1. Introduction - acfr.aut.ac.nz Web viewIn recent years, Interest rate swaps are widely traded over...

Hedging Effectiveness and Price Discovery in the Interest Rate Swap Market

Alex Frinoa*, Michael Garciaa

a The University of Wollongong, Wollongong, 2522 Australia

DraftAs at 7/5/2017

Abstract

This study examines the effectiveness of hedging an Australian 1-year interest rate swap using the 90-days bank bills futures contracts (90-days BABs), as well as, price discovery between these two markets. Using a unique over the counter (OTC) data set on interest rate swaps, this study presents three important findings – First, the hedge ratio between interest rate swaps and futures approaches unity as the hedge duration increases from 1 to 30 days, thus price movements between the swaps and futures are highly correlated for longer hedge durations. Second, an outright position in the swaps can be effectively hedged with futures contracts. To measure how effective futures contracts are at hedging interest rate swaps, we compare the average absolute returns of an unhedged position in the swaps to a hedged position using the futures. We find that the average absolute return of the hedged position is close to zero and the hedge strategy performs better for longer durations. Finally, similar to previous studies, we find that information flows between the swap and futures market is highly contemporaneous. These findings confirm that, although volume and liquidity in the interest rate swap market has increased considerably in recent years, futures contracts remain as an important instrument to access the yield curve and a preferred benchmark for the pricing and hedging of other interest rate products.

Keywords: price discovery, hedging effectiveness, swap market, interest rate futures.

**Corresponding author. Alex Frino. Tel: +61 (2) 8088 4238. Email: [email protected], University of Wollongong, Northfields Ave, Wollongong NSW 2522, Australia.

1. Introduction

In recent years, Interest rate swaps are widely traded over the counter by private investors and banks

in volumes similar or higher to other financial instruments such as equities or government debt (see

Appendix 1). As a result of higher liquidity in the swap market, institutions are increasingly using

interest rate swaps to gain exposure to the yield curve and shifting to swaps for the pricing and

hedging of other interest rate products (this is known as Benchmark Tipping; McCauley, 2001). In

order to understand the importance of swaps in the modern financial world, this paper investigates

the relation between interest rate swaps and futures while examining hedging effectiveness and price

discovery between the two markets.1 The aim of this study is to explain the extent to which swaps

have overcome futures as an important medium to access the yield curve and a preferred benchmark

in the interest rate market.

Hedging effectiveness has been widely studied on different securities such as equities (Laws and

Thompson, 2004), bonds (Wilkinson et.al., 1999; Young et.al., 2004), commodities (Witt, Schroeder

and Hayenga, 1987) and currencies (Hill and Schneeweis, 1982), which provides a framework that

can be applied to interest rate swaps.2 Studies on hedging effectiveness are divided on whether the

hedge ratio is assumed to be constant or time-varying. Under the assumption that the hedge ratio is

constant over time, hedging effectiveness is estimated using linear regression models as in Young,

Hogan and Batten (2004), Holmes (1996), Laws and Thompson (2004), Frino, Wearing and Fabre

(2004), Witt, Schroeder and Hayenga (1987), and Brown (1985).3 Young, Hogan and Batten (2004)

1 Interest rate swaps are a security commonly used by banks, companies and financial institutions to gain exposure to the interest rate market. The plain vanilla interest rate swap is an agreement between two firms to exchange cash flows determined by the different between a fixed and a floating interest rate during a period specified by the swap tenure (Litzenberger, 1992). The Australian 1-year interest rate swap has 4 fixed for floating exchange of cash flows that occur every three months, in which the fixed leg is the rate agreed at the beginning of the swap and the floating leg is represented by the BBSW rate reported daily by the Australian Financial Markets Association (AFMA). Litzenberger (1992) describes two motivations for investors to enter on a swap agreement – motivation for borrowing short and swapping into fixed, and motivation for borrowing long and swapping into floating (refer to Appendix 2 for more literature on swaps pricing).2 There are few studies on hedging effectiveness for the swaps market. Rendleman (2004) provides a general model for hedging swaps with Eurodollar futures. This model which is drawn on the cubic spline interpolation methodology in Rendleman (2004) shows that the difference between Eurodollar futures and forward rates is defined by convexity and it proves to be effective in hedging the interest rate risk of LIBOR swaps. 3 Laws and Thompson (2004) studies the effectiveness of hedging stock portfolios with futures stock indices for a sample period from 1995 to 2001 on the London stock exchange. To estimate the hedge ratio, this paper uses Ordinary Least Squares (OLS), as well as Exponential Weighted Moving Average (EWMA), and concludes that the EWMA method

investigate the effectiveness of the 10-years JGB bond futures contracts to hedge Japanese bonds of

different maturities and credit quality. OLS regression in price levels between the bonds and futures

is implemented to show that the 10-years JGB futures provides a good hedge for the 10-years bond

(as it would be expected since they both have the same maturity). Holmes (1996) examines the

hedging effectiveness of the FTSE100 stock index futures contract in hedging a spot portfolio that

underlying the index from 1984 to 1992 while comparing three methods for estimating the hedge

ratio between the two portfolios. These methods include an OLS technique, an Error Correction

Model (ECM) and the Generalised ARCH approach (GARCH). Holmes (1996) shows that OLS

outperforms other econometric techniques and the FTSE100 index reduces the risk and provides a

good hedge for a portfolio of stocks, especially for a hedge duration beyond four weeks.

A related set of authors propose different techniques on how to estimate hedging effectiveness

between two instruments under the assumption that the hedge ratio is time-varying.4 Choudhry

(2002) investigates the long-run relationship between the stock cash index and its futures index in 6

different markets using a hedge ratio implied from the GARCH and GARCH-X models. The results

demonstrate that hedging effectiveness increases after considering short-run deviations between the

cash and futures price. Hatemi and Roca (2006) suggest that among all the time-varying methods,

the Kalman Filter generates estimated parameters with better statistical properties. However, the

time-varying nature of the ratio implies that the hedge must be rebalanced every period which causes

high transaction costs, therefore, futures contracts should not be used to hedge the underlying

instrument. Wilkinson, Rosa and Young (1999) present a time-varying technique using cointegration

which is applied to the New Zealand and Australian 90-days, 3-years and 10-years government debt

and futures market. The hedge ratio parameters estimated from the cointegration method is compared

to estimates from a OLS regression that assumes a constant ratio. They confirm that time-varying

models such as univariate and multivariate error correction models do not provide better parameter

estimates than traditional OLS regression. Although the literature is ambiguous and don’t agreed on

whether hedge ratios are constant or time-varying, previous studies comparing the performance of

provides the best estimation of the hedge ratio and the FTSE250 futures index is the best hedging instrument for these portfolios. Frino, Wearing and Fabre (2004) perform a similar study on the relation between returns on stock index futures and stock indices that deliver capital gains, dividends and franking credits in Australia. Witt, Schroeder and Hayenga (1987) implement an OLS regression in price level, price change and percentage change to estimate the optimal hedge ratio for hedging barley and sorghum cash prices using corn futures. They suggest that the correct selection of a hedge ratio method depends on the function of the hedger and the type of hedge considered. For example, for a high-risk hedger, the hedge can be estimated implementing a price level regression. But if the hedger aims to maximize expected utility then none of the techniques can achieve this result. Brown (1985) constructs a sample of Friday closing spot and futures prices for wheat, corn and soybeans traded on the CBOT between 1978 and 1980 to find that better parameter estimates can be obtained regressing returns or price changes instead of price levels (OLS). 4 Some of these econometric techniques include the Generalised ARCH approach (GARCH) and GARCH-X.

the two hedging models do not find significant difference between the effectiveness of the hedge

under the two assumptions. Therefore, our study implements a similar model to Holmes (1996) and

estimates the hedge ratio assuming the ratio to be constant over time.

Different methods have been used to study price discovery between two financial securities.

However, the ECM Granger causality (Engle and granger, 1987) and Lead/Lag model (Sims, 1972)

remain the two most popular models. Poskitt (1999) uses the Garbade-Silber (GS) and ECM Granger

Causality model in the New Zealand interest rate market to find how information flows from the

futures to the cash market. Similarly, Frino, et.al. (2012) implement a Granger causality test to

investigate whether order flows coming from overseas influence price discovery in the Australian

futures markets and confirm that transactions that originate in Sydney and Chicago contribute the

most to price discovery of the SPI futures contracts. Poskitt (2007) presents an interesting price

discovery study on swaps that explains the relation between the interest rate sterling swaps and

futures while implementing a cross-correlation analysis and Sims (1972) model. Poskitt (2007)

shows that, even though the flow of information between the swap and futures market is

bidirectional, in the very short term the futures market remains the primary source of price discovery

in the UK interest rate market.5 Based on previous literature, we design a method that includes two

different models to assess whether price discovery occurs in the interest rate swap or futures market

– First, we conduct a lead/lag model similar to sims (1972) which includes a dimension for testing

the contemporaneous relation between the two markets.6 Finally, using a popular technique to

examine the lead/lag relation between two time series, we perform a ECM Granger causality test

appropriate if the two variables are co-integrated. The remainder of this paper is organized as

follows: Section 2 describes the data and method, section 3 sets out the empirical results, while

section 4 provides the conclusion and suggestions for future research.

2. Data and Method

The data for this study is obtained from the Thomson Reuters Tick History Data Base (TRTH)

maintained by the Securities Industries Research Centre of Asia-Pacific (SIRCA). This dataset

contains intraday trade data on the Australian 90-days Bank Accepted Bills futures contracts (90-

days BABs futures) traded at the Australian Security Exchange (ASX) from 1 January 2008 to 31

5 it is important to assess whether in Australia price discovery also occurs in the futures markets, given that the Australian interest rate swaps market is considerably big and liquid which might cause information to flow from the swaps to the futures. 6 Other methods such as VAR, Granger causality and VEC approach ignore this dimension (Poskitt, 2007).

December 2013.7 The data includes the contract code, date and time of each trade, along with the

price and volume transacted for all the BABs contracts on the quarterly expiration cycle (March,

June, September and December). The over the counter (OTC) quote data for the Australian 1-year

interest rate swaps and Australian deposits with maturities of 1 day, 7 days, 1 month, 2 months and 3

months, is also collected from TRTH on an intraday basis for the same sample period (1 January

2008 – 31 December 2013), this data includes indicative bid and ask quotes supplied by different

dealers and contributors which are used as a proxy for transaction prices.8 The hedging effectiveness

and price discovery analysis for the 90-days BABs futures and 1-year interest rate swaps are

conducted on a daily basis using the last traded price and prevailing bid and ask quotes at 4:30 pm on

days when the deposits, swaps and futures markets were open for trading.9

2.1. Theoretical swap pricing

In order to analyze the relation between the interest rate swap and futures market, we design a

method that recognizes the implicit relation that exists between the two markets, given that swap

rates can be constructed from a combination of in-array futures contracts (see Appendix 2). The

swap rate implied from the futures strip (henceforth referred to as the theoretical swap rate) is used

in combination with the swap rate collected from the OTC market (henceforth referred to as the

actual swap rate) to analyze hedging effectiveness and price discovery between the interest rate

swaps and futures.

To calculate the theoretical swap rate derived from the futures strip, we follow the floating rate note

method (FRN) described by Miron and Swannell (1991), Flavell (2002) and Poskitt (2007). Under

this method, the theoretical swap rate is estimated from the following equation:

7 After 2013, OTC data for swaps and deposits shows a dramatic reduction in the number of quotes at the intraday level. Therefore, we omit the period after 2013 to improve the quality of the dataset. 8 Although actual transaction price and volume are not used in this study given that trade data is not available for swaps, bid and ask mid-quotes can be used as a proxy for actual transaction prices since OTC dealers avoid giving false or misleading quotes as their reputation is valuable in the OTC market (Goodhart and Figliuoli, 1991). However, in a fast-moving environment, indicatives bid and ask quotes may lag behind actual transactions as dealers are trading rather than maintaining the quotes (Poskitt, 2007).9 The 90-days BABs futures contracts trade from 8:28 am to 4:30 pm at the Australian Security Exchange (ASX) whereas the deposits and swaps markets trade 24-hours at the OTC market.

TSR1Y=1−d4

(d α 0 ,d 1+d2 α d 1 ,d 2+d3α d 2 , d3+d4 α d3 , d4) (1)

where dn are the discount factors for each of the 4 fixed for floating exchange of cash flows that

occur in an Australia 1-year interest rate swap.10 Since the discount factor is calculated out of the

futures strip, the theoretical swap rate incorporates the information contain in the futures rates,

therefore, it is possible to study the relation between the swap and the futures market using the

actual swaps rate collected from the OTC market and the theoretical swap rate implied from the

futures strip (refer to Appendix 3 for more information on interest rate swap pricing).

Although we should apply a convexity adjustment to the theoretical swap rate given the positive

convexity of swaps compared to futures, the convexity adjustment for a 1-year interest rate swap

with 4 fixed for floating exchange of cash flows is very small (less than one basis point) and it does

not change significantly over time (Poskitt, 2007). Therefore, the convexity adjustment is omitted in

this study.11 Table 1 reports the descriptive statistics for the actual swap rate - theoretical swap rate

differentials measured on a daily basis over the sample period. The actual swap rate is the bid and

ask mid-quote collected from the OTC market whereas the theoretical swap rate is the rate implied

from the futures contracts. Table 1 shows that the mean differential is close to zero at -0.16 basis

points and 98% of the differentials are within 8.6 and -11.6 basis points (99 th and 1st percentile)

which confirms that the theoretical swap pricing model properly estimates the swap rate implied

from the futures strip.12

<INSERT TABLE 1 HERE>

2.2. Hedging effectiveness

10 If the time to expiration of the nearest contract is exactly 3 months, the theoretical swap price is estimated using the current 3-month deposits rate and the forward rates implied by the nearest three futures contracts. However, If the time to expiration of the nearest contract is less than 3 months, the calculation of the theoretical swap price involves interpolation and the following instruments from the future strip: the current deposit rate for the time to the nearest expiration futures contract and forward rates represented by the nearest four future contracts. The rates implied from these instruments are necessary for the calculation of the discount factors used in Equation 1 (refer to Appendix 3 for more information on interest rate swap pricing). 11 Gupta and Subrahmanyam (2000) examine the existence of the convexity bias in the pricing of interest rate swaps, and find that during the early 1990s, there was a mispricing of swap contracts as the convexity adjustment was not considered for the pricing of interest rate swaps implied from the futures strip. However, this mispricing was eliminated over time. 12 Previous studies using intraday data present similar results – Gupta and Subrahmanyam (2000) report mean differential and standard deviation of -4.2 and 4 basis points, respectively. Similarly, Poskitt (2007) finds mean differential and standard deviation of 0.3 and 1.5 basis points, respectively.

The effectiveness of interest rate futures in hedging interest rate swaps is evaluated over a number of

periods following three steps – First, we estimate the hedge ratio between the interest rate swaps and

futures as in Holmes (1996) and Young, Hogan and Batten (2004). Second, we calculate the mean

absolute return of an unhedged position in the swaps and the same position hedged implementing a

rolling hedge ratio strategy with the futures contracts. Finally, we compare the mean absolute returns

between the outright and hedged position for different hedge durations, and estimate the difference in

percentage change between the two portfolios.13 Using different hedge durations allow us to

compare whether the effectiveness of implementing a hedging strategy varies according to the

duration of the hedge since a daily hedge duration might be too frequent and a monthly duration too

infrequent. Therefore, the hedge ratio is calculated for durations of 1, 3, 7, 15 and 30 days using OLS

regressions in price difference as described in equation 2:

DSt=β0+ β1 DFt+E t (2)

where DSt is the first difference on the actual swap price for all hedge durations, DF t is the first

difference on the theoretical swaps price for all hedge durations, and β1 is the hedge ratio between

the swaps and futures.14

2.3. Price discovery

Two methods of price discovery are implemented to analyze how information is transmitted between

the interest rate swap and futures market – Sims (1972) and Error Correction Granger Causality

(ECM). The former includes a level in the regression to test for the bi-directional flow of information

between the two securities whereas the latter is one of the most popular lead/lag model.15 Sims

(1972) measures information transmission between the swap and futures market using the following

Ordinary Least Squares (OLS) model:

∆ St=α+ ∑k=−20

20

β t+k ∆ F t+ k+u t

13 If futures contracts are effective in hedging interest rate swaps, we would expect the mean absolute return of the hedged position to approach zero. This study evaluates hedging effectiveness over the main period from 1 January 2008 to 31 December 2013 and three sub-periods: sub-period 1 (1 Jan 2008 – 31 Dec 2009), sub-period 2 (1 Jan 2010 – 31 Dec 2011), and sub-period 3 (1 Jan 2012 – 31 Dec 2013). 14 Actual and theoretical swap prices are inferred from an index of 100 minus the yield of the actual and theoretical swap rates, respectively. 15 Although we expect both methods to yield similar results, Sims (1972) gives a better perspective since previous research have found information flows between the swaps and the futures to be contemporaneous.

(3)

where ∆ St is the change in the actual swap price over day t, ∆ F t is the change in the theoretical

swap price over day t, and ut is the random error term. Under this model, if the futures market leads

the swap market, the coefficients of the lagged theoretical swap price (k < 0) will be significant

different from zero while the coefficients of the lead theoretical swap price (k > 0) will be

insignificant. On the contrary, if the swaps market leads the futures market, the coefficients of the

lagged theoretical swap price (k < 0) will be insignificant different from zero while the coefficients

of the lead theoretical swap price (k > 0) will be significant. In addition, we test for the bidirectional

flow of information between the two markets examining the size and significance level of the neutral

coefficient (k = 0) and using Wald test on the coefficients for the following hypotheses – H1: the

coefficients of the leads 1 to 10 are equal to zero (β t+1=0), which evaluates whether the swap market

leads the futures market; H2: the coefficients of the lags 1 to 10 are equal to zero (β t−1=0), which

evaluates whether the futures market leads the swap market; H3: the sum of the coefficients of the

first 5 leads is equal to the sum of the coefficients of the first 5 lags (∑i=1

5

β t+1=∑i=−1

−5

βt+1), this

hypothesis suggests that the strength of the information flow between the two markets is similar. The

rejection of H1 and H2 while the failure to reject H3 gives a strong evidence that price discovery

occurs simultaneously in the swap and futures markets.

The ECM Granger causality also measures the lead/lag relation between the interest rate swaps and

futures. However, it does not include a level to test the contemporaneous relation between the two

markets. Under this method, if two time series are cointegrated of order (1,1), the residuals from the

cointegrating regression can be used to estimate the error correction model as:

∆ St=α+β u t−1+∑i=1

n

δ i ∆ F t−i+∑j=1

n

γi ∆ St−i+e1 t

(4)

∆ F t=α+β ut−1+∑i=1

m

δi ∆ St−i+∑j=1

m

γi ∆ F t−i+e2 t

(5)

where ∆ St is the daily change in the actual swap price, ∆ F tis the daily change in the theoretical

swap price, and ut−1 is the lagged residual from the cointegrating regression.16 Equation 4 infers that

current changes in swap rates are determined by the lagged values of ∆ St and ∆ F t whereas equation

5 postulates that current changes in futures rates are determined by the lagged values of ∆ St and ∆ F t

.17 The changes in the futures price (represented by the theoretical swap price) granger cause the

changes in the swaps price, if some of the δ i in equation 4 are nonzero while all the δ i in equation 5

are equal to zero so that the futures market leads the swap market. On the contrary, the changes in

the swap price granger cause the changes in the futures price, if some of the δ i in equation 5 are

nonzero while all the δ i in equation 4 are equal to zero so that the swap market leads the futures

market.

3. Results

3.1 Hedging effectiveness

Table 2 presents hedge ratio estimates between the interest rate swaps and futures for hedge duration

ranging from 1 to 30 days. hedge ratios are estimated for a main sample period from 1 January 2008

to 31 December 2013, and three sub-periods: (1) 1 January 2008 to 31 December 2009; (2) 1 January

2010 to 31 December 2011; and (3) 1 January 2013 to 31 December 2013. For all periods, the hedge

ratio approaches unity as the duration increases from 1 to 30 days, as a result, the hedge ratio applied

to a hedge ratio strategy must be adjusted for the duration of the hedge since a 1:1 classic hedging

strategy would not accurately reduce the risk of the position. It is important to mention that, although

the hedge ratio is not stable across periods (especially for the shortest hedge durations), there is low

variation in the hedge ratio over the sub-periods for hedge durations higher than 15 days.


Table 3 compares an unhedged portfolio in the 1-year interest rate swap to the same portfolio hedged

with the 90-days BABs futures contracts. Using the hedge ratios previously estimated, a hedge ratio

strategy is implemented for hedge durations of 1, 7 and 30 days over the main sample period and

16 Before undertaking the cointegration test, we must evaluate whether the time series for the theoretical and actual swap price are integrated of the same order. Using the Augmented Dickey Fuller test (ADF), we can infer the number of unit roots in each time series to determine whether both variables are integrated of order I (1). If both time series are integrated of order I(1), it is possible to measure whether the series are cointegrated by estimating the long run equilibrium between the two variables using OLS at price levels and testing the regression residuals for the presence of a unit root with an ADF test. If the residuals are stationary, we conclude that the two series are cointegrated of order (1,1) and the residuals from the equilibrium regression can be incorporated into equation 4 and 5 to estimate the ECM granger causality model. 17 The optimal lag length for the ECM model is estimated using the Schwarz criterion.

three sub-periods. The results demonstrate that, the average price change and standard deviation of

the hedged portfolio are much lower than the estimates of the unhedged position for all hedge

durations. Therefore, hedging interest rate swaps with futures effectively reduces the risk involve in

the outright position. In addition, the performance of the hedge varies under different durations and it

is more effective as the hedge duration increases. For example: during the main sample period (2008

- 2013), the average price change of the unhedged portfolio in the swaps decreases by 38% after

hedging with the futures for a 1-day hedge duration. However, there is a reduction of approximately

87% in the average price change of the unhedged portfolio after hedging with the futures for a 30-

days hedge duration. This shows that, hedging interest rate swaps with futures contracts yields better

results for longer hedge durations.


3.2 Price discovery

Table 4 presents the results of the coefficients for the Sims (1972) lead/lag model implemented to

study the flow of information between the interest rate swap and futures market. Panel A shows that

there are four significant coefficients in the lead size of the regression (k= +1, k = +2, k= +3, k= +19)

and three in the lag side (k= -1, k = -2, k= -11) which confirm that that there is a contemporaneous

relation between the swap and the futures market. This result is also explained while examining the

magnitude of the coefficient for k = 0 (0.78) which is larger than the magnitude for the adjacent lead

and lag coefficients, 0.14 (k = +1) and 0.02 (k = -1), respectively. Panel B presents the Wald test

results on the coefficients which provide a better insight into the relation between the swaps and the

futures. The rejection of hypothesis 1, 2 demonstrates that there is a bi-directional relation between

the two markets.


Table 5 presents the estimation results of the ECM Granger Causality test, a popular lead/lag model

for studying causality between time series.18 The results show that the coefficients of the residuals

(β) are significant for equation 4 and 5, which suggest that there is a contemporaneous flow of

18 Before implementing the ECM Granger Causality model, we need to test whether the two time series are cointegrated. First, we confirm that both series are integrated of order I (1) using ADF test. Given that we find both series to be I (1), the residuals from the long-run relationship between the swaps and futures are tested using ADF which confirms that the two series are cointegrated. Since the two series are cointegrated, the ECM granger causality model can be used to estimate information flows between the swaps and futures.

information between the swaps and futures markets, therefore, confirming our previous findings

under the Sims (1972) model.19 In addition, a significant δ and high R2 in the regression with ∆F as

the dependent variable suggests that the change in the theoretical swap price is explained by the

lagged values of the actual swap prices over the very short term. As a result, although the overall

relation between the swap and futures market is bidirectional, the swap market leads the futures over

the very short period.


4. Conclusion and Suggestions for Future Research

This paper explains the relation that exists between the interest rate swap and futures market. In

terms of hedging effectiveness, we demonstrate that a theoretical swap constructed from a

combination of 90-days interest rate futures contracts, effectively hedges the risk of an outright

position in the 1-year interest rate swap (actual swap), and the effectiveness of the hedge increases

for longer hedge durations. Similarly, our study on price discovery finds a bi-directional flow of

information between the swap and futures market which demonstrates that the transmission of

information occurs simultaneously in both markets and one market does not strongly lead the other.

These findings confirm that, even though interest rate swaps have grown in importance in recent

years, the 90-days futures contract is still a relevant instrument that provides similar exposure to the

yield curve as interest rate swaps, as well as, an important source of price discovery for the interest

rate market.

19 Using the Schwarz criterion, we estimate the optimal number of lags to be used in the ECM model to be 1.

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Table 1: Descriptive Statistics of the Actual / Theoretical Swap Rate Differential (2008 – 2013)Table 1 reports the descriptive statistics of the actual swap rate/theoretical swap rate differential between 2008 and 2013. The actual swap rate is collected from the OTC market as the mid-quote of indicative bid and ask prices contributed by banks. The theoretical swap rate is estimated using swap pricing theory with rates implied from the futures strip. All figures are reported in basis points.

Panel A: Statistics

Mean -0.16

Median 0.11

Standard Deviation 3.87

Maximum 19.34

Minimum -19.94

Panel B: Percentiles

99th 8.69

75th 1.95

50th 0.11

25th -1.89

1st -11.68

Table 2: Hedge Ratio Estimates for Different Hedge Durations and Sub-periods Table 2 reports hedge ratios estimated using OLS regression in price difference for hedge duration of 1, 3, 7, 15 and 30 days. The hedge ratio estimates and regression R squared are calculated for the main sample period from 1 January 2008 to 31 December 2013, while the sub-periods are (1) 1 January 2008 to 31 December 2009; (2) 1 January 2010 to 31 December 2011; and (3) 1 January 2013 to 31 December 2013.

2008-2013 2008-2009 2010-2011 2012-2013

Hedge Duration

Hedge Ratio

R Squared (%) Hedge

RatioR Squared

(%) Hedge Ratio

R Squared (%) Hedge

RatioR Squared

(%)

1 0.80 0.75 0.86 0.70 0.71 0.63 0.75 0.66

2 0.89 0.87 0.92 0.84 0.84 0.79 0.87 0.81

3 0.94 0.92 0.96 0.89 0.91 0.86 0.88 0.86

4 0.95 0.93 0.97 0.91 0.92 0.88 0.89 0.88

7 0.97 0.96 0.99 0.95 0.94 0.92 0.91 0.92

15 0.98 0.98 0.99 0.98 0.97 0.96 0.96 0.96

30 0.99 0.99 0.99 0.99 1.01 0.97 0.98 0.97

Table 3: Hedging Effectiveness – Comparison of an Unhedged and Hedged PortfolioTable 3 reports the average and standard deviation of price changes (returns) for an unhedged portfolio of interest rate swaps and a hedged portfolio after implementing a hedge ratio strategy using the interest rate futures contracts. The period from 1 January 2008 to 31 December 2013 is the main sample period for this study, while the sub-periods are (1) 1 January 2008 to 31 December 2009; (2) 1 January 2010 to 31 December 2011; and (3) 1 January 2013 to 31 December 2013. The estimates are calculated for hedge duration of 1, 7 and 30 days and are presented in basis points.

Hedge Duration

One Day Seven Days Thirty Days

Panel A: 2008 - 2013

Unhedged Portfolio

Avg. price change 3.90 12.17 31.15

SD of price changes 4.80 15.54 40.05 Hedged Portfolio


SD of price changes 2.37 3.04 3.58

Decrease in Avg. price change -38% -74% -87% Panel B: 2008 - 2009

Unhedged Portfolio





Decrease in Avg. price change -42% -77% -90% Panel C: 2010 - 2011

Unhedged Portfolio





Decrease in Avg. price change -35% -70% -84% Panel D: 2012- 2013

Unhedged Portfolio





Decrease in Avg. price change -37% -73% -83%

Avg. and SD of price changes are in basis point

Table 4: Results of Regression Analysis for the Sims (1972) Lead/Lag Model Table 4 reports the regression coefficients of the Sims (1972) lead/lag model for the period 1 January 2008 to 31 December 2013. Panel A presents the coefficients estimated using a OLS regression with daily observations where the dependent and independent variables are the change in the actual and theoretical swap price, respectively. Panel B reports the F-statistics of Wald tests on coefficient restrictions for the three hypotheses.

Panel A: Coefficients from OLS lead/lag regression

Intercept 0.0000 𝞫 t 0.7832***𝞫 t+20 0.0056 𝞫 t-1 0.0287**𝞫 t+19 0.0299** 𝞫 t-2 0.0322**𝞫 t+18 -0.0126 𝞫 t-3 -0.0009𝞫 t+17 0.0073 𝞫 t-4 -0.0169𝞫 t+16 -0.0089 𝞫 t-5 -0.0012𝞫 t+15 -0.0193 𝞫 t-6 0.0182𝞫 t+14 -0.0034 𝞫 t-7 -0.0190𝞫 t+13 0.0176 𝞫 t-8 0.0176𝞫 t+12 -0.0216 𝞫 t-9 -0.0044𝞫 t+11 0.0048 𝞫 t-10 0.0001𝞫 t+10 0.0079 𝞫 t-11 -0.0225*𝞫 t+9 -0.0120 𝞫 t-12 0.0063𝞫 t+8 -0.0060 𝞫 t-13 0.0094𝞫 t+7 0.0043 𝞫 t-14 -0.0029𝞫 t+6 0.0139 𝞫 t-15 0.0128𝞫 t+5 0.0191 𝞫 t-16 -0.0060𝞫 t+4 0.0062 𝞫 t-17 0.0125𝞫 t+3 -0.0589*** 𝞫 t-18 -0.0042𝞫 t+2 0.0415** 𝞫 t-19 -0.0077𝞫 t+1 0.1412*** 𝞫 t-20 0.0091

Panel B: Hypothesis tests

F-test

H1: 𝞫 t+1 = 0; for all first 10 leads 14.79***

H2: 𝞫 t-1 = 0; for all first 10 lags 1.83*

H3: ∑i=1

i=5

β t+1=∑i=−1

i=−5

βt+1 7.59***

* p < 0.1, ** p < 0.05, *** p < 0.01

Table 5: ECM Granger Causality Test Table 5 reports the error correction granger causality test which measures the lead/lag relationship between the actual and theoretical swap price series. The dependent variables ∆S and ∆F are the daily change in the actual and theoretical swap prices, respectively. T-statistics and significance levels are presented in parenthesis.

Dependent variable

∆S ∆F

α 0.0027 0.0025

(1.79)* (1.66)*

β -0.0815 0.2573

(-1.69)* (5.34)***

δ 0.0194 0.3967

(0.38) (7.45)***

γ 0.1063 -0.2222

(1.99)** (-4.38)***

R Squared 0.016 0.100

t-statistics are reported in parentheses * p < 0.1, ** p < 0.05, *** p < 0.01

Appendix

1. Swaps and Futures Background

Swaps were first traded in the 1980s among companies looking to avoid capital controls from the

British government. Since then, the swaps market has grown rapidly and expanded into different

types and countries. As of 2015, swaps have become one of the most important financial instrument

in Australia with an annual turnover of 12 trillion AUD and an average transaction size that ranges

between $50 and 100 million, this represents an 80% increase from 2010 according to the Australian

Financial Markets Report (2015) and the Reserve Bank of Australia.20 Bicksler and Chen (1986)

argue that the popularity of interest rate swaps reflects how simple swaps can be executed by

companies and financial institutions, which explains why interest rate swaps have become one of the

most used vehicle to hedge against interest rate risk (more effective than futures or options).

In recent years, the rise of interest rate swaps has increased the risk of manipulation by some market

participants. In 2016, major news agencies in Australia exposed conversations between swaps traders

at the big Australian banks in which they agreed to manipulate the Australian Bank Bill Swap Rate

(BBSW) to profit on their open swaps positions. This type of market manipulation is not particular to

Australia, in 2013, UK and US regulators fined Barclays, UBS, Royal Bank of Scotland, Deutsche

Bank and JPMorgan over charges for manipulating the London Inter-Bank Offered Rate (LIBOR).

As a response, market regulators are introducing new regulations to prevent the manipulation of the

market such as creating an alternative risk-free benchmark and asking prime banks to disclose live

and executable prices used to estimate the benchmark.

Since the focus of this study is on two securities – interest rate swaps and futures, it is also important

to describe the 90-days bank accepted bill futures contracts which was launched in 1979 and has

become one of the ten most liquid contracts in the world with an average daily turnover of 83.000

contracts in 2012, seven times higher than the turnover of the cash market. The 90-days BABs

trades between 8:28 am - 4:30 pm (day session) and 5:08 pm – 7:00 am (night session) at the ASX

Trade24 with four expiry month (March, June, September and December).

2. Literature review on Interest Rate Swaps Pricing

There are two main methods for pricing interest rate swaps using futures contracts – the forward rate

model (Basal, Ellis and Marshall, 1993) and the floating rate note (FRN) described by Smith,

Smithson and Wakeman (1988), Miron and Swannell (1991) and Flavell (2002). The forward rate 20 In 2015, the annual turnover for equities and government debt securities was 1.3 and 1.8 trillion, respectively.

model presented by Basal, Ellis and Mashal (1993), examines the pricing of short-dated interest rate

swaps in which the fix rate of the swap is set against the floating rate represented by the Eurodollar

futures strip. This pricing model is valid as long as there are enough futures contracts actively trading

with high liquidity. The floating rate note (FRN) explained by Miron and Swannel (1991), assumes

that under this method, swaps can be viewed as a portfolio of in-arrears forward rate agreements

which can be adapted to price long-dated interest rate swaps for which there are not actively trading

futures contracts. Although the two methods are similar, the floating rate note (FRN) is more flexible

than the forward rate model, especially if the fixed leg and floating leg of the swaps are exchange at

different periods (Miron et.al, 1991; Flavell, 2002). For example, the pricing of a 1-year interest rate

swap with a semi-annual floating leg and annual fixed leg can be priced just under the FRN method,

not the forward rate model.

3. Theoretical Swap Pricing – Details

The pricing of interest rate swaps implied from the futures strip (theoretical swap pricing) follows

three steps. First, we must determine the time to expiration of the nearest future contract (which is 3

months or less since the 90-days BABs futures contracts expiry every 3 months) in order to

determine how many futures contracts are needed to price the swap. Second, the discount factors for

each of the four exchange of cash flows in a 1-year swap are calculated using the futures strip.

Finally, the theoretical swap rate can be estimated using the four discount factors previously

calculated.

If the time to expiration of the nearest contract is exactly 3 months, the theoretical swap price is

estimated using the current 3-months deposits rate and the forward rates implied by the nearest three

futures contracts. However, If the time to expiration of the nearest contract is less than 3 months, the

calculation of the theoretical swap price involves interpolation and the following instruments: the

current deposit rate for the time to the nearest expiration future contract and forward rates

represented by current rates on the nearest four future contracts.

Following basic bond pricing theory to determine the present value of the swap, we apply a discount

factor to each of the four exchange of cash flows that occur in an Australian 1-year interest rate

swap. The determination of this discount factor varies depending on the time to the nearest expiration

future contract. As shown in Figure 1 (Panel A), if the time to expiration of the nearest contract is

exactly 3 months, the exchange of cash flows in the swap matches the expiry date of the futures

contract, therefore, we can apply the discount factor to each of the forward rates implied from the

futures contracts without interpolation. However, Figure 1 (Panel B) shows that if the time to

expiration of the nearest contract is less than 3 months, the exchange of cash flows in the swap

occurs in between the expiration date of the futures contract, therefore, we use interpolation to

estimate the discount factor for each exchange of cash flows.21

Figure 1: A one year interest rate swap with quarterly exchange of cash flowsFigure 1 presents the number of futures contracts involved in the estimation of the discount factors for each of the 4 exchange of cash flows that occur in an Australian 1-year interest rate swap. Panel A shows that if the time to expiration of the nearest contract is exactly 3 months, the theoretical swap price is estimated using the current deposits rate and the nearest three futures contracts. Panel B shows that if the time to expiration of the nearest contract is less than 3 months, the calculation of the theoretical swap price involves the current deposit rate and the nearest four future contracts. CF i

represents the four exchange of cash flows in a 1-year interest rate swap whereas d i is the discount factor applied to each of these exchange of cash flows.

Panel A: Exactly 3 months to expiration of the nearest futures contract

Panel B: Less than 3 months to expiration of the nearest futures contract

The discount factor for each of the four exchange of cash flows in an Australian 1-year interest rate

swap is estimated using the following equation (Miron and Swannell, 1991; Flavell, 2002):

dnd=d(n−1 )d

1+(100−Pn−1)α ( n−1 ) d , nd (A1)

21 We calculate the discount factors at the expiration date of the futures contracts (grid points) before using the exponentially interpolated discount function to find the discount factors for the exchange of cash flows located in between the grid points (Miron and Swannell, 1991).

α nd ,(n−1)d=Dnd−D(n−1 ) d

36500 (A2)

where dndis the discount factor at the n cash flow, Pn−1 is the price of the (n−1 )th future contract,

Dnd and D ( n−1 ) d represent the number of days elapsed between the cash flows nd and (n−1 ) d,

respectively .22 To determine the theoretical swap rate, we incorporate the discount factors for each

of the cash flows into the following equation:

TSR1Y=1−d4

(d α 0 ,d 1+d2 α d 1 ,d 2+d3α d 2 , d3+d4 α d3 , d4) (A3)

where dn are the discount factors estimated from equation A1. Equation A3 finds the swap rate

implied from the futures contracts which is compared to the swap rate collected from the OTC

market to analyze hedging effectiveness and price discovery between the swaps and the futures.

22 The 90-days BABs futures contract is quoted as the yield deducted from an index of 100 (ASX Interest Rate Markets Fact Sheet, 2014).

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