Csv Analysis - Qwafafew

8/13/2019 Csv Analysis - Qwafafew

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Jose Menchero

Global Cross-Sectional

Volatility Analysis


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2009. All rights reserved.

Outline

Global Factor Model

Industry versus Country

Diversification Potential, Correlation, and MAD

Regional and Size Differences

Cross-Sectional Volatility (CSV) Analysis

Why is CSV important?

CSV Factor Decomposition

Empirical Results: Styles, Industries, Countries

2


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Global Factor Model


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Global Factor Model

Model derived from Barra Global Equity Model (GEM2):

1 World factor

Country factors with (0,1) exposure

24 Industry Groups (GICS) with (0,1) exposure

8 style factors (derived from GEM2)

Estimate factor returns by regression:

4

n

s

sns

i

ini

c

cncwn ufXfXfXfr


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Factor Models for Study

Build separate factor models for each region:

48 countries in MSCI ACWI IMI

24 emerging markets in MSCI ACWI IMI

16 countries in MSCI Developed Europe (ACWI IMI)

Use global-relative standardization for style factors

Estimate models using cap-weighted (WLS) and equal-

weighted (OLS) regression

5


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Estimating Factor Returns

6

is the weight of stock n in factor portfolio k

n

s

sns

i

ini

c

cncwn ufXfXfXfr

nnknk rf Pure factor returns

Constraint: 0c c

c

w f Cap-weighted country factor returnssum to zero

Constraint: 0i ii

w f Cap-weighted industry factor returnssum to zero

kn


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Interpreting Factor Portfolios

Pure country factor portfolios go long the country and go

short the World; they have zero industry exposure

Pure industry factor portfolios go long the industry and go

short the World; they have zero country exposure

Pure style factor portfolios have unit exposure to the style

and zero exposure to all other factors

Adding World factor to country (industry) factor creates

100% net-long factor with neutral industry (country)

exposures

7


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Pure Pure Pure Pure PureMarket World Japan US Auto Volatility

Segment Factor Factor Factor Factor Factor

World (Net) 100.00 0.00 0.00 0.00 0.00

Long 100.00 109.75 66.03 128.46 62.32

Short 0.00 -109.75 -66.03 -128.46 -62.32

Japan (Net) 10.72 89.28 -10.72 0.00 0.00

Long 10.72 89.28 0.35 45.98 5.76Short 0.00 0.00 -11.07 -45.98 -5.76

US (Net) 35.42 -35.42 64.58 0.00 0.00

Long 35.42 6.31 64.64 20.30 22.91

Short 0.00 -41.73 -0.06 -20.30 -22.91

Auto (Net) 2.41 0.00 0.00 97.59 0.00

Long 2.41 6.71 0.84 97.59 1.29

Short 0.00 -6.71 -0.84 0.00 -1.29Japan Auto (Net) 1.15 6.71 -0.47 45.98 0.16

Long 1.15 6.71 0.09 45.98 0.41

Short 0.00 0.00 -0.56 0.00 -0.25

US Auto (Net) 0.18 -0.90 0.55 8.18 0.45

Long 0.18 0.00 0.55 8.18 0.46

Short 0.00 -0.90 0.00 0.00 0.00

Example of Pure Factor Portfolios (6-30-2009)

Country factorshave zero

exposure to

industries.

Industry factors

have zeroexposure to

countries.

Adding World

factor to country

factors produces100% net-long

portfolio in a single

country, with

neutral industry

exposures

8


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Industry vs Country


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The Algebra of Country/Industry Risk

10

wf (return of World factor)

kf (return of long/short country/industry factor)

return of net long country/industry factork w kf f f

1/22 2

,2k w k w k k w Volatility of net long

country/industry factor

World factor can be added to country (industry) factor to create

100% net long factor with neutral industry (country) exposure


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The Geometry of Country/Industry Risk

11

k k

kk

w

2 2 2

,2k w k w k k w Variance of net long factor

cosk k

cosk k

Correlation of long/short factor with World

Correlation of net long factor with World

kAs decreases, net longfactor becomes more

correlated with the World


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Diversification Potential (DP) and Correlation

Diversification Potential measures volatility reduction that canbe achieved by investing in the World portfolio rather thanthe country factor or industry factor

Use either equal-weighted or regression-weighted averages

12

kk

w

DP

k

k

k w

DP w

DiversificationPotential

k k

k

w Mean correlation between countriesor industries and the World


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DP and Correlation for World (48 Countries)

13

Countries dominated

from 1997-1999

Industries dominated

from 2000-2002

Overall, the two effects

are comparable strength

DPwas high during

internet bubble period

DP is now at an all-time

low

Year

1997 1999 2001 2003 2005 2007 2009

Value

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Countries (World)Industries (World)


Correlation

Cap-weighted Results


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DP and Correlation for EM (24 Countries)

For emerging markets,

country effects always

dominate industries

Even before Oct 2008,DPseemed to be in

secular decline

DP is now at an all-time

low

14

Year

1997 1999 2001 2003 2005 2007 2009

Value

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Countries (EM)Industries (EM)


Correlation



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DP and Correlation for Dev. Europe (16 Countries)

For developed Europe,

industry effects clearly

dominate countries

Industry diversificationwas particularly strong

during internet bubble

15

Year

1997 1999 2001 2003 2005 2007 2009

Value

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Countries (Euro 16)Industries (Euro 16)


Correlation



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Diversification Potential: Empirical Results

Period: Jan-97 to Jul-09, Cap-Weighted Regression

Industries dominate countries in Europe

Countries dominate industries in emerging markets

Country DPincreases for equal-weighted case due to

effect of highly volatile small countries

16

Country (Cap Weighted) (Equal Weighted)

Scheme Countries Industries Countries Industries

48 ACWI 1.21 1.19 1.68 1.18

16 Europe 1.11 1.22 1.22 1.26

24 Emerging 1.41 1.17 1.54 1.21


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Diversification Potential: Small-cap vs Large-cap

Sample period: Jan-97 to Jul-09 (151 months)

OLS probes small-cap stocks, WLS probes large-caps

Countries dominate industries when using OLS regression

Country effects remain strong for small-cap stocks

Industry effects are weaker at the small-cap level

17

Country Regression (Regression Weighted)

Scheme Scheme Countries Industries

48 ACWI WLS 1.21 1.19

48 ACWI OLS 1.38 1.09


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World Volatility: Cap-weighted vs Equal-weighted

Volatility of World

portfolio is largely

insensitive to stock-

weighting scheme

18

Year

1997 1999 2001 2003 2005 2007 2009

WorldFactorVo

latility

0

5

10

15

20

25

30

35

40

45

Cap Weighted (WLS)

Equal Weighted (OLS)


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Volatility Ratio of OLS-to-WLS (48 Countries)

Country factors retain

strength in small-cap

segment

Industry factors weaken

in the small-cap regime

19

Year

1997 1999 2001 2003 2005 2007 2009

V

olatilityRatio(OLS/WLS)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Countries (OLS/WLS)

Industries (OLS/WLS)

(OLS)

(WLS)

kk

k

VR

1k

k

VR VRK


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Mean Absolute Deviation (MAD) Measure

MAD measures the cap-weighted active return from

tactical allocation to the segment with perfect foresight

Compute rolling 12-month average

20

( ) k kk C

MAD C w f

( ) k kk I

MAD I w f

Mean Absolute Deviation, Countries

Mean Absolute Deviation, Industries


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MAD for World (48-Country Model)

Use 12-month rolling

average

Countries dominate prior to1999

Industries dominate from

2000-2003

Industries and countries

are comparable since 2003

21

Year

1997 1999 2001 2003 2005 2007 2009

MAD(percentmonthly)

0

1

2

3

4

5

Countries (World)

Industries (World)


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MAD for Developed Europe (16-Country Model)

At start of period,

industries and countries

were comparable

Industries have stronglydominated countries in

Europe since 1998

22

Year

1997 1999 2001 2003 2005 2007 2009

MAD(percentmo

nthly)

0

1

2

3

4

5

Countries (Dev. Europe)

Industries (Dev. Europe)


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MAD for Emerging Markets (24-Country Model)

Country effects were

strongest in 1998-1999

For Emerging Markets,

countries stronglydominate industries over

entire sample period

23

Year

1997 1999 2001 2003 2005 2007 2009

MAD(percentmo

nthly)

0

1

2

3

4

5

6

7

8

Countries (EM)

Industries (EM)


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Cross-Sectional Volatility

(CSV) Analysis


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What is Cross-Sectional Volatility (CSV)?

25

Return (percent)

-100 -80 -60 -40 -20 0 20 40 60 80 100

Count

0

200

400

600

800

1000

1200

MSCI All Country

World Investable

Market Index(ACWI IMI)

October 2008:

Mean Return: -23%

CSV: 18%

Return Distribution


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Why is CSV Important?

26

CSV measures the opportunity for active management:

Aggressiveness Opportunity Skill

AA n nn

R w r R Active Return

22

22

1( )

( )

A

n nA nA n n

An nn n

n n

w r RR N w r R

N w r R


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Active Weight (Percent)

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5

RelativeReturn(Percent)

-80

-60

-40

-20

0

20

40

60

80

100

120

Example: October 2008

27

Portfolio: MSCI World ValueBenchmark: MSCI ACWI IMI

Portfolio Return -15.80%Benchmark Return -17.36%

Aggressiveness 5.11

Opportunity (CSV) 17.80%

Skill 0.0172

Active Return 1.56%


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A Brief Digression: Risk Attribution

Identifies three drivers of time series volatility

Risk contributions are intuitive and fully additive

Aligns risk attribution model with investment process

28

t m mt

m

R x g Return Attribution, Period t

mx Source Exposure;

,m m mm

R x g g R Risk Attributionx-sigma-rho formula

mtg Source Return


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Exact CSV Decomposition

Identifies three drivers of cross-sectional volatility

Volatility contributions are intuitive and fully additive

CSV can be attributed to individual factors!

29

n n nr u Return Decomposition (factor vs specific)

Explained CS Volatility

x-sigma-rho formula ( ) ,k k k

k

f X X

n k nk

k

f X Linear Factor Structure


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Approximate CSV Decomposition

Collinearity among GEM2 factors is typically small

Reasonable and useful approximation:

Contribution to explained CSV is roughly proportional tothe squared factor return and the variance of factor

exposures

30

22( ) k

k

k

Xf

No-collinearity

Approximation


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Percent in Segment (p)

0 10 20 30 40 50

VarianceofExposures

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Variance of Factor Exposures

31

Style factors have cross-

sectional variance of 1

Country & Industry factors have

maximum CS variance of 0.25

2var( ) /100kX p p

TypicalCS variance of Country

& Industry factors may be 0.02


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Explained vs Total CSV (12m Rolling Average)

32

Year

1997 1999 2001 2003 2005 2007 2009

MonthlyCSV(Percent)

0

2

4

6

8

10

12

14

16

Explained CSV

Total CSV

Wide variation in

CSV over time:

CSV peaks above

14% in 2000

CSV dips below 7%

from 2005-2007


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Explained-to-Total CSV Ratio

33

Year

1997 1999 2001 2003 2005 2007 2009

CSVRatio(rolling1

2maverage)

0.3

0.4

0.5

0.6

0.7

CSV Ratio (Explained/Total)

CSV Ratio is

remarkably stable

about 0.5

Square of CSV

ratio is the Relative

R-squared of model


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Explained CSV Attributed by Factor Type

34

Year

1997 1999 2001 2003 2005 2007 2009

MonthlyCSV(Percent)

0

2

4

6

8

10

Explained CSV

Countries

Industries

Styles

Contributions to

explained CSV vary

greatly over time

Countries dominate

prior to 1999

Styles dominatefrom 2000-2004


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Attribution of Styles CSV

35

Year

1997 1999 2001 2003 2005 2007 2009

MonthlyCSV(Percent)

0

1

2

3

4

5

Styles

Volatility

Momentum

Volatility factor islargest contributor to

Styles CSV

In 2001, Volatility

contributes one-fourth

of total explained CSV

(about 2% of 8%):

2

2 21

48

kk

Xf

Monthly volatility of

Volatility factor


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Year

1997 1999 2001 2003 2005 2007 2009

MonthlyCSV(P

ercent)

0

1

2

3

Countries

Japan

USA

Attribution of Countries CSV

36

In 2006, Japan

contributes one-tenth of

the total explained CSV

Thats 40 bps (of 4%)

2

2 2 (0.1)4

4

k

k

Xf

Monthly volatility of

Japan factor


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Summary

CSV represents the opportunity for active management

CSV can be attributed to individual factors

Styles, countries, and industries dominate over different periods

The relative strength of countries versus industries can be

measured by the Diversification Potential (DP) or MAD

Countries dominate industries in EM, vice versa in Dev. Europe

Country factors persist in small-cap regime; industries weaken

Recent decline of DP due to increased volatility of World factor,

not decline in volatility of country or industry factors

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MSCI Barra 24 Hour Global Client Service

39

Asia Pacific

China North 10800.852.1032 (toll free)

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Hong Kong +852.2844.9333

Singapore 800.852.3749 (toll free)

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[email protected]

Barra Knowledge Base Online Answers to Barra Questions: www.barra.com/support


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40

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