Performance Measurement of Exchange Traded Funds

Department of Banking and Finance

Performance Measurement of Exchange

Traded Funds

Master Thesis in Banking and Finance

Lodged with Prof. Dr. Markus Leippold

Under the supervision of Nikola Vasiljevic

Lodged at Chair of Financial Engineering

Author Thomas Schär

Alte Bernstrasse 75b

3075 Rüfenacht BE

E-Mail: [email protected]

Matriculation number: 08-125-684

Zurich, August 18th, 2014

i

Executive Summary

The selection of actively managed funds aims at identifying an investment that is likely to

outperform a selected benchmark. In contrast, excess performance is not a focus in choosing

Exchange Traded Funds (ETFs). This paper argues that the performance measures of active

funds are often not only irrelevant, but may be misleading when being applied to passively

managed ETFs. Investors of ETFs want to buy and sell a diversified bundle of assets with the

same return profile as the benchmark which is replicated. Since investing directly into the

benchmark is not possible, unlevered, passive ETFs aim to mirror, or track the performance of

the benchmark. Therefore the ETFs’ performance relative to the benchmark and the

competing ETFs is more significant than absolute returns. The key research question of this

study is therefore how to comprehensively measure and assess the tracking ability of ETFs. The

thesis aims to design an intuitive efficiency measure that helps selecting the most efficient ETF

amongst its peers replicating the same benchmark. The most distinctive feature of this paper is

that it does not only take several statistical considerations into account, but also adjusts for a

selection of typical trading strategies on the ETFs primary and secondary market.

As suggested by Hassine and Roncalli (2013), the theoretical framework of the ETF efficiency

measure is based on the Value-at-Risk (VaR) methodology and combines tracking difference,

tracking error and the bid-ask spread. The theoretical processing of the efficiency measure is

completed with empirical research conducted on unlevered, passively managed ETFs listed on

SIX. ETFs replicating the Swiss Market Index and the EURO STOXX 50 over the observation

period from May 2013 to May 2014 are considered. The VaR framework is extended

throughout this study by considering both the underlying assumptions about the distributions

of relative returns and the measurement methods of ETF risk-factors. Alternative calculation

techniques, robust and unilateral measures of tracking error are applied. Gaussian and non-

Gaussian distribution assumptions as well as intra-horizon risk are taken into account by

considering the historical VaR, Cornish-Fisher VaR, Expected Shortfall and Intra-Horizon VaR.

The empirical evidence in this study suggests that the ETF rankings according to the efficiency

measures are largely consistent across the data sample. More efficient funds tend to perform

better in most of the methods considered. However, the results of strongly depend on the

underlying statistical assumptions of the risk metrics as well as the trading characteristics of

the investor. The sample data is found to suffer from strong non-normality and data outliers.

The findings show that investors need to consider several ETF performance measurement

alternatives in their ETF selection process while adjusting the efficiency measures to their

underlying investment objectives and trading circumstances.

ii

Contents

List of Figures ............................................................................................................................... iv

List of Tables .................................................................................................................................. v

Chapter 1 Introduction ................................................................................................................ 1 1.1 Outline ........................................................................................................................................................ 2

Chapter 2 Exchange Traded Funds .............................................................................................. 3 2.1 Delimitation .............................................................................................................................................. 3 2.2 Historical Background ............................................................................................................................ 4 2.3 Replication Strategies ............................................................................................................................ 5

2.3.1 Physical Replication .............................................................................................................................. 6 2.3.2 Synthetic Replication ............................................................................................................................ 7 2.3.1 Net Asset Value ...................................................................................................................................... 8

2.4 ETF Costs .................................................................................................................................................... 8 2.4.1 Internal Costs ........................................................................................................................................... 9 2.4.2 External Costs .......................................................................................................................................... 9

2.5 Extra Revenue – Securities Lending ................................................................................................ 10 2.6 Indices ....................................................................................................................................................... 11 2.7 Market Environment ............................................................................................................................ 12

2.7.1 Providers ................................................................................................................................................. 12 2.7.2 Authorized Participants .................................................................................................................... 13 2.7.3 Creation- Redemption Process ...................................................................................................... 13 2.7.4 Investors and Trading Strategies ................................................................................................. 15

Chapter 3 ETF Risk Metrics ........................................................................................................ 16 3.1 Delimitation ............................................................................................................................................ 16 3.2 Tracking Efficiency: Tracking Difference and Tracking Error .................................................. 17

3.2.1 Tracking Difference ............................................................................................................................ 17 3.2.2 Tracking Error - Based on the Standard Deviation ............................................................... 18 3.2.3 Sources of Tracking Difference and Tracking Error .............................................................. 18

3.3 Liquidity Metrics .................................................................................................................................... 20 3.3.1 Delimitation: Relative versus Absolute Liquidity ................................................................... 20 3.3.2 AuM and Trading Volume ............................................................................................................... 21 3.3.3 Bid-Ask Spread ..................................................................................................................................... 21 3.3.4 Market Impact Costs and the Notional Traded ...................................................................... 23

3.4 Pricing Efficiency .................................................................................................................................... 24

Chapter 4 Literature Review ...................................................................................................... 25 4.1 ETF Performance ................................................................................................................................... 25 4.2 Tracking Efficiency, Liquidity and Pricing Efficiency ................................................................... 27

Chapter 5 Performance Measurement ...................................................................................... 30 5.1 ETF Selection Principles ....................................................................................................................... 30 5.2 Sharpe Ratio and Information Ratio ............................................................................................... 31

5.2.1 Pitfalls of the Information Ratio ................................................................................................... 33 5.3 The ETF Efficiency Measure by Hassine and Roncalli ................................................................ 35

iii

Chapter 6 Empirical Research .................................................................................................... 39 6.1 Data Sample ............................................................................................................................................ 39 6.2 Data Treatment ...................................................................................................................................... 40 6.3 Sample Statistics .................................................................................................................................... 41 6.4 Results for the ETFs on SMI ............................................................................................................... 42 6.5 Results for the ETFs on EURO STOXX 50 ........................................................................................ 45

6.5.1 Information Ratio versus Efficiency Measure ......................................................................... 48

Chapter 7 Adjustments to the Efficiency Measure .................................................................... 49 7.1 Pricing Efficiency .................................................................................................................................... 49 7.2 Alternative Tracking Error Measures .............................................................................................. 50

7.2.1 TE – Based on Correlation of Returns ......................................................................................... 50 7.2.2 Tracking Error based on the Residuals of a Linear Regression ........................................ 53 7.2.3 Tracking Error based on Robust Measures .............................................................................. 54 7.2.4 Tracking Error based on Semi-Variance .................................................................................... 57 7.2.1 Autocorrelation ................................................................................................................................... 61

7.3 Alternative Bid-Ask Spread Measurement .................................................................................... 63 7.4 Alternative Value-at-Risk Measures ................................................................................................ 66

7.4.1 Cornish-Fisher Value-at-Risk .......................................................................................................... 70 7.4.1 Historical Value-at-Risk .................................................................................................................... 72 7.4.2 Intra-horizon Value-at-Risk ............................................................................................................ 74 7.4.1 Expected Shortfall ............................................................................................................................... 78

7.5 Alternative Interpretation of the Efficiency Measure ............................................................... 80

Chapter 8 Conclusion and Outlook ............................................................................................ 81

iv

List of Figures

Figure 1: ETP Classification ............................................................................................................ 4

Figure 2: Global ETP Numbers and AuM ....................................................................................... 5

Figure 3: ETF Replication Strategies .............................................................................................. 6

Figure 4: Internal and External Costs ............................................................................................ 8

Figure 5: Dividend Distribution ................................................................................................... 12

Figure 6: Creation - Redemption Process .................................................................................... 14

Figure 7: Tracking and Pricing Efficiency ..................................................................................... 16

Figure 8: Sources of Tracking Error and Tracking Difference ...................................................... 19

Figure 9: Impact Factors on Bid-Ask Spread................................................................................ 22

Figure 10: Information Ratio based on Benchmark .................................................................... 32

Figure 11: Information Ratio based on Tracker .......................................................................... 34

Figure 12: Illustration of the Efficiency Measure ........................................................................ 36

Figure 13: Larger Tracking Difference ......................................................................................... 37

Figure 14: Larger Bid-Ask Spread ................................................................................................ 37

Figure 15: Larger Tracking Error .................................................................................................. 37

Figure 16: Percentage Spread ETF 2# SMI................................................................................... 43

Figure 17: Tracking Difference ETF 2# SMI .................................................................................. 43



Figure 20: Tracking Difference ETF 7# EURO STOXX 50 .............................................................. 46

Figure 21: Percentage Spread ETF 2# EURO STOXX 50 ............................................................... 47

Figure 22: Sample Regression with Data Outliers ....................................................................... 52

Figure 23: Sample Regression without Data Outliers ................................................................. 52



Figure 26: Autocorrelation Function ETF 3# SMI ........................................................................ 62

Figure 27: Autocorrelation Function ETF 1# EURO STOXX 50 ..................................................... 62

Figure 28: Relative Tracking Difference Distribution .................................................................. 66

Figure 29: Absolute Tracking Difference Distribution ................................................................. 69

Figure 30: Cumulative Tracking Error ETF 1# and 3# on SMI ...................................................... 74

Figure 31: Decision Tree of ETF Efficiency Measures .................................................................. 85

Figure 32: Time Series ETF Tracking Difference ........................................................................ 107

Figure 33: ETF Autocorrelation Function .................................................................................. 113

Figure 34: Percentage Bid-Ask Spreads ..................................................................................... 117

v

List of Tables

Table 1: Information Ratio .......................................................................................................... 31

Table 2: Results for the ETFs on SMI ........................................................................................... 42

Table 3: Results for the ETFs on EURO STOXX 50 ........................................................................ 46

Table 4: Information Ratio ETF SMI............................................................................................. 48

Table 5: Information Ratio ETF EURO STOXX 50 ......................................................................... 48

Table 6: Pricing Efficiency ETF SMI .............................................................................................. 49

Table 7: Pricing Efficiency ETF EURO STOXX 50 .......................................................................... 49

Table 8: Tracking Error ................................................................................................................ 51

Table 9: Alternative TE ETF SMI .................................................................................................. 53

Table 10: Data Outliers ETF SMI .................................................................................................. 54

Table 11: Data Outliers ETF EURO STOXX 50 .............................................................................. 54

Table 12: Robust TE ETF SMI ....................................................................................................... 55

Table 13: Robust TE ETF EURO STOXX 50 .................................................................................... 56

Table 14: IQR ETF SMI ................................................................................................................. 57

Table 15: IQR ETF EURO STOXX 50 .............................................................................................. 57

Table 16: Semi-Variance ETF SMI ................................................................................................ 59

Table17: Semi-Variance ETF EURO STOXX 50 ............................................................................. 60

Table 18: Adjusted Spread ETF SMI ............................................................................................. 64

Table 19: Adjusted Spread ETF EURO STOXX 50 ......................................................................... 65

Table 20: Normality Test ETF SMI ............................................................................................... 68

Table 21: Normality Test ETF EURO STOXX 50 ............................................................................ 69

Table 22: Cornish-Fisher VaR ETF SMI ......................................................................................... 70

Table 23: Cornish-Fisher VaR ETF EURO STOXX 50 ..................................................................... 71

Table 24: Historical VaR ETF SMI ................................................................................................. 72

Table 25: Historical VaR ETF EURO STOXX 50 ............................................................................. 72

Table 26: Intra-horizon VaR ETF SMI ........................................................................................... 76

Table 27: Intra-horizon VaR ETF EURO STOXX 50 ....................................................................... 77

Table 28: Expected Shortfall ETF SMI .......................................................................................... 79

Table 29: Expected Shortfall EURO STOXX 50 ............................................................................. 79

Table 30: EURO STOXX 50 ......................................................................................................... 100

Table 31: Swiss Market Index .................................................................................................... 101

Table 32: ETF Sample ................................................................................................................ 102

Table 33: Fund Information ....................................................................................................... 103

Table 34: Trading Information .................................................................................................. 105

Table 35: Efficiency Measures Overview .................................................................................. 121

Table 36: Efficiency Measures Overview without Spread ......................................................... 123

vi

Abbreviations

AP Authorized Participant

AuM Asset under Management

Bps Basis Points

CHF Swiss Franc

CESR Committee of European Securities Regulators

ES Expected Shortfall

ESMA European Securities and Markets Authority

ETF Exchange Traded Fund

ETI Exchange Traded Instrument

ETN Exchange Traded Note

ETP Exchange Traded Product

FINMA Swiss Financial Market Supervisory Authority

iid independent and identically distributed

iNAV indicative Net Asset Value

IQR Interquartile Range

IOSCO International Organization of Securities Commissions

IR Information Ratio

LOB Limit Order Book

LPM Lower Partial Moment

MAD Median Absolute Deviation

MiFID Markets in Financial Instruments Directive

NAV Net Asset Value

OTC Over-the-Counter

PnL Profit and Loss

SIX SIX Swiss Exchange

SMI Swiss Market Index

TD Tracking Difference

TE Tracking Error

TER Total Expense Ratio

UCITS Undertakings for Collective Investment in Transferable Securities Directives

USD United States Dollar

VaR Value-at-Risk

Chapter 1 Introduction

1


Over the past decade, Exchange Traded Products (ETP) have experienced a surge in popularity

whereas the possibilities of their application has increased. iShares, being the largest ETP

provider in the world with more than 440 funds and over USD 480 billion of Assets under

Management (AuM), estimates that the ETP industry grew from worldwide 106 products with

USD 79,4 billion AuM in 2002 to 5’025 ETPs with USD 2’300 billion AuM in January 2014

(iShares, 2014, p.5). This trend seems to continue as the industry grows across all markets and

segments.

Above all, the subcategory of Exchange Traded Funds (ETF) was responsible for a large amount

of the growth in ETPs (Blackrock, 2012, p.4). In Switzerland, the number of ETFs increased from

888 listed products in 2012 to 940 in 2013 with a rise in volume of roughly 20% (SIX, 2013a,

p.3). Moreover, during the financial crisis in 2008 ETFs boosted their volume unlike any other

investment class (SIX, 2009, p.5). Institutional as well as retail investors gained interest in these

products, which offer index tracking, the main purpose of ETFs, at relative modest costs.

In accordance with the enormous increase in size, came an increase in variety and complexity

of ETFs. Nevertheless, ETFs are praised for their high level of transparency and are thus

awarded a special role in comprehensive due diligence procedures and risk management to

investors. Guidelines from regulatory bodies such as the Undertakings for Collective

Investment in Transferable Securities Directives (UCITS) in Europe on the one hand and

enhanced due diligence procedures by the ETF providers on the other hand, helped to increase

the investment knowledge on ETFs. Nevertheless investors need to be aware of several factors

when looking for ETFs suiting their portfolio and investment needs. They not only need to take

into account investor-related factors such as the underlying investment objective, horizon and

universe, they also need to compare and contrast ETFs from a range of providers according to

their structure, tradability, risk and performance.

As selecting the most excellent fund is core for any investor, the efficiency and performance1

of an ETF is a primary concern. Where traditional mutual funds are judged by how much they

outperform their opponents and benchmark, the performance measurement of ETFs is not

straightforward, as their aim is not to beat the performance of their underlying benchmark,

1 ETF Efficiency and performance are used as synonyms in the context of this thesis. In order to achieve a consistent terminology

throughout the study, the official ETF terminologies by the European Securities and Markets Authority (ESMA) and the naming of

the ETFs according to SIX Swiss Exchange are applied. If not stated otherwise, the term ETF refers to long only, passively managed,

unlevered exchange traded funds. ETF performance and ETF efficiency measurement are used conterminously.


2

but to replicate it as close as possible. Since many tools developed for traditional funds fail

when being applied to ETFs, standalone measures such as the tracking error and the tracking

difference are used to compare the ETF’s tracking ability. However, little is known about their

consolidation and joint interpretation as one comprehensive ETF performance measure.

1.1 Outline

The overall structure of the study takes the form of eight chapters, including this introductory

chapter. In order to acquire a fundamental knowledge about the ETFs history, replication

strategies, costs, revenues, market environment and trading characteristics, Chapter 2

presents thorough discussion of the specific features of the ETFs. As for every section of the

thesis, the theoretical outlay in Chapter 2 focuses on factors relevant for efficiency

measurement.

Chapter 3 holds the processing of both qualitative and quantitative performance

measurement and provides the full mathematical framework of the ETFs performance metrics.

Chapter 4 will complement the theoretical insight on the performance of ETFs with an

extensive literature review.

Looking at existing performance figures, Chapter 5 presents both empirical as well as

mathematical assessment on existing funds evaluation methods. Ultimately, the framework

for the efficiency measurement of ETFs, initially designed by Hassine and Roncalli (2013), will

be set up.

Chapter 6 presents the data sample processed in this study and calculates the efficiency

measure for the ETFs selected. Moreover, comprehensive insight on the data sample and data

treatment is given.

The analysis in Chapter 7 enhances the basic model by applying Gaussian and non-Gaussian

efficiency measures, as well as liquidity risk and alternative tracking error measures.

The conclusion Chapter 8 summarizes and critically evaluates the empirical and mathematical

findings. As a final point, areas for further ETF research are identified.

Chapter 2 Exchange Traded Funds

3


According to the European Securities and Markets Authority (ESMA), ETFs are open-ended

collective investment schemes that trade throughout the day like a stock on the secondary

market, which takes place on the exchange. Generally, ETFs seek to mirror the performance of

a target benchmark and are structured and operate in a similar way. Like operating companies,

ETFs register subscriptions and redemptions of shares and list their shares for trading (ESMA,

2011, p.9). From a legal perspective, ETFs are considered to be special assets not included in

the bankruptcy assets, should the ETF provider become insolvent. Unlike index funds which

are priced only once at the end of each trading session, ETF prices adjust throughout the day

and can be bought without any direct subscription and redemption fee on the secondary

market (Picard & Braun, 2010, p.2).

2.1 Delimitation

Since the inception of the first ETP, a large number of products have been introduced in the

financial market. Whereas ETFs have to pursue strict guidelines the widening of the ETP

product universe put forth many, partially regulated products such as Exchange Traded Notes

(ETNs). For the sake of clarity, it is crucial to consistently distinguish these instruments

according to their types. The classification in this paper generally follows the suggestion by

iShares (2014, p.17).

ETPs are understood as an umbrella term of three subcategories. Besides the mentioned ETFs,

the second subcategory subsumes ETNs as well as Exchange Traded Commodities (ETCs),

whereas the third subcategory covers the remaining Exchange Traded Instruments (ETIs). ETNs

are structured products that are issued as non-interest paying debt instruments, whose prices

fluctuate with an underlying index or an underlying basket of assets. Because they are debt

obligations, ETNs are backed by the issuer and subject to the solvency of the issuer (ESMA,

2012b, p.10). The remaining ETP-spectrum that is neither defined as funds nor as notes, is

classified as ETIs. Here included are listed options, warrants and hybrid instruments (iShares,

2014, p.11). Figure 1 highlights the important distinction of these product classes.


4

Figure 1: ETP Classification

The distinction of ETPs is illustrated. The term Exchange Traded Product covers Exchange Traded Funds, Exchange Traded Notes/ Exchange Traded Commodities and Exchange Traded Instruments. (Source: Own illustration following iShares, 2014)

The subcategories, ETNs, ETCs and ETIs will not be subject to analysis in this paper.

2.2 Historical Background

Eugene Fama set the cornerstone for passive management in 1965 with his study on market

efficiency. He suggested that, since the prices of securities instantly and fully reflect all public

and inside information available, price movements cannot be predicted using past prices. In

consequence, investors on average can only perform the same as the market. They come off

best by simply buying and holding a diversified basket of stocks, whilst minimizing fees and

taxes (Fama, 1965). Following the idea by Fama, Wells Fargo, an American banking and

financial services company, commercially adapted a passive strategy and launched the first

institutional index fund in 1976. The first index fund available for retail investor was launched

by Vanguard only five years later (Hehn, 2006, p.120).

Nonetheless, it was not until 1993 that ETFs initially became a viable investment opportunity.

Indeed, the first registered index-tracker was launched that year by State Street Global

Advisors under the name of SPDR tracking the US-Stock index S&P 500. Today, this fund

remains one of the most heavily traded funds in the world, with more than USD 37 billion AuM

(Picard & Braun 2010, p.17).

Whereas the story of success of ETFs in Europe began in the 2000, the total amount of ETFs

available globally had grown to 169 a year later only, whereby 103 of ETFs were traded

exclusively on U.S. markets (Wiandt & McClatchy, 2001, p.73). Apart from Switzerland, it was

Germany, Great Britain and Sweden who were the vanguards by offering ETFs in Europe

(Picard & Braun, 2010). Deutsche Börse emerged as the most important trading platform for

ETFs in Europe, significantly contributing to its success story (Hehn, 2006, p.120). In 2004 the

first ETFs on Emerging Markets, Real Estate and Commodities were introduced, whereas two

Exchange Traded Products (ETPs)

Exchange Traded Funds (ETFs)

Exchange Traded Notes (ETNs) /

Exchange Traded Commodities

(ETCs)

Exchange Traded Instruments (ETIs)


5

years later, the first ETFs taking short positions have been launched (Picard & Braun, 2010,

p.17). Figure 2 presents the global development of number and AuM of both ETFs and ETPs

since 1993. Only the financial crisis in 2008 resulted in a yearly decrease AuM of both ETFs and

ETPs. The amount of products on the market however steadily increased since the first

inception of an ETF.

Figure 2: Global ETP Numbers and AuM

The development of ETP and ETF AuM and the number of products are illustrated over the period from 1993 to June 2014. The ETF AuM figures for June 2014* are estimations, as official figures are not available. (Source: Own illustration following Blackrock 2009, 2012 & 2014)

2.3 Replication Strategies

ETFs can be categorized by their way of replicating a benchmark. Two main types of index

replication, namely physical and synthetic replication, can be differentiated. Physically

replicating ETFs hold all or a selection of constituents of an index, whereas synthetic

replication refers to the usage of derivatives in order to achieve benchmark returns. Synthetic

ETFs deliver the performance of a benchmark through the use of swaps and other derivatives

(IOSCO, 2013, p.2).

The style of replication has a significant influence on the ETFs tracking ability and subsequently

is explained in more detail. The explanations follow the principles for the regulation of ETFs,

issued in 2013 by the board of the International Organization of Securities Commission

(IOSCO), which regulates more than 95% of the world’s securities markets. Figure 3 gives an

overview on the commonly used segmentation of ETFs according to their replication strategy.

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013June

2014*

ETF AuM 0.8 1.1 2.3 5.3 8.2 17.6 39.6 74.3 105 142 212 310 412 566 796 711 1036 1311 1351 1644 2010 2207

ETP AuM 0 0 0 0 0 0 2 79.4 109 146 218 319 428 598 851 772 1156 1483 1525 1944 2396 2632

# of ETFs 3 3 4 21 21 31 33 92 202 280 282 336 461 713 1170 1595 1944 2460 3011 3297 3490 3650

# of ETPs 0 0 0 0 0 0 2 106 219 297 300 357 524 883 1541 2220 2694 3543 4311 4759 4988 5217

0

1000

2000

3000

4000

5000

0

500

1000

1500

2000

2500

3000

Nu

mb

er

of

pro

du

cts

Au

M i

n m

illi

on

US

D


6

Figure 3: ETF Replication Strategies

The ETF Replication Strategies are depicted. Physical and synthetic replication is differentiated. Physical replication can be further split into the full replication and the sampling methods, which furthermore comprises the representative and optimized sampling. Synthetic replication includes the unfunded and the fully funded swap model. (Source: Own illustration following the classification by IOSCO, 2013; iShares, 2014; Picard & Braun, 2010)

2.3.1 Physical Replication

Physically replicating ETFs can be segmented according to the share of benchmark constituents

they hold. ETFs which contain all elements of a benchmark are referred to as fully replicating.

Whereas ETFs that hold a selection of the underlying constituents are denoted as optimized or

partially replicating (IOSCO, 2013, p.2). If the physically replicating ETF does not conduct

securities lending, a process described later on in more detail, the strategy generally does not

expose an investor to counterparty risk (Hehn, 2006, p.16). Derivatives are only used in order

to equitize cash dividends of the constituents. In this process, the ETF avoids building up

unprofitable cash-positions by reinvesting the cash trough futures and other derivatives

(Wiandt & McClatchy, 2001, p.42).

2.3.1.1 Full Replication

A fully replicating ETF generally invests in the component securities of the underlying

benchmark in the same approximate proportions as in the benchmark itself. In consequence,

this type of ETF commonly displays a high degree of transparency (IOSCO, 2013, p.2).

Besides offering relatively close tracking of the benchmark, certain methodical problems might

arise with full replication as Benchmark constituents often are published with rounded down

decimal places only. Furthermore, dividend distributions may result in a higher cash

component of the ETFs. The reason is that the ETF distributes dividends each quarter or

semester only, whereas the benchmark may assume to distribute dividends on a daily basis.

Replication

strategies

Physical replication

Full replication

Sampling methods

Representative sampling

Optimized sampling

Synthetic replication

Unfunded swap model

Fully funded swap model


7

Replicating broad indices such as the MSCI World furthermore is costly, as more securities

have to be bought in order to fully replicate the index. On the one hand this increases

corresponding transaction costs, on the other hand, it leads to frequent rebalancing within the

index. The cancellation and admission of new benchmark constituents increases the

rebalancing costs for the ETF. Finally, if the index holds illiquid constituents, prices might be

driven up by the additional demand triggered by the ETF (Picard & Braun, 2010, p.47-48).

2.3.1.2 Replication by Sampling

With sampling techniques, the ETF overcomes some of the problems previously mentioned.

The ETFs thus acquires only a subset of the underlying indexes constituents whilst adding

securities that exhibit similar return patterns as the constituents omitted (IOSCO, 2013, p.2).

This method has the advantage of lower management fees and administrative costs but the

ETF may suffer from more inaccurate return tracking (Picard & Braun, 2010, p.42).

2.3.2 Synthetic Replication

Synthetic or derivative replicating ETFs invest in a diversified basket of assets while entering

into a derivative contract, typically through a total return swap (IOSCO, 2013, p.2). The swap

counterparty guarantees to deliver the return of the index in exchange for a variable swap

spread (Picard & Braun, 2010, p.52).

Although this replication strategy avoids the high rebalancing costs and tracking inaccuracy

associated with physical replication, it exposes the investor to counterparty risk. Regulatory

requirements reduce the risk arising. A UCITS fund in Europe e.g. is allowed to maximally

allocate 10% of its total assets into derivatives such as swaps (ESMA, 2012b, p.7). In case of

default of the swap counterparty, the ETF should be fully covered by the collateral of the swap

contract (Picard & Braun, 2010, p.61).

According to IOSCO Guidelines, the unfunded and the funded structure of a synthetic

replicating ETF can be further differentiated. In an unfunded structure, the ETF manager

invests in a substitute or reference basket of securities. This baskets return is used as collateral

in the derivative contract in exchange for the return of the index (IOSCO, 2013, p.3). In the

funded model, synthetic ETFs engage in a swap in exchange for cash without the creation of a

substitute basket (IOSCO, 2013, p.3). The fund transfers the cash proceeds from investors to

the counterparty, which in return provides collateral in excess of the subscription value and

further guarantees the performance of the benchmark (iShares, 2014, p.14).


8

2.3.1 Net Asset Value

The value of an ETFs underlying constituents is described by its Net Asset Value (NAV). The

NAV is calculated by summing the value of all constituents of the fund including cash positions

and deducting all liabilities. The sum is divided by the amount of outstanding ETF shares on a

daily basis, in order to receive the NAV (iShares, 2014, p.50). A unique feature of ETFs is that a

so-called indicative Net Asset Value (iNAV) is issued. It is calculated throughout the day from

current market prices and is published every 15 seconds (iShares, 2014, p.50). This process

allows for real-time tradability of an ETF. Conversely, traditional mutual funds are prices once

a day (Picard & Braun, 2010, p.6).

2.4 ETF Costs

ETFs attract a broad range of investors due to their diversification benefits coming at low fees.

Depending on the provider, the benchmark and the replication method, ETF costs may

however diverge and therefore need to be watched closely (Picard & Braun, 2010, p.8). This

section therefore assesses the total costs of ETF ownership. In line with the classification of

iShares (2014, p.44), internal cost, being ongoing charges to the ETF, are differentiated from

external costs, which are costs incurred at the time of trading the ETF. Figure 4 presents the

classification of costs for both physically and derivative replicating ETFs.

Figure 4: Internal and External Costs

The internal cost of holding the ETF and the external cost from trading the ETF are listed for both physical and synthetic replicating ETFs. (Source: Own illustration following iShares, 2014, p.44)

Fund structure

Physical replicating

synthetic replicating

Internal costs

- Total expense ratio

- Rebalancing Costs

-Additional factors

- Total expense Ratio

- Swaps Spread

-Additional factors

External costs

-Bid- / Ask -Spreads

-Transaction Costs

- Taxation


9

2.4.1 Internal Costs

The set of internal costs include all expenses of the ETF on an ongoing basis. The most

prominent, being the Total Expense Ratio (TER) and the rebalancing costs, are discussed

subsequently.

TER is expressed in percentages and includes all ongoing fees charged to the ETF (Picard &

Braun, 2010, p.27). The TER must be officially published by the ETF provider and has to

comprise the following indicative, but not exhaustive list of charges:

It has to include all payments to the management company, directors, depositary, custodians,

investment adviser as well as any outsourced services of the ETF. The management fee hereby

covers all costs arising from ETF administration, maintenance and management (Picard &

Braun, 2010, p.27). Furthermore, registration and regulatory fees as well as audit fees must be

included in the TER. Entry and exit charges, as well as performance related fees are not

covered by the TER (Committee of European Securities Regulators, 2010). The TER is deducted

from a fund’s NAV on a daily basis and therefore influences an ETFs daily tracking performance

(iShares, 2014, p.45).

Rebalancing cost arise when a change in the benchmark requires a reweighting of the ETFs

constituents. Equivalently, costs arising from a change in the variable swap spread are

regarded as internal costs for synthetic ETFs (iShares, 2014, p.45). Both cost types negatively

influence an ETFs tracking performance.

2.4.2 External Costs

External costs are defined as costs that are charged to the investor only at the time of ETF

trading. They include trading costs such as the bid-ask spread and transaction costs as well as

any taxes levied on the ETF trade.

Bid and ask prices indicate the best price at which a security can be sold and bought at a given

point in time (Picard & Braun, 2010, p.88). The bid-ask spread of an ETF is defined as the

difference between the bid price and the ask price. The bid-ask spread is always positive as the

maximal price for which an investor is willing to sell his ETF shares is always larger than the

price for which he is willing to buy them (Picard & Braun, 2010, p.28). The spread does not

directly influence the tracking performance of the ETF. However, it is crucial factor in ETF

liquidity measurement and will be subject to profound evaluation in Chapter 3.


10

Transaction costs comprise all additional costs that arise when an ETF is sold or bought. Such

costs include brokerage and custody feed and provisions for banks and brokerage dealers

(Picard & Braun, 2010, p.102).

The taxation of an investment in an ETF may occur on the ETF, the underlying securities and

the investor level.

On a fund level the applicable jurisdiction of the domicile country as well as the legal structure

of the ETF are relevant (iShares, 2014, p.21). For all ETF structures in Switzerland, income and

capital taxes have to be paid only on a dividend and investor level, as ETFs do not represent a

legal entity (Picard & Braun, 2010, p.83). Withholding taxes on income or on capital gains

received by the fund are charged at the ETF constituents’ level. They arise in the country

where the underlying securities are situated and strongly depend on the treaty between the

country of the securities and the country in which the ETF is domiciled. Those two layers of

taxation become especially important as the benchmark and the ETF may have diverging

taxation principles. Benchmarks such as gross total return indices assume that dividends are

reinvested without any tax deductions, whereas the ETF will have to pay withholding taxes

when disbursing dividends. Net total return indices may assume that withholding taxes are

paid on dividends, whereas the ETF is able to reclaim its taxes partially. This practice, known as

dividend tax enhancement, may boosts ETF returns relative to the benchmark (Johnson et al.,

2013, p.6). An additional example of tax optimization is called dividend tax arbitrage. In this,

ETFs lend stocks that are subject to dividend withholding taxes to counterparties located in

more tax-efficient jurisdictions during dividend season (Bioy & Rose, 2013, p.6).

Taxes levied on an investor level are not subject to ETF performance measurement. In

consequence the taxation of investors is not discussed in this thesis.

2.5 Extra Revenue – Securities Lending

Apart from the revenues generated trough the rise in value of the underlying constituents, an

ETF can generate additional revenue from securities lending. Securities lending refers to

additional revenue trough the transfer of securities from the ETF to a third party, who will

provide collateral to the lender and pay a fee. The extra revenue can be used to partially offset

the internal costs the ETF. It even can lead to an over performance of the ETF with respect to

the benchmark, which does not exert securities lending (Picard & Braun, 2010, p.68). However,

since lending activities can be executed in direct agreements between the lender and the

borrower, true magnitude is difficult to assess (Bioy & Rose, 2013, p.3). In Europe, the UCITS


11

regulation requires all revenues, net of direct and indirect operational costs, to be returned to

the ETF (ESMA, 2012a, p.7).

Securities lending may be undertaken in physical as well as synthetic replicating ETFs. As the

lending in physically replication ETFs is more straightforward, securities lending possibilities for

synthetic ETFs are more complex. Physically lending the securities inherits the risk that the

borrower of the security becomes insolvent and is unable to return the loaned securities.

Therefore physical ETFs engaged in lending expose investors to counter party risk.

In synthetic ETFs, the lending process takes place within the reference basket and thus does

expose the investor to counterparty risk. (iShares, 2014, p.49). Securities lending is an

important factor in total return assessment of an ETF and has to be kept in mind when

evaluating the tracking performance of an ETF.

2.6 Indices

Even though ETFs are found to replicate a variety of benchmarks, this thesis is confined to ETFs

replicating equity indexes only. Picard and Braun (2010, p.33) define an index as a statistical

figure, representing a basket of financial assets, which can only be bought by investors through

the use of ETFs or index-certificates.

The underlying assumptions of the index thereby have an important impact on the relative

performance of the ETF. In this context, the indexes’ most relevant feature is their dividend

reinvestment assumption. Divergent assumption on the dividend treatment of ETF and index

result in tracking dissimilarity. In general, price and total return indices are differentiated. Price

indices only return the prices of the underlying assets whilst assuming that all dividends of the

constituents are distributed. Total return indices on the other hand assume that all dividends,

interest payments and other income are reinvested (Picard & Braun, 2010, p.36). They can be

further separated according to their assumption on taxation on the dividends reinvested. A net

total return index assumes that dividends are taxed at the biggest available rate, whereas

gross total return indexes assume that no taxes are levied on the reinvested dividends (iShares

2014, p.22). These assumptions are particularly important as they results in performance

differences of the ETF and the index whenever dividends are paid or reinvested (Hassine &

Roncalli, 2013).

The timing of dividend reinvestment can lead to further performance differences between ETF

and its benchmark. Whereas many indices assume dividends to be disbursed at ex-dividend

dates of the corresponding constituents, the dividend payouts by ETFs are often cumulatively

administered (Picard & Braun 2010, p.24).


12

From the time series of the SMI price index and the DB X-TRACKERS SMI UCITS ETF in Figure 5,

it can for instance be seen that the ETFs dividend payment on July 25th, 2013 results in an

instant drop of NAV compared to the NAV of the benchmark. By the end of March 2014

however, the NAV of the ETF and the benchmark return to similar values, as the SMI price

index distributes dividends throughout the investment horizon.

Figure 5: Dividend Distribution

The development of the NAV of the SMI price index and the DB X-TRACKERS SMI UCITS ETF are illustrated. The period covers May 2013 to May 2014. The red circle indicates the period of the dividend payment of the ETF. (Source: Own calculations/ illustrations)

2.7 Market Environment

Due to its size, distinctive structure and easy accessibility, the ETF market consists of various

types of participants. In the following, the most relevant, market participants and market

characteristics are presented.

2.7.1 Providers

The ETF provider is in charge of all defining aspects of an ETF such as the replication strategy,

pricing and dividends attribution. Therefore, he is the main responsible for the ETF

performance (Picard & Braun 2010, p.29).

Following a recent statistic by Deutsche Bank (2014, p.37), by the end of 2013, a total of 180

ETF providers existed across the globe. However, 85.8% of the ETF industries total assets were

concentrated amongst the top 10 providers only. Blackrock, the mother company of iShares, is

the largest ETP provider with 40.3% of total market share, followed by State Street GA (17%)

and Vanguard (15.1%). Holding a total of 72.4% of the global ETF market in 2013, those three

big players provide nine of the ten biggest ETFs by AuM.

Deutsche Bank AG (2.3%) is the biggest provider located in Europe, whereas UBS, the biggest

Swiss provider, holds USD 16 billion AuM (0.7%). The ETF market is mainly dominated by banks

7000

7200

7400

7600

7800

8000

8200

8400

8600

8800

9000

SMI

ETF SMI


13

and bank-owned providers such as Deutsche Bank, Lyxor of Société Général, UBS and Zürcher

Kantonalbank (Deutsche Bank, 2014, p.41). In Switzerland iShares covers 53.36% of the Swiss

ETF market by the end of 2013. Out of a total of 18 ETF providers, the five biggest providers

including UBS (19.3%), Zürcher Kantonalbank (6.4%), Lyxor (6.25%) and db x-trackers (6%)

covered 97.5% of the ETF market (SIX, 2013a, p.3).

2.7.2 Authorized Participants

Authorized participants (AP), also referred to as Market Makers, govern the ETFs creation-

redemption process in which ETF shares are issued or redeemed. Typically being large

investment banks or brokerage businesses, APs conclude participation agreements with the

ETF, which allow the AP to subscribe and redeem units of the ETF on an in-kind basis. APs may

act as distributors of the ETF shares on various stock exchanges as well (Hehn, 2006, p.96). The

process in its details will be explained in chapter 2.7.3.

On the Swiss exchange platform SIX, at least one AP is employed for each ETF. APs are obliged

provide continuous liquidity in the ETF (Picard & Braun, 2010, p.30). APs have to provide bid

and ask prices for a fixed minimum of trading volume and have to avoid prices, which exceed a

maximum bid-ask spread of 5% in the case of an inexistent Over-the-Counter (OTC)2 market or

2% where a functioning OTC market exists (SIX, 2014).

As the spread is going to be integral part of the performance analysis, it’s important to

understand the role of APs in the ETF market. By providing liquidity through their so-called

Limit Order Books (LOB) 3, APs have an important influence on the prices that need to be paid

when trading an ETF. According to Roncalli and Zheng (2014), during a trading day, all selling

and buying orders are matched against the best order of their counterpart. If the volume of

the market order is larger than the quantity available at the corresponding best limit order, the

best limit price will be adapted and executed on the second limit order. Therefore the spread

between the best bid and the best ask price increases with the ETF notional traded (Roncalli &

Zheng, 2014).

2.7.3 Creation- Redemption Process

The creation- redemption process of ETF shares is administered through several steps.

At the beginning of the trading day, the portfolio manager of the ETF designates the APs with

the basket of securities to be taken into the fund at the closing of the market in exchange for

new units of the ETF. The AP will buy the corresponding basket of securities on the capital

2 OTC trades are administered on the primary market directly between the AP and the ETF. The final price for the ETF share is negotiated directly between the two counterparties. 3 LOB is the set of all active trading order of buyers and sellers of ETFs listed on any electronic system (Gould et al., 2013).


14

markets. The AP exchanges this basket against the equivalent amount of ETF-shares, which he

now is able to sell on the secondary market or OTC (Picard & Braun, 2010, p.63-65). This

process eliminates transaction fees and avoids tax events borne by the ETF, as the ETF does

generally not need to buy and sell component securities directly (Hehn, 2006, p.96). The main

benefit of the creation-redemption process is that it causes the market price of an ETF to

remain closely linked to its NAV, despite being priced continuously (Charupat & Miu, 2011,

p.968). If the price of the ETF moves sufficiently far outside the bid and ask band of the

underlying basket of securities, an arbitrage opportunity arises. If for example the price of the

ETF is sufficiently below the price of the underlying basket, the AP takes advantage of this

opportunity by buying ETF shares and selling the basket of securities short. At the end of the

day the AP uses the ETF shares to receive the underlying basket of securities and employ those

to cover the short position previously entered. By doing so, the AP receives the difference

between the two prices. The AP exploits the arbitrage opportunity until the price difference

between ETF and the underlying basket erode. As a consequence, the ETF is traded within the

bid-ask-spread of the underlying basket in normal market conditions. Figure 6 gives an

overview on how the primary and secondary markets are interlinked and how the creation-

redemption process is administered through the AP.

Figure 6: Creation - Redemption Process

The process of creating and redeeming ETF shares is depicted. The AP administers the process and acts as an intermediary of the capital markets, the ETF management and the Investors. Institutional investors can trade directly with the AP, on the primary as well as on the secondary market. Retail investors generally are only able to trade on exchange. (Source: Own Illustration following Hehn, 2006, p.123)

Institutional

Investor

Retail

Investor

Au

tho

rize

d P

arti

cip

ant

Capital

markets:

Stocks, ETFs,

Futures etc.

ETF / Fund manager

Cash

ETFs

ETFs

Securitie

s Secu

riti

es

ETFs

Redemption

Subscription

Cash

Securiti

OTC trading

Secondary Market Primary Market

Bro

kers

/ B

anks

Exch

ange

Cash

ETFs


15

2.7.4 Investors and Trading Strategies

Retail as well as institutional investors gained interest in ETFs as they use ETFs as an effective

mean of asset allocation by combining investments throughout different markets and asset

classes. Pension funds, insurance companies, foundations and other corporates typically use

ETFs in order to track selected markets precisely and transparently. As indicated in Figure 6,

institutional investors furthermore have the possibility to acquire ETF directly on the primary

market through OTC transactions. By trading OTC at the NAV of the ETF, an investor can get

ETF units created or redeemed at a premium only, without paying the bid-ask spread. The

investor however bears the risk that the constituents of the ETF might lose in value by the

official close of trading (Picard et al., 2014, p.16).

ETFs can be used as building blocks in a variety of strategies such as in core-satellite portfolios.

Hereby, ETFs are suitable for the core portfolio, which tries to achieve the broadest possible

diversification across the various asset classes. In the satellite portfolio the ETFs can be used to

build up diversified satellite positions in emerging markets, specific sectors or alternative asset

classes (Picard et al., 2014, p.10). ETFs can furthermore be used as a hedging tool against

declining markets, as they either can be sold short or short-ETFs can be bought (Picard &

Braun, 2010, p.11). Similar to the derivatives used to equitize cash, ETFs can be used to

manage short or medium-term cash holdings.

The variety of trading strategies indicates that investors may have completely heterogonous

interest in ETFs. The span reaches from buy-and-hold investors, who profit from a ETFs low

fees, tax efficiency and broad diversification, to a frequent trader who benefits from the low

volatility of ETFs compared to individual equities (Wiandt & McClatchy, 2001, p.98).

Having discussed the ETFs history, replication strategies, costs, revenues and market

environment, the following chapter will focus on the most prominent ETF performance

metrics. Both tracking and liquidity measures are considered.

Chapter 3 ETF Risk Metrics

16


As indicated in the preceding chapters, ETFs combine many advantageous features such as

security, good transparence, permanent pricing and trading, diversification as well as dividend

participation for relatively low costs. However, ETFs do also bear risks. In fact, many of the

existing statistical performance measures of ETFs are in fact risk figures due to the fact that

ETFs do not aim to outperform, but replicate a benchmark as closely as possible (Hassine &

Roncalli, 2013). This section hence provides the mathematical framework of key ETF risk

figures and reviews their sources. The most common metrics are the tracking difference

(subchapter 3.2), tracking error (subchapter 3.2), liquidity measures (subchapter 3.3) and the

pricing efficiency (subchapter 0). Besides pricing efficiency, those risk factors jointly depict the

building blocks for the efficiency measure derived in this thesis.

3.1 Delimitation

Much of the literature considered does not clearly distinguish tracking efficiency from pricing

efficiency. The term tracking efficiency refers to how closely the NAV of an ETF corresponds to

the NAV of the benchmark, whereas pricing efficiency measures how closely the price of the

ETF follows the NAV of the ETF. Figure 7 presents the difference between pricing and tracking

efficiency.

Figure 7: Tracking and Pricing Efficiency

The difference of pricing efficiency, measuring the equality of the ETFs price and NAV, and the tracking efficiency, measuring the equality of the ETFs NAV and benchmarks NAV are illustrated. (Source: Own illustration following Charupat & Miu, 2011)

By analyzing daily or even intraday data, pricing efficiency is concerned about the prevalence

of market inefficiencies such as failures in the creation-redemption process and its underlying

arbitrage mechanisms. However, resulting premiums or discounts over the NAV are not

expected to persist over the long run and are likely to lie within transaction costs (Charupat &

Miu, 2011). While tracking difference may be accounted to the ETF management, pricing

deviations are more likely to be market inefficiencies caused by the AP and therefore need to

be distinguished strictly.

Pricing Efficiency Tracking Efficiency

Price ETF NAV ETF NAV

Benchmark


17

3.2 Tracking Efficiency: Tracking Difference and Tracking Error 4

The ESMA Guidelines on ETFs and other UCITS defines Tracking Difference (TD) as the total

return difference of the annual return of the ETF and the annual return of the tracked

benchmark. Tracking Error (TE) is defined as the average daily volatility of the difference

between the return of the ETF and the return of the tracked benchmark (ESMA, 2012, p.4).

Both backward-looking coefficients measure the quality of benchmark tracking, whereas the

closer their values are to zero, the better is the tracking. There exist several methodologies to

calculate TE, whereas the calculation of TD is generally consistent across studies. To begin

with, Subchapter 3.2.2 provides the most prominent calculation method of TE following Pope

and Yadav (1994). In a later chapter, additional methods to compute TE are presented.

Calculating both the TD and TE requires the calculation of ETF and benchmark returns. The

mathematical formulas applied in the herein thesis are illustrated below, where and

denote the NAV of the ETF and of the benchmark at the time respectively. The returns

of the ETF and of the benchmark compute as indicated below.

(1)

(2)

3.2.1 Tracking Difference

The difference in ETF and benchmark returns, denoted by in formula (3) is calculated

according to Pope and Yadav (1994). The vector of weights of the ETF and the benchmarks

constituents are denoted with and respectively, whereby it is assumed that the number

of ETF and benchmark constituents is the same for the funds considered in this thesis.

(3)

4 Tracking Error is labeled differently in academic literature. Pope and Yadav (1994) as well as Frino and Gallagher (2001) define TE as the standard deviation of the difference between ETF returns and benchmark returns. Roll (1992) as well as Hassine and Roncalli (2013) define TE as the difference in portfolio and benchmark returns. In the herein thesis, the term TD will be used to describe the difference in returns, whereas TE refers to the standard deviation of the return differences.


18

The annual TD in returns computes as the return difference of ETF and the benchmark over the

time period of one year. The expression in the below formula denotes the vector of expected

return differences

| (4)

3.2.2 Tracking Error - Based on the Standard Deviation

The most widely used methodology used in the ETF industry is based on the day-to-day

variability of the difference in returns between a fund and its benchmark (Frino & Gallagher,

2001; Pope & Yadav, 1994). The TE | is calculated as the standard deviation of the

difference in daily returns as indicated below. The term hereby denotes the covariance

matrix of asset returns.

| √ (5)

Pope and Yadav (1994) indicate an estimation bias arising from the usage of the above formula

with daily or weekly data, inflating the TE measured. The issue can be resolved by either using

monthly data (Pope & Yadav, 1994) or make use of the correction based on the Lo and

MacKindlay (1988) analysis. iShares (2014, p.27) suggest the usage of at least 30 observation

points in order to receive a significant TE coefficient. In consequence the calculation of TE

based on monthly data requires a track record of at least two and a half years. As this trading

horizon may not reflect the average holding period of an ETF, this paper calculates TE on a

daily basis, as the average over one trading year.

3.2.3 Sources of Tracking Difference and Tracking Error

In order to get a sense for what may cause TD and TE, the sources ETF and benchmark return

differences are discussed in the following. Figure 8 lists the causes of TD and TE for both

physically and synthetically replicating ETF. The illustration additionally indicates the direction

of impact of the various factors. Whereas it can be seen from formula (3) and (4) that TD can

take both positive and negative values, TE, by squaring the return differences, only takes

positive values. A positive TD is desirable as it indicates an outperformance of the ETF over the

benchmark, whereas a high TE indicates many deviations in the returns. Thus Figure 8

allocates the direction negative to all factors increasing TE, whereas the classification negative

(positive) indicates a resulting excess performance of the benchmark (ETF).


19

Figure 8: Sources of Tracking Error and Tracking Difference

The causes of TD and TE for both physical and synthetic ETFs are depicted, indicating the direction of their impact. Negative impact indicates that the TD and TE increase. No influence* for synthetic ETFs indicates that the impact may be compensated indirectly through the swap price quoted by the swap counterparty. (Source: Own illustration following Johnson et al., 2013)

The illustration indicates an unambiguous relationship between the method how an ETF

replicates his benchmark and the quantity of potential TD and TE sources. Continuous factors

such as the daily deduction of the TER influence TD, but do generally not inflate TE. Non-

recurring and impermanent sources as for instance transaction and rebalancing costs, taxes

and diverging dividend reinvestment assumptions may influence both measures.

Many of the factors listed and their direction of impact on tracking have been discussed in the

previous chapters and thus will not be discussed again. An additional source of tracking

deviation comes from different cash holdings due to time lags during index composition

changes, where the ETF is forced to hold returns from cancelled constituents in cash (Johnson

et al., 2013, p.5). Another reason is that the ETF daily deducts a fraction of the annual

management fee. This will result in the fund holding smaller amounts of cash until payout.

Finally cash drag can arise from the lag between dividend or coupon payments by the index

constituents and the distribution of dividends to the ETF investors. Cash drag influences TE

negatively in up- and positively in down markets (Picard & Braun, 2010, pp. 22 - 23).

Cause

TER

Transaction and Rebalancing Costs

Dividend reinv. assumption

Taxation

Securities Lending

Swap Spread

Sampling method

Cash Drag

Tracking Difference

physical ETFs

Negative

Negative

Negative / Positive

Negative / Positive

Positive

No Influence

Negative / Positive

Negative / Positive

Tracking Difference

Synthetic ETFs

Negative

No influence*

No influence*

No influence*

No influence*

Negative / Positive

No influence*

No influence*

Tracking Error

physical ETFs

No Influence

Negative

Negative

Negative

Negative

No Influence

Negative

Negative

Tracking Error

Synthetic ETFs

No Influence

No influence*

No influence*

No influence*

No influence

Negative

No influence*

No influence*


20

3.3 Liquidity Metrics

Not only do the ETF constituents and their sizes have an important impact on an ETFs liquidity,

but it is likewise important to look at the property of the platforms on which the ETFs are

traded and the functioning of the underlying arbitrage mechanism. In the following, common

liquidity metrics and their applicability in the context of efficiency measurement are discussed.

Firstly, it is important to distinguish the absolute and the relative liquidity of ETFs (Roncalli &

Zheng, 2014).

Depending on the investment horizon of an investor, liquidity becomes a key criterion. The

investment of the investor determines whether to invest in a liquid or illiquid asset. A short

investment horizon may require an asset to be regularly traded at no or little discount,

whereas a long-time investor may benefit from higher returns by investing in illiquid assets

(Amihud & Mendelson, 1991). In addition, liquidity is important for risk-management purposes

in order to react quickly to changing market situations (Picard & Braun, 2010, p.9).

The subscription and redemption of ETF shares may become at risk in times of financial

distress. Recent events such as the downgrading of Greece to a non-investment grade, as well

as the earthquake in Japan in 2011 showed that ETF benchmarked to the corresponding

indices became difficult to trade (Hassine & Roncalli, 2013). Finally the liquidity of an ETF may

indicate the liquidity cost at which the ETF is traded.

3.3.1 Delimitation: Relative versus Absolute Liquidity

Relative liquidity refers to a comparison of both the ETFs and the underlying indexes liquidity.

As the liquidity of the index may be crucial when deciding for a benchmark, relative liquidity is

not relevant for intra-provider comparison as the benchmarks’ liquidity is same for all ETFs and

providers. Absolute liquidity on the other hand refers to the liquidity of the ETF himself and

does not relate to the liquidity of the underlying benchmark (Roncalli & Zheng, 2014). As

absolute liquidity is relevant in the context of this study, a selection of absolute liquidity

measures are presented.

In practice, there exist a range of measures to approximate the absolute liquidity of a fund,

however not all are appropriate when it comes to measuring the liquidity of an ETF. Why some

traditional liquidity metrics such as the AuM and the trading volume may be misleading in the

context of ETFs is explained subsequently. In order to design a comprehensive measure in

combination with TE and TD, the liquidity measure should furthermore allow for precise

scaling of ETF liquidity cost. The bid-ask spread and market impact costs are hereby found to

be the most relevant.


21

3.3.2 AuM and Trading Volume

The simplest approach to approximate the liquidity of an ETF is to look at total AuM.

Comparing the proportion of trades in the ETF allows to a certain extend to approximate how

liquid and costly trading the ETF is. Practitioners however argue, that the fund size and trading

volume allow little inference on the true liquidity of an ETF, as it is the constituent’s tradability

and their availability on the exchange that determines the liquidity of an ETF (iShares, 2013,

p.34; Justice & Rawson, 2012, p.4). Especially for ETFs, it is advisable to apply those two

measures with caution. As previously mentioned, the so-called on-screen activity coming from

trades on the secondary market which is measured and published by the exchange platforms

may only be a fraction of what is actually traded in the ETF due to OTC trades on the primary

market. Calamia, Devilla and Riva (2013) and iShares (2013, p.45) indicate that significant

portions of the ETF turnover is traded on the primary market. As those trades are not

consistently reported, overall ETF liquidity measurement with trading volume and AuM may be

misleading and are therefore not used to draw inference about the ETFs liquidity in this thesis.

3.3.3 Bid-Ask Spread

It is important to understand, that depending on whether a trade is executed on the primary

or secondary market, different liquidity costs arise. OTC trading orders can be entered at a

fixing with no bid-ask spread, whereas the price is at the discretion of the AP and the investor.

Such orders are generally handled at the NAV, meaning on the closing price of the benchmark

index plus a fee negotiated with the AP. While these fees certainly depend on the taxes, the

hedging costs as well as any operational costs of the AP, it certainly may also depend on the

negotiation power the investors.

The bid-ask spread to be paid on the secondary market is calculated throughout the day and is

generally not negotiable. Amundi (2011) stated, that the bid-ask spread for buying the ETF

MSCI World for the year 2010 on NYSE Euronext was 0.20%, whereas set-up and redemption

fees at the NAV were only 0.045%. Figure 9 lists again some of the most common factors which

influence the size of the bid-ask spread.


22

Figure 9: Impact Factors on Bid-Ask Spread

The factors influencing the bid-ask spread are illustrated. They include the costs of buying/- selling the securities, taxes levied, foreign exchange and hedging costs, the costs of holding the ETF shares and the margin of the AP. Larger trading volume and AuM furthermore are expected to have an impact on the size of the bid-ask spread. (Source: Own illustration following Amundi, 2011; Amihud & Mendelson, 1991)

From a mathematical point of view, the bid-ask spread is calculated as the difference of the bid

price and the ask price

In order to incorporate the bid-ask spread into the design of

an efficiency measurement, the relative bid-ask spread has to be calculated. This spread

measures the percentage difference in prices. Following the suggestions by Hassine and

Roncalli (2013), the relative bid-ask-spread | is calculated as the difference between the

quoted bid price and the quoted ask price

divided by their mid-price :

|

(6)

The mid-price is thereby defined as the average of both prices.

(7)

Formula (6) indicates the costs of a full market cycle, meaning purchasing an ETF share for the

bid price and consequently selling it for the ask price on the market. Whenever an investor is

more concerned with just the cost of only one transaction side, meaning either only selling or

only buying the ETF, the measure can be reduced to the half-spread by dividing the spread

| by two. In the herein thesis a full market cycle is assumed.

Impact Factors

Buying/ - selling the securitites

Taxation

Foreign Exchange/ Hedging costs

Cost of carrying the ETF

AP Margin

Trading Volume / Notional

Assets under Management


23

3.3.4 Market Impact Costs and the Notional Traded

Market impact cost arises when large trading volumes cause price in- or decreases in the

underlying assets of the ETF due to changed demand and supply on the markets (Amihud &

Mendelson, 1991). Practitioners such as Morningstar measures market impact cost by the

average market price movement in percent caused by a USD 100’000 trade in the ETF. Market

impact costs are expected to be larger the more volatile market prices are, the smaller and less

traded the ETF is and the more liquid the underlying securities are (Justice & Rawson 2012,

p.4). This costs impact becomes a key criterion for larger investors, who trade large amounts.

Not only the prices of the constituents, but also the bid-ask spread of the ETF may widen with

larger trading amounts. The best bid-ask spread may not be available as a large order generally

cannot be executed via the first best limit order in limited order book of an AP. Market impact

costs and the bid-ask spreads therefore are both influenced by the notional that is traded on

the market. The theoretical relationship between the bid-ask spread and the notional traded is

positive, meaning an increase in the notional traded results in an increase in the spread. In a

solely theoretical setting, the spread becomes infinite once the order size becomes large

enough to not be executable (Hassine & Roncalli, 2013).

In this paper however, market impact cost as well as bid-ask spreads for second or lower limit

orders will not be computed due to several reasons. Firstly, measuring those costs requires

accurate high frequency data on the bid- ask prices of the ETFs constituents, the ETF itself and

on the limited order book of the APs. Secondly, measuring the price impact of an ETF trade is

not straightforward due to many additional influential factors such as the liquidity of the ETF

and benchmark, the market microstructures as well as the capacity of the AP (Justice &

Rawson, 2012). Complementary mathematical background and exemplary calculation methods

are given in Stoll (2000), Roncalli and Zheng (2014) as well as Hassine and Roncalli (2013) and

references therein.


24

3.4 Pricing Efficiency

Closing Chapter 3 on ETF Risk metrics, this subchapter will discuss how to measure the pricing

efficiency of an ETF. Pricing efficiency, being part of microstructure analysis of an ETF,

measures how well the price of the ETFs mirrors the value of the NAV. It focuses on the

efficient functioning of exchange platforms and the products traded thereon. In this concept,

the APs’ role of providing liquidity and efficient pricing by acting as a dealer, broker and

exchange official is important.

According to Charupat and Miu (2011) the pricing efficiency of an ETF can be computed as the

percentage deviation of the end-of-day prices of an ETF from its NAV

(8)

According to Flood (2010), an issue with the above risk factor arises as closing prices are of the

noisiest prices in the day due to arbitrage trades at closing. A remedy is to use the midpoint of

closing quotes instead of the day-end prices as defined in formula (8).

(9)

Frictionless pricing is ensured by the arbitrage mechanism in the creation-redemption process

described in chapter 2.7.3. As this study assumes normal market conditions and frictionless

pricing, the pricing efficiency is anticipated to be within transaction costs. How robust pricing

and arbitrage mechanisms of ETFs are in volatile markets is yet subject to research.

This chapter mathematically evaluated the methods used to assess the risks and performance

characteristics of an ETF relative to its benchmark. Turning now to the empirical evidence on

the metrics discussed, the next chapter will review the literature on ETF performance

measurement.

Chapter 4 Literature Review

25


A selection of authors providing comprehensive background on ETF structure, risks, trading

characteristics and costs has been mentioned in the previous chapters (Picard & Braun, 2010;

Wiandt & McClatchy, 2001; Hehn, 2006). Likewise, there is a large body of studies describing

specific fields of ETFs. The herein literature review accordingly is confined on most relevant

topics for performance measurement of unleveraged, passively managed ETFs. In particular,

the focus is laid on ETF characteristics that facilitate intra-provider comparison. As a

complement to the theoretical examinations of ETFs in the previous and subsequent chapters,

this chapter takes a look at the existing empirical evidence. Section 4.1 gives an overview of

ETFs overall performance and Section 4.2 evaluates the specific risk metrics previously

discussed.

4.1 ETF Performance

Being a relatively new financial product, there has not only been an increasing amount of

literature on the performance of different ETFs types, but also lots of comparisons of ETFs to

similar instruments in recent years. Several studies investigate the performance of ETFs

respectively to traditional mutual funds. Due to their similarity, ETF have however most

prominently been contrasted to index funds. Rompotis (2005) presents evidence that the two

instruments produce very similar results with respect to average return and mean risk levels as

well as tracking ability. Considering German passively managed ETFs, the author deems ETFs to

be hybrids between index funds and equities. Blitz, Huij and Swinkels (2010) find that both

European index funds and ETFs underperform their benchmarks due to dividend taxes, but not

necessarily due to expense ratios. Harper, Madurab and Schnusenberg (2006) on the other

hand, report from their cross-country studies higher mean returns and sharp ratios than

closed-end funds due to the lower expense ratios of ETFs. The extensive study by Svetina

(2008), which evaluates domestic equity, international equity as well as fixed income ETFs,

reports that ETFs deliver better performance than retail index funds and similar performance

than institutional index funds. Roncalli and Zheng (2014) consider the liquidity of an ETFs to be

the main advantage compared to index mutual funds.

Several authors however find that ETFs display poorer returns than index funds as their

structure and management processes are reluctant not to recapture transaction costs during

benchmark changes (Gastineau, 2004; Elton, Gruber & Busse, 2002). Looking at the relative

performance of US ETF from 2011 to 2013, Qiao (2013) discovers excess performance, but


26

larger TE of ETFs compared to mutual funds. In consequence ETFs did not outperform mutual

funds, despite having lower management fees.

Raising the question whether the two instruments are complements rather than substitutes,

Svetina (2008) suggests that only 83% of ETFs in the US track the same index as index funds.

Guedj and Huang (2010) similarly find by virtue of their equilibrium model, that for well-

diversified, broad indices, ETFs and index funds indeed can be regarded as substitutes,

whereas for narrower and less liquid indexes ETFs are more suitable. These results are

consistent with the findings by Agapova (2011), who compares flows into the two instruments

and does not find cannibalization effects of ETF and index funds. Contrarily, Roncalli and Zheng

(2014) suggest that ETFs are not used as pure substitutes of index funds as the trading activity

of ETFs is spread throughout the day and not centered at the market close.

Comparing European and Swiss ETFs with their benchmarks, Rompotis and Milonas (2006)

identify a positive correlation of the management fees and the risk of the ETF. The authors

report that ETFs perform poorer and encumber investors with greater risk than their

benchmark. Gallagher and Segara (2006) examine ETFs traded on the Australian stock

exchange and argue that the ETFs produce the same return as their underlying benchmark

before costs.

Studying the cost features of ETFs and index funds, Dellva (2001) reports a cost advantage of

ETFs compared to index funds due to lower management fees. Gastineau (2001) confirms

those findings and identifies the size and the lack of transfer agency functions as the reason for

the ETFs cost efficiency. Elton et al. (2004) investigate the informational efficiency of index

funds and conclude that higher expenses such as a higher management fees does not increase

performance adequacy. Justice and Rawson (2012) incorporate holding costs as well as market

impact costs of ETFs in their total cost analysis and provide a range of results. By grouping ETFs

according to their size, they show that total costs are lower the larger and more heavily traded

the ETFs are. Moreover, they find that older ETFs have lower estimated holding costs and

tracking volatility.

Securities lending is found to be consequently used to enhance or completely offset TER

(Picard & Braun, 2010, p.55). According to a survey conducted by Morningstar, roughly 45% of

physical replicating ETFs in Europe engage in securities lending. The survey reveals that

revenue sharing arrangements and disclosure to investors vary greatly across providers. The

portion of revenues returned to the fund hereby ranges from 45% to 75% of gross revenue

(Bioy & Rose, 2013).


27

4.2 Tracking Efficiency, Liquidity and Pricing Efficiency

Frino, Gallagher, Neubert & Oetomo (2004) point out that causes of mismatches in tracking

may have exogenous as well as endogenous reasons. Exogenous TD arises from index rules and

preservation procedures such as revision of the index composition, share issuance and

repurchases and spin-offs and are beyond the fund manager’s control. Endogenous TD is

induced from the individual activities of the funds. Despite being evaluated on be basis of

index funds, those distinctions are valid for ETFs as well. Research by Johnson et al. (2013, p.9)

suggests that TD of ETFs is usually negative as an ETF should underperforms its benchmark by

its TER when assuming perfect tracking.

A number of authors compare the TE of various ETF types based on their replication style.

Meinhardt, Mueller and Schoene (2012) argue in their study about the German ETF market,

that contrary to the general belief, synthetic ETFs regardless of their appropriation and asset

class, do not have a smaller TE and do not offer superior tracking compared the full replicating

ETFs. Synthetic fixed income ETFs however, seem to have persistently lower TE. Johnson et al.

(2013, pp.5-7) suggest, that despite the reduced set of potential source for TD in synthetic

ETFs, the tracking quality may however be influenced indirectly by the swap pricing. The

authors observe lower TE with synthetic replicating ETFs tracking the S&P 500 index. Physical

replication however offers less underperformance, meaning a lower TD, than the synthetic

funds. Furthermore TD tends to vary significantly over the time period considered. Due to the

fact that the index return is guaranteed by the swap agreement, TE is genuinely lower than

with physically replicating ETFs. According to the authors, benefits from lower TE are offset by

the exposure to counterparty risk. Meinhardt et al. (2012) argue in their study about the

German ETF market, that contrary to the general belief, synthetic ETFs regardless of their

appropriation and asset class generally do not have a smaller TE and do not offer superior

tracking compared the full replicating ETFs. Synthetic fixed income ETFs however seem to have

persistently lower TE. This result stands in contrast to the findings by Johnson et al. (2013),

which find lower TE with synthetic replicating ETFs tracking the S&P 500 index.

Several studies examine the liquidity in ETFs and try to conceptualize the rather impalpable

term. According to the survey by Ernst and Young (2014), the depth of the secondary market,

approximated by the tightness of bid-ask spreads and the level of trading turnover are often

used as approximations of liquidity. To some extent, the size of the fund can be used to draw

inference about liquidity as well. The bid-ask spread and price impact are the two measures

mostly focused on in statistical literature on liquidity (Brennan & Subrahmanyam, 1996).


28

A number of studies however suggest that as the AuM and liquidity do not show high

correlation, simply looking at the ETFs’ total assets may be misleading. According to Roncalli

and Zheng (2014) this is especially true for the European ETF market, as it is mainly

institutional investors who hold large volumes of ETF for their strategic asset allocation. Other

authors contrarily find that the fund size and the amount of trading volume actually is an

indication of tighter spreads (Calamia et al., 2013). Looking at the traded volume on exchanges

as a proxy for liquidity, may however be misleading as it does not reveal the true liquidity, of

the underlying constituents of the ETF. Moreover it is the APs obligation to provide liquidity

which is relevant (Picard & Braun, 2010, p.9). Furthermore Roncalli and Zheng (2014) show

that for the EURO STOXX 50 index, trading activity is concentrated in only a small number out

of all available ETFs.

Aggrawal and Clark (2009) develop a five-factor scoring model for ETF liquidity and

consequently rank over 500 ETFs according to their underlying liquidity in the secondary

market. They find that a lower bid-ask spread, a higher market capitalization, a lower expense

ratio and higher average trading volume are the strongest indicators for high liquidity in the

ETF. Hassine and Roncalli (2013) find that the changes in spread in relation to the notional

traded depend on the markets. In their two dimensional study, Sanchez and Wei (2010)

examine bid-ask spreads and holding periods of ETFs. They use the inverse of the turnover

ratio as a proxy for the trading intensity since for ETFs the amount of shares in the market is

not fixed. The main two result of their research are, that ETFs replicating broad benchmarks

have lower spreads and that the overall liquidity of an ETF is not necessarily better than the

liquidity of their top holdings. Calamia et al (2013) find in their extensive study, that the

liquidity of ETFs not only depends on the liquidity of the benchmark, but trading volumes,

market fragmentation and AuM of ETFs result in tighter bid-ask spreads.

Furthermore, Roncalli and Zheng (2014) observe that the intraday spreads of the ETF and the

index are not related, yet there exists a positive relationship between the liquidity of the

underlying constituents and the ETF. Additionally, the competition and number of APs in the

ETF market are found to be important as they narrow the quoted bid-ask spreads (iShares,

2014, p.37). Petersen and Fialkowski (1994) show that posted and effective spreads on the

New York Stock Exchange often diverge, implicating that the quoted spreads are not what the

investors can expect in reality.

With respect to the pricing of ETFs, Ackert and Tian (2008) demonstrate that the relationship

between liquidity and pricing efficiency generally is positive for domestic ETFs as more liquid

markets tend to be more efficient. For international ETFs however, this relationship is found to


29

be non-linear. Moreover, they find that holdings of international ETFs often are not listed at

domestic markets, which hinders the efficient creation-redemption process and harms pricing

efficiency of ETFs. The authors find that mispricing of country ETFs is related to momentum,

illiquidity as well as the ETFs size. Petajisto (2013) discovers that the prices of ETFs may

fluctuate significantly, reaching a difference of 260 bps, despite the prevalence of arbitrage

mechanisms in the creation-redemption process.

Engle and Sarkar (2006) look as the daily as well as intraday transaction of US listed domestic

and international ETFs. They conclude that price deviations of domestic ETFs are generally

small and temporary, while international ETFs suffer from larger and more persistent discounts

or premiums.

Overall, the results from the comprehensive body of literature on ETF performance suggests

that the empirical evidence often is inconclusive. The purpose of this chapter was to review

the literature on ETF performance measurement, whereas the subsequent chapter will

thoroughly discuss how to measure ETF performance quantitatively.

Chapter 5 Performance Measurement

30


Markowitz (1952) was the first to provide a methodology of portfolio evaluation by maximizing

the expected return of a portfolio for a given level of market risk. Subsequent theories such as

the Capital Market Line by Tobin (1985) and the Two Fund Separation Theorem by Sharpe

(1994) laid the cornerstone for passive management. The concept of Jensen’s Alpha

established by Jensen (1968) ultimately questioned the value added of active management. In

his research on mutual funds, the author investigated the performance of 115 actively

managed mutual funds. He concluded that they do not only underperform a simple buy-and

hold approach, but found little evidence that an actively managed fund was able to perform

better than a random choice strategy. Alongside the alpha measure, other figures with the

purpose of measuring the performance of mutual funds such as the Sharpe- and Information

Ratio have been established.

This chapter will therefore illustrate why many of the tools developed up till now are not

suited to evaluate passively managed funds and may moreover return incorrect results in the

context of ETFs. The first subsection will open up this chapter b evaluating the quality features

important for an ETF investor. The subsequent sections prove why traditional metrics are

unsuited to evaluate ETF performance. Finally a performance measure based on the

framework by Hassine and Roncalli (2013), which is specifically tailored to ETFs is elaborated.

5.1 ETF Selection Principles

Fund picking for passive funds largely deviates from fund picking for actively managed funds.

Investors in ETFs generally are neither concerned about over-performing their benchmark, nor

do they need to narrow down their investment universe, as they simply try to replicate the

benchmark selected (Hassine & Roncalli, 2013). In order to understand which performance

measures are useful to compare ETFs, it is important to understand that passive investors do

not seek absolute performance, but want to buy and sell a diversified bundle of instruments at

the exact same return as the benchmark. Furthermore close-up tracking is a necessity when

ETFs are used for hedging purposes or mandates of an asset manager (Justice & Rawson,

2012).

In a global survey in 2014 representing 87% of the ETF industries global assets, Ernst and

Young (2014) determined the most important selection criteria when choosing an ETF.

Amongst the most relevant factors were the promoter’s reputation, which roughly 30% of the

participants chose to be relevant, the management fee (17%), tracking error (20%), the


31

liquidity/size (23%) and the level of spreads (13%) were chosen to be the most relevant (Ernst

and Young, 2014, p,9). Whereas an isolated assessment of those features may be practicable,

their joint evaluation is less straightforward. An ideal ETF therefore is a fund that tracks the

benchmark perfectly and at the same time exposes the investor with no risk of suffering from

bigger losses than the benchmark at any time. The following subchapter does explain why the

Sharpe- and Information Ratio are not suited to evaluate ETFs.

5.2 Sharpe Ratio and Information Ratio

Combating both the dimension of risk as well as performance, the Sharpe Ratio and

Information Ratio are often used to directly compare the performance comparable funds. They

both capture the excess return per unit of risk associated with this excess return. The Sharpe

Ratio measures the excess return of a portfolio over the risk-free rate (Sharpe, 1994) whereas

the Information Ratio measures the excess return of the investment with respect to a given

benchmark (Grinold & Khan, 2000). Both measures can be applied either to a single asset as

well as a portfolio of assets such as a fund or an ETF. The Sharpe Ratio has little indicative

value for ETF performance comparison as the ETF does not try to outperform the benchmark.

The Information Ratio may be a better measure as it captures how much the returns of the ETF

deviate from the benchmark returns and puts it into relation of the risk associated risk with

this deviation. Expressed in the mathematical terms previously established, the Information

Ratio calculates as the ratio of the TD and TE.

| |

| (10)

To illustrate the concept, the following fictional funds and their values for the Information

Ratio are considered.

Table 1: Information Ratio

Fictional examples of ETF TD, TE and Information Ratio are presented. The metrics take the value zero for the benchmark, as they measure the relative tracking with respect to the benchmark itself. (Source: Own calculations/ illustrations)

ETF Number Symbol | | |

Benchmark 0% 0% n/a

1 3.6% 3% 1.2

2 4.5% 3% 1.5

3 2.4 % 1.6% 1.5

4 2% 2.5% 0.8


32

Taking the Information Ratio as a measure, fund two is preferred to fund number one as it

displays a higher excess return | for the same level of risk | . On the other hand,

fund number one offers better performance than fund number three, but exhibits almost

double the volatility in TD. In consequence, fund three is more favorable as indicated by the

higher Information Ratio. If fund number one and four are compared, fund number four offers

a lower excess return over the benchmark and a lower risk, but nevertheless is inferior to fund

number one. Finally fund three offers a lower excess return, but also lower TE than fund

number two but has the same Information Ratio of 1.5. According to the Information Ratio, an

investor will be indifferent between the two most favorable funds number two and three.

The graphical proof of the examples considered is presented in Figure 10 below.

Figure 10: Information Ratio based on Benchmark

The Information Ratio for the four fictional Funds calculated relative to the benchmark is illustrated. The vertical axis depicts the TD and the horizontal axis indicates the TE. (Source: Own illustration following Hassine & Roncalli, 2013)

It becomes evident that fund number two is preferable to fund one as it offers better TD for

the same TE. Furthermore it can be seen that fund number three, having the same Information

Ratio of 1.5, can be constructed as a linear combination of fund number two and the

benchmark. In consequence fund number two is superior to funds number one and four as

well. Mathematically, the linear combination of fund number two and the benchmark is

defined by formula (11).

Benchmark

X3

X1

X2

X4

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

Tra

ckin

g D

Iffe

ren

ce

Tracking Error

IR 1.2

IR 0.8

IR 1.5


33

(11)

The Information Ratio then can be calculated as a linear combination of fund number two and

the benchmark.

| | (12)

The ability to combine benchmark and the fund presumes that the benchmark can be

replicated perfectly. If this requirement is fulfilled, the following proposition about the

performance of two funds and and their Information Ratio can be made according to

Hassine and Roncalli (2013).

(13)

5.2.1 Pitfalls of the Information Ratio

As it is neither is possible to invest in the benchmark directly nor to replicate it perfectly, a

tracker has to be used in order to approximate the benchmark.

(14)

In consequence the proposition (13) does no longer hold and the calculation of the

Information Ratio of fund number three becomes less trivial.

( | ) | |

√ | | | (15)

The mathematical proof of the above equation is given in Appendix 1. Whenever the TD of the

tracker is negative, due to management fees or other costs for example, the Information

Ratio of fund three is smaller than the Information Ratio of fund two , as the TE is

positive by its mathematical definition (Hassine & Roncalli, 2013). In consequence, the

subsequent relationship holds for | and .


34

( | ) | (16)

Graphically it can be seen from Figure 11 that the Information Ratio of fund three

being a linear combination of the fund and a tracker may be misleading as it

indicates to be inferior to fund . Due to the fact that could not be reached, fund

conversely is superior to fund , even though its Information Ratio is lower.

Figure 11: Information Ratio based on Tracker

The Information Ratio is calculated using a tracker, which serves as a proxy for the benchmark. The vertical axis depicts the TD and the horizontal axis indicates the TE. (Source: Own illustration following Hassine & Roncalli, 2013)

According to Hassine and Roncalli (2013) this issue becomes more severe for benchmarked

funds with low levels of TE. By looking at the increasing gap between the dotted and the

drawn-trough line in Figure 11, the authors’ proposition becomes evident. The linear

approximation gets less accurate for lower TD and TE levels.

An additional drawback of the Information Ratio in the context of ETFs is that it ignores the

magnitude of the TE. Whereas the investor may be interested in a ETF which replicates its

benchmark as close as possible. A fund that has lower TE and at the same time lower TD levels

does a better replication job than a fund with the same Information Ratio but higher TD and TE

values.

X1

X2

X3

X3 proxy

X0

-0.05

0

0.05

0.1

0.15

0.2

0 0.1 0.2 0.3 0.4 0.5 0.6

Tra

ckin

g D

iffe

ren

ce

Tracking Error


35

5.3 The ETF Efficiency Measure by Hassine and Roncalli

Hassine and Roncalli (2013) incorporate the most important ETF metrics, the TE, TD and the

bid-ask spread into a single performance measure, allowing for consistent intra-ETF

comparison. The mathematical outlay of their efficiency measure is presented in the following.

Assuming a model with two time periods, the authors define an investor’s Profit and Loss (PnL)

function of buying an ETF at time and selling it at as the difference of the TD and

the bid-ask spread of the ETF.

| | (17)

The loss function of the investor is defined as all negative events in | .

| | { | } (18)

The efficiency measure finally is a risk measure applied to the loss function of the ETF based on

the Value-at-Risk (VaR) for a given probability level .

| { { | } } (19)

VaR is defined as the threshold value, such that the loss over the given time horizon does not

exceed this value for the given probability . In other words, the investor has a probability of

of losing an amount greater than - | . By switching sings, the authors make use of

the opposite of the loss in order to achieve an ascending order of the efficiency measure.

Therefore, opposite to traditional VaR interpretation, higher values of the efficiency are more

favorable.

The relevant percentiles do depend on the probability level selected. depicts the

probability distribution function of | and is assumed to be normal in this base-scenario.

The efficiency measure is then described by the inverse of the probability distribution function

at a given level of probability.

| (20)


36

Assuming that asset returns are normal distributed, the probability distribution function takes

the values of the inverse of the standard normal distribution denoted by the Greek letter phi

.

| | | | (21)

The closed-form expression of the efficiency measure is computed by taking the TD |

and subtracting both the costs of trading the ETF measured by the bid-ask spread | and

the inverse of the standard normal probability distribution function multiplied with the TE

| . The full mathematical derivation of formula (21) is presented in Appendix 2.

In order to illustrate the intuition of the efficiency measure, Figure 12 exemplifies the

efficiency measure at a confidence level of 95%. At this quantile, the expression

takes the rounded value of For the computation, the following fictional values are

assumed: | , | and | .

Figure 12: Illustration of the Efficiency Measure

The efficiency measure is illustrated. A positive TD shifts the mean of the normal curve to the right, the bid-ask spread shifts it to left. The inverse of the inverse of the standard normal probability distribution function at the 95% percentile, multiplied by the TE finally indicates the VaR on the horizontal axis. (Source: Own illustration following Hassine & Roncalli, 2013)

As it can be seen from Figure 12, the graph takes the form of a normal distribution. The

difference between the TD and the spread shifts the curve to the right. Consequently the PnL

distribution is centered around 20 bps. Looking at the 95% percentile, the efficiency measure

takes the value of | . The investor in this example therefore has a 95%

s(x │ b)

μ(x │ b)

1.65*σ(x │ b)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-1.0

0

-0.9

0

-0.8

0

-0.7

0

-0.6

0

-0.5

0

-0.4

0

-0.3

0

-0.2

0

-0.1

0

0.0

0

0.1

0

0.2

0

0.3

0

0.4

0

0.5

0

0.6

0

0.7

0

0.8

0

0.9

0

1.0

0

1.1

0

1.2

0

1.3

0

Value-at-Risk


37

chance of not losing an amount greater than 30 bps or reciprocally a 5% chance of losing an

amount greater than 30 bps.

Figure 13: Larger Tracking DifferenceFigure 13 to Figure 15 illustrate how the efficiency measure

adapts to changes in the underlying risk factors.

Figure 13: Larger Tracking Difference Figure 14: Larger Bid-Ask Spread

The dashed line illustrates an increase in the TD. The horizontal axis depicts the VaR. The dashed lines indicate the shift in the probability distribution function as compared to the initial fund. (Source: Own illustration following Hassine & Roncalli, 2013)

The dashed line illustrates an increase in the spread. The horizontal axis depicts the VaR. The dashed lines indicate the shift in the probability distribution function as compared to the initial fund. (Source: Own illustration following Hassine & Roncalli, 2013)

In Figure 13 the TD has been increased to 50 bps, meaning that the fund outperforms his

benchmark by an additional 10 bps and therefore is favorable to the initial fund. Consistent

with this interpretation, the efficiency measure takes a value of -10 bps. Figure 13 illustrates a

widening in the spread of 20 bps as the efficiency measure deteriorates to -50 bps, the initial

fund is preferred.

Figure 15: Larger Tracking Error

The dashed line illustrates an increase in the TE. The horizontal axis depicts the VaR. The dashed lines indicate the shift in the probability distribution function as compared to the initial fund. (Source: Own illustration following Hassine & Roncalli, 2013)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-1.0

0

-0.8

5

-0.7

0

-0.5

5

-0.4

0

-0.2

5

-0.1

0

0.0

5

0.2

0

0.3

5

0.5

0

0.6

5

0.8

0

0.9

5

1.1

0

1.2

5

1.4

0u1(x|b) < u2(x|b)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-1.0

0

-0.8

5

-0.7

0

-0.5

5

-0.4

0

-0.2

5

-0.1

0

0.0

5

0.2

0

0.3

5

0.5

0

0.6

5

0.8

0

0.9

5

1.1

0

1.2

5

1.4

0

s1(x|b) < s2(x|b)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-1.0

0

-0.8

5

-0.7

0

-0.5

5

-0.4

0

-0.2

5

-0.1

0

0.0

5

0.2

0

0.3

5

0.5

0

0.6

5

0.8

0

0.9

5

1.1

0

1.2

5

1.4

0

σ1(x|b) < σ2(x|b)


38

In Figure 15, the altered fund has a greater TE of 40 bps, which means that the distribution of

TD is more scattered and exhibits fatter tails. In consequence the fund is more likely to deliver

bigger. The lower value of the efficiency measure -46 bps confirms this presumption and

therefore the initial fund is preferred.

According to Hassine and Roncalli (2013), it can be concluded that if and are two ETFs

benchmarked against the same index, is preferred to if and only if the efficiency measure

of fund | is larger than the efficiency measure of fund | .

| | (22)

This chapter described which factors are most relevant for an ETF investor and argued why

traditional performance metrics may fail in the context of ETFs. It suggested that a

comprehensive ETF performance measure should include the bid-ask spread, TD and TE in

order to cover all relevant ETF performance dimensions. The next chapter will apply the

procedures and methods previously derived to the ETF data sample.

Chapter 6 Empirical Research

39


This chapter follows on from the previous chapter, which laid out the mathematical framework

of the efficiency measure | , turning now to the empirical evidence on Swiss and

European ETFs. The first subsection provides details on the ETF sample and data treatment.

The second subchapter prepositions the sample statistics and the last subchapter calculates

the efficiency measure based on the ETF data sample.

6.1 Data Sample

The sample period covers one trading year of an ETF. It starts on May 1st, 2013 and ends on

April 30th, 2014. For all calculations the perspective of a Swiss investor is adopted. In

consequence, solely ETF which were active on SIX Swiss Exchange throughout the entire study

period are eligible. ETFs liquidated or not incepted at the beginning of the study period are

excluded from the analysis. Even though investors are able to trade ETFs internationally,

additional expenses from on-site storage or costly transfer to the home stock exchange justify

the above confinement of only considering the funds quoted on the Swiss exchange.

The ETF sample is restricted to all funds replicating the Swiss Market Index (SMI) and the EURO

STOXX 50, whereas currency hedged share classes are not part of the data sample. For the

SMI, ETFs benchmarked against both the prices as well as the net total return index are

considered. For EURO STOXX 50, due to tax-efficiency reasons, only ETFs on the net total

return index are on the market. Regardless of the fact that certain providers issue multiple

ETFs with diverging share classes on the same benchmark, all ETFs are considered. The

different share classes are specially designed for either institutional or retail investors and in

consequence have varying management fees, TER, minimum investment and finally tracking

efficiency.

All calculations are held in the corresponding base currency of the benchmark, which is Swiss

Francs (CHF) for the SMI and Euros (EUR) for the EURO STOXX 50. As iShares (2014, p.29)

indicates, calculating TE in a different currency results in marginally different volatility and

additionally comprises currency risk. Such risk is not part of the analysis in this study.

In total, five ETFs benchmarked against the SMI and seven ETFs replicating the EURO STOXX 50

are evaluated. Further information regarding the constituents and weights of the considered

benchmarks are given in the Appendix 3. An overview of the sample ETFs, including additional


40

information on e.g. management fees, inception dates, fund sizes and dividend appointments

can be found in Appendix 4, 5 and 6.

6.2 Data Treatment

The relevant data is extracted from Bloomberg and merged with the information available on

the provider websites. If not stated otherwise, all data is measures at the closing of the

corresponding trading day. The bid (ask) prices available on Bloomberg are defined as the

highest (lowest) price a seller will accept for a security. They correspond to the last bid (ask)

price from the last day the market was open. As receiving the data from an index may be

costly for ETF providers, they often avoid costs by purchasing data either from the total return

or the price index. In the herein data sample, three distributing ETFs are therefore

benchmarked against the SMI total return index. In the case of EURO STOXX 50, due to fiscal

optimization, all providers of the sample chose to replicate the EURO STOXX 50 total return

Index. In consequence three distributing ETFs have deviant dividend assumptions from their

benchmark.

In order to receive significant and consistent statistics, the following definitions and numerical

adjustments are applied to the data sample:

For each ETF a number between 1# and 7# is assigned in order to obtain anonymous and

provider-independent results. The concrete ETF names can be found in Appendix 4, whereby

the order of the funds in the appendix does not correspond to the order of the numbers

assigned.

With the purpose of receiving consistent and comparable results, the confidence level for the

VaR is set at throughout the whole analysis.

Whenever an ETF treats dividend payments differently than the benchmark, TD and TE arise

and distort calculations. In order to compute commensurable metrics, the daily performance

of the ETF is corrected every time a dividend is paid. Hereto the dividends are added back to

the NAV of the ETF at the dividend date and are assumed to exhibit the same percentage

return as the NAV for the remaining observation period.


41

Due to divergent holidays of the ETF and the benchmark, partially no NAV is quoted. In

consequence, such days are excluded in the calculations of both ETF and benchmark returns.

Additionally, whenever there was no trading activity in an ETF and thus no bid and ask prices

placed, those days are not considered for the calculations of the spread.

6.3 Sample Statistics

The study period is denoted by [ ] and includes daily observations. The corresponding

value of the inverse of the 95%-percentile of the standard normal probability distribution

is 1.645. For the data sample, the efficiency measure takes the following closed-form

expression

| | | | (23)

where the sample mean | , TD | the bid-ask spread | and the TE |

are calculated according to Hassine and Roncalli (2013) over the whole observation period.

The annual TD | is calculated as the annual return difference between ETF and

benchmark returns, whereas corresponds to one year.

| (

)

(

)

(24)

The sample mean | is measured as the average of the daily return difference of the ETF

and the benchmark.

|

(25)

The calculation of the percentage spread is based on the day end bid and ask,

prices. It is assumed, that all the trading orders are executed at the best available prices,

indicated by the superscripted number one.

|

(26)


42

The sample annual average spread is the sum of all spreads divided by the amount of trading

days observed in the sample.

|

|

(27)

The sample TE calculates as the annualized daily standard deviation from the sample mean.

| √

|

√ (28)

In order to consistently calculate the VaR for all ETFs, the daily TE is annualized by being

multiplied with the factor √ As suggested by Hassine and Roncalli (2013), the number 260

depicts the standardized amount of trading days a year. Although only being an appropriate

procedure, when assuming Brownian motion in returns, it is a universally accepted rule to

annualize the daily TE by multiplying it with the square root of the amount of trading days

(Duffie & Pan, 1997).

6.4 Results for the ETFs on SMI

Table 2 presents the descriptive statistics of all sample variables as well as the result of the

efficiency measure for the ETFs on SMI.

Table 2: Results for the ETFs on SMI5

The summary annual statistics of the TD, the sample mean, the bid-ask spread, the TE and the efficiency measure are presented. The measures are calculated on a daily basis from May 2013 to May 2014, whereas the numbers depict annualized results. The statistics are rounded to two decimal places and measured in basis points (bps), where one percentage corresponds to 100 bps. (Source: Own calculations/ Illustrations)

ETF on SMI | | | | |

1# -30.39 0.67 15.34 78.15 -174.28

2# -112.12 -0.43 62.21 46.97 -251.59

3# -69.35 -0.26 10.92 39.04 -144.47

4# -43.30 -0.16 4.95 4.40 -55.49

5# -32.98 -0.12 6.94 7.95 -53.01

Average -57.63 -0.06 20.07 35.30 -135.77

5 The empirical data analysis and computation framework are held in Microsoft Excel and are enclosed to this thesis. If not stated otherwise, all subsequent results are measured in basis points. For all calculations the explanations laid out in subchapter 6.1 and 6.2 apply.


43

According to the efficiency measure for the ETFS on the SMI, ETF 5# is the most efficiently

tracking ETF amongst all funds. With fund number 5#, an investor has a 95% chance of not

losing an amount greater than 53 bps by the end of the study period. ETF 4# exhibits similar

results. Looking at the magnitude of the sample calculations, ETF 2# not only underperforms

his benchmark more than its peers, but comes at the highest bid-ask spread of 62.2 bps. The

evolution of the bid-ask spread of fund number 2# can be seen in Figure 16. In comparison to

the spread development of the other ETFs, fund 2# exhibits much higher and step-like spread

values. One of the potential reasons for this distortion could be the previously discussed

problem of taking day-end prices, instead of e.g. intra-day bid and ask prices.

Figure 16: Percentage Spread ETF 2#6 SMI

The percentage spread development for ETF 2# on SMI is illustrated. The observation period covers May 2013 to May 2014. (Source: Own calculations / illustrations)

The second reason for the large underperformance of fund number 2#, is the large TD of more

than 112 bps caused by three large negative spikes in on the February 27th 2014, March 6th,

2014 and April 14th 2014. These negative outliers are illustrated in the figure below.

Figure 17: Tracking Difference ETF 2# SMI

The TD development for ETF 2# on SMI is illustrated. The observation period covers May 2013 to May 2014. The red circle indicates the three negative outliers towards the end of the observation period. (Source: Own calculations / illustrations)

6 For graphical intra-ETF analysis it is important to bear in mind that scales of the vertical axis of the subsequent illustrations diverge across the exhibits. An overview of all graphs scaled consistently is given in Appendix 7 and 10.

0.20%0.30%0.40%0.50%0.60%0.70%0.80%0.90%1.00%

-0.25%-0.20%-0.15%-0.10%-0.05%0.00%0.05%0.10%0.15%


44

Interestingly, the other ETFs on SMI exhibit similar deviations in returns around the same

dates. The reason is, that as the SMI is a market capitalization-weighted index, the three big

weights Nestlé, Roche and Novartis each make out about 18-21% of the index. Whenever one

of these companies pays dividends, (Roche on March 4th and 5th, 2014; Novartis on February

25th, 2014; Nestlé on April 10th, 2014) TD as well as TE arise. Curiously, the synthetic replicating

ETF 2# seems not to be protected against distortions from dividend payments in the index. The

physically replicating ETFs number 4# and 5# adjust to the index dividend schedule by

distributing their dividends at the exact same dates. Presumably those dates are chosen in

order to avoid cash drag from the constituents’ dividends. Fund 1#, being a distributing and

physically replicating fund on the other hand exhibits large positive TD as he is benchmarked

against the SMI price index. In consequence fund number 1# exhibits the largest TE of all funds

considered, but also the most favorable TD characteristics as depicted in Figure 18.


The TD development for ETF 1# on SMI is illustrated. The observation period covers May 2013 to May 2014. The red circle indicates the four positive outliers towards the end of the observation period. (Source: Own calculations / illustrations)

An example of the TD over the observation period without large outliers can be seen from

fund 5# in Figure 19. Due to the lack of large data outliers, the annual TE of fund 5# is the

second lowest. In consequence, the fund is rated the most efficient tracking fund out of the

ETF on SMI data sample.

-0.10%

0.00%

0.10%

0.20%

0.30%

0.40%

0.50%


45


The TD development for ETF 5# on SMI is illustrated. The observation period covers May 2013 to May 2014. (Source: Own calculations / illustrations)

In conclusion, none of the ETFs on the SMI considered are able to outperform their benchmark

and attain a positive TD. ETF 1# was the only fund which attained a positive value for the

sample mean, indicating the large proportion of positive TE.

From the sample calculations, it becomes apparent that the TE has the biggest influence on

the efficiency measure and the ETF tracking performance. On average, the ETFs tracking the

SMI exhibited an annualized TE of roughly 35.3 bps. Nevertheless both TE and the bid-ask

spread play an important role by making out the difference amongst ETFs with similar TE

values.

6.5 Results for the ETFs on EURO STOXX 50

Largely consistent with the results reported by Hassine and Roncalli (2013) for the study period

of November 2011 to November 2012, the TD for all ETFs on EURO STOXX 50 suggest an

outperformance of the benchmark. The average TD takes a value of 43 bps. Fund number 7#

performs best by beating the benchmark by 73 bps over the course of one trading year. The

results for the ETFs on EURO STOXX 50 are reported in Table 3. Astonishingly, fund 7# does

expose an investor with a 95% chance of not gaining an amount less than 26.65 bps by the end

of the observation period. According to the efficiency measure, fund 1# is ranked the most

efficient ETF, while part of its excess-performance may be explained by securities lending. ETFs

4#, 5# and 7# profit from securities lending as well and consequently outperform the

benchmark. ETF 1# is ranked second by exhibiting the second lowest TE of all ETFs. Fund 4# is

the least favorable ETF by exposing an investor to a loss not greater than 102 bps. The reason

of the by far weakest performance is the low TD, large bid-ask spread and highest TE.

-0.03%-0.02%-0.02%-0.01%-0.01%0.00%0.01%0.01%0.02%


46

Table 3: Results for the ETFs on EURO STOXX 50

The summary annual statistics of the TD, the sample mean, the bid-ask spread, the TE and the efficiency measure are presented. The measures are calculated on a daily basis from May 2013 to May 2014, whereas the numbers depict annualized results. The statistics are rounded to two decimal places and measured in basis points (bps), where one percentage corresponds to 100 bps. (Source: Own calculations/ Illustrations)

ETF on EURO STOXX 50

| | | | |

1# 45.97 0.15 15.30 10.95 12.67

2# 41.76 0.14 59.75 9.95 -34.35

3# 12.86 0.23 25.86 12.10 -32.90

4# 17.87 0.24 52.73 41.20 -102.62

5# 67.28 0.22 13.82 32.45 0.09

6# 42.34 0.14 14.01 11.17 9.95

7# 73.01 0.24 15.68 18.71 26.55

Average 43.02 0.20 28.17 19.50 -17.23

Johnson et al. (2013) which investigated on the excess-performance of ETFs on EURO STOXX

50 find that much of the outperformance can be explained by the choice of the benchmark.

The reason is that the net return version of the index assumes certain withholding taxes on the

dividends paid, whereas most ETFs in fact achieve lower withholding tax rates in their country

of domicile. The authors furthermore report significant and higher than average performance

deviation around May of each year as a result of dividend optimization. Those findings are

consistent with most of the results obtained from the sample analysis. As it can be seen from

ETF 7# in Figure 20, the TD is especially volatile around the period of Mai 2013. With the

exception of ETF 4#, the other funds exhibited similar in TD.

Figure 20: Tracking Difference ETF 7# EURO STOXX 50

The TD development for ETF 1# on EURO STOXX 50 is illustrated. The observation period covers May 2013 to May 2014. The red circle indicates the higher volatility at the beginning of the observation period. (Source: Own calculations / illustrations)

Finally, the ETFs outperformance partially helps to explain the higher than average TE due to

the positive deviation from the benchmark. Overall, results show evidence that synthetic

replicating ETFs such as funds number 1#, 2# & 6# indeed produce lower TE than those using

-0.04%

-0.02%

0.00%

0.02%

0.04%

0.06%

0.08%

0.10%

0.12%


47

physical replication. In the sample average, physical replicating ETFs had a greater TE of about

43 bps.

With respect to the bid-ask spread, funds 2# and 4# show a particularly high spread. Fund 2#

hereby exhibits an inexplicable development in the spread, as the bid-ask spread level takes a

leap around September 05th and December 1st, 2013 as illustrated in Figure 21. Interestingly,

the development of the percentage spread does exhibit two breaks in the trend line at the

dates where no spread was quoted on Bloomberg.

Figure 21: Percentage Spread ETF 2# EURO STOXX 50

The percentage spread development for ETF 2# on EURO STOXX 50 is illustrated. The observation period covers May 2013 to May 2014. The red circles illustrate the inexplicable leap in the percentage spread levels. (Source: Own calculations / illustrations)

The illustration of the spread development of the other funds in the sample can be found in

appendix 10, whereas they do not exhibit such anomalies in the development of the spread.

The jumps and high spread levels raise the suspicion, that the data on the quoted spreads may

be incorrect. For the subsequent calculations it is important to bear in mind the potential bias

stemming from the exceptionally large spread of ETF 2#.

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%


48

6.5.1 Information Ratio versus Efficiency Measure

This subchapter evaluates whether the ranking according to the previously discussed

Information Ratio corresponds to the ranking according to the efficiency measure. The bid-ask

spread is therefore added back to the efficiency measure, as it is not accounted for in the

Information Ratio. The sample results are reported in Table 4 and Table 5.

Table 4: Information Ratio ETF SMI Table 5: Information Ratio ETF EURO STOXX 50

The Information Ratio in absolute terms and the efficiency measure in bps are presented. (Source: Own calculations / illustrations)

The Information Ratio in absolute terms and the efficiency measure in bps are presented. (Source: Own calculations / illustrations)

ETF on SMI | |

# -0.39 -174.28

2# -2.39 -251.59

3# -1.78 -144.47

4# -9.83 -55.49

5# -4.15 -53.01

Average -3.71 -135.77


| |

1# 4.20 27.96

2# 4.20 25.40

3# 1.06 -7.04

4# 0.43 -49.89

5# 2.07 13.91

6# 3.79 23.96

7# 3.90 42.23

Average 2.81 -10.93

The ranking of the ETFs according to the Information Ratio is different than the ranking

according to the efficiency measure values. This highlights the drawback of the Information

Ratio in connection with passive fund evaluation, as it not account for the absolute levels of TE

and TD but only looks at their ratio. From the Information Ratio of ETF 2# and 3# on EURO

STOXX 50, it becomes evident that even though fund 3# performs worse than fund 2# by

exhibiting a higher TE, the ETF compensates by having a much larger TD. In conclusion, the

funds 2# is favored when looking at the Information Ratio, whereas fund 3# performs slightly

better when looking at the ETF efficiency.

In this chapter, the empirical evidence on the ETF efficiency measure has been presented for

the sample ETFs on the SMI and the EURO STOXX 50. As the sample calculations indicate

asymmetric in the TE distribution, the VaR method applied needs to be further evaluated. The

viability of the model and its underlying assumptions thus will be further evaluated in the

subsequent chapter.

Chapter 7 Adjustments to the Efficiency Measure

49


Building on the basic framework presented in Chapter 6, this chapter enhances the

mathematical assumptions and calculation methods of the ETF efficiency measure by taking

into account a set of statistical considerations and adjustments. To begin with, the first

subchapter discusses pricing efficiency. Comparing alternative ways of calculating TE,

subchapter 7.2 evaluates on the one hand whether the results differ significantly across the

calculation methods and on the other hand how robust those results are to data outliers.

Additionally, the concept of semi-volatility is introduced. Finally, the second subchapter will

cut into potential errors arising from autocorrelation in TD. The third subchapter discusses

alternative approaches to measure the bid- ask spread. Adjusting the underlying assumptions

of the VaR framework, subchapter 7.4 applies alternative risk measures such as the historical

VaR, Cornish-Fisher VaR, intra-horizon VaR as well as the Expected Shortfall.

7.1 Pricing Efficiency

Before looking at potential adjustments of the factors and the framework of the efficiency, this

subsection will look at the previously discussed pricing efficiency. It evaluates, whether the

efficiency measure can be enhanced by including pricing efficiency of an ETF. As day end prices

tend to be the most volatile, the average daily pricing deviation is calculated as the

percentage difference of the midpoint spread and the NAV of the ETF. Table 6 and Table 7

present the sample calculations.

Table 6: Pricing Efficiency ETF SMI Table 7: Pricing Efficiency ETF EURO STOXX 50

The average daily pricing efficiency measured in bps is presented. (Source: Own calculations / illustrations)

The average daily pricing efficiency measured in bps is presented. (Source: Own calculations / illustrations)

ETF on SMI

1# 0.37

2# 0.60

3# -0.25

4# 0.10

5# 1.41

Average 0.45


1# -0.50

2# -2.89

3# 1.56

4# 0.98

5# 3.40

6# -1.54

7# 1.20

Average 0.32

Negative values for the pricing efficiency indicate that the NAV is larger than the midpoint

spread, whereas positive values suggest that the midpoint spread on average was higher.


50

The results show that the daily prices do not deviate more than half a basis point from their

NAV. Only ETF 2# and 5# on EURO STOXX 50 deviate significantly, which indicates that the ETF

pricing and markets function efficiently. Furthermore, APs seem to generally step in, which

closes arbitrage opportunities from deviating prices.

Pricing efficiency will not be included in the efficient measure for three reasons. Firstly the

above values indicate that at normal market conditions, pricing deviations tend to be small

and within transaction costs. Secondly, due to the usage of day-end prices, it is uncertain that

the data on the bid and ask prices is representative. Finally, as the pricing efficiency highly

depends on the efficient functioning of the markets rather than on the ETFs tracking ability

itself, the measures will not be included.

7.2 Alternative Tracking Error Measures

Besides the computation method previously presented, there exist alternative ways to

calculate TE. The methods vary either on what kind of volatility is measured or how TE is

computed. In order to keep the various measures apart, the different TE measures will be

labeled with a subscript. TE from formula (28), based on the standard deviation of return

differences is referred to as . Measuring the same type of volatility, but with alternative

calculation methods, TE based on the correlations of returns will be denoted as and TE

based on the residuals of a linear regression is labeled as The robust measure considered is

based on the Median Absolute Deviation (MAD) and is labeled . Finally TE measured as

the standard deviation below a certain threshold will be referred to as semi-volatility .

7.2.1 TE – Based on Correlation of Returns

According to Hwang and Satchell (2001), the daily TE can be calculated based on the values of

covariance of the benchmark and the ETF returns as well as their variances

and .

| √

(29) The covariance can be further disseminated into the product of correlation and standard

deviations. The annualized sample TE is calculated based on the values of correlation of

ETF and benchmark returns as well as their variances and standard deviations .

| √

√ (30)


51

Again the annualized TE is received by multiplying the daily TE with the factor √ . The

sample values for the alternative TE measure | can be seen in Table 8 and Table 9.

Table 8: Tracking Error

The summary statistics of the ETF and benchmark variances and the covariance of ETF and benchmark are reported in absolute values. The TE measures based on the standard deviation and the correlation of returns in bps are presented. (Source: Own calculations / illustrations) Panel A: ETF on SMI

ETF on SMI | |

1# 0.70515 0.70932 0.99834 78.31 78.15

2# 0.73433 0.73798 0.99942 47.07 46.97

3# 0.68211 0.70095 0.99967 39.12 39.03

4# 0.70088 0.70095 0.99999 4.41 4.40

5# 0.69968 0.70095 0.99998 7.97 7.95

Average 0.70 0.71 1.00 35.38 35.30

Panel B: ETF on EUTO STOXX 50


| |

1# 0.9390 0.9392 0.99998 10.97 10.95

2# 0.9485 0.9514 0.99998 9.97 9.95

3# 0.9649 0.9701 0.99997 12.12 12.10

4# 0.9176 0.9392 0.99971 41.28 41.20

5# 0.9358 0.9356 0.99978 32.51 32.45

6# 0.9383 0.9356 0.99997 11.20 11.17

7# 0.9340 0.9389 0.99993 18.75 18.71

Average 0.9407 0.9452 0.99990 19.85 19.50

From the tables above it can be seen that the correlation coefficient of ETF and

benchmark returns is approximately one for all ETFs, indicating an approximately perfect

correlation of their returns. When jointly plotting the ETF and benchmark returns, their

positive linear relationship becomes evident. Taking ETF 1# on SMI as an example, Figure 19

illustrates the match of ETF and benchmark returns. Except for the four previously discussed

outliers from dividend payment in the SMI, all returns lie perfectly aligned on the regression

line.


52

Figure 22: Sample Regression with Data Outliers

The regression of ETF and benchmark returns for ETF 1# on SMI is presented. The vertical axis depicts the ETF returns and the horizontal axis depicts the index returns. The equation of and the coefficient of determination in the top left corner indicate that the ETF and benchmark returns fit the linear regression very well. The red circle indicates the four outliers in the data sample. (Source: Own calculation / illustrations)

Figure 23 exemplifies an approximately perfect correlation of 0.99997 between the ETF and

benchmark returns of fund 3# on EURO STOXX 50.

Figure 23: Sample Regression without Data Outliers

The regression of ETF and benchmark returns for ETF 1# on SMI is presented. The vertical axis depicts the ETF returns and the horizontal axis depicts the index returns. The equation of and the coefficient of determination in the top left corner indicate that the ETF and benchmark returns fit the linear regression very well. (Source: Own calculation / illustrations)

Looking at the difference between measure | and | , there is no significant

change in TE values associated with the alternative calculation method. Overall, the resulting

values for | differ from the original calculations for less than one bps only. As the

values of the efficiency indicator do not change significantly, the ranking of the ETFs is not

altered as well.

y = 0.9954x + 7E-05 R² = 0.9967

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

-0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04

ET

F R

etu

rns

Index Returns

y = 0.9996x + 2E-05 R² = 0.9999

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

-0.04 -0.02 0 0.02 0.04

ET

F R

etr

un

s

Index Returns


53

7.2.2 Tracking Error based on the Residuals of a Linear Regression

Using the concept of correlation alike, Treynor and Black (1973) measure the daily TE by

analyzing the regression of the return of the ETF on the return of the benchmark. The standard

deviations of the residuals of the linear regression are then used as an estimate of TE.

(31)

| (32)

| √ (33)

The daily TE of a portfolio can be computed from both formula (32) and (33) yielding the same

results. The annualized sample TE is calculated by multiplying the daily TE with the square root

of the standardized amount of trading days 260.

In Table 9 the sample statistics for the alternative TE based are listed. As expected, |

and | do return exact same TE values. Furthermore, strong evidence is found that

none of the three alternative calculation methods does significantly deviate. The ranking of the

ETFs according to the efficiency measure remains the same, independent of the TE measure

considered.

Table 9: Alternative TE ETF SMI

The summary statistics of the ETF TE measures based on the standard deviation, the correlation of returns and the residuals of a linear regression are presented. The final row depicts the alternative way of calculating the TE based on a linear regression. All results are reported in basis points. (Source: Own calculation / illustration)

Panel A: ETF on SMI

ETF on SMI | | | |

1# 78.15 78.31 78.06 78.06

2# 46.97 47.07 46.88 46.88

3# 39.04 39.12 34.35 34.35

4# 4.40 4.41 4.41 4.41

5# 7.95 7.97 7.87 7.87

Average 35.30 35.38 34.32 34.32


54

Panel B: ETF on EURO STOXX 50


| | | |

1# 10.95 10.97 10.97 10.97

2# 9.95 9.97 9.68 9.68

3# 12.10 12.12 12.10 12.10

4# 41.20 41.28 36.98 36.98

5# 32.45 32.51 32.37 32.37

6# 11.17 11.20 11.17 11.17

7# 18.71 18.75 18.28 18.28

Average 19.50 19.54 19.79 18.79

7.2.3 Tracking Error based on Robust Measures

TD and TE are strongly affected by data outliers from e.g. diverging dividend payments

schedules, holidays, missing or misaligned data and rounding errors. Such data outliers may

inflate the TE of an ETF, despite its fairly good tracking of the benchmark. In the herein study,

data outliers are understood according to the three-sigma rule following Duda, Hart and Stork

(1997). The authors state, that in a normal distribution, 99.73% of all values lie within three

standard deviations of the sample mean. Table 10 and Table 11 indicate how many outliers

were found according to the three-sigma rule over the whole study period.

Table 10: Data Outliers ETF SMI Table 11: Data Outliers ETF EURO STOXX 50

The amount of data outliers in the data sample according to the three-sigma rules. (Source: Own calculations / illustrations)

The amount of data outliers in the data sample according to the three-sigma rules. (Source: Own calculations / illustrations)

ETF on SMI Number of

outliers

1# 4

2# 1

3# 1

4# 2

5# 1

Average 1.80


Number of outliers

1# 7

2# 8

3# 6

4# 2

5# 1

6# 3

7# 2

Average 4.14

Simply removing outliers may erroneously distort the TE test statistics. Additionally data

outliers may mask other deviants, which would fall under the three-sigma rule after the

removal of the initial outliers. Furthermore, accurate data outliers from e.g. different dividend

appointment should be included in the efficiency measure whenever they reflect the actual

ETF tracking.


55

Instead of removing outliers from the data sample, a robust measure of TE is applied. The

measure allows to assess the TD volatility of an ETF in its essence. It furthermore may be a

better metric to draw long term inference about the TD volatility, not affected by singular

outlier points. For the herein data sample, it is expected that all ETFs will display improved

sample statistics, due to a reduction in TE.

Following the definition by Hwang and Satchell (2001), a way of measuring robust TE is based

on the Median Absolute Deviation (MAD). The resulting TE | is defined as the

median of the absolute deviations from the data’s median . The median is defined as the

middle value, separating the upper from the lower half of the empirical sample TD.

|

| |

(34)

Compared to the previous efficiency measure the is no longer calculated with respect

to the sample mean | but to the median in absolute terms. Data outliers drag the

mean towards them, away from the true center of the data. By arranging all observations

according to their magnitude and picking the middle value, the median is robust to data

outliers.

The results, illustrated in Table 12 and Table 13, indicate an overall decrease of TE based on

the calculations on MAD. On average, the switch to the robust measure improves the TE of the

ETFs on SMI for approximately 30 bps.

Table 12: Robust TE ETF SMI

The summary statistics of the TE measures based on the standard deviation and on MAD as well as the corresponding efficiency measures are presented for the ETFs on SMI. (Source: Own illustrations/ calculations)

ETF on SMI | | | |

1# 78.15 20.74 -174.28 -79.85

2# 46.97 13.47 -251.59 -196.48

3# 39.04 18.06 -144.47 -109.96

4# 4.40 2.07 -55.49 -51.66

5# 7.95 6.14 -53.01 -50.02

Average 35.30 12.09 -135.77 -98.08

Nevertheless, the reduction in TE did not affect all ETFs alike. ETF 5# is still the most favorable

fund with respect to the TE as well as the corresponding efficiency indicator | . ETF 4#

and ETF 1# become the second and third most efficient fund. As suggested by the amount of


56

data outliers, the TE of ETF 1# is reduced by more than 70%. Fund number 3#, previously

having a lower VaR of roughly 30bps than fund number 1#, dismounts in the rating.

Table 13: Robust TE ETF EURO STOXX 50

The summary statistics of the TE measures based on the standard deviation and on MAD as well as the corresponding efficiency measures are presented for the ETFs on EURO STOXX 50. (Source: Own illustrations/ calculations)


| | | |

1# 10.95 4.63 12.67 23.06

2# 9.95 4.52 -34.55 -25.62

3# 12.10 6.30 -32.90 -23.36

4# 41.20 27.51 -102.62 -80.11

5# 32.45 6.66 0.09 42.50

6# 11.17 3.72 9.95 22.20

7# 18.71 8.72 26.55 42.99

Average 19.503 8.87 -17.26 0.24

Similarly, the rankings for the ETFs on EURO STOXX 50 change. On average, the robust

measure | reduces TE of all funds for about 11 bps. Fund 5# profits the most from

an improvement in the TE and is now ranked the second most efficient fund, only half a bps

behind fund 7#. Although ETF 5# only exhibits one data outlier, it can be seen from the

distribution of TE in Figure 24 that the magnitude of the outlier causes the mean as well as the

TE to inflate. This exemplifies that the robust TE measure based on MAD does not only account

for the amount, but the magnitude of outliers as well.


The TD development for ETF 5# on EURO STOXX 50 is illustrated. The observation period covers May 2013 to May 2014. (Source: Own calculations / illustrations)

-0.05%

0.00%

0.05%

0.10%

0.15%

0.20%

0.25%

0.30%

0.35%


57

In order to supplement the intuition of the results received from | and to get a

feeling about the symmetry of the TD distribution, a complementary robust measure called the

Interquartile Range (IQR) is introduced. The IQR measures the difference between the 75th

percentile and the 25th percentile of the empirical TD data sample. Therefore it captures 50%

of the distribution of the TD.

(35)

The larger the IQR, the more spread is the TD. IQR can be regarded as a nonparametric

equivalent to the standard deviation (Hyndman & Fan, 1996). However, the IQR only considers

half of the data sample and therefore will not be included in the design of the efficiency

measure. The resulting IQR values are reported in Table 14 and Table 15 and are compared

with the | values.

Table 14: IQR ETF SMI Table 15: IQR ETF EURO STOXX 50

The IQR in absolute terms and the efficiency measure measured based on MAD are presented. (Source: Own calculations / illustrations)

The IQR in absolute terms and the efficiency measure measured based on MAD are presented (Source: Own calculations / illustrations)

ETF on SMI |

1# 1.28 0.97

2# 0.84 0.78

3# 1.12 1.14

4# 0.13 0.17

5# 0.38 0.60 Average 0.75 0.73


|

1# 0.29 0.17

2# 0.28 0.17

3# 0.39 0.32

4# 1.71 2.55

5# 0.41 0.28

6# 0.23 0.06

7# 0.54 0.47

Average 0.55 0.57

Interestingly, the ranking of the ETFs based on MAD and the IQR are not entirely consistent for

the ETFs on SMI. Furthermore, a lower | does not necessarily indicate a lower IQR.

For the ETFs on EURO STOXX 50 however, the ranking according to the robust TE measure

correspond to the ranking according to the IQR.

For a symmetric distribution of TD, | should be equal to half of the IQR. Since this

property is not given for any of the ETFs, it is expected that they exhibit an asymmetric

distribution in TD. The asymmetry property will be accounted for the subsequent chapters.

7.2.4 Tracking Error based on Semi-Variance

Following the suggestions of Markowitz (1959), Fishburn (1977), Harlow (1991) and Estrada

(2007), Hassine and Roncalli (2013) suggest measuring risk by using semi-variance, instead


58

variance. The underlying principle of semi-variance questions the usage of variance as a risk

measure, since it depends on both positive and negative values of TD. The investor however

might only be interested in the negative deviations from a certain threshold. In the traditional

setting of the efficiency measure, positive deviations are punished by a higher TE and may

results in a lower efficiency measure score. Accounting for only the negative deviations from

e.g. the mean or zero, semi volatility is defined as a special case of lower partial moments. The

mathematical derivation following Bawa (1975) as well as Casella and Berger (2001) is given in

appendix 8.

Contrary to the application of the mean suggested by Hassine and Roncalli (2013), the median

is assumed to be a more suitable threshold in this thesis. The reason is the previously

discussed robustness of the median to outliers. The corresponding formula for the semi-

variance with respect to the median is illustrated by formula (36). It calculates the expected

variance by looking at the negative deviations from the median only.

| [ ] (36)

The semi-variance in relation to the threshold of zero calculates identically.

| [ ] (37)

The semi-standard deviation with respect to the median becomes the square root of the semi-

variance. In order to illustrate the intuition of the efficiency measure graphically Figure 25

presents the TD captured by the semi-variance measure.


The TD development for ETF 3# on EURO STOXX 50 is illustrated. The observation period covers May 2013 to May 2014. The dotted line illustrated all the TD values not accounted for by the semi-variance TE measure and the green line depicts the threshold zero. (Source: Own calculations / illustrations)

-0.02%

-0.01%

0.00%

0.01%

0.02%

0.03%

0.04%

0.05%


59

With respect to the adjustment of the efficiency measure, Hassine and Roncalli (2013) indicate

that the ratio of the standard deviation and semi standard deviation is equal to √ , whenever

the distribution of TD is symmetric around the threshold.

√ (38)

The modified ETF efficiency measure based on the semi-standard deviation becomes:

| | | √ | (39)

The results for the ETFs on SMI for both semi-variance with respect to the median and zero are

reported in Table 16. In order to compare the results to the initial TE measures, | and

| are listed as well.

Table 16: Semi-Variance ETF SMI

The TE and the corresponding efficiency measure based on the standard deviation, the semi-variance with threshold median and the semi-variance with threshold zero are presented. (Source: Own calculations / illustrations)

threshold = median threshold = zero

ETF on SMI

| | | | ) |

|

1# 78.15 -174.28 6.80 -61.57 7.29 -62.69

2# 46.97 -251.59 43.88 -276.40 44.10 -276.91

3# 39.04 -144.47 21.21 -129.61 22.26 -132.04

4# 4.40 -55.49 3.60 -56.61 3.80 -57.09

5# 7.95 -53.01 4.73 -50.93 5.36 -52.40 Average 35.30 -135.77 16.48 -115.02 16.56 -116.23

Looking at the magnitude of the results, the semi TE measure generally reduces the TE values

for ETF 1#, 3# and 5#, whereas it increases the efficiency indicator for ETF 2#, 4# on SMI. Apart

from the move of ETF 5#, the relative rankings for the ETFs based on the semi standard

deviation do not change. Furthermore, the rankings do not depend on whether the median or

zero is selected as the threshold. Since ETF 2#, 3# 4# and 5# exhibit a negative median, they

reveal lower TE at the median as compared to the threshold zero. Thus, the efficiency measure

for ETF 2# and 4# deteriorate given that multiplying the semi-standard deviation with √

penalizes negative outliers over-proportionally.

Fund 1#, having four large positive TD values at the end of the study period, profits the most

from the change to the downside risk measure. The fund now is ranked the third most efficient


60

ETF as the four outliers are not captured by the semi-volatility. ETF 2# on the other hand,

exhibits three large negative TD values, which are included in the semi-variance measure and

thus the ETF keeps his lowest ranking.

Generally, the results from the ETFs on SMI suggest applying the semi-volatility efficiency

measure carefully. Whereas the concept of downside risk may be suitable in e.g. alternative

pricing models based on downside beta (Estrada, 2007), it is less suitable in the context of ETF

tracking efficiency measurement. The short time horizon as well as the persistence of data

outliers makes the application of VaR based on semi-variance cumbersome and potentially

misleading.

Turning to the results for the ETFs on EURO STOXX 50, Table17 lists the sample statistics for

the efficiency measure based on the semi standard deviation with threshold zero and the

median, as well as the initial volatility measure | .

Table17: Semi-Variance ETF EURO STOXX 50

The TE and the corresponding efficiency measure based on the standard deviation, the semi-variance with threshold median and the semi-variance with threshold zero are presented. (Source: Own calculations / illustrations)

threshold = median threshold = zero

ETF on EURO

STOXX 50 | | |

| | |

1# 10.95 12.67 1.06 28.20 1.30 27.64

2# 9.95 -34.55 2.00 -22.85 2.09 -23.06

3# 12.10 -32.90 2.05 -17.77 2.01 -17.66

4# 41.20 -102.62 19.40 -79.98 18.86 -78.73

5# 32.45 0.09 1.86 49.13 2.07 48.65

6# 11.17 9.95 1.71 24.35 1.77 24.22

7# 18.71 26.55 3.95 48.14 4.12 47.76 Average 19.50 -17.26 4.58 28.20 4.60 4.12

With the new TE measure, the ranking for the ETFs change due to a large improvement of fund

5# whereas the relative position of the other funds remain the same. The results show that

ETF 5# now ranks as the most efficient ETF, followed by fund 7# and 1#. Fund 5# exhibits a

large positive TD on January 09th, 2014 and thus profits from an improved TE. Overall, all funds

reach lower TE values with the semi-variance measure. The choice of the threshold does not

influence the ranking of the ETFs. Since all ETFs reveal positive outliers only, the efficiency

measures | improves for all sample ETFs.


61

In addition to the previously mentioned drawbacks of the TE based on semi-volatility, investors

concerned about the tracking ability of the ETF may dislike both the negative as well as the

positive deviations from the benchmark. For those investors, the efficiency measure based on

the semi-volatility is an inaccurate risk concept, especially if TD is not centered on the

threshold.

7.2.1 Autocorrelation

To conclude the section about alternative TE measures, it is tested whether the return

difference of benchmark and ETFs are subject to serial correlation, also called autocorrelation.

However, it is not the purpose of this study to statistically correct the efficiency measure for

autocorrelation. Instead, it should give an indication of how to interpret the empirical results

in the prevalence of autocorrelation.

Autocorrelation refers to the correlation of a value with its own past or future value. It is

computed based on the general correlation function. Autocorrelation is measured as the

correlation of TD between two dates, TD at time and TD at time , where is referred

to as the number of lagged days tested for. In the herein sample, a total of 25 lags are

considered in order to incorporate the time of a full trading month.

(40)

According to Chatfield (2004), if the time series is random and the sample size is large, the

autocorrelation coefficients are approximately normal distributed with mean zero and

variance , where depicts the amount of trading days. The null hypothesis of no

autocorrelation is rejected at the 95% level whenever exhibits values above (below)

the upper (lower) test statistics, given by

√ (41)

Although formula (41) gives a rough estimation of the true statistics only, it is sufficient to give

an indication about the prevalence of autocorrelation in the ETF data sample.

Out of the whole ETF sample, all ETFs except for fund 5# on EURO STOXX 50 and fund 3# on

SMI exhibit significant autocorrelation. Figure 26 illustrates the different autocorrelation


62

values for ETF 3# on SMI as well as the upper and lower critical values. The values in the graph

suggest that the null hypothesis of no autocorrelation cannot be rejected.

Figure 26: Autocorrelation Function ETF 3# SMI

The autocorrelation function for the first 25 lags for the ETF 3# on SMI is illustrated. The dotted red lines correspond to the test statistics at which the null hypothesis of no autocorrelation is rejected. (Source: Own calculations / illustrations)

Figure 27 gives the autocorrelation value for ETF 5# on SMI for which the null hypothesis of no

autocorrelation is rejected at the first seven lags. This indicates that the TD values from up to

seven days ago, influence present values and thus bias the results. The complementary graphs

for all ETFs on SMI and EURO STOXX 50 are presented in appendix 9.

Figure 27: Autocorrelation Function ETF 1# EURO STOXX 50

The autocorrelation function for the first 25 lags for the ETF 3# on SMI is illustrated. The dotted red lines correspond to the test statistics at which the null hypothesis of no autocorrelation is rejected. (Source: Own calculations / illustrations)

Pope and Yadav (1994) show that autocorrelation in TE can bias the estimate of TE upwards.

The authors argue that delayed adjustments of prices due to changes of the investors’

expectations and obligations by APs to stabilized prices, will lead to positive serial correlation.

Although the sources for autocorrelation are difficult to identify in this data sample, it is

furthermore assumed that autocorrelation is caused by lagged portfolio adjustments lagged

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lag k

Autocorrelation

U-Critical Val

L Cirtical Val

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lag k

Autocorrelation

U-Critical Val

L Cirtical Val


63

dividend payment schedules of the ETF. In order to receive unbiased results, the so called

heteroskedasticity and autocorrelation consistent estimations of covariance matrices

suggested by Andrews (1991) or the long run variance suggested by Phillips (1991) may be

applied.

7.3 Alternative Bid-Ask Spread Measurement

This subsection evaluates an alternative method of measuring the bid-ask spread | . The

discussion provides the mathematical framework and reasoning behind the adjusted spread

measure.

Roncalli and Zheng (2013) as well as Flood (2010) argue that using intraday prices instead of

day-end prices is more relevant in the context of ETFs, as they tend to be less volatile.

Furthermore the previously discussed bid-ask spread assumes all trades to be executed at the

first limit order, meaning the best spread available. As Hassine and Roncalli (2013) indicate,

this may be an appropriate assumption for retail investors, since they generally trade smaller

amounts. For large institutional investors however, trading large notional in ETFs may result in

an increase in the spread, especially when liquidity in the ETF is limited. Therefore, using day

end prices for the first limit order may not reflect the true trading conditions. Hassine and

Roncalli (2013) in consequence weight each spread by the number of trades executed at that

spread. They compute the intraday spreads weighted by the duration between two ticks for a

given notional, where a tick is defined as the minimum change in price of the ETF.

|

) (42)

In formula (44), depicts the spread of the tick in order to trade a notional N and

is the elapsed time between two consecutive ticks. The ETF efficiency measure

adjusts according to the distribution of the spread .

| | | (43)

Hassine and Roncalli (2013) report, that depending on the notional traded, ranking for their

ETFs evaluated changes. However, in order to empirically calculate the adjusted spread

measure, high frequency data on the spreads at the microsecond level in combination with

changes in the limit order book of APs and the amount of trades is needed. Although


64

Bloomberg does provide historical intraday data going back six month, the required data is not

available for the whole observation period. Furthermore, the processing of the data requires

large computational capacity. For example, the intraday data for fund 4# on SMI counts

486’892 price data points in April 2014 only. Analyzing the full trading year in order to receive

comprehensive and significant results would require processing roughly 5.8 million bid and ask

prices. In consequence, the adjusted spread measure is not empirically calculated in this

thesis. Exemplary calculations and statistical analysis are explained in Roncalli and Zheng

(2014), Degryse, De Jong and Van Kervel (2011) as well as Hassine and Roncalli (2013).

Instead of calculating the adjusted spread measure, this thesis looks the influence spread on to

the ETF ranking. Table 18 compares the initial spread and efficiency measure to the efficiency

measure where the spread was calculated based on the median instead of the daily average

spread. Additionally the efficiency indicator is calculated without including the bid-ask spread.

As discussed previously, certain investors are able to trade ETF shares OTC and thus do not pay

the full bid-ask spread. For an investor trading on the primary markets, the spread becomes

irrelevant and should be neglected in the ETF ranking.

Table 18: Adjusted Spread ETF SMI

The summary statistics of the efficiency measure incorporating the initial spread measure, the spread measure based on the median and no spread are presented. (Source: Own calculations / illustrations)

median No Spread

ETF on SMI | | | | |

1# 15.34 -174.28 7.45 -166.39 -158.94

2# 62.21 -251.59 64.34 -253.73 -189.39

3# 10.92 -144.47 9.02 -142.58 -133.56

4# 4.95 -55.49 4.80 -55.34 -50.54

5# 6.94 -53.01 6.15 -52.21 -46.06

Average 20.07 -135.77 18.35 -134.05 -115.70

This study does not reveal an altered ranking for the ETFs on SMI, neither when the median

spread is included nor when the spread is omitted completely. Except for fund 1#, the spread

values based on the mean or on the robust median do not indicate the prevalence of data

outliers as they are alike. Even though ETF 2# does exhibit an average spread which is almost

four times as high as the second highest average spread, the ETF furthermore exhibits the

largest negative TD and large TE. In consequence it is still ranked the least efficient tracker,

even when omitting the spread.

Table 19 illustrates the results for the ETF on EURO STOXX 50.


65

Table 19: Adjusted Spread ETF EURO STOXX 50

The summary statistics of the efficiency measure incorporating the initial spread measure, the spread measure based on the median and no spread are presented. (Source: Own calculations / illustrations)

threshold = median No Spread


| | | | |

1# 15.30 12.67 11.52 16.45 27.96

2# 59.95 -34.55 49.22 -23.81 25.40

3# 25.86 -32.90 16.26 -23.30 -7.04

4# 52.73 -102.62 56.17 -106.06 -49.89

5# 13.82 0.09 14.09 -0.18 13.91

6# 14.01 9.95 12.87 11.09 23.96

7# 15.68 26.55 14.21 28.02 42.23 Average 28.19 -17.26 24.91 -13.97 10.93

For those ETFs, excluding the bid-ask spread changes the rankings. Fund 2#, previously having

the largest bid-ask spread of all ETFs, now is ranked the third most efficient ETF. Even though

fund 4# exhibits a large bid-ask spread as well, the other risk metrics for ETF 4# suggest inferior

tracking. Therefore the ETF does not improve its ranking.

Taking the median spread, does not alter the ranking according to the efficiency measure. The

similarity of the mean and the median spread in the data sample indicates that the distribution

of daily spreads is approximately symmetrical.

To conclude this section about the importance of the spread, it is to say that this thesis

assumes one trade throughout the whole observation period. It therefore assumes that the

ETF is bought at the beginning and sold at the end of the observation period. However, the

bid-ask spread has to be paid each time a full trade cycle is accomplished. A cycle comprises

buying and selling the ETF and is depicted by the factor in the below formula.

| | | | (44)

Despite playing a minor role in the initial efficiency measure setting, the spread measure may

become the most important cost factor for a high frequency ETF trader. Hassine and Roncalli

(2013) therefore suggest that in the limit, the investor is only interested in the spread. TD and

TE become less relevant the more often an investor trades the ETF on the secondary market.

| | (45)


66

7.4 Alternative Value-at-Risk Measures

The underlying assumptions of the VaR framework have a significant influence on which

possibility of loss is essentially accounted for. This subsection extends the mathematical

assumptions of the basic VaR framework with four alternative measurement methods of VaR.

Each method takes a different point of view of VaR and eliminates some of the drawbacks of

the other methods considered. The discussion starts with assessing the so-called delta-normal

VaR. The initial efficiency measure makes use of the delta-normal VaR, proposed by Jorion

(2007, pp.249-251). In this method, the calculations are based on the assumption that the TD

are normally distributed | | with mean | and

variance | .

The empirical distributions of TD as well as the figures for the IQ and the median suggest that

the normality assumption most likely does not hold. Out of the entire ETF sample, only fund 5#

on SMI exhibits an approximate normal distribution. Figure 28 illustrates the relative TD

distribution in comparison to an arbitrary normal distribution with the same mean and

variance.

Figure 28: Relative Tracking Difference Distribution

The relative frequency distribution of TD (blue bars) for the ETF 5# on SMI and the corresponding normal distribution (red line) are presented. The vertical axis depicts the relative frequency of TD and the horizontal axis depicts the absolute TD values. (Source: Own calculations / illustrations)

The sample distribution of TD from all other funds show clear signs non-normality. This is a

severe issue, as the delta-normal VaR based on a normal distribution is likely to misestimate

the true potential loss on the empirical distribution. Furthermore, the efficiency measure

0

0.01

0.02

0.03

0.04

0.05

0.06


67

based on VaR underestimated the potential loss, as it measures the percentile, but not the

property of the tail below the confidence interval. In order to statistically test whether the

normality assumption holds, the third and fourth moments as described in appendix 8 are

examined. Being commonly referred to as the skewness of a distribution, the sample statistics

based on the third moment | is calculated according to Bai and Ng

(2005).

| [ ]

[ ]

|

| (46)

The skewness measures how symmetric the distribution is around the mean. It can take both

positive and negative values. A negative skew indicates that the tail on the left side of a

distribution is longer whereas a positive skew suggests that the distribution is tailed to the

right. In order for the normality assumption to hold, the values of the skewness should be

close to 0 (Bai and Ng, 2005).

The fourth moment | is used to calculate the kurtosis of a distribution.

| [ ]

[ ]

|

| (47)

Formula (47) shows how peaked the distribution TD is and furthermore indicates the heaviness

of the tails in the distribution. Even though the interpretation of the absolute kurtosis values is

rather cumbersome, higher values indicate a more pointed and fat tailed distribution. As the

normal distribution exhibits a kurtosis of three, the above formula often is reduced by three to

receive the excess kurtosis | . For the normality assumption to hold, | should

take values close to 0 (Bai & Ng, 2005).

In order to statistically test whether the normality assumption holds for the ETF sample, the

Jarque-Bera-Test is applied. The test statistics by Jarque and Bera (1987) is based on the

skewness | , excess kurtosis | as well as the sample size .

|

( | )

(48)


68

The Jarque-Bera test statistics has a chi-square distribution with two degrees of

freedom. The corresponding null hypothesis suggests, that the sample distribution is normally

distributed. The alternative hypothesis states that the TD are not normally distributed. The

quantile of the chi-square distribution at the 95% probability level takes the value of 5.99. For

values of above 5.99, the null hypothesis is rejected at the 95% significance level. Large

values indicate that the null hypothesis of normal distribution in TD can be rejected at even

higher probability levels. Table 20 presents the relevant sample statistics for the ETFs on SMI.

Table 20: Normality Test ETF SMI

The summary statistics of the skewness, the kurtosis and the Jarque-Bera test statistics for the ETFs on SMI are presented. (Source: Own calculations / illustrations)

ETF on SMI | |

1# 7.36 57.69 1969993.28

2# -6.60 57.97 1958435.53

3# 4.03 55.11 1729827.64

4# -2.57 30.91 305387.57

5# -0.19 0.47 2.54

Average 0.41 40.43 1192729.31

It becomes evident that except for ETF 5# on SMI, for all funds the null hypothesis of normal

distribution is rejected at the 95% probability level. Furthermore it can be seen, that fund

number 1# and 3# exhibit positive skewness, suggesting that the distribution of TD is tailed to

the right. Consequently, the delta normal VaR may in fact overestimates the risk for those two

funds, whereas it underestimates the risk for the funds 2#, 4# and 5#. The large excess kurtosis

suggests a leptokurtic distribution, meaning a strong peak around the mean and fat tails.

Those fat tails suggest that extreme TD are likely to be milder in the normal compared to the

fat-tailed distributions.

The intuition of a negative skew (-2.57) and a large excess kurtosis (30.91) can be seen from

ETF 4# in Figure 29. It is assumed that the large negative outliers inflate the kurtosis whereas

more TD on the left of the sample mean cause negative skewness.


69

Figure 29: Absolute Tracking Difference Distribution

In order to illustrate skewness and kurtosis, the absolute frequency distribution of TD for the ETF 4# on SMI is presented. The vertical axis depicts the absolute frequency of TD and the horizontal axis depicts the TD values. (Source: Own calculations / illustrations)

The ETFs on EURO STOXX 50 all display a positive skewness, meaning that the TD is skewed to

the left. This is in favor of the investor as it indicates the prevalence of more positive TD on the

right side of the sample mean. Those results are consistent with the findings by Hassine and

Roncalli (2013) who find high skewness in their data sample. The null hypothesis of normally

distributed TDs can be rejected for all funds according to the Jarque-Bera Test.

Table 21: Normality Test ETF EURO STOXX 50

The summary statistics of the skewness, the kurtosis and the Jarque-Bera Test for the ETFs on EURO STOXX 50 are presented. (Source: Own calculations / illustrations)


| |

1# 4.49 27.41 213717.53

2# 4.33 28.92 244629.92

3# 2.96 11.67 16531.69

4# 2.55 18.73 68121.69

5# 14.20 214.92 102596534.30

6# 6.93 69.00 3396863.42

7# 5.02 36.98 519455.95

Average 5.91 61.78 17756066.42

Together these results provide important insight on the ETFs TD distribution, suggesting that

the distribution of TD is non-normal. The next section discusses an alternative method of VaR

which does relax the statistical assumption of normality.

0

5

10

15

20

25

30


70

7.4.1 Cornish-Fisher Value-at-Risk

Cornish and Fisher (1937) propose an extension of the delta-normal VaR which approximates

the percentiles of a normal distribution function of TD adjusted to its primary four moments,

TD | , TE | , skewness | and excess kurtosis | .

The Cornish-Fisher expansion allows the assessment of the VaR even if the normality

assumption is violated. The adjusted factor hereby replaces the previously applied inverse

of the standard normal distribution function and is calculated as below:

|

( ) |

( ) | (49)

As we are consistently interested in the 95% percentile, takes the value 1.645. From

formula (49) it can be seen that whenever the skewness as well as the excess kurtosis takes

the value zero, as it is the case in the normal distribution, collapses to .

Given and the standard deviation of TD | , the efficiency indicator then adjust as

depicted below.

| | | | (50)

In Table 22 the Cornish-Fisher expansion is used to compute the efficiency measure | .

Counterintuitively, the measure indicates an advantage to fund 2# and 4# which both

exhibited negative sample skewness and high kurtosis, indicating that the tail on the loss side

is longer. Fund 4# now even is regarded to be the best tracker, raising suspicion that the

expansion may not be suitable for distributions with great skewness and kurtosis.

Table 22: Cornish-Fisher VaR ETF SMI

The summary statistics for the sample skewness, kurtosis and the Cornish-Fisher factor as well as the corresponding efficiency measure based on the Cornish-Fisher expansion are presented. The last row lists the efficiency measure based on the delta-normal VaR. (Source: Own calculations / illustrations)

ETF on SMI | | | |

1# 7.36 57.69 1.56 -167.29 -174.28

2# -6.60 57.97 -2.22 -70.01 -251.59

3# 4.03 55.11 1.37 -133.87 -144.47

4# -2.58 30.91 0.16 -48.97 -55.49

5# -0.19 0.47 1.58 -52.50 -53.01

Average 0.40 40.43 0.49 -94.52 -135.77


71

The most surprising aspect of the data is that even though large kurtosis values suggested the

existence of fat tails, the Cornish-Fisher expansion translates into an improvement in the

efficiency measure score | score even for the funds with negative skewness. For

example, the large negative skewness and the high kurtosis resulted in a negative value for

ETF 2# on SMI.

Table 23: Cornish-Fisher VaR ETF EURO STOXX 50

The summary statistics for the sample skewness, kurtosis and the Cornish-Fisher factor as well as the corresponding efficiency measure based on the Cornish-Fisher expansion are presented. The last row lists the efficiency measure based on the delta-normal VaR. (Source: Own calculations / illustrations)


| | | |

1# 4.49 27.41 1.99 8.90 12.67

2# 4.33 28.92 1.94 -37.48 -34.55

3# 2.96 11.67 2.09 -38.23 -32.90

4# 2.55 18.73 1.87 -111.84 -102.62

5# 14.20 214.92 -2.44 132.71 0.09

6# 6.93 69.00 1.32 13.58 9.95

7# 5.02 36.98 1.85 22.67 26.55

Average 5.91 61.78 1.13 1.04 -24.56

For the ETFs on EURO STOXX 50, the results seem somewhat more consistent with the theory

on the Cornish-Fisher VaR. Even though funds exhibit positive skewness, they suffer from the

large kurtosis values and in consequence inferior efficiency measure values. Nevertheless, the

results suggest that those implausibly large kurtosis values positively influence the efficiency

measure values. ETF 5# exhibits the most extreme and dubious result by exhibiting negative

value and improving his ranking to the first position.

The empirical results not only lay in strong contrast to the findings by Hassine and Roncalli

(2013), which found nearly consistent rankings for both, the delta normal as well as the

Cornish-Fisher efficiency measure, but they suggest that the Cornish-Fisher expansion fails

when the TD distribution is strongly non-normal. Jaschke (2002) confirms this suspicion and

points out that monotonicity and the convergence are not certain for the Cornish-Fisher

expansion. The author points out that the approximation is only suitable when the returns are

sufficiently close to being normal. Maillard (2012) further calculates the domain of validity of

the transformation which is | | (√ ) | | (√ ) . Except

for ETF 5# on SMI, none of the sample ETFs fall within domain of validity.

The fact that neither the skewness nor the kurtosis is a robust measure may be the reason why

such high values are found in the empirical analysis. Even though the Cornish-Fisher approach


72

adjusts for the shape of the distribution of TE, it may actually fail to estimate the true VaR in

the existence of data outliers. A solution to this problem would be to use robust skewness and

kurtosis measures as discussed by Moors (1988).Another alternative is to consider the

historical VaR which does estimate the ETF risk from the empirical distribution of TD.

7.4.1 Historical Value-at-Risk

The historical simulation of the VaR is a remedy to the delta-normal and the Cornish-Fisher

method, as it makes no specific assumption about the distribution of TD, but draws samples

from historical data (Jorion, 2007, p.253). The historical VaR uses empirical percentiles from

the observation period by arranging the historical TD over the last trading days according to

their size. The value representing the -% percentile will be the corresponding historical

VaR. Following Hassine and Roncalli (2013) the efficiency measure based on the historical VaR

is defined as follows, whereas depicts the historical probability distribution function of

centered TD.

| | | (51)

The approach generally requires a larger data sample than the delta normal method in order

to return significant results. A 99% daily VaR estimated over a time period of 100 days only

produces one observation in the tail. For the ETF 3# on SMI for example, the observation

period counts 252 observations, which means that the 95% percentile is the 12.4th largest loss

observed in the data sample.

The efficiency measures for the ETFs on SMI derived from the delta-normal as well as the

historical VaR are reported in Table 24 and for the ETF on EURO STOXX 50 in Table 25.

Table 24: Historical VaR ETF SMI Table 25: Historical VaR ETF EURO STOXX 50

The efficiency measure based on the delta-normal VaR and the historical VaR are presented. (Source: Own calculation / illustration)

The efficiency measure based on the delta-normal VaR and the historical VaR are presented. (Source: Own calculation / illustration)

ETF on SMI |

1# -174.28 -64.59

2# -251.59 -193.48

3# -144.47 -121.68

4# -55.49 -54.54

5# -53.01 -55.05

Average -135.77 -98.02


|

1# 12.67 26.84

2# -34.55 -24.26

3# -32.90 -17.72

4# -102.62 -85.67

5# 0.09 47.83

6# 9.95 26.00

7# 26.55 48.53 Average -24.56 -5.18


73

For the ETFs on SMI especially fund 1# improves his efficiency measure values. The ETF profits

from a low negative TD values at the 95% percentile and now is ranked the third most efficient

ETF. Except for fund 5#, all ETF exhibit better efficiency measure values. This suggests that the

VaR based on a normal distribution overestimates the risks in the ETFs.

For the ETFs on EURO STOXX 50, fund 7# remains the most efficient ETF. Compared to the

measurement based on the delta-normal method, all ETFs profit from improved measures.

Especially ETF 5# improved his ranking and is now the second most efficient ETF. The low

ranked funds 2#, 3# and 4# remain to be the worst performing funds.

From the above described method it can be seen that some issues of historical VaR remain.

Firstly, historical VaR does not indicate how large the losses are below the 95% percentile.

Secondly, historical VaR generally assumes that returns are independent and identically

distributed (iid), meaning that every TD has the same probability distribution and that they are

mutually independent. Historical VaR thus does not account for time-varying volatility. Diebold

et al. (1998) show that high frequency and daily returns are often not iid. The shortcoming is

an issue when the daily historical VaR is scaled to an annualized measure. According to

Hendricks (1996) historical simulations cannot be easily transformed between multiple

percentiles and study periods. The author states that it is not uncommon to use up to five

years of data in order to circumvent the matter.

Another key shortcoming of the efficiency measure based on historical VaR is that historical

scenarios are assumed to fully represent future observations. The problem is, that the

approach weights recent data the same as outdated observations. If current market trends

such as higher volatility in returns occur, the historical VaR is an inappropriate measure to

evaluate performance. This issue can partly be resolved by weighting recent returns more

strongly.

In conclusion, the absolute values of the efficiency measure based on the historical VaR need

to be interpreted with caution. A reasonable approach to tackle the issues discussed is to

simply consider the corresponding ranking of ETFs, but not the efficiency measures absolute

values. An alternative is to use a statistical improvement of the delta-normal method, which

does not rely on the empirical distribution of returns, but adjusts the normal distribution

function in the delta-normal Var for the sample distribution function.


74

An overall weakness of all the VaR methods considered so far is, that they generally fail to

indicate how the TD behaves over the observation horizon. Therefore the next subchapter will

introduce the concept of intra-horizon risk.

7.4.2 Intra-horizon Value-at-Risk

The issues of intra-horizon risk was already under discussion in the context of minimum capital

requirement by the Basel 3 committee (1996, p.4). The Overview of the amendment to the

capital accord to incorporate market risks (1996) finally suggested the usage of a multiplication

factor of three in order to take into account the weaknesses of end-of-horizon VaR. The

reports suggest the importance of a continuous measure of risk for minimum capital

requirements. Amongst others, Kritzman and Rich (2002) and Bakshi and Panayotov (2010)

argue that the traditional calculation of VaR allows estimating the probability of loss at the

end, but not along the investment period. The authors suggest a measure which incorporates

information about the dynamic path of potential losses, taking into consideration the losses

incurred before the end of a specified horizon.

Intra-horizon risk is relevant for any investor. However, it is particularly important for stop-loss

investors who follow the strategy to sell their assets whenever their value falls below a

predefined hurdle rate. Furthermore intra-horizon risk may be essential for pension funds or a

portfolio manager, who needs to rebalance of his portfolio, once the value of an investment

falls below a certain threshold. In the context of ETFs, previous VaR methods do not allow

inference about the likelihood and the maximum negative tracking outcome throughout the

whole study period. In a situation where the ETF investor is forced to sell his fund before the

due date, he may suffer from the current low return. The intuition behind the measurement of

intra-horizon risk is illustrated in Figure 30 at the examples of ETF 1# and 3# on SMI.

Figure 30: Cumulative Tracking Error ETF 1# and 3# on SMI

The evolution of the cumulative TE for ETF 1# and ETF 3# on SMI are illustrated. The observation period covers May 2013 to November 2013. (Source: Own calculations / illustrations)

-0.20%

-0.15%

-0.10%

-0.05%

0.00%

0.05%

0.10%

0.15%

1#

3#


75

The investment horizon for the herein illustration is arbitrarily chosen from May 2nd until

October 2nd 2014. It can be seen, that according to the cumulative TD, both funds perform

equally well at the end of the observation period, as both end up at the same cumulative TD

value, indicating that VaR is concerned about the likelihood of the distribution of returns at

the end of the investment period. In the above example it is expected that the volatility partly

punishes the higher deviations of fund 3# as compared to ETF 1#. If fund 1# would however

exhibits positive deviations, but end up at the same cumulative TD level at the end of the

investment horizon, the efficiency measure would fail to indicate which fund is more efficient.

If the investor is forced to sell either ETF 1# or 3# one month prior to the end of the

investment horizon, he would experience a much greater loss when being invested with ETF 3#

than with ETF 1#.

Kritzman and Rich (2002) discuss a measure of intra-horizon VaR that is calculated based on

the probability of maximum loss at any time during the investment period at some given

confidence level. In order to obtain an intuition of this method, Kritzman and Rich (2002) firstly

derive the end-of-horizon VaR ( ), based on the formula below.

√ (52)

depicts the probability of loss, calculated by the difference between the cumulative

percentage loss in continuous units and the annualized expected return , meaning the

annual TD, divided by the annualized standard deviation of continuous returns √ , being the

annualized TE. is measured in terms of years. Finally the normal distribution function is

applied to convert the standardized distance from the mean to a probability estimate. As we

are considering the probability of loss, is the 5% percentile in order to correspond to the

95% probability of not losing an amount greater than . The end-of-horizon VaR then is

derived by rearranging the formula (52) and solving for .

√ (53)

The efficiency measure with the above VaR including the bid-ask spread is calculated as:

| | (54)


76

In order to capture the probability of intra-horizon loss , Kritzman and Rich (2002) apply a

statistic called first-passage time probability. The method captures the probability that the

return will hit a particular hurdle rate during the investment horizon. Alternatively it estimates

the maximum loss during the period at the given confidence level of 95%. The probability

that an investment will fall under a particular value while being constantly monitored is

(

√ )

(

√ )

(55)

The first part of the equation is equal to the end-of-horizon VaR from formula (53), whereas

the second part of the equation only takes positive values, making the probability of intra-

horizon loss always larger than end-of-horizon loss . In contrast to the tradition VaR

probability measure, furthermore increases for a longer investment horizon, thus arguing

against the benefit of time diversification of risk.

As solving for cannot be administered analytically, numerical optimization is applied in

order to derive intra-horizon VaR . The efficiency measure finally measures the worst trade

at a chosen probability to any time during the investment horizon.

| | (56)

The results of the efficiency measure based on the delta-normal VaR | , the alternative

method of calculating the end-of horizon VaR | as well as the intra-horizon VaR

| are presented in Table 26 and Table 27.

Table 26: Intra-horizon VaR ETF SMI

The sample statistics for the efficiency measure based on the delta-normal, the end of horizon and the intra-horizon VaR are presented. (Source: Own calculations / illustrations)

ETF on SMI | |

|

1# -174.28 -173.07 -193.14

2# -251.59 -250.43 -256.53

3# -144.47 -143.83 -149.86

4# -55.49 -55.46 -55.65

5# -53.01 -52.95 -53.68

Average -135.77 -135.15 -141.77


77

As expected, the end-of-horizon VaR calculation method by Kritzman and Rich (2002),

returned efficiency measure values that deviate by not more than one basis point from the

traditional delta-normal method | . Considering the intra-horizon risk | does

however change absolute values significantly. As suggested by the definition of formula (55),

intra-horizon risk is greater for all ETFs than end-of-horizon risk. Particularly fund 1# exposes

an investor with greater risk throughout the study period, increasing the continuously

measured loss for about 20 bps. The reason can be found in its TE, being the largest of all ETFs

considered. Intuitively, it is the volatility of the TD that has the biggest influence weather a

fund exposes an investor to greater risk throughout the investment horizon.

Table 27: Intra-horizon VaR ETF EURO STOXX 50

The sample statistics for the efficiency measure based on the delta-normal, the end of horizon and the intra-horizon VaR are presented. (Source: Own calculations / illustrations)


| |

|

1# 12.67 12.60 -19.21

2# -34.55 -34.60 -63.51

3# -32.90 -32.91 -40.08

4# -102.62 -102.51 -118.89

5# 0.09 -0.13 -37.02

6# 9.95 9.89 -18.43

7# 26.55 26.37 -22.89

Average -17.26 -17.33 -45.72

Similarly the ETFs on EURO STOXX 50 do not exhibit larger deviations by more than half a basis

point for the delta normal | and the end-of-horizon VaR | . The intra-horizon

VaR again reduces the efficiency measures, suggesting that the risk during the trading horizon

is substantially larger than at the end of the observation period. Other than for the ETFs on

SMI, the ranking of the efficiency measure | largely changes for the ETFs on EURO

STOXX 50. Fund 6# exposes an ETF investor to the smallest loss at the 95% probability level

during the whole study period. ETF 7# and 8# are ranked second and third. Especially ETF 7#

deteriorated for more than 40 bps. This indicates that even though the fund gives the best

result at the end of the investment horizon, it exposes an investor to substantial intra-horizon

risk.

Unfortunately, the intra-horizon VaR does not indicate how large the loss will be in the worst

cases occurring outside of the probability scenario. The method furthermore assumes

approximate normality in the distribution of TD.


78

Although being largely accepted as a market risk measure, the VaR calculation methods

considered so far suffer from an additional shortcoming with respect the magnitude of the loss

in the tail. The VaR methods give e.g. the maximal loss at the 95% probability level, but do not

indicate how big the loss is in the remaining 5% cases. The next subchapter therefore discusses

a method which addresses this issue.

7.4.1 Expected Shortfall

Although being largely accepted as a market risk measure, VaR suffers from additional

shortcomings with respect the magnitude losses in the tail and the fact that it is generally not

considered to be a coherent measure of risk. The herein subchapter discusses those drawbacks

and evaluates a method that provides a remedy.

According to Atzner, Delbaen, Eber and Heath (1999), VaR is not a coherent measure as it

considers the risk of a portfolio to be higher than the sum of risk of its individual asset. In other

words, the VaR concept implicitly revokes the benefits of diversification and is largely criticized

for not being sub-additive. Furthermore, VaR is concerned about the probability level at which

a certain loss will not be exceeded only, but does not indicate how big the loss in the

remaining events will be. Expected Shortfall (ES), alternatively referred to as the conditional

VaR, is a measure that explicitly includes tail risk (Acerbi & Tasche, 2002). ES measures how big

the expected loss will be on average, in case the worst events occur. In the herein

setting, ES looks at the average of the losses that fall outside the 95% percentile of the VaR.

[ | ] (57)

According to Hassine and Roncalli (2013), the efficiency measure adjusts as follows:

| | | [ | ] (58)

In Table 28 and Table 29 the results for | on the ETFs from both benchmarks are

reported. Furthermore the efficiency measure based on the historical VaR is listed. The

comparison to the historical VaR is especially informative, as it indicates how big the negative

TEs are, that fall out of the 95% empirical quantile, which is depicted by the historical VaR.


79

Table 28: Expected Shortfall ETF SMI Table 29: Expected Shortfall EURO STOXX 50

The sample statistics of the efficiency measure based on the historical VaR and on the ES are presented. (Source: Own calculations / illustrations)

The sample statistics of the efficiency measure based on the historical VaR and on the ES are presented. (Source: Own calculations / illustrations)

ETF on SMI

1# -64.43 -72.52

2# -193.48 -301.76

3# -121.68 -164.34

4# -54.26 -62.11

5# -55.05 -58.94

Average -97.78 -131.93


1# 26.84 26.15

2# -24.26 -26.76

3# -17.72 -19.83

4# -85.67 -102.63

5# 47.83 46.09

6# 26.00 22.64

7# 48.53 41.85 Average -4.50 -9.06

Large deviations of the efficiency measure based on the historical VaR and the ES indicate that

the loss in the tails indeed reach significantly higher values. For the ETFs on SMI, it is fund 2#

and 3# that exhibit large losses in the tail. The ranking of the bottom ETFs however is not

changed. Only ETF 5# performs relatively better and ranks as the most efficient ETFs amongst

all ETFS on SMI. By definition the measure based on ES is expected to reveal lower efficiency

measure scores as the historical VaR is lower than ES. For the ETFs on SMI, the average

measures deteriorate for roughly 23bps.

The ranking for the ETFs on EURO STOXX 50 did not change by any means. The reason is that

none of those funds exhibits large negative TD and thus large losses in their empirical tails. On

average, the measure corrupts the tracking efficiency for about 4bps only as compared to

the historical VaR. Those results are largely consistent with the findings by Hassine and

Roncalli (2013), which observe the ETFs on EURO STOXX 50 over the period of November 2012

until November 2013.

Similarly to the drawbacks of the historical VaR, the ES values have to be interpreted with

caution as again the √ rule is applied in order to receive annual results. It is advisable to

use the results for ranking purposes only. In order to receive significantly absolute VaR figures,

entropic VaR suggested by Ahmadi-Javid (2011) can be applied. Entropic VaR is a coherent risk

measure, which is defined as an upper bound for the delta-normal VaR and the ES.

Furthermore the efficiency measure based on ES indicates the maximal loss at the end of the

period, but does fail to indicate how big the maximal loss will be at any time during the

observation period. The same drawback can be found in the other VaR methods considered so

far.


80

It can be concluded that even thought the computation methods jointly account for the main

shortcomings of VaR, none of them is able to completely offset all drawbacks. It is thus

important to consider several efficiency measures. The closing section of Chapter 7 will discuss

the interpretation of the efficiency measure.

7.5 Alternative Interpretation of the Efficiency Measure

To conclude, the adjustments of the ETF efficiency measure, the interpretation suggested by

Hassine and Roncalli (2013) is discussed critically. The authors propose that if the efficiency

measure of ETF is larger than the efficiency indicator for ETF , fund should be preferred to

fund . A major limitation of this interpretation is that it does not indicate how efficient the

fund actually mimics the returns of the benchmark. Large but steady excess performance

increases the efficiency measure and makes a fund more favorable in the traditional

understanding. The question that needs to be asked is which value for the efficiency measure

actually indicates efficient tracking. A perfectly replicating ETF has no TD, no TE and preferably

comes at no bid-ask spread. In consequence, the most efficient tracker would have an

efficiency measure of zero.

Whereas negative values in the TE certainly are undesirable, positive values indicate an over

performance possibly coming from securities lending. Close up tracking becomes a necessity

when ETFs are used for example hedging purposes or in a mandate of an asset manager.

Depending on the objective of the investor, it makes sense to consider the negative absolute

values of the tracker and evaluate how much the value deviates from zero.

| | | (59)

The above application may have the side benefit that providers are less likely to choose an

inaccurate benchmark in order to boost the excess-performance of the ETF. When applying

the above proposition to the ETFs in the herein sample, 5# on SMI and fund 5# on EURO

STOXX 50 are generally regarded as the most efficiently tracking ETFs. Overall, they exhibit the

least deviation from the benchmark.

From the previous discussion, it can be seen that the design of an appropriate efficiency

measure is not straightforward. The mathematical assumptions of the models and the

backdrop of the efficiency measure have to be borne in mind. The subsequent conclusion

therefore again sums the main results derived in this thesis and gives recommendations on the

application of the efficiency measure.

Chapter 8 Conclusion and Outlook

81


This research paper provides profound investigation of ETF performance measurement

following the research by Hassine and Roncalli (2013). After gaining in-depth insight on the

structure and functioning of ETFs, the thesis shows that traditional performance not only are

inappropriate, but may be misleading when being applied to passively managed ETFs.

Subsequently, the efficiency measure based on VaR is established. Empirical research on

unlevered, passively managed, equity ETF on SMI and the ETFs on EURO STOXX 50 is

conducted. The subsequent analysis on TE applies alternative computation methods of TE and

evaluates robust and semi-variance measures. After discussing the liquidity metrics ETFs, the

efficiency measure is adjusted for normal and non-normal TD distribution as well as ES and

intra-horizon risk. Finally alternative interpretations of the efficiency measure are discussed.

To conclude the analysis from the previous chapters, the subsequent sections give case-by-

case recommendations for the design and application of the efficiency measure. Suggestions

are given by taking into account the different types of ETF investors and trading strategies as

well as the underlying mathematical assumptions of the efficiency measure. To begin with, the

ETF performance characteristics are discussed. Subsequently, some of the rule-in and rule-out

criteria’s of ETF investors are highlighted. The conclusion elaborates on the insights from the

theoretical and empirical analysis of this thesis and gives concrete recommendations on which

efficiency measure is most suitable in a particular scenario. As a final point, an outlook on

potential fields of ETF performance measurement is held.

Before looking at any ETF efficiency measure, the investors need to determine the risk metrics

most relevant in the context of their underlying ETF investment strategy. The span of ETF

investors may reach from a buy-and-hold investor, who profits from the ETFs low fees and tax

efficiency, to a frequent trader who benefits from the ETFs liquidity, lower volatility and broad

diversification. Moreover, eligible investors are able to trade ETF shares OTC, whereas others

only are able to trade on the exchange. The corresponding trading circumstances and the

underlying investment objective therefore jointly influence which efficiency measure is most

suitable for the investor.


82

How ETF performance is measured largely depends on whether the ETF is traded on the

secondary or the primary market. The major difference in ETF performance measurement

either market stems from the different liquidity costs of trading the ETF. Analyzing the ETF

liquidity costs by looking at the spread and pricing efficiency only, fails to take into account

that investors with access to the primary market in fact trade OTC directly with the AP. Large

institutional investor for example may subscribe or redeem their shares at the NAV plus

spread, while potentially negotiating favorable conditions. As the costs of OTC trades are not

publicly available and may depend on the investor’s negotiation power, it is advisable to

evaluate the ETFs based on the efficiency measures without the spread. Appendix 12 presents

all efficiency measure values without including the bid-ask spread. For the ETFs on SMI,

especially fund 4# and 5# perform consistently well. ETF 1# exhibits most favorable results for

the semi-volatility VaR and ES efficiency measure. For the ETFs on EURO STOXX 50, its fund 5#

and 7# that constantly probe to be the most efficient.

The efficiency measure including the bid-ask spread most likely is suitable for secondary

market trading only. In order to approximate to cost of trading the ETF on the exchange,

investors should look at the bid-ask spread measure which takes the average of intraday prices

and not day-end prices as reference. For investors, who trade ETF volumes, it additionally

advisable to adjust the spread for the notional traded and estimate the market impact costs

caused by their trades in the ETF and

Finally investors from both the primary and secondary market are interested in how closely

the ETF replicates its benchmark. Evaluating both the TE and the TD therefore is vital for

efficiency measurement. Nevertheless, the relative importance of each of these metrics

depends on the investment purpose of the investor. A high frequency trader, investing short

term in order to e.g. equitize cash positions or profit from short term market developments,

may be more concerned about the relative deviation of the ETF returns on a daily basis,

measures by TE. Additionally, the bid-ask spread becomes highly important for the frequent

trader, as for every ETF trade the spread has to be paid. In the limit, the investor may solely

care about the ETF trading costs.

A buy and hold investor may be mostly concerned about the long term performance difference

of the ETF relative to the benchmark measured by TD, but not so much about the short term

volatility measured by TE. A buy and hold investor cares tracking deviation in the long run,

caused by fees and additional charged, instead of the short term deviations caused by e.g.

dissimilar dividend payment schedules.


83

After eliminating unsuitable ETFs and determining which risk metrics are the most important,

the investor is faced with selecting the best performing product. As this thesis has shown ETFs

may in fact track the same benchmark, however, differ largely regarding their performance

relative to the benchmark as well as the underlying investment risks. In order to compare like

with like, it is crucial to have a close look at the ETFs and the benchmarks underlying dividend

assumptions. Quite frequently ETFs are benchmarked against different types of the same

benchmark, as ETF providers generally acquire data from one benchmark type only. An

accumulating ETF benchmarked against a net total return index may track less accurately than

a distributing ETF benchmarked against price index version of the same benchmark. Correcting

the daily performance of the ETF every time a dividend is paid is at risk of exhibiting return

abnormalities due to diverging taxation assumptions or timing. Investors need to be aware

that data outliers from any source strongly influence ETF efficiency measurement. One large

outlier may inflate the TE and indicate low quality tracking, even though the ETF mirrors his

benchmark fairly well. Especially non-robust measures as the mean, volatility, Skegness and

the kurtosis have to be interpreted carefully.

Finally the underlying assumptions of the various VaR methodologies have to be kept in mind.

The decision tree in Figure 31: Decision Tree of ETF Efficiency MeasuresFigure 31 assists

investors in choosing the most suitable VaR method in the ETF performance measurement

process.


84

After determining which risk metrics are the most important, the investor is faced with

selecting the best performing ETF. As this thesis has shown, ETFs may track the same

benchmark, however, differ largely regarding their performance and underlying investment

risks. In order to compare like with like, it is therefore crucial to have a close look at the ETFs

and the benchmarks underlying dividend assumptions. Quite frequently ETFs are benchmarked

against different types of the same benchmark. An accumulating ETF benchmarked against a

net total return index may track less accurately than a distributing ETF benchmarked against

the price index version of the same benchmark. Correcting the performance of the ETF every

time a dividend is paid is at risk of resulting in return abnormalities due to diverging taxation

assumptions. Investors need to be aware that data outliers strongly influence ETF efficiency

measurement. One large outlier may inflate the TE and indicate low quality tracking, even

though the ETF mirrors his benchmark fairly well in 99% of the cases. Especially non-robust

measures as the mean, volatility, Skegness and the kurtosis have to be interpreted carefully.

Finally the underlying assumptions of the various VaR methodologies have to be kept in mind.

The decision tree in Figure 31: Decision Tree of ETF Efficiency MeasuresFigure 31 assists

investors in choosing the most suitable VaR method for ETF performance comparison.


85

Figure 31: Decision Tree of ETF Efficiency Measures

The decision tree for the efficiency measures based on the different VaR methods is presented. Starting from the square on the top left, the drawn-out lines represent eligible options. The rhombuses represent the corresponding VaR measure on which the efficiency measure should be based on. (Source: Own calculations / illustrations)

If the relative return of the ETF is not allowed to fall below a certain threshold at any time

during the investment horizon, the efficiency measure based on the intra-horizon risk is

appropriate. If investors are only concerned about the probability of loss at the end of the

observation period and the TD are normally distributed, the efficiency measure based on the

delta-normal VaR is most suitable. When the distribution of TD is sufficiently close to a normal

distribution and the skewness as well as the kurtosis are within their domain of validity, the

ETF performance measure based on the Cornish-Fisher VaR complements the delta-normal

VaR. The historical VaR based on the empirical distribution of TD is suitable whenever large

skewness and kurtosis and finally non-normality in TD bias the statistical VaR approach. To

complement any VaR efficiency measure, the efficiency measure based on the expected

No

Are the ETFs tracking differences

normally distributed? Delta-normal

VaR

Are the ETFs tracking differences

approximately normally distributed? Cornish-Fisher

VaR

Are the ETFs tracking differences not

normally distributed? Historical VaR

Is the investor concerned about the

loss in the tails?

Is the investor concerned about the

expected loss at any time along the

investment horizon?

Intra-Horizon

VaR

Expected

Shortfall

Yes

No

Yes

Yes

Yes

Yes

No

No


86

shortfall indicates the losses in the tails and is relevant for investors which are concerned

about the losses occurring outside of the 95% scope.

Despite the fact that the branches Figure 31 indicate that each option is mutually exclusive, it

is highly advisable to consider several measures in order to select the most sufficient ETF. The

reason is that none of the measures considered is entirely free of drawbacks, and no single

measure can account for the full range of investor’s objectives.

The distinctive feature of this thesis is that it does not only evaluate single risk factors, but

presents an integral performance measure, incorporating the most important metrics in ETF

performance measurement. The analysis conducted is independent of any product provider

and ads to the considerations by Hassine and Roncalli (2013) by introducing robust measures

of risk as well as intra-horizon risk. This is the first study to look at ETF performance

measurement for both, ETFs traded on exchange and OTC. Therefore, the thesis not only takes

several statistical considerations into account, but furthermore adjusts to a selection of typical

ETF trading strategies on the ETFs primary and secondary market.

Whereas many studies focus on either the US or the European ETF market, this thesis is one of

the few to analyze parts of the Swiss ETF market. The randomized results suggest that the

rankings according to the various efficiency measures are largely consistent across the data

sample, where more efficient funds tend to perform better for most methodologies applied.

For the ETFs on EURO STOXX 50, the analysis generally confirms the results received by other

authors. However it does not find the same consistency across ETF ratings than suggested by

Hassine and Roncalli (2013). Especially the results for the Cornish-Fisher VaR deviate from the

results in their study, indicating larger skewness and excess kurtosis in the data sample. The

results in this thesis show that the efficiency measure is susceptible to the statistical

assumptions of the underlying TD distribution and suffers from other drawbacks such as non-

robustness. Overall, the measurement of ETF tracking efficiency is very precarious. It is

essential for investors not only to have transparent measures sourcing from high quality data,

but moreover to receive in-depth education about the risks and the shortcomings of ETF

efficiency measurement.


87

It is subject to further research whether the methods in the herein thesis give consistent

results when being extrapolated to ETF replicating e.g. fixed income, real estate, commodity or

hedge fund indexes. Additionally, research has to be conducted in order to test the viability of

the measures in different markets such as the US or Asia.

The ETF-market is one of the most growing markets within the asset management industry.

Not only new providers and ETF variations enter the market on a regular basis, but also the set

of potential index benchmarks increases. The rise in complexity jeopardizes the highly praised

simplicity and transparency of ETFs. The applicability of the efficiency measures framework to

different types of ETFs and indexes needs to be investigated going forward. With new products

such as leveraged and actively managed funds, the variety of ETFs increases. This further

evokes the need to have expedient efficiency indicators. As measures such as the TE and TD

may fail in the context of these products, additional risk metrics need to be developed.

88

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97

Appendix 1 – Proof of Equation (15)

Proof of equation (15) following Hassine and Roncalli (2013):

|

The weights of the linear combination of the tracker and are

Where the weights with respect to the benchmark adjust as follows

Consequently the TD is

| | |

And the TE calculates as follows

|

| |

| | |

| | |

98

The Information Ratio therefore is the following:

| |

|

| |

√ | | |

99

Appendix 2 – Derivation of the Efficiency Measure

Derivation of the efficiency measure based on the VaR framework following Hassine and

Roncalli (2013) as well as Jorion (2007).Starting from the general expression for VaR

| { { | } }

We have

{ | }

{ }

{ }

{ |

|

|

| }

Or

{ |

|

|

| }

( |

| )

|

|

Solving for

| |

And since

|

We get

| |

100

Appendix 3 – Index Information

Table 30: EURO STOXX 50

The constituents of the EURO STOXX 50 net total return index are depicted. The reference date is May 30

th 2014 and the name, the corresponding industry, the country of domicile and the percentage of the

constituents are presented. (Source: STOXX, 2014) No. Name Industry Country Percentage as of 30.05.2014

1

AIR LIQUIDE Chemicals FR 1.60% 2 AIRBUS GROUP NV Industrial Goods & Services FR 1.58% 3 ALLIANZ Insurance DE 2.84% 4

ANHEUSER-BUSCH INBEV Food & Beverages BE 2.88% 5 ASML HLDG Technology NL 1.35% 6

ASSICURAZIONI GENERALI Insurance IT 1.11% 7 AXA Insurance FR 2.02% 8

BASF Chemicals DE 3.75% 9 BAYER Chemicals DE 4.24%

10 BCO BILBAO VIZCAYA RGENTARIA Banks ES 2.64% 11 BCO SANTANDER Banks ES 3.86% 12 BMW Automobiles & Parts DE 1.49% 13

BNP PARIBAS Banks FR 3.15% 14 CARREFOUR Retail FR 0.90% 15

CRH Construction & Materials IE 0.76% 16 DAIMLER Automobiles & Parts DE 3.39% 17 DANONE Food & Beverages FR 1.51% 18 DEUTSCHE BANK Banks DE 1.72% 19 DEUTSCHE POST Industrial Goods & Services DE 1.27% 20

DEUTSCHE TELEKOM Telecommunications DE 1.83% 21 E.ON Utilities DE 1.45% 22

ENEL Utilities IT 1.34% 23 ENI Oil & Gas IT 2.52% 24

ESSILOR INTERNATIONAL Healthcare FR 0.83% 25 GDF SUEZ Utilities FR 1.56% 26 GRP SOCIETE GENERALE Banks FR 1.87% 27 IBERDROLA Utilities ES 1.30% 28 Industria de Diseno Textil SA Retail ES 1.20% 29

ING GRP Insurance NL 2.03% 30 INTESA SANPAOLO Banks IT 1.68% 31

L'OREAL Personal & Household Goods FR 1.44% 32 LVMH MOET HENNESSY Personal & Household Goods FR 1.80% 33 MUENCHENER RUECK Insurance DE 1.30% 34 ORANGE Telecommunications FR 1.03% 35 PHILIPS Industrial Goods & Services NL 1.19% 36

REPSOL Oil & Gas ES 0.76% 37 RWE Utilities DE 0.73% 38

SAINT GOBAIN Construction & Materials FR 1.01% 39 SANOFI Healthcare FR 4.70% 40

SAP Technology DE 2.81% 41 SCHNEIDER ELECTRIC Industrial Goods & Services FR 1.87% 42 SIEMENS Industrial Goods & Services DE 4.25% 43 TELEFONICA Telecommunications ES 2.32% 44 TOTAL Oil & Gas FR 5.91% 45

UNIBAIL-RODAMCO Real Estate FR 0.96% 46 UNICREDIT Banks IT 1.83% 47

UNILEVER NV Food & Beverages NL 2.32% 48 VINCI Construction & Materials FR 1.46% 49 VIVENDI Media FR 1.31% 50 VOLKSWAGEN PREF Automobiles & Parts DE 1.35%

101

Table 31: Swiss Market Index

The constituents of the SMI price index are depicted. The reference date is December 12th

2013 and the name, the corresponding industry and the percentage of the constituents are presented. (Source: SIX, 2013b)

No. Name Industry Percentage as of

30.12.2013

1 ABB Industrials 5.44%

2 Actelion Health Care 0.84%

3 Adecco Industrials 0.95%

4 Credit Suisse Financials 4.13%

5 Geberit Industrials 1.02%

6 Givaudan Basic Materials 1.06%

7 Holcim Industrials 1.51%

8 Julius Baer Group Financials 0.96%

9 Nestlé food products 21.08%

10 Novartis Health Care 19.29%

11 Richemont clothing and accessories 4.13%

12 Roche Health Care 17.53%

13 SGS Industrials 1.13%

14 Swatch Group clothing and accessories 1.82%

15 Swiss Re Financials 2.82%

16 Swisscom Telecommunications 1.06%

17 Syngenta Basic Materials 3.31%

18 Transocean Oil & Gas 1.47%

19 UBS Financials 6.09%

20 Zurich Insurance Group Financials 3.85%

102

Appendix 4 – ETF Sample

Table 32: ETF Sample

The sample fund names, the International Securities Identification Number (ISIN) as well as the corresponding product provider are presented. The funds are arranged in a random order and do not correspond to the sequence of numbers used in the main body of the thesis as well as the listing in Appendix 5. (Source: Provider Factsheets available on provider websites and Bloomberg)

Panel A: ETF on SMI

Names ISIN Product provider

ISHARES SMI DE DE0005933964 iShares

COMSTAGE SMI UCITS ETF LU0392496427 ComStage ETF

ISHARES SMI CH CH0008899764 iShares

DB X-TRACKERS SMI UCITS ETF LU0274221281 db x-trackers

UBS ETF CH-SMI CHF A CH0017142719 UBS

DB X-TRACKERS SMI UCITS ETF LU0943504760 db x-trackers

UBS ETF CH-SMI CHF I CH0200721360 UBS

SMI Price Index CH0009980894 SIX Swiss Exchange

SMI Total Return Index CH0000222130 SIX Swiss Exchange

Panel B: ETF on EURO STOXX 50

Names ISIN Product provider

COMSTAGE ETF DJ EUR STOXX 50 NR UCITS ETF LU0378434079 ComStage ETF SICAV

LYXOR UCITS ETF (FCP) EURO STOXX 50 FR0007054358 Lyxor International Asset Management

ISHARES EURO STOXX50 UCITS ETF (DE) DE0005933956 BlackRock Asset Management Deutschland AG

UBS ETF (LU) EURO STOXX 50 UCITS ETF LU0136234068 UBS ETF

ISHARES Core EURO STOXX 50 UCITS ETF IE00B53L3W79 iShares VII plc

HSBC EURO STOXX 50 UCITS ETF IE00B4K6B022 HSBC ETFs PLC

AMUNDI ETF EURO STOXX 50 UCITS ETF FR0010654913 AMUNDI

EURO STOXX 50 Net Total Return Index EU0009658145 STOXX

103

Appendix 5 – ETF Facts

Table 33: Fund Information

The ETF facts as of April 2014 are depicted. The illustration covers the ETF status, share class, the ETF domicile, inception date, replication strategy, whether the fund distributes or accumulates dividends and whether the ETF conducts securities lending. (Source: Provider Factsheets available on provider websites and Bloomberg)

Panel A: ETFs on SMI

ETF on SMI Status Share class Domicile Inception

Date Replication Acc./ Dist.

Securities lending

1# active 1D Luxembourg 14.05.2007 Full Distributing No

2# active I Luxembourg 04.11.2009 synthetic Accumulating Unknown

3# active A Germany 29.08.2001 Full Distributing No

4# active A Switzerland 15.03.2001 Full Distributing Yes

5# active A Switzerland 05.12.2003 Full Distributing Yes

104

Panel B: ETFs on EURO STOXX 50


Status Share class Fund

Domicile Inception

Date Replication Acc./ Dist.

Securities lending

1# active C France 13.04.2010 synthetic Accumulating No

2# active I Luxembourg 01.06.2010 synthetic Accumulating Unknown

3# active A Ireland 11.04.2011 full Distributing No

4# active A Germany 12.09.2003 full Distributing Yes

5# active B Ireland 26.01.2010 full Accumulating Yes

6# active D France 15.09.2004 synthetic Accumulating

and /or Distribution

No

7# active A Luxembourg 13.11.2001 full Distributing Yes

105

Appendix 6 – ETF Trading Information

Table 34: Trading Information

The trading facts as of April 2014 are presented. The illustration covers the ETF trading information symbol, Bloomberg ticker and benchmark. In addition, the responsible APs on the SIX Swiss Exchange and the current registrations within the European Union and Switzerland are listed. Furthermore the AuM, the trading currency, the management fees and the total expense ratio are depicted. (Source: Provider Factsheets available on provider websites and Bloomberg)


ETF on SMI Symbol Bloomber

g ticker Benchmark

(Symbol) APs on SIX

Current Listing

EU & CH

AuM in Mio

Trading Currency

Mgmt. fee

TER

1# XSMI XSMI SW SMI

Deutsche Bank AG London Branch; Flow Traders B.V.; Commerzbank AG; Optiver V.O.F; Susquehanna; KCG

Europe Limited

AT, CH, DE, ES,

FR, IE, IT, LU, UK

465 CHF 0.30% 0.30%

2# CBSSMI CBSSMI SW SMIC Commerzbank AG;

Susquehanna

AT, CH, DE, LU

59.64481

CHF 0.25% 0.25%

3# SMIEX SMIEX SW SMIC Flow Traders B.V.;

Commerzbank AG; Optiver V.O.F; Susquehanna

CH, DE, LI 255 CHF 0.50% 0.50%

4# CSSMI CSSMI SW SMIC

Credit Suisse AG; Susquehanna; Commerzbank

AG; Flow Traders B.V.; Optiver V.O.F; KCG Europe Limited;

Zürcher Kantonalbank

CH, DE, LI 3319.99

1 CHF 0.39% 0.39%

5# SMICHA SMICHA

SW SMIC

UBS; Commerzbank AG; Optiver V.O.F; Flow Traders

B.V.; Credit Suisse AG; Timber Hill (Europe) AG; Zürcher

Kantonalbank; Susquehanna

CH, LI 1050.05

7 CHF 0.20% 0.20%

106



Symbol Bloomberg

ticker Benchmark

(Symbol) APs on SIX

Current Listing EU &

CH

AuM in Mio

Trading Currency

Mgmt. fee

TER

1# C50 C50 SW SX5T Flow Traders B.V.; BNP Paribas; Susquehanna

CH, DE, ES, FR, IT, UK

980.8394 EUR 0.15% 0.15%

2# CBSX5E CBSX5EEU SW SX5T Commerzbank AG;

Susquehanna AT, CH, DE, LU 234.3195 EUR 0.10% 0.10%

3# H50E H50EEUR SW SX5T HSBC Bank Plc;

Susquehanna; Flow Traders B.V.

AT, CH, DE, SP, FR, UK, IT, NL,

SW 69.42362 EUR 0.15% 0.15%

4# DJSXE SX5EEX SW SX5T Commerzbank AG; Flow

Traders B.V.; Susquehanna

AT, CH, DE FR, LI, LU

4955.333 EUR 0.15% 0.16%

5# CSSX5E CSSX5E SW SX5T

Credit Suisse AG; Timber Hill (Europe)

AG; Flow Traders B.V.; Susquehanna

AT, CH, DE, ES, FR, IE, IT, UK

122.3061 EUR 0.20% 0.20%

6# MSE MSE SW SX5T

Société Générale; Commerzbank AG; Flow

Traders B.V.; Susquehanna

AT, BE, CH, DE, ES, FR, IT, UK

4780.819 EUR 0.20% 0.20%

7# E50EUA E50EUA SW SX5T UBS; Commerzbank AG;

Flow Traders B.V.; Susquehanna

At, CH, DE, FR, IT, LI, LU, SG,

UK 614.0051 EUR 0.15% 0.15%

107

Appendix 7 – Tracking Differences Figure 32: Time Series ETF Tracking Difference

The TD development for the sample ETFs is illustrated. The observation period covers May 2013 to May 2014 and is illustrated on the horizontal axis. In order to receive comparable illustrations, the vertical axis is scaled consistently across all ETFs and depicts the TD in percentage. (Source: Own calculations / illustrations)

Panel A.1: ETF 1# on SMI



-0.05%

-0.03%

-0.01%

0.01%

0.03%

0.05%

03

.05

.13

17

.05

.13

31

.05

.13

14

.06

.13

28

.06

.13

12

.07

.13

26

.07

.13

09

.08

.13

23

.08

.13

06

.09

.13

20

.09

.13

04

.10

.13

18

.10

.13

01

.11

.13

15

.11

.13

29

.11

.13

13

.12

.13

27

.12

.13

10

.01

.14

24

.01

.14

07

.02

.14

21

.02

.14

07

.03

.14

21

.03

.14

04

.04

.14

18

.04

.14

-0.05%

-0.03%

-0.01%

0.01%

0.03%

0.05%

03

.05

.13

17

.05

.13

31

.05

.13

14

.06

.13

28

.06

.13

12

.07

.13

26

.07

.13

09

.08

.13

23

.08

.13

06

.09

.13

20

.09

.13

04

.10

.13

18

.10

.13

01

.11

.13

15

.11

.13

29

.11

.13

13

.12

.13

27

.12

.13

10

.01

.14

24

.01

.14

07

.02

.14

21

.02

.14

07

.03

.14

21

.03

.14

04

.04

.14

18

.04

.14

-0.05%

-0.03%

-0.01%

0.01%

0.03%

0.05%

03

.05

.13

17

.05

.13

31

.05

.13

14

.06

.13

28

.06

.13

12

.07

.13

26

.07

.13

09

.08

.13

23

.08

.13

06

.09

.13

20

.09

.13

04

.10

.13

18

.10

.13

01

.11

.13

15

.11

.13

29

.11

.13

13

.12

.13

27

.12

.13

10

.01

.14

24

.01

.14

07

.02

.14

21

.02

.14

07

.03

.14

21

.03

.14

04

.04

.14

18

.04

.14

108



Panel B.1: ETF 1# on EURO STOXX 50

-0.05%

-0.03%

-0.01%

0.01%

0.03%

0.05%

03

.05

.13

17

.05

.13

31

.05

.13

14

.06

.13

28

.06

.13

12

.07

.13

26

.07

.13

09

.08

.13

23

.08

.13

06

.09

.13

20

.09

.13

04

.10

.13

18

.10

.13

01

.11

.13

15

.11

.13

29

.11

.13

13

.12

.13

27

.12

.13

10

.01

.14

24

.01

.14

07

.02

.14

21

.02

.14

07

.03

.14

21

.03

.14

04

.04

.14

18

.04

.14

-0.05%

-0.03%

-0.01%

0.01%

0.03%

0.05%

03

.05

.13

17

.05

.13

31

.05

.13

14

.06

.13

28

.06

.13

12

.07

.13

26

.07

.13

09

.08

.13

23

.08

.13

06

.09

.13

20

.09

.13

04

.10

.13

18

.10

.13

01

.11

.13

15

.11

.13

29

.11

.13

13

.12

.13

27

.12

.13

10

.01

.14

24

.01

.14

07

.02

.14

21

.02

.14

07

.03

.14

21

.03

.14

04

.04

.14

18

.04

.14

-0.01%

0.00%

0.01%

0.02%

0.03%

0.04%

0.05%

0.06%

3.0

5.1

3

17

.05

.13

31

.05

.13

14

.06

.13

28

.06

.13

12

.07

.13

26

.07

.13

9.0

8.1

3

23

.08

.13

6.0

9.1

3

20

.09

.13

4.1

0.1

3

18

.10

.13

1.1

1.1

3

15

.11

.13

29

.11

.13

13

.12

.13

27

.12

.13

10

.01

.14

24

.01

.14

7.0

2.1

4

21

.02

.14

7.0

3.1

4

21

.03

.14

4.0

4.1

4

109




-0.01%

0.00%

0.01%

0.02%

0.03%

0.04%

0.05%

0.06%

03

.05

.13

17

.05

.13

31

.05

.13

14

.06

.13

28

.06

.13

12

.07

.13

26

.07

.13

09

.08

.13

23

.08

.13

06

.09

.13

20

.09

.13

04

.10

.13

18

.10

.13

01

.11

.13

15

.11

.13

29

.11

.13

13

.12

.13

27

.12

.13

10

.01

.14

24

.01

.14

07

.02

.14

21

.02

.14

07

.03

.14

21

.03

.14

04

.04

.14

-0.01%

0.00%

0.01%

0.02%

0.03%

0.04%

0.05%

0.06%

03

.05

.13

17

.05

.13

31

.05

.13

14

.06

.13

28

.06

.13

12

.07

.13

26

.07

.13

09

.08

.13

23

.08

.13

06

.09

.13

20

.09

.13

04

.10

.13

18

.10

.13

01

.11

.13

15

.11

.13

29

.11

.13

13

.12

.13

27

.12

.13

10

.01

.14

24

.01

.14

07

.02

.14

21

.02

.14

07

.03

.14

21

.03

.14

04

.04

.14

-0.03%

-0.02%

-0.01%

0.00%

0.01%

0.02%

0.03%

0.04%

0.05%

0.06%

03

.05

.13

17

.05

.13

31

.05

.13

14

.06

.13

28

.06

.13

12

.07

.13

26

.07

.13

09

.08

.13

23

.08

.13

06

.09

.13

20

.09

.13

04

.10

.13

18

.10

.13

01

.11

.13

15

.11

.13

29

.11

.13

13

.12

.13

27

.12

.13

10

.01

.14

24

.01

.14

07

.02

.14

21

.02

.14

07

.03

.14

21

.03

.14

04

.04

.14

110




-0.01%

0.00%

0.01%

0.02%

0.03%

0.04%

0.05%

0.06%

03

.05

.13

17

.05

.13

31

.05

.13

14

.06

.13

28

.06

.13

12

.07

.13

26

.07

.13

09

.08

.13

23

.08

.13

06

.09

.13

20

.09

.13

04

.10

.13

18

.10

.13

01

.11

.13

15

.11

.13

29

.11

.13

13

.12

.13

27

.12

.13

10

.01

.14

24

.01

.14

07

.02

.14

21

.02

.14

07

.03

.14

21

.03

.14

04

.04

.14

-0.01%

0.00%

0.01%

0.02%

0.03%

0.04%

0.05%

0.06%

03

.05

.13

17

.05

.13

31

.05

.13

14

.06

.13

28

.06

.13

12

.07

.13

26

.07

.13

09

.08

.13

23

.08

.13

06

.09

.13

20

.09

.13

04

.10

.13

18

.10

.13

01

.11

.13

15

.11

.13

29

.11

.13

13

.12

.13

27

.12

.13

10

.01

.14

24

.01

.14

07

.02

.14

21

.02

.14

07

.03

.14

21

.03

.14

04

.04

.14

-0.01%

0.00%

0.01%

0.02%

0.03%

0.04%

0.05%

0.06%

03

.05

.13

17

.05

.13

31

.05

.13

14

.06

.13

28

.06

.13

12

.07

.13

26

.07

.13

09

.08

.13

23

.08

.13

06

.09

.13

20

.09

.13

04

.10

.13

18

.10

.13

01

.11

.13

15

.11

.13

29

.11

.13

13

.12

.13

27

.12

.13

10

.01

.14

24

.01

.14

07

.02

.14

21

.02

.14

07

.03

.14

21

.03

.14

04

.04

.14

111

Appendix 8 – Semi-Variance as a Special Case of LPM

According to Bawa (1975) semi-variance is a special case of lower partial moments (LPM).

Starting from as a random variable with distribution , the mathematical expectation of is

defined according to Casella & Berger (2001)

[ ]

∫ ∫

Casella and Berger (2001) provide the full mathematical framework the moments of a

distribution. The centered moment of order , which essentially measures the shape of a set

of points around the media is defined as:

[ ]

∫

The first four moments are then defined as follows:

Formula Mathematical Sign Numerator for

[ ]

[ ]

[ ]

[ ]

According to Bawa (1975), the lower Partial Moment (LPM) of the above distribution is defined

as follows, where denotes the threshold:

[ ]

∫

Semi-variance then is defined as the second lower partial moments with respect to

the threshold of the mean

112

[ ]

∫

Whenever the distribution of is symmetric around the theshold, the semi-variance is half of

the variance.

∫

∫

∫

∫

113

Appendix 9 – Autocorrelation

Figure 33: ETF Autocorrelation Function

The autocorrelation function for the first 25 lags is presented. The dotted red lines correspond to the coefficients in order to reject the null hypothesis of no autocorrelation. (Source: Own calculations / illustrations).




-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lag k

Autocorrelation

U-Critical Val

L Cirtical Val

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lag k

Autocorrelation

U-Critical Val

L Cirtical Val

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lag k

Autocorrelation

U-Critical Val

L Cirtical Val

114




-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lag k

Autocorrelation

U-Critical Val

L Cirtical Val

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lag k

Autocorrelation

U-Critical Val

L Cirtical Val

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lag k

Autocorrelation

U-Critical Val

L Cirtical Val

115




-0.15

-0.05

0.05

0.15

0.25

0.35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lag k

Autocorrelation

U-Critical Val

L Cirtical Val

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lag k

Autocorrelation

U-Critical Val

L Cirtical Val

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lag k

Autocorrelation

U-Critical Val

L Cirtical Val

116




-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lag k

Autocorrelation

U-Critical Val

L Cirtical Val

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lag k

Autocorrelation

U-Critical Val

L Cirtical Val

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lag k

Autocorrelation

U-Critical Val

L Cirtical Val

117

Appendix 10 – Bid-Ask Spread

Figure 34: Percentage Bid-Ask Spreads

The percentage spread development for all ETFs are presented. The observation period covers May 2013 to May 2014. (Source: Own calculations / illustrations).




0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

02

.05

.13

16

.05

.13

30

.05

.13

13

.06

.13

27

.06

.13

11

.07

.13

25

.07

.13

08

.08

.13

22

.08

.13

05

.09

.13

19

.09

.13

03

.10

.13

17

.10

.13

31

.10

.13

14

.11

.13

28

.11

.13

12

.12

.13

26

.12

.13

09

.01

.14

23

.01

.14

06

.02

.14

20

.02

.14

06

.03

.14

20

.03

.14

03

.04

.14

17

.04

.14

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

02

.05

.13

16

.05

.13

30

.05

.13

13

.06

.13

27

.06

.13

11

.07

.13

25

.07

.13

08

.08

.13

22

.08

.13

05

.09

.13

19

.09

.13

03

.10

.13

17

.10

.13

31

.10

.13

14

.11

.13

28

.11

.13

12

.12

.13

26

.12

.13

09

.01

.14

23

.01

.14

06

.02

.14

20

.02

.14

06

.03

.14

20

.03

.14

03

.04

.14

17

.04

.14

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

02

.05

.13

16

.05

.13

30

.05

.13

13

.06

.13

27

.06

.13

11

.07

.13

25

.07

.13

08

.08

.13

22

.08

.13

05

.09

.13

19

.09

.13

03

.10

.13

17

.10

.13

31

.10

.13

14

.11

.13

28

.11

.13

12

.12

.13

26

.12

.13

09

.01

.14

23

.01

.14

06

.02

.14

20

.02

.14

06

.03

.14

20

.03

.14

03

.04

.14

17

.04

.14

118




0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

02

.05

.13

16

.05

.13

30

.05

.13

13

.06

.13

27

.06

.13

11

.07

.13

25

.07

.13

08

.08

.13

22

.08

.13

05

.09

.13

19

.09

.13

03

.10

.13

17

.10

.13

31

.10

.13

14

.11

.13

28

.11

.13

12

.12

.13

26

.12

.13

09

.01

.14

23

.01

.14

06

.02

.14

20

.02

.14

06

.03

.14

20

.03

.14

03

.04

.14

17

.04

.14

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

02

.05

.13

16

.05

.13

30

.05

.13

13

.06

.13

27

.06

.13

11

.07

.13

25

.07

.13

08

.08

.13

22

.08

.13

05

.09

.13

19

.09

.13

03

.10

.13

17

.10

.13

31

.10

.13

14

.11

.13

28

.11

.13

12

.12

.13

26

.12

.13

09

.01

.14

23

.01

.14

06

.02

.14

20

.02

.14

06

.03

.14

20

.03

.14

03

.04

.14

17

.04

.14

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

02

.05

.13

16

.05

.13

30

.05

.13

13

.06

.13

27

.06

.13

11

.07

.13

25

.07

.13

08

.08

.13

22

.08

.13

05

.09

.13

19

.09

.13

03

.10

.13

17

.10

.13

31

.10

.13

14

.11

.13

28

.11

.13

12

.12

.13

26

.12

.13

09

.01

.14

23

.01

.14

06

.02

.14

20

.02

.14

06

.03

.14

20

.03

.14

03

.04

.14

119




0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

02

.05

.13

16

.05

.13

30

.05

.13

13

.06

.13

27

.06

.13

11

.07

.13

25

.07

.13

08

.08

.13

22

.08

.13

05

.09

.13

19

.09

.13

03

.10

.13

17

.10

.13

31

.10

.13

14

.11

.13

28

.11

.13

12

.12

.13

26

.12

.13

09

.01

.14

23

.01

.14

06

.02

.14

20

.02

.14

06

.03

.14

20

.03

.14

03

.04

.14

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

02

.05

.13

16

.05

.13

30

.05

.13

13

.06

.13

27

.06

.13

11

.07

.13

25

.07

.13

08

.08

.13

22

.08

.13

05

.09

.13

19

.09

.13

03

.10

.13

17

.10

.13

31

.10

.13

14

.11

.13

28

.11

.13

12

.12

.13

26

.12

.13

09

.01

.14

23

.01

.14

06

.02

.14

20

.02

.14

06

.03

.14

20

.03

.14

03

.04

.14

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

02

.05

.13

16

.05

.13

30

.05

.13

13

.06

.13

27

.06

.13

11

.07

.13

25

.07

.13

08

.08

.13

22

.08

.13

05

.09

.13

19

.09

.13

03

.10

.13

17

.10

.13

31

.10

.13

14

.11

.13

28

.11

.13

12

.12

.13

26

.12

.13

09

.01

.14

23

.01

.14

06

.02

.14

20

.02

.14

06

.03

.14

20

.03

.14

03

.04

.14

120




0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

02

.05

.13

16

.05

.13

30

.05

.13

13

.06

.13

27

.06

.13

11

.07

.13

25

.07

.13

08

.08

.13

22

.08

.13

05

.09

.13

19

.09

.13

03

.10

.13

17

.10

.13

31

.10

.13

14

.11

.13

28

.11

.13

12

.12

.13

26

.12

.13

09

.01

.14

23

.01

.14

06

.02

.14

20

.02

.14

06

.03

.14

20

.03

.14

03

.04

.14

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

02

.05

.13

16

.05

.13

30

.05

.13

13

.06

.13

27

.06

.13

11

.07

.13

25

.07

.13

08

.08

.13

22

.08

.13

05

.09

.13

19

.09

.13

03

.10

.13

17

.10

.13

31

.10

.13

14

.11

.13

28

.11

.13

12

.12

.13

26

.12

.13

09

.01

.14

23

.01

.14

06

.02

.14

20

.02

.14

06

.03

.14

20

.03

.14

03

.04

.14

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

02

.05

.13

16

.05

.13

30

.05

.13

13

.06

.13

27

.06

.13

11

.07

.13

25

.07

.13

08

.08

.13

22

.08

.13

05

.09

.13

19

.09

.13

03

.10

.13

17

.10

.13

31

.10

.13

14

.11

.13

28

.11

.13

12

.12

.13

26

.12

.13

09

.01

.14

23

.01

.14

06

.02

.14

20

.02

.14

06

.03

.14

20

.03

.14

03

.04

.14

121

Appendix 11 – Efficiency Measure Values

Table 35: Efficiency Measures Overview

The summary statistics of all efficiency measure calculation methods is presented. The measures are calculated in bps on an annual basis from May 2013 to May 2014. For each efficiency measure, the number of the corresponding formula is indicated. The coloring in the cells illustrates the ranking of the fund according to the efficiency measure considered. Orange coloring indicates a lower ranking and yellow coloring suggest a better ranking amongst the ETFs considered. (Source: Own calculations / illustrations)


Formula 1# 2# 3# 4# 5#

| with | 23 & 28 -174.28 -251.59 -144.47 -55.49 -53.01

| with | 29/30 -174.54 -251.76 -144.60 -55.51 -53.03

| with | 32/33 -174.13 -251.44 -136.77 -55.51 -52.87

| 34 -79.85 -196.48 -109.96 -51.66 -50.02

| 36 -61.57 -276.40 -129.61 -56.61 -50.93

| 37 -62.69 -276.91 -132.04 -57.09 -52.40

Median Spread 43 -166.39 -253.73 -142.58 -55.34 -52.95

No Spread 43 -158.94 -189.39 -133.56 -50.54 -46.06

49 -64.43 -193.48 -143.83 -54.26 -55.05

| 51 -167.29 -70.01 -133.87 -48.97 -52.50

52 -72.52 -301.76 -164.34 -62.11 -58.94

| 53 -173.07 -250.43 -219.21 -55.46 -52.95

| 58 -193.14 -256.53 -149.86 -55.65 -53.68

Average -132.53 -232.30 -144.98 -54.94 -52.64

122


Formula 1# 2# 3# 4# 5# 6# 7#

| with | 23 & 28 12.67 -34.55 -32.90 -102.62 0.09 9.95 26.55

| with | 29/30 12.63 -34.58 -32.94 -102.76 -0.02 9.91 26.49

| with | 32/33 12.63 -34.11 -32.91 -95.68 0.22 9.95 27.26

| 34 23.06 -25.62 -23.36 -80.11 42.50 22.20 42.98

| 36 28.20 -22.85 -17.77 -79.98 49.13 24.35 48.14

| 37 27.64 -23.05 -17.67 -78.73 48.65 24.22 47.76

Median Spread 43 16.45 -23.81 -23.30 -106.06 -0.18 11.09 28.02

No Spread 43 27.96 25.40 -7.04 -49.89 13.91 23.96 42.23

49 26.84 -24.26 -17.72 -85.67 47.83 26.00 48.53

| 51 8.90 -37.48 -38.23 -111.84 132.71 13.58 22.67

52 26.15 -26.76 -19.83 -102.63 46.09 22.64 41.85

| 53 -19.21 -63.51 -40.08 -118.89 -37.02 -18.43 -22.89

| 58 -3.91 -3.55 -14.21 -66.15 -23.20 -4.42 -7.21

Average 15.38 -25.29 -24.46 -90.85 24.67 13.46 28.64

123

Appendix 12 – Efficiency Measure without Bid-Ask Spread

Table 36: Efficiency Measures Overview without Spread

The summary statistics of all efficiency measure versions without incorporating the bid-ask spread is presented. The measures are calculated on an annual basis from May 2013 to May 2014 and are measured in Basis points. For each efficiency measure, the number of the corresponding formula is indicated. The coloring in the cells illustrates the ranking of the fund according to the efficiency measure considered. Orange coloring indicates a lower ranking and yellow coloring suggest a better ranking amongst the ETFs considered. (Source: Own calculations / illustrations)


Formula 1# 2# 3# 4# 5#

| with | 23 & 28 -158.94 -189.39 -133.56 -50.54 -46.06

| with | 29/30 -159.20 -189.55 -133.69 -50.56 -46.09

| with | 32/33 -158.79 -189.24 -125.85 -50.56 -45.92

| 34 -64.51 -134.27 -99.05 -46.71 -43.07

| 36 -46.22 -214.20 -118.69 -51.66 -43.99

| 37 -47.35 -214.71 -121.12 -52.14 -45.46

49 -49.09 -131.28 -143.83 -49.31 -55.05

| 51 -151.95 -7.80 -122.95 -44.02 -45.55

52 -57.18 -239.55 -153.42 -57.16 -51.99

| 53 -157.73 -188.23 -208.29 -50.51 -46.01

| 58 -177.80 -194.33 -138.95 -50.71 -46.73

Average -111.71 -172.05 -136.31 -50.35 -46.90

124


Formula 1# 2# 3# 4# 5# 6# 7#

| with | 23 & 28 27.96 25.40 -7.04 -49.89 13.91 23.96 42.23

| with | 29/30 27.93 25.37 -7.08 -50.02 13.80 23.93 42.16

| with | 32/33 27.93 25.84 -7.04 -42.95 14.04 23.96 42.93

| 34 38.36 34.33 2.50 -27.37 56.33 36.21 58.66

| 36 43.50 37.10 8.09 -27.25 62.95 38.36 63.82

| 37 42.94 36.90 8.20 -26.00 62.47 38.23 63.44

49 42.14 35.69 8.15 -32.93 61.65 40.01 64.20

| 51 24.20 22.47 -12.37 -59.11 146.53 27.59 38.35

52 41.44 33.19 6.03 -49.90 59.91 36.65 57.53

| 53 -3.91 -3.55 -14.21 -66.15 -23.20 -4.42 -7.21

| 58 11.38 56.40 11.65 -13.42 -9.38 9.59 8.47

Average 15.38 -25.29 -24.46 -90.85 24.67 13.46 28.64

Performance Measurement of Exchange Traded Funds

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