Hedging Effectiveness and Price Discovery in the Interest Rate Swap Market
Alex Frinoa[*], Michael Garciaa
aThe University of Wollongong, Wollongong, 2522 Australia
Draft
As at 7/5/2017
Abstract
This studyexamines the effectiveness of hedgingan 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,thusprice movements between the swaps and futuresarehighly correlatedfor longer hedge durations. Second, an outright position in the swapscan 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 strategyperforms 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 contractsremain 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.
1. Introduction
In recent years, Interest rate swaps are widely traded over the counterby 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 ofhigher liquidity in the swap market, institutions are increasingly using interest rate swaps to gain exposure to the yield curve and shifting toswapsfor the pricing and hedging of other interest rateproducts (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.
Hedgingeffectiveness has been widely studied on different securities such as equities(Laws and Thompson, 2004), bonds(Wilkinsonet.al., 1999; Younget.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 isassumed 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 inYoung, 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) 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 hedgefor 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 usinga 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 usingcointegrationwhich 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 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, theECM Granger causality (Engle and granger, 1987) andLead/Lag model(Sims, 1972) remain the two most popular models. Poskitt (1999) uses the Garbade-Silber (GS) and ECM Granger Causalitymodel 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 andconfirm 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 therelation 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 swapand futures market is bidirectional,in the very short term the futures market remains the primary source of price discoveryin 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 swapor 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 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, isalso 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 analysisfor the 90-days BABs futures and 1-year interest rate swapsare 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 toanalyze 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 acombination of in-array futures contracts (see Appendix 2). Theswap rate implied from the futures strip (henceforth referred to as the theoretical swap rate)isused 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:
/ (1)where are the discount factors for each of the 4 fixed for floating exchange of cash flowsthat 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 relationbetween the swap and the futures marketusing the actual swaps rate collected from the OTC market and the theoretical swap rateimplied 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 rateis the bid and ask mid-quote collected from the OTC market whereas the theoretical swap rateis 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 (99th 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
The effectiveness of interest rate futures in hedging interest rate swaps is evaluatedover 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 comparewhether 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 differenceas described in equation 2:
/ (2)where is the first difference on the actual swap pricefor all hedge durations, is the first difference on the theoretical swaps pricefor all hedge durations,and 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 theinterest 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) measuresinformation transmission between the swap and futures market using the following Ordinary Least Squares (OLS) model:
/ (3)where is the change in the actual swap priceover day t, is the change in the theoretical swap priceover day t, and 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 areequal to zero (),whichevaluates whether the swap market leads the futures market; H2: the coefficients of the lags 1 to 10 areequal to zero (), 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 (),this hypothesis suggests that the strength of the information flow between the two markets is similar. The rejection of H1 and H2 whilethe 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:
/ (4)/ (5)
where is the daily change in the actual swap price, is the daily change in the theoretical swap price, and 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 and whereas equation 5 postulates that current changes in futures rates are determined by the lagged values of and .[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 in equation 4 are nonzero while all the 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 in equation 5 are nonzero while all the 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.