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The impact of interest rate reset period on the bid-offer rates in an interest rate swap contract — an empirical investigation
Journal
of Multinational 8 (1998)
ELSEVIER
Financial 79-88
Journal of MULTINATIONAL FINANCIAL MANAGEMENT
Management
The impact of interest rate reset period on the bid-offer rates in an interest rate swap contract - an empirical investigation D.K. Malhotra * Philadelphia
College
of Textiles
Received
and Science,
30 September
Philadelphia,
1997; accepted
PA 19144-5497,
30 January
USA
1998
Abstract Although numerous studies have analyzed the interest rate swap market, the major influences on the swap spreads have not been fully examined. Using bi-weekly interest rate swap quotations from a swap dealer, this study documents the impact of semi-annual versus annual interest payments on the bid and offer rate quotations in the interest rate swap market. A univariate analysis indicates that the bid-offer spreads over the Treasuries in a one-year London Interbank Offer-Rate (LIBOR) indexed interest rate swap contract bracket similar spreads in a six-month LIBOR-indexed swap contract. Also, the spread between the bid and offer rate in an annual interest rate swap is also higher than the spread in a semi-annual interest rate swap contract. In addition, a one-year LIBOR-indexed all-in swap rate incorporates higher term premiums in comparison to a six-month LIBOR-indexed swap contract. 0 1998 Elsevier ScienceB.V. All rights reserved. JEL class$cation: Keywords:
E4; E43; G2
Interest rate swap; Bid-offer rates
1. Introduction An interest rate swap is an agreement between two parties to exchange a series of interest payments on a notional principal that is not exchanged. These payments are tied to different indexes such as the London Interbank Offer Rate (LIBOR), the Treasury rate, etc. Further, instead of being traded on organized exchanges, interest rate swaps are arranged by commercial and investment banks. Thus, they are classified as over-the-counter contracts. Dealers in interest rate swaps act as market makers and readily quote interest rates at which they stand ready to take either side * Corresponding
author.
Fax:
+ 1 215 951 2652.
1042-444X/98/$19.00 0 1998 Elsevier PI1 SlO42-444X(98)00019-X
Science
B.V. All rights
reserved
80
D. K. Malhotra
/ Journal
of’Multinationa1
Financial
Manugrmcnt
8 (I 998) 79-88
of the interest rate swaps with simple structures and standard maturities (typically two to ten years with semi-annual interest payments). If the dealer makes fixed interest rate payments and receives floating interest rate payments, the dealer is said to be on the bid side of the swap contract. Conversely, the dealer that pays a floating rate and receives a fixed rate is said to be on the offer side of the swap contract. In a fixed-for-floating interest rate swap, the fixed-rate side of the swap is usually stated as a spread over the prevailing yields on-the-run U.S. Treasury securities. Moreover, interest rate swaps priced as a spread over the Treasuries assume semi-annual interest payments. Therefore, when the dealer’s client requires annual payments instead of semi-annual payments, the dealer adjusts the fixed rate of interest to reflect this difference. Although numerous studies have analyzed the swap market, none of these studies examined the significance of semi-annual versus annual interest payments on the bid-offer rates in an interest rate swap contract. According to the expectations hypothesis of the term structure of interest rates, the bid-offer spreads over the Treasuries in a semi-annual and annual interest rate swap contract should be similar; otherwise there exists an opportunity for arbitrage. Therefore, this study compares a one-year LIBOR-indexed interest rate swap contract to a six-month LIBOR-indexed interest rate swap contract in three areas: the bid-offer spreads over the Treasuries, the spread between the bid and offer rates, and the spread of longerterm swaps versus swaps maturing in two years. An empirical analysis indicates that the bid-offer spreads over the Treasuries in a one-year LIBOR-indexed interest rate swap contract bracket similar spreads in a six-month LIBOR-indexed interest rate swap contract. Also, the spread between the bid and offer rates in an annual swap contract is higher than the spread in a semi-annual swap contract. The rest of the paper is organized as follows. Section 2 discusses the theoretical foundation of this paper. Section 3 includes data description and analysis of the empirical results. Section 4 concludes and summarizes this study.
2. Theoretical foundation Academic research on interest rate swaps mainly focused on: the growth of the swap market, the pricing of interest rate swaps, the default risk in interest rate swap contracts, and the regulation of the swap market. ’ Very few studies empirically analyzed the swap market. Sun et al. (1993) (SSW) conducted an empirical analysis of the interest rate swap market using daily quotations from two interest rate swap dealers. They used swaps in which fixed U.S. dollar interest rates were exchanged for a six-month LIBOR and documented that the spreads between swap rates and the Treasury yields generally increase significantly with maturities. They also found the bid-offer spread in interest rate swaps to be large and statistically significant. In ’ Bicksler and Chen (1986); Smith et al. ( 1986); Arak et al. ( 1988); Wall and Pringle (1989) discussed reasons for the growth of the swap market. Studies conducted by Whittaker (1986); Felgran ( 1988); Wall et al. (1990); and Aggarwal (1990) focused on the uses, risks, and regulatory aspects of swaps. Whittaker ( 1987); Abken (1991); and Cooper and Mello (1991) analyzed default risk in a swap contract.
D. K. Malhotra
/ Journal
of Multinational
Financial
Management
8 (I 998) 79-88
81
addition, the SSW study also showed that swap rate quotations appeared to incorporate term premiums, because the spread over the Treasuries increased with an increase in the maturity of the swap contract. Malhotra (1997) re-examined the empirical aspects of the swap market and confirmed the results of the SSW study. Malhotra’s study covered swaps indexed to one-year LIBOR. These studies, however, did not analyze the impact of semi-annual versus annual interest payments on the bid and offer rate quotations in the swap market. Assuming that the expectations hypothesis of the term structure of interest rates holds, a one-year LIBOR-indexed interest rate swap contract is expected to have the same all-in swap fixed rate payments as an equivalent maturity six-month LIBOR-indexed interest rate swap contract.2 Thus, a swap indexed to a one-year LIBOR should trade at the same spread over the Treasuries as the swap indexed to a six-month LIBOR. If the one-year LIBOR-indexed all-in swap bid-offer rates do not equal the six-month LIBOR-indexed all-in swap bid-offer rates, there exists an opportunity for arbitrage. For example, if the one-year LIBOR-indexed interest rate swap carries higher bid-offer spreads over the Treasuries than a six-month LIBORindexed swap contract, a party can enter into a one-year LIBOR-indexed swap to pay one year LIBOR and receive fixed interest rate payments on the notional principal. At the same time, the party can also enter into an equivalent maturity six-month interest rate swap contract to receive six-month LIBOR and make semiannual fixed interest rate payments on the notional principal. Further, in a swap contract with a semi-annual exchange of interest payments, rates are reset frequently in contrast to a swap indexed to one-year LIBOR. Consequently, the probability of the six-month indexed swap contract assuming a large negative value before the reset date is lowered. This should cause the swap spreads for a six-month LIBOR-indexed swap to be lower in comparison to a oneyear LIBOR-indexed swap contract. However, changes in mark-to-market value of a swap, and hence its credit exposure, will be largely driven by changes in the value of the fixed interest rate payments with the floating rate component being quite small in comparison. Thus, the noise being generated by time varying volatility associated with the fixed-interest component would likely swamp any reduction in the uncertainty associated with the floating-rate component.3 Consequently, there should not be a statistically significant difference in the spreads over the Treasuries for a six-month LIBOR-indexed and a one-year LIBOR-indexed interest rate swap contract.
Thus, the null hypothesis is that the bid and offer spreads over the Treasuries in a one-year LIBOR-indexed swap equal similar spreads in a six-month LIBORindexed swap, and the interest rate reset period has no impact on the bid-offer rates in an interest rate swap contract. The alternate hypothesis is that the bid-offer rates ’ According to the unbiased expectations hypothesis of the term structure of interest rates, the total return that an investor will realize by rolling over short-term bonds to some investment horizon will be the same as holding a zero-coupon bond with a maturity that is the same as that investment horizon, 3 In addition, the credit spreads themselves are generally very small and should not cause statistically significant difference in the bid-offer rates of one-year LIBOR-indexed and six-month LIBOR-indexed interest rate swap contracts.
82
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1 Journal
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in a one-year LIBOR-indexed interest rate swap contract exceed the bid-offer rates in a six-month LIBOR-indexed interest rate swap contract and the reset period impacts the swap rate quotations.
3. Data description and analysis
To conduct the empirical analysis, this study uses the data from various issues of the Swaps Monitor.” The data set contains information for the all-in swap bid-offer rates, the Treasury rate of equivalent maturity, and the maturity of the swap contract. The data is on a bi-weekly basis from 1 October 1987 to 2 November 1991 for a swap with a maturity of two, three, four, five, seven, and ten years. These rates apply to interest rate swaps that are indexed to a six-month LIBOR and swaps that are indexed to a one-year LIBOR.’ Fig. l(a) plots the bid rate spread over the Treasuries for semi-annual and annual two-year maturity interest rate swap contracts, and Fig. l(b) plots the bid-rate spread over the Treasuries for semi-annual and annual ten-year maturity interest rate swap contracts. As illustrated in Fig. 1 (a,b), the bid rate spread over the Treasuries for an annual interest rate swap contract is higher than the bid rate spread over the Treasuries for a semi-annual interest rate swap contract throughout the sample period.6 Table 1 summarizes the characteristics of the spread between the Treasuries and the all-in swap bid-offer rates for the period between October 1987 and November 1991. As illustrated in Table 1, the bid-offer spreads over the Treasuries increase with an increase in the maturity of the swap contract. Also, a univariate analysis indicates that the bid and offer spreads in an annual LIBOR-indexed swap exceed similar spreads in a six-month LIBOR-indexed swap for all swap maturities. However, according to the t-statistic, the difference is not statistically significant at the 1% level of significance for any swap maturity. To examine the statistical significance of the difference between the bid-offer rates of annual and semi-annual swap contracts, we also use the Wilcoxon rank sum test.’ Although the average bid-offer spread over the Treasuries in a one-year LIBOR-indexed interest rate swap contract 4 Swaps Monitor is a bi-weekly publication of Swaps Monitor, New York, NY 10276. Data is based on quotations provided by Tullet and Tokyo Forex. 5 The empirical analysis incorporates the difference between the money market and the bond-yield conventions. In an interest rate swap where LIBOR is exchanged for a fixed interest rate, the fixed-rate payments typically follow bond-yield convention, whereas the LIBOR payments are subject to the money-market convention. 6 Similarly, the bid rate spread over the Treasuries was higher for an annual swap contract than the similar spread for a semi-annual swap contract for all other swap maturities. ‘We use a non-parametric test to analyze the statistical significance of the difference between the bidoffer rate quotations in a semi-annual and annual interest rate swap, because a non-parametric test requires fewer assumptions regarding the distribution of the sample. Moreover, a parametric test statistic allows small persistent differences in the spreads to be swamped by the overall variability of the spreads over the sample period. Therefore, the use of a non-parametric test, such as the Wilcoxon rank sum test, is appropriate to check the robustness of the results.
D. K. Malhotra
/ Journal
of’ Multinational
Financial
Management
8 (1998)
79-88
83
‘---Annual ( :. . Semisnnual \
140
,
I
0:
(b)
Time
Fig. 1. (a) The bid rate spread over the Treasuries for a two-year maturity semi-annual and annual interest rate swap contract. The spread is in basis points. (b) The bid rate spread over the Treasuries for a tenyear maturity semi-annual and annual interest rate swap contract. The spread is in basis points.
exceeds the average bid-offer spread in a six-month LIBOR-indexed interest rate swap contract by two to four basis points only, the difference is statistically significant according to the z-statistic at the 1% level of significance. Therefore, we reject the null hypothesis that the bid-offer spreads over the Treasuries in a six-month LIBORindexed swap contract equal the spreads in a one-year LIBOR-indexed swap con-
Bid
68.5 12.4 1.6* -s.9+**
Swaps indexed to k-month LIBOR Mean 61.6 56.4 Standard deviation 16.3 14.8 r-Statistics I.1 1.1 z-Statistics -8.9*** -s.9***
*** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level.
11.2 12.8
58.7 15.6
Offer
Bid
contract 3-year
of the swap
63.5 12.4 1.9** -8,7***
67.0 14.4
Offer
71.5 12.4 1.6** -8,9***
74.4 12.9
Bid
4-year
66.6 11.6 1.6** -8.9***
69.3 12.1
Offer
73.8 13.6 1.6** -8,9***
76.8 14.2
Bid
5-year
69.0 13.1 1.5* -8,9***
71.8 13.5
Offer
74.5 13.7 1.6** -8,9***
77.6 14.2
Bid
7-year
in semi-annual and annual interest rate swap contracts. The semi-annual interest rate swap contract is indexed to a one-year LIBOR. The data covers the period
2-year
Maturity
Svaps indcued to one-year LIBOR Mean 63.8 Standard deviation 16.9
Statistics
Table 1 The bid-offer spread over the Treasuries six-month LIBOR. The annual interest 1991. The spread is in basis points
69.4 13.0 1.6* -8,9***
72.3 13.5
Offer
77.8 13.7 1.8** -8.9***
81.2 14.4
Bid
IO-year
72.9 13.4 1.7** -8.9***
75.8 13.7
Offer
rate swap contract is indexed to a from October 1987 to November
D. K. Malhotra
J Journal
of’kfultinational
Financial
Management
8 (1998)
a5
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tract. However, a pure arbitrage in the sense of earning a positive rate of return on a position that requires no net investment and contains no risk does not exist. Due to the nature of the swap contracts, the arbitrage does involve some risk, because six-month LIBOR may move significantly during a six-month period and could generate losses. Higher bid-offer spreads over the Treasuries in a one-year LIBORindexed interest rate swap contract can be partially explained by term premiums at the short-end of the LIBOR market. In addition, the large bid-offer spreads in a one-year LIBOR-indexed swap over the similar spreads in a six-month LIBORindexed swap also highlight the fact that the two types of swaps have different market structures and different users. The customized nature of the one-year LIBORindexed swap instead of the standardized nature of the six-month LIBOR-indexed swap contract may also partially explain the statistically significant difference in the bid-offer spreads of the two types of swaps. In addition, a statistically significant difference between the bid-rate spreads over the Treasuries for the two types of swap markets also points towards differences in the liquidity of the two markets. Further, as mentioned above, the convention in the swap market is to price interest rate swaps as a spread over the Treasuries assuming semi-annual interest payments. However, if a client requires annual payments, the swap dealer will customize the swap by adjusting the all-in swap rate. Therefore, this study also analyzes the spread between the all-in swap bid and offer rates to examine any differences in the transaction costs and, consequently, the liquidity of the two markets. Table 2 gives the summary statistics for the spread between the swap bid and offer rates. The spread between the bid and offer rates is significantly different from zero for all swap maturities. In addition, the bid-offer spread is significantly high for swaps with seven- and ten-year maturities. Less liquidity at the higher maturity spectrum explains high bid-offer spread in this segment of the interest rate swap market. The spread between the bid and offer rates in a swap indexed to one-year LIBOR exceeds the spread in a swap indexed to a six-month LIBOR by 0.14 to 0.23 basis points. Table 2 A comparison of the bid-otherspreadin a swapindexedto a one-yearLIBOR to the bid-offer spread in a swap indexed to a six-month LIBOR. The data set covers the period from October 1987 to November 1991. The spread is in basis points Swap
maturity
One-year Indexed
2-year 3-year 4-year 5-year 7-year ***
Significant
LIBOR
Six-month
swap
Mean
Standard
5.09 5.12 5.06 5.08 5.27
1.51 1.20 1.37 1.17 1.30
at the 0.01 level.
Indexed deviation
LIBOR
Z-Statistic
swap
Mean
Standard
4.95 4.96 4.88 4.79 5.08
1.36 1.17 1.28 1.08 1.30
deviation 3.s7*** 3.24*** 4.15*** 4.99*** 4.03***
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In fact, as the maturity of the swap contract increases, the difference in the bid-offer spreads of semi-annual and annual swaps increases. According to the z-statistic constructed through the Wilcoxon rank sum test, the difference in the bid-offer spreads of the two markets is statistically significant for all swap maturities at the 1% level of significance. Thus, in terms of transaction costs, liquidity and depth of the market, there is a statistically significant difference between a six-month LIBORindexed and a one-year LIBOR-indexed interest rate swap contract.8 In a rising yield curve environment, the all-in swap rate for a two-year maturity swap should be lower than the all-in swap rate for a higher maturity swap due to the term premiums in a higher maturity swap contract. Term premiums represent the difference between the swap spreads over the Treasuries for any swap maturity and the corresponding spread for a two-year maturity swap.’ If the expectations hypothesis of the term structure of interest rates holds, the term premium in a semiannual swap contract should not be statistically different from the term premiums in an annual swap contract. Table 3 illustrates the term premiums of swap spreads for different swap maturities. Table 3 shows that the term premiums are significantly different from zero for all maturities for both the samples. The term premiums for a swap indexed to one-year LIBOR exceed the term premiums for a swap indexed to a six-month LIBOR by Table 3 Term premiums of spreads between swap offer rates and the Treasury yields for a swap indexed to a sixmonth LIBOR and a swap indexed to a one-year LIBOR. The term premiums are in basis points for the period between October 1987 and November 199 1. The term premium of spread is the difference between the spread concerned and the corresponding two-year swap period Statistics
Maturity Z-year
Sltap indexed to one-.vear Mean Standard deviation Sbvap indexed to si.u-month Mean Standard deviation
Significant
contract
3-year
4-year
5-year
7-year
1O-year
8.29 12.27
10.58 IO.03
13.03 11.17
13.61 12.35
17.08 13.91
7.11 7.17
10.21 9.59
12.53 11.73
13.01 11.83
16.28 13.39
- 3.97***
-0.58***
-5.61***
-6.17***
-7.10***
LIBOR
LIBOR
=-Statistics ***
of the swap
at the 0.01 level
’ We have argued in the paper that credit spreads are unlikely to explain differences in bid-ask spreads, because most of the credit risk is driven by the volatility of the fixed-interest component. However, if payment intervals match reset frequencies then swaps using one-year LIBOR should contain more credit risk. The significant difference in the spreads of a six-month LIBOR-indexed and one-year LIBORindexed swap could be due to credit risk, or differences in liquidity in the swap market or both. ’ For example, suppose the swap other rate for a two-year maturity swap equals 65 basis points over Treasuries. while the swap offer rate for a seven-year maturity swap equals 75 basis points over Treasuries. The term premium equals IO basis points (75 bp-65 bp).
D. K. Malhotru /Journal of’ Multinational Financial Management 8 (199X) 79-88
RI
0.37 to 1.18 basis points for different swap maturities and the difference is statistically significant. In fact, except for a two-year swap, as the maturity of the swap increases, the difference between the term premiums of the swap indexed to a one-year LIBOR and the swap indexed to a six-month LIBOR rises. Higher term premiums in a oneyear LIBOR-indexed swap can be due to the time varying credit risk premium that is incorporated in the floating rate LIBOR used in the swap contracts. This adds strength to the argument that the interest rate reset period impacts the bid-offer rate quotations in the swap market, because one-year LIBOR-indexed swaps and sixmonth LTBOR-indexed swaps represent two different types of market structures.
4. Summary and conclusions This study examined the impact of semi-annual versus annual interest payments on the bid-offer quotations in an interest rate swap contract. Using bi-weekly interest rate swap quotations from October 1987 to November 1991, this study documented that the bid-offer rates in an interest rate swap indexed to a one-year LIBOR bracketed the bid-offer rate quotations of an interest rate swap indexed to a sixmonth LIBOR. The difference in the swap rate quotations for a one-year and sixmonth LIBOR-indexed swap contract was statistically significant. The spread between the bid and offer rates in annual interest rate swap was also higher than the spread between the bid and offer rates in a semi-annual swap contract. Thus, semi-annual and annual interest rate swap contracts appeared to be significantly different in transaction costs, liquidity, and depth of the market. In addition, the term premiums in one-year LIBOR-indexed swaps were also higher than the term premiums in six-month LIBOR-indexed swap contracts.
References Abken, P.F., 1991. Valuing default-risky interest rate swaps. Advances in Futures and Options Research 6, 933116. Aggarwal, R., 1990. Assessing default risk in interest rate swaps. In: Beidleman, C. (Ed.), Interest Rate Swaps. Business One-Irwin, Homewood, IL. Arak, M., Estrella, A., Goodman, L., Silver, A., 1988. Interest rate swaps: An alternative explanation. Financial Management 17, 12-18. Bicksler, J., Chen, A.H., 1986. An economic analysis of interest rate swaps. J. Finance 41, 6455655. Cooper, I., Mello, J.F., 1991. Default risk in swaps. J. Finance 46, 597-620. Felgran, SD., 1988. Interest rate swaps: Uses, risk, and prices. New England Economic Review 22,22 -33. Malhotra, D.K., 1997. An empirical examination of the interest rate swap market, Quarterly J. Business and Economics 36, 19-29. Smith, C.W., Smithson, C.W., Wakeman, L.M., 1986. The evolving market for swaps. Midland Corporate Finance J. 3, 20-32. Sun, T.-S., Sundaresan, S., Wang, C., 1993. Interest rate swaps - An empirical investigation. J. Financial Economics 34, 7799. Wall, L.D., Pringle, J.J., 1989. Alternative explanations of interest rate swaps: A theoretical and empirical analysis. Financial Management 18, 59973.
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Wall, L.D., Pringle, J.J., McNulty, J.E., 1990. Capital requirements for interest-rate hedges. Economic Review, Federal Reserve Bank of Atlanta, May/June, 14-28. Whittaker, J.G., 1986. Interest rate swaps: Risk and regulation. Economic Review, of Kansas City. March, 3-13. Whittaker, J.G., 1987. Pricing interest rate swaps in an options pricing framework. of Kansas City Working Paper, Missouri, May.
79-88 and foreign-exchange Federal
Reserve
Bank
Federal
Reserve
Bank
of Multinational 8 (1998)
ELSEVIER
Financial 79-88
Journal of MULTINATIONAL FINANCIAL MANAGEMENT
Management
The impact of interest rate reset period on the bid-offer rates in an interest rate swap contract - an empirical investigation D.K. Malhotra * Philadelphia
College
of Textiles
Received
and Science,
30 September
Philadelphia,
1997; accepted
PA 19144-5497,
30 January
USA
1998
Abstract Although numerous studies have analyzed the interest rate swap market, the major influences on the swap spreads have not been fully examined. Using bi-weekly interest rate swap quotations from a swap dealer, this study documents the impact of semi-annual versus annual interest payments on the bid and offer rate quotations in the interest rate swap market. A univariate analysis indicates that the bid-offer spreads over the Treasuries in a one-year London Interbank Offer-Rate (LIBOR) indexed interest rate swap contract bracket similar spreads in a six-month LIBOR-indexed swap contract. Also, the spread between the bid and offer rate in an annual interest rate swap is also higher than the spread in a semi-annual interest rate swap contract. In addition, a one-year LIBOR-indexed all-in swap rate incorporates higher term premiums in comparison to a six-month LIBOR-indexed swap contract. 0 1998 Elsevier ScienceB.V. All rights reserved. JEL class$cation: Keywords:
E4; E43; G2
Interest rate swap; Bid-offer rates
1. Introduction An interest rate swap is an agreement between two parties to exchange a series of interest payments on a notional principal that is not exchanged. These payments are tied to different indexes such as the London Interbank Offer Rate (LIBOR), the Treasury rate, etc. Further, instead of being traded on organized exchanges, interest rate swaps are arranged by commercial and investment banks. Thus, they are classified as over-the-counter contracts. Dealers in interest rate swaps act as market makers and readily quote interest rates at which they stand ready to take either side * Corresponding
author.
Fax:
+ 1 215 951 2652.
1042-444X/98/$19.00 0 1998 Elsevier PI1 SlO42-444X(98)00019-X
Science
B.V. All rights
reserved
80
D. K. Malhotra
/ Journal
of’Multinationa1
Financial
Manugrmcnt
8 (I 998) 79-88
of the interest rate swaps with simple structures and standard maturities (typically two to ten years with semi-annual interest payments). If the dealer makes fixed interest rate payments and receives floating interest rate payments, the dealer is said to be on the bid side of the swap contract. Conversely, the dealer that pays a floating rate and receives a fixed rate is said to be on the offer side of the swap contract. In a fixed-for-floating interest rate swap, the fixed-rate side of the swap is usually stated as a spread over the prevailing yields on-the-run U.S. Treasury securities. Moreover, interest rate swaps priced as a spread over the Treasuries assume semi-annual interest payments. Therefore, when the dealer’s client requires annual payments instead of semi-annual payments, the dealer adjusts the fixed rate of interest to reflect this difference. Although numerous studies have analyzed the swap market, none of these studies examined the significance of semi-annual versus annual interest payments on the bid-offer rates in an interest rate swap contract. According to the expectations hypothesis of the term structure of interest rates, the bid-offer spreads over the Treasuries in a semi-annual and annual interest rate swap contract should be similar; otherwise there exists an opportunity for arbitrage. Therefore, this study compares a one-year LIBOR-indexed interest rate swap contract to a six-month LIBOR-indexed interest rate swap contract in three areas: the bid-offer spreads over the Treasuries, the spread between the bid and offer rates, and the spread of longerterm swaps versus swaps maturing in two years. An empirical analysis indicates that the bid-offer spreads over the Treasuries in a one-year LIBOR-indexed interest rate swap contract bracket similar spreads in a six-month LIBOR-indexed interest rate swap contract. Also, the spread between the bid and offer rates in an annual swap contract is higher than the spread in a semi-annual swap contract. The rest of the paper is organized as follows. Section 2 discusses the theoretical foundation of this paper. Section 3 includes data description and analysis of the empirical results. Section 4 concludes and summarizes this study.
2. Theoretical foundation Academic research on interest rate swaps mainly focused on: the growth of the swap market, the pricing of interest rate swaps, the default risk in interest rate swap contracts, and the regulation of the swap market. ’ Very few studies empirically analyzed the swap market. Sun et al. (1993) (SSW) conducted an empirical analysis of the interest rate swap market using daily quotations from two interest rate swap dealers. They used swaps in which fixed U.S. dollar interest rates were exchanged for a six-month LIBOR and documented that the spreads between swap rates and the Treasury yields generally increase significantly with maturities. They also found the bid-offer spread in interest rate swaps to be large and statistically significant. In ’ Bicksler and Chen (1986); Smith et al. ( 1986); Arak et al. ( 1988); Wall and Pringle (1989) discussed reasons for the growth of the swap market. Studies conducted by Whittaker (1986); Felgran ( 1988); Wall et al. (1990); and Aggarwal (1990) focused on the uses, risks, and regulatory aspects of swaps. Whittaker ( 1987); Abken (1991); and Cooper and Mello (1991) analyzed default risk in a swap contract.
D. K. Malhotra
/ Journal
of Multinational
Financial
Management
8 (I 998) 79-88
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addition, the SSW study also showed that swap rate quotations appeared to incorporate term premiums, because the spread over the Treasuries increased with an increase in the maturity of the swap contract. Malhotra (1997) re-examined the empirical aspects of the swap market and confirmed the results of the SSW study. Malhotra’s study covered swaps indexed to one-year LIBOR. These studies, however, did not analyze the impact of semi-annual versus annual interest payments on the bid and offer rate quotations in the swap market. Assuming that the expectations hypothesis of the term structure of interest rates holds, a one-year LIBOR-indexed interest rate swap contract is expected to have the same all-in swap fixed rate payments as an equivalent maturity six-month LIBOR-indexed interest rate swap contract.2 Thus, a swap indexed to a one-year LIBOR should trade at the same spread over the Treasuries as the swap indexed to a six-month LIBOR. If the one-year LIBOR-indexed all-in swap bid-offer rates do not equal the six-month LIBOR-indexed all-in swap bid-offer rates, there exists an opportunity for arbitrage. For example, if the one-year LIBOR-indexed interest rate swap carries higher bid-offer spreads over the Treasuries than a six-month LIBORindexed swap contract, a party can enter into a one-year LIBOR-indexed swap to pay one year LIBOR and receive fixed interest rate payments on the notional principal. At the same time, the party can also enter into an equivalent maturity six-month interest rate swap contract to receive six-month LIBOR and make semiannual fixed interest rate payments on the notional principal. Further, in a swap contract with a semi-annual exchange of interest payments, rates are reset frequently in contrast to a swap indexed to one-year LIBOR. Consequently, the probability of the six-month indexed swap contract assuming a large negative value before the reset date is lowered. This should cause the swap spreads for a six-month LIBOR-indexed swap to be lower in comparison to a oneyear LIBOR-indexed swap contract. However, changes in mark-to-market value of a swap, and hence its credit exposure, will be largely driven by changes in the value of the fixed interest rate payments with the floating rate component being quite small in comparison. Thus, the noise being generated by time varying volatility associated with the fixed-interest component would likely swamp any reduction in the uncertainty associated with the floating-rate component.3 Consequently, there should not be a statistically significant difference in the spreads over the Treasuries for a six-month LIBOR-indexed and a one-year LIBOR-indexed interest rate swap contract.
Thus, the null hypothesis is that the bid and offer spreads over the Treasuries in a one-year LIBOR-indexed swap equal similar spreads in a six-month LIBORindexed swap, and the interest rate reset period has no impact on the bid-offer rates in an interest rate swap contract. The alternate hypothesis is that the bid-offer rates ’ According to the unbiased expectations hypothesis of the term structure of interest rates, the total return that an investor will realize by rolling over short-term bonds to some investment horizon will be the same as holding a zero-coupon bond with a maturity that is the same as that investment horizon, 3 In addition, the credit spreads themselves are generally very small and should not cause statistically significant difference in the bid-offer rates of one-year LIBOR-indexed and six-month LIBOR-indexed interest rate swap contracts.
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in a one-year LIBOR-indexed interest rate swap contract exceed the bid-offer rates in a six-month LIBOR-indexed interest rate swap contract and the reset period impacts the swap rate quotations.
3. Data description and analysis
To conduct the empirical analysis, this study uses the data from various issues of the Swaps Monitor.” The data set contains information for the all-in swap bid-offer rates, the Treasury rate of equivalent maturity, and the maturity of the swap contract. The data is on a bi-weekly basis from 1 October 1987 to 2 November 1991 for a swap with a maturity of two, three, four, five, seven, and ten years. These rates apply to interest rate swaps that are indexed to a six-month LIBOR and swaps that are indexed to a one-year LIBOR.’ Fig. l(a) plots the bid rate spread over the Treasuries for semi-annual and annual two-year maturity interest rate swap contracts, and Fig. l(b) plots the bid-rate spread over the Treasuries for semi-annual and annual ten-year maturity interest rate swap contracts. As illustrated in Fig. 1 (a,b), the bid rate spread over the Treasuries for an annual interest rate swap contract is higher than the bid rate spread over the Treasuries for a semi-annual interest rate swap contract throughout the sample period.6 Table 1 summarizes the characteristics of the spread between the Treasuries and the all-in swap bid-offer rates for the period between October 1987 and November 1991. As illustrated in Table 1, the bid-offer spreads over the Treasuries increase with an increase in the maturity of the swap contract. Also, a univariate analysis indicates that the bid and offer spreads in an annual LIBOR-indexed swap exceed similar spreads in a six-month LIBOR-indexed swap for all swap maturities. However, according to the t-statistic, the difference is not statistically significant at the 1% level of significance for any swap maturity. To examine the statistical significance of the difference between the bid-offer rates of annual and semi-annual swap contracts, we also use the Wilcoxon rank sum test.’ Although the average bid-offer spread over the Treasuries in a one-year LIBOR-indexed interest rate swap contract 4 Swaps Monitor is a bi-weekly publication of Swaps Monitor, New York, NY 10276. Data is based on quotations provided by Tullet and Tokyo Forex. 5 The empirical analysis incorporates the difference between the money market and the bond-yield conventions. In an interest rate swap where LIBOR is exchanged for a fixed interest rate, the fixed-rate payments typically follow bond-yield convention, whereas the LIBOR payments are subject to the money-market convention. 6 Similarly, the bid rate spread over the Treasuries was higher for an annual swap contract than the similar spread for a semi-annual swap contract for all other swap maturities. ‘We use a non-parametric test to analyze the statistical significance of the difference between the bidoffer rate quotations in a semi-annual and annual interest rate swap, because a non-parametric test requires fewer assumptions regarding the distribution of the sample. Moreover, a parametric test statistic allows small persistent differences in the spreads to be swamped by the overall variability of the spreads over the sample period. Therefore, the use of a non-parametric test, such as the Wilcoxon rank sum test, is appropriate to check the robustness of the results.
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83
‘---Annual ( :. . Semisnnual \
140
,
I
0:
(b)
Time
Fig. 1. (a) The bid rate spread over the Treasuries for a two-year maturity semi-annual and annual interest rate swap contract. The spread is in basis points. (b) The bid rate spread over the Treasuries for a tenyear maturity semi-annual and annual interest rate swap contract. The spread is in basis points.
exceeds the average bid-offer spread in a six-month LIBOR-indexed interest rate swap contract by two to four basis points only, the difference is statistically significant according to the z-statistic at the 1% level of significance. Therefore, we reject the null hypothesis that the bid-offer spreads over the Treasuries in a six-month LIBORindexed swap contract equal the spreads in a one-year LIBOR-indexed swap con-
Bid
68.5 12.4 1.6* -s.9+**
Swaps indexed to k-month LIBOR Mean 61.6 56.4 Standard deviation 16.3 14.8 r-Statistics I.1 1.1 z-Statistics -8.9*** -s.9***
*** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level.
11.2 12.8
58.7 15.6
Offer
Bid
contract 3-year
of the swap
63.5 12.4 1.9** -8,7***
67.0 14.4
Offer
71.5 12.4 1.6** -8,9***
74.4 12.9
Bid
4-year
66.6 11.6 1.6** -8.9***
69.3 12.1
Offer
73.8 13.6 1.6** -8,9***
76.8 14.2
Bid
5-year
69.0 13.1 1.5* -8,9***
71.8 13.5
Offer
74.5 13.7 1.6** -8,9***
77.6 14.2
Bid
7-year
in semi-annual and annual interest rate swap contracts. The semi-annual interest rate swap contract is indexed to a one-year LIBOR. The data covers the period
2-year
Maturity
Svaps indcued to one-year LIBOR Mean 63.8 Standard deviation 16.9
Statistics
Table 1 The bid-offer spread over the Treasuries six-month LIBOR. The annual interest 1991. The spread is in basis points
69.4 13.0 1.6* -8,9***
72.3 13.5
Offer
77.8 13.7 1.8** -8.9***
81.2 14.4
Bid
IO-year
72.9 13.4 1.7** -8.9***
75.8 13.7
Offer
rate swap contract is indexed to a from October 1987 to November
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tract. However, a pure arbitrage in the sense of earning a positive rate of return on a position that requires no net investment and contains no risk does not exist. Due to the nature of the swap contracts, the arbitrage does involve some risk, because six-month LIBOR may move significantly during a six-month period and could generate losses. Higher bid-offer spreads over the Treasuries in a one-year LIBORindexed interest rate swap contract can be partially explained by term premiums at the short-end of the LIBOR market. In addition, the large bid-offer spreads in a one-year LIBOR-indexed swap over the similar spreads in a six-month LIBORindexed swap also highlight the fact that the two types of swaps have different market structures and different users. The customized nature of the one-year LIBORindexed swap instead of the standardized nature of the six-month LIBOR-indexed swap contract may also partially explain the statistically significant difference in the bid-offer spreads of the two types of swaps. In addition, a statistically significant difference between the bid-rate spreads over the Treasuries for the two types of swap markets also points towards differences in the liquidity of the two markets. Further, as mentioned above, the convention in the swap market is to price interest rate swaps as a spread over the Treasuries assuming semi-annual interest payments. However, if a client requires annual payments, the swap dealer will customize the swap by adjusting the all-in swap rate. Therefore, this study also analyzes the spread between the all-in swap bid and offer rates to examine any differences in the transaction costs and, consequently, the liquidity of the two markets. Table 2 gives the summary statistics for the spread between the swap bid and offer rates. The spread between the bid and offer rates is significantly different from zero for all swap maturities. In addition, the bid-offer spread is significantly high for swaps with seven- and ten-year maturities. Less liquidity at the higher maturity spectrum explains high bid-offer spread in this segment of the interest rate swap market. The spread between the bid and offer rates in a swap indexed to one-year LIBOR exceeds the spread in a swap indexed to a six-month LIBOR by 0.14 to 0.23 basis points. Table 2 A comparison of the bid-otherspreadin a swapindexedto a one-yearLIBOR to the bid-offer spread in a swap indexed to a six-month LIBOR. The data set covers the period from October 1987 to November 1991. The spread is in basis points Swap
maturity
One-year Indexed
2-year 3-year 4-year 5-year 7-year ***
Significant
LIBOR
Six-month
swap
Mean
Standard
5.09 5.12 5.06 5.08 5.27
1.51 1.20 1.37 1.17 1.30
at the 0.01 level.
Indexed deviation
LIBOR
Z-Statistic
swap
Mean
Standard
4.95 4.96 4.88 4.79 5.08
1.36 1.17 1.28 1.08 1.30
deviation 3.s7*** 3.24*** 4.15*** 4.99*** 4.03***
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In fact, as the maturity of the swap contract increases, the difference in the bid-offer spreads of semi-annual and annual swaps increases. According to the z-statistic constructed through the Wilcoxon rank sum test, the difference in the bid-offer spreads of the two markets is statistically significant for all swap maturities at the 1% level of significance. Thus, in terms of transaction costs, liquidity and depth of the market, there is a statistically significant difference between a six-month LIBORindexed and a one-year LIBOR-indexed interest rate swap contract.8 In a rising yield curve environment, the all-in swap rate for a two-year maturity swap should be lower than the all-in swap rate for a higher maturity swap due to the term premiums in a higher maturity swap contract. Term premiums represent the difference between the swap spreads over the Treasuries for any swap maturity and the corresponding spread for a two-year maturity swap.’ If the expectations hypothesis of the term structure of interest rates holds, the term premium in a semiannual swap contract should not be statistically different from the term premiums in an annual swap contract. Table 3 illustrates the term premiums of swap spreads for different swap maturities. Table 3 shows that the term premiums are significantly different from zero for all maturities for both the samples. The term premiums for a swap indexed to one-year LIBOR exceed the term premiums for a swap indexed to a six-month LIBOR by Table 3 Term premiums of spreads between swap offer rates and the Treasury yields for a swap indexed to a sixmonth LIBOR and a swap indexed to a one-year LIBOR. The term premiums are in basis points for the period between October 1987 and November 199 1. The term premium of spread is the difference between the spread concerned and the corresponding two-year swap period Statistics
Maturity Z-year
Sltap indexed to one-.vear Mean Standard deviation Sbvap indexed to si.u-month Mean Standard deviation
Significant
contract
3-year
4-year
5-year
7-year
1O-year
8.29 12.27
10.58 IO.03
13.03 11.17
13.61 12.35
17.08 13.91
7.11 7.17
10.21 9.59
12.53 11.73
13.01 11.83
16.28 13.39
- 3.97***
-0.58***
-5.61***
-6.17***
-7.10***
LIBOR
LIBOR
=-Statistics ***
of the swap
at the 0.01 level
’ We have argued in the paper that credit spreads are unlikely to explain differences in bid-ask spreads, because most of the credit risk is driven by the volatility of the fixed-interest component. However, if payment intervals match reset frequencies then swaps using one-year LIBOR should contain more credit risk. The significant difference in the spreads of a six-month LIBOR-indexed and one-year LIBORindexed swap could be due to credit risk, or differences in liquidity in the swap market or both. ’ For example, suppose the swap other rate for a two-year maturity swap equals 65 basis points over Treasuries. while the swap offer rate for a seven-year maturity swap equals 75 basis points over Treasuries. The term premium equals IO basis points (75 bp-65 bp).
D. K. Malhotru /Journal of’ Multinational Financial Management 8 (199X) 79-88
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0.37 to 1.18 basis points for different swap maturities and the difference is statistically significant. In fact, except for a two-year swap, as the maturity of the swap increases, the difference between the term premiums of the swap indexed to a one-year LIBOR and the swap indexed to a six-month LIBOR rises. Higher term premiums in a oneyear LIBOR-indexed swap can be due to the time varying credit risk premium that is incorporated in the floating rate LIBOR used in the swap contracts. This adds strength to the argument that the interest rate reset period impacts the bid-offer rate quotations in the swap market, because one-year LIBOR-indexed swaps and sixmonth LTBOR-indexed swaps represent two different types of market structures.
4. Summary and conclusions This study examined the impact of semi-annual versus annual interest payments on the bid-offer quotations in an interest rate swap contract. Using bi-weekly interest rate swap quotations from October 1987 to November 1991, this study documented that the bid-offer rates in an interest rate swap indexed to a one-year LIBOR bracketed the bid-offer rate quotations of an interest rate swap indexed to a sixmonth LIBOR. The difference in the swap rate quotations for a one-year and sixmonth LIBOR-indexed swap contract was statistically significant. The spread between the bid and offer rates in annual interest rate swap was also higher than the spread between the bid and offer rates in a semi-annual swap contract. Thus, semi-annual and annual interest rate swap contracts appeared to be significantly different in transaction costs, liquidity, and depth of the market. In addition, the term premiums in one-year LIBOR-indexed swaps were also higher than the term premiums in six-month LIBOR-indexed swap contracts.
References Abken, P.F., 1991. Valuing default-risky interest rate swaps. Advances in Futures and Options Research 6, 933116. Aggarwal, R., 1990. Assessing default risk in interest rate swaps. In: Beidleman, C. (Ed.), Interest Rate Swaps. Business One-Irwin, Homewood, IL. Arak, M., Estrella, A., Goodman, L., Silver, A., 1988. Interest rate swaps: An alternative explanation. Financial Management 17, 12-18. Bicksler, J., Chen, A.H., 1986. An economic analysis of interest rate swaps. J. Finance 41, 6455655. Cooper, I., Mello, J.F., 1991. Default risk in swaps. J. Finance 46, 597-620. Felgran, SD., 1988. Interest rate swaps: Uses, risk, and prices. New England Economic Review 22,22 -33. Malhotra, D.K., 1997. An empirical examination of the interest rate swap market, Quarterly J. Business and Economics 36, 19-29. Smith, C.W., Smithson, C.W., Wakeman, L.M., 1986. The evolving market for swaps. Midland Corporate Finance J. 3, 20-32. Sun, T.-S., Sundaresan, S., Wang, C., 1993. Interest rate swaps - An empirical investigation. J. Financial Economics 34, 7799. Wall, L.D., Pringle, J.J., 1989. Alternative explanations of interest rate swaps: A theoretical and empirical analysis. Financial Management 18, 59973.
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Wall, L.D., Pringle, J.J., McNulty, J.E., 1990. Capital requirements for interest-rate hedges. Economic Review, Federal Reserve Bank of Atlanta, May/June, 14-28. Whittaker, J.G., 1986. Interest rate swaps: Risk and regulation. Economic Review, of Kansas City. March, 3-13. Whittaker, J.G., 1987. Pricing interest rate swaps in an options pricing framework. of Kansas City Working Paper, Missouri, May.
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Reserve
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Bank