- Email: [email protected]
Interest rate swaps
Journal
of Financial
Interest
Economics
rate swaps
An empirical Tong-sheng Columhiu
Received
investigation
Sun, Suresh Sundaresan,
Unirrrsii~~,
November
34 (1993) 77-99. North-Holland
New
York. NY
and Ching Wang*
10027, USA
1991. final version
received
December
1992
Using quotations from two interest rate swap dealers with different credit ratings (AAA and A), we examine the effect of dealers’ credit reputations on swap quotations and bid-offer spreads. The AAA offer rates are significantly higher than the A offer rates, and the AAA bid rates are significantly lower than the A bid rates. We also document the relation between swap rates and par bond yields estimated from London interbank offered rate (LIBOR) and bid rate (LIBID) data. We identify some of the problems in testing the implications of swap pricing theory.
1. Introduction Interest rate swaps are agreements between two institutions in which each commits to make periodic payments to the other based on a predetermined amount of notional principal for a predetermined life, called the maturity. The periodic payments may either be fixed or may float with an agreed-upon floating index such as the six-month London interbank offered rate (LIBOR). The two institutions engaging in the swap transaction are called counterparties. In most cases, transactions are arranged and intermediated by swap dealers, which are typically investment or commercial banks. Swap dealers that act as intermediaries absorb the counterparties’ credit risks and receive the bid-offer spread. Dealers may also receive up-front fees for arranging swap transactions. The
Correspondencr to: Suresh York, NY 10027, USA.
Sundaresan,
Graduate
School
of Business, Columbia
University,
New
*We thank John Breit, William Broeksmit, and Brian Herring for providing us with the swap data and for their comments and suggestions. We have also benefited from the comments and suggestions of participants in the faculty workshops at Baruch College, the University ofToronto, the Universite Catholique de Louvain, and the Hebrew University. Special thanks go to John Hull and Alan White for their suggestions. Comments and suggestions made by Clifford Smith and an anonymous referee significantly improved the paper. 0304-405X/93/$06.00
:i
1993-E]
sevier Science Publishers
B.V. All rights
reserved
78
T.-s. Sun et al., Intrrest
rate swaps
credit reputations of swap dealers differ widely, with some dealers enjoying an AAA credit rating and others a rating of A or less. In interest rate swaps no principal amounts change hands. In so-called generic interest rate swaps one counterparty pays a fixed and the other a floating rate, with the payment frequency coinciding with the term of the floating index. To illustrate the market conventions, we provide in fig. 1 an example of an intermediated swap transaction. The dealer that makes fixed payments and receives floating payments is said to be on the bid side of the transaction. Thus, in fig. 1, the swap dealer has a bid rate of Treasury plus 15 basis points. If the swap has a term of five years, the five-year Treasury yield will be used as the benchmark. Conversely, the dealer that pays a floating rate and receives a fixed rate is said to be on the offer side of the transaction. In the example in fig. 1, the dealer has an offer rate of the five-year Treasury yield plus 25 basis points. Swap dealers charge bid-offer spreads for their services: they pay less on the bid side and receive more on the offer side. It is intuitive to expect that, all else being equal, the bid-offer spreads depend on the swap dealers’ credit reputations. The interest rate swaps market is now estimated at about $3 trillion in notional principal amount outstanding and thus represents one of the major segments of the capital market.’ The significance of this growth is perhaps best understood in the context that this market did not exist before 1980. The importance of the swap market in managing risk is now well recognized in the academic literature, as evidenced by the extensive treatment of swaps in a recent text by Smith, Smithson, and Wilford (1990).
Offer
Bid Side
Fig. I. A five-year
Intermediated
interest
Side
rate swap
Interest rate swaps are agreements between two institutions, called counterparties, in which one counterparty pays a fixed and the other a floating rate based on a predetermined notional principal for a predetermined maturity. The most common index for the floating rate is the six-month London interbank offered rate (LIBOR). Most swaps are arranged and intermediated by swap dealers. The dealer that pays a fixed rate and receives a floating rate is on the bid side of the transaction, and the dealer that pays a floating rate and receives a fixed rate is on the offer side. In this five-year swap, on the bid side the dealer receives the six-month LIBOR and pays a swap bid rate equal to the five-year Treasury yield plus I5 basis points. On the offer side the dealer pays the six-month LIBOR and receives a swap offer rate equal to the five-year Treasury yield plus 25 basis points.
‘InternatIonal
Swap Dealers’ Association
(ISDA) survey
1990.
T.-s. Sun ei al.. Inreresi rate .wups
79
To our knowledge, no empirical investigation of interest rate swaps has appeared in the literature. This is the principal motivation for our paper. Using daily interest rate swap quotations from a swap dealer with a credit rating of AAA and another dealer with a credit rating of A, we provide some stylized facts about the behavior of swap rates. We also describe how the swap rates and their biddoffer spreads are related to the swap dealers’ credit reputations. The bid-offer spreads of the A dealer are much smaller than those of the AAA dealer, and the A swap rates are typically bracketed by the AAA rates. Interestingly, the midpoints (or the average of bid and offer) of swap quotations for the two dealers are not statistically significantly different from each other for swaps with a life of four or more years. A second motivation for our paper is that swap pricing theory offers potentially testable implications. For example, under simplifying assumptions (no transactions costs or default), swap pricing theory implies that the arbitrage-free rate for a generic interest rate swap should equal the yield on a par bond with the same maturity. This proposition assumes away the risk of default. When there is a default risk, swap pricing theory implies that the par bond yield is greater than the swap rate. The par bond yields are therefore either greater than or equal to the swap rates. Since default risk and transactions costs are unlikely to change daily, the changes in swap rates should be closely related to (or tracked by) the changes in par bond yields. We investigate the presence of default risk in swaps. This investigation turns out to be considerably more difficult, because of data limitations and the nature of swap and interbank markets. The data limitations are easily understood in the context of fig. 1. To investigate the implications of default risk in swaps, we can compare either the par bond yield of counterparty Y (in fig. 1) with the swap offer rate or the par bond yield of the swap dealer with the swap bid rate. Data on the par bond yields of various counterparties, however, are simply unavailable. We are thus forced to pursue this inquiry indirectly by examining the relation between the swap rates and the estimated par bond yields in the interbank market. Specifically, the counterparties of the swap dealers are assumed to be represented by the participants in the interbank market whose LIBOR and LIBID (London interbank bid rate) are used to estimate the par bond yields. The swap and interbank markets also differ in liquidity. Swap quotes are typically keyed off respective benchmark Treasury yields. as illustrated in fig. 1. Since the Treasury benchmark issues are very actively traded, swap quotes change frequently. The interbank market, on the other hand, is relatively thin. The bid-offer spreads in the interbank market, as measured by the difference between LIBOR and LIBID, are around 12.5 basis points for all maturities and the quotes tend to change less frequently. The implications of these data problems for our study are addressed later in the paper. To mitigate this difficulty at least partially, we conduct our empirical work using LIBOR data from two sources, Data Research Incorporated (DRI)
80
T.-s. Sun et al.. Interest rate swaps
and Data Stream. We also obtain data on LIBID from Data Stream. Later in the paper we discuss in detail these data sets and the inferences one can draw from them. Our empirical evidence shows that the swap offer rates of both dealers are significantly less than the LIBOR par bond yields. The deviations of AAA swap offer rates from the par bond yields vary on average from about 8 to 12 basis points, and the deviations of A swap offer rates vary from about 12 to 15 basis points. The average deviations for each dealer are, for most part, within the bid-offer spread in the interbank market, which is about 12.5 basis points. Comparisons of (a) swap bid rates with LIBID par bond yields and (b) swap midpoints with the par bond yields estimated from the midpoints in the interbank market also show that the par bond yields on average are greater than swap rates, albeit the differences are less pronounced. A comparison of swap offer rates with LIBID par bond yields indicates a sharp contrast between AAA and A swap quotes. The AAA swap offer rates exceed LIBID par bond yields in three out of four swap maturities, whereas the A swap offer rates are below the LIBID par bond yields in three out of four swap maturities. We further examine the extent to which the par bond yields are able to track swap quotes by regressing the changes in the par bond yields with the changes in swap quotes. Regressions based on weekly changes perform much better than regressions based on daily changes. This points to the presence of asynchronicity in quotes. We view our results in this context as an attempt to highlight some regularities and alert researchers to potential problems in testing the implications of swap pricing theory. Clearly, it is desirable to use transactions data on swaps and actual par bond yields of counterparties to examine the implications of swap pricing theory. The paper is organized as follows. Section 2 briefly reviews the literature and swap pricing theory. In section 3 we provide summary information on swap rates of the two dealers, and discuss the LIBOR and LIBID data. Section 4 presents the empirical evidence. We first examine the effect of the dealers’ credit reputations on the bid-offer spreads of swap quotations. Then we compare the swap rates with the LIBOR and LIBID par bond yields. We also explore how well the Treasury yields and the LIBOR par bond yields track swap rates. Section 5 concludes and discusses the directions for future research in the light of our evidence.
2. Swap pricing theory Academic research in swap markets focuses on many papers explore the economic rationale for the of interest rate swap markets, principles of swap interest rates and credit risks on the structure and
three distinct issues. First, existence and the evolution pricing, and the impact of valuation of swaps. Papers
in this category include Bicksler and Chen (1986) Smith, Smithson, and Wakeman (1986, 1988) and Turnbull (1987). Second, a number of papers examine how swap contracts can be valued in an arbitrage-free setting. The groundwork for pricing swaps is laid in the valuation of floating-rate instruments by Cox, Ingersoll, and Ross (1980) and Ramaswamy and Sundaresan (1986). Interest rate swaps can be valued by finding the level of fixed payments that will have the same present value as the floating payments. Smith, Smithson, and Wakeman (1986) also suggest a valuation procedure. Papers by Hull (1989) Sundaresan (1991) and Cooper and Mello (199 1) provide approaches to pricing interest rate and currency swaps that are subject to either interest rate or default risk or both. Finally, a number of papers explore the regulatory framework for swaps and capital adequacy for swap market makers. Hull (1989) discusses the issue of capital determination for off-balance-sheet commitments using contingentclaims valuation principles, and Whittaker (1987) examines the regulatory aspects of swap markets. The issue of capital adequacy is addressed by Smith, Smithson, and Wilford (1990). For our empirical work, the key insight from swap pricing theory is the implication that, under certain assumptions to be discussed, the rate for a generic interest rate swap must equal the yield on a par bond issued by the counterparty that is making the fixed payments. This insight follows readily from the work of Smith, Smithson, and Wakeman (1986, 1988) and Sundaresan (1991). We establish the swap pricing proposition under the following assumptions: (A.l)
Reset index (A.2) There (A.3) There (A.4) There
dates precede the payment dates with a lag equal maturity. are no transactions costs, taxes, or other frictions. are no arbitrage opportunities. is no default risk.
to the floating
Generic interest rate swaps satisfy assumption (A.1). Assumption (A.2) implies perfect market conditions, and assumption (A.3) implies that the swaps are priced identically to a replicating portfolio that duplicates the cash flows of the swap. Assumption (A.4) which ignores default risk, is clearly restrictive: we examine whether the major pricing implication derived under this assumption is broadly consistent with the data on swap quotes. We also explore the directional bias introduced when this assumption is relaxed. Swap Pricing Proposition. Under ussumptions (A.I)-(A.4), the arbitrage-free swap rate on the settlement date should equal the yield on a par bond that makes 0 fixed payments on the sume dates as thejloating leg of the swap. The intuition generic interest
behind this result is easy to understand. Consider the five-year rate swap in fig. I between the swap dealer and counterparty Y.
Counterparty Y is long in the floating leg and short in the fixed leg. On the settlement date, the position of counterparty Y can be replicated as follows: issue at par a five-year fixed-rate note with a principal amount equal to the notional principal and invest the notional principal in the LIBOR maturing on the next reset date. The interest to be received on the next reset date equals the principal amount times LIBOR. The interest is withdrawn and the principal is rolled into the LIBOR that matures on the next reset date and so on. On the last date, the maturing notional amount is used to cover the balloon payment of the fixedrate note. This strategy replicates all the cash flows of the generic swap. Therefore the swap rate on the settlement date must be the yield (or the coupon) on the fixed-rate note issued at par. A fuller discussion of this result appears in Smith, Smithson, and Wakeman (1986). It is instructive to examine this proposition further. The proposition ignores default risk, but clearly, both the swap dealer and the counterparties carry such risk. The par bond issued by the counterparty is riskier than the swap, since it has a balloon payment at maturity that is also subject to default risk. In addition, with a par bond only the issuer (in fig. 1, counterparty Y) can default. In swaps, both parties to the transaction can default. As pointed out by Smith, Smithson, and Wakeman (1988), in swaps it is the joint probability that counterparty Y is in financial distress and the value of the swap is negative to counterparty Y that defines default. This risk is smaller than the default risk associated with a loan. Most swap structures also provide for netting arrangements whereby only the difference between the fixed rate and the floating rate is paid by the counterparties. In addition, swaps typically provide for ‘offsets’ whereby the solvent counterparty is relieved of its obligations if the other counterparty defaults. Hence the default risk is likely to have a smaller impact in swap transactions. The swap pricing proposition also assumes away transactions costs and bidoffer spreads. The swaps we study are intermediated by dealers who absorb the credit risk and guarantee performance. For this service, they typically charge a fee that is embodied in the swap bid-offer spreads. Swap markets tend to have narrower bidoffer spreads than the interbank market, however. As argued by Amihud and Mendelson (1986), higher transactions costs lead to higher quoted yields. Both these factors (transactions costs and default risk) introduce the same directional bias in the basic pricing proposition: the par bond yields of counterparties will be higher than the swap rate to reflect higher transactions costs and higher default risk. So, we regard the basic proposition that equates swap rates with par bond yields as the null hypothesis. The alternative hypothesis is that the par bond yields will exceed the swap rates when default risk is important.’ In addition, default risk has a significant impact on the bid-offer spreads of swap dealers with different credit ratings. Suppose that the credit quality of the ‘A
proof of the alternative
hypothesis
will be made available
to interested
readers
upon request.
T.-s. Sun
et ul., Interestrate swups
83
counterparties is the same for different swap dealers, and that the swap contracts do not differ in other characteristics such as the up-front fee and collateral. Then the swap bid rates of AAA-rated dealers should be lower than those of A-rated dealers. For a swap dealer, swap bid rates pertain to obligations to make fixed payments in the future. Other things being equal, the present value of fixed payments from a dealer with better credit is higher. Swap dealers with a credit rating of AAA are therefore able to pay lower fixed rates. On the other hand, the swap offer rates of AAA-rated dealers should be higher than those of A-rated dealers. For a swap dealer, swap offer rates pertain to obligations to make floating payments in the future. Payments from a dealer with better credit have a higher present value, which implies that AAA swap dealers can demand higher fixed rates. The requirement that the credit quality of the counterparties is the same is only a sufficient condition and is not necessary. As long as the credit quality of the counterparties of an AAA-rated dealer is not significantly better than that of the counterparties of an A-rated dealer, our arguments will hold. In our empirical investigation, we examine the relationship between the bid-offer spreads of the two swap dealers.
3. Data description and diagnostics We obtain swap quotations from AIG Financial Products and Merrill Lynch. The short-term debt (commercial paper) is rated PI+ for AIG and Pl for Merrill Lynch, whereas the long-term debt is rated AAA for AIG and A for Merrill Lynch. We refer to the AIG swap quotes as AAA quotes and the Merrill Lynch quotes as A quotes. Our data set contains 605 daily swap bid and offer rates from October 11, 1988 to April 15, 1991. These rates apply to interest rate swaps in which fixed U.S. dollar rates are exchanged for the six-month LIBOR. The swap rates are available for two-, three-, four-, five-, seven-, and ten-year maturities. AIG also provided us with the corresponding Treasury benchmark yields. To estimate the par bond yields, we obtain LIBOR quotes from DRI for the same sample period for the following maturities: six months, one year, two years, three years, four years, and five years. The data for intermediate maturities and extended maturities are unavailable. To assess the quality of LIBOR quotations from DRI, we also obtain LIBOR and LIBID data from Data Stream for the same sample period. In the rest of this section we first describe the swap rates and the Treasury yields. Then we discuss the LIBOR and LIBID data and examine the quality of the data sets. 3. I. Swaps und Treasuries Figs. 2 and 3 provide the surfaces of the Treasury yield curves and the AAA swap offer rates for the entire sample period. The sample period includes periods
T.-s. Sun
et cd.. Interestrute swaps
Maturity lo-year -year
Fig. 2. U.S. Treasury
yield curve.
MawritY
10-w
Fig. 3. AAA
swap offer rates.
T.-s. Sun et
al.. Intere.s~ rate
swaps
85
of upward-sloping Treasury yield curve as well as inverted yield curve. Of 605 daily yield curve observations, 405 pertain to an upward-sloping Treasury yield curve and the remaining 200 (from December 14, 1988 to October 11, 1989) correspond to an inverted Treasury yield curve. The yield curve is defined as inverted when the ten-year Treasury yield is less than the two-year yield. The close association between swap quotes and the respective Treasury benchmark yields is evident from these figures. The two figures also indicate that inversions in the Treasury yield curve are accompanied by inversions in the swap curve. The average Treasury yields for the overall sample increase from 8.24% for a maturitiy of two years to 8.5% for a maturity of ten years, implying a term premium of 26 basis points. The corresponding AAA swap offer rates rise from 8.88% to about 9.32%, with a term premium of 44 basis points. The top panel of table 1 provides the summary statistics for the spreads between AAA swap offer rates and Treasury yields. The spreads are significantly positive at all maturities irrespective of the shape of the Treasury yield curve. The lower panel describes the corresponding term premiums of swap spreads _ the differences between the spread concerned and the two-year spread. The results here are striking: the term premiums are significantly positive for the overall sample, whereas most of the premiums are not significantly different from zero when the yield curve is inverted. Following Fama (1984), we use Hotelling T2 statistics to test the hypothesis that all premiums are zero. [See Fama (1984) or Anderson (1984) for more details of the statistics.] The joint hypothesis that the term premiums at all maturities are the same is decisively rejected for both the whole sample period and the subperiod when the yield curve is inverted. The behavior of the A swap rates is similar (and therefore not reported here). The term premiums of swap spreads for the overall sample increase significantly with maturities; the increase is much smaller when the Treasury yield curve is inverted.
3.2. LIBOR
and LIBID
As pointed out earlier, one of our goals is to compare the swap quotes with the estimated par bond yields based on LIBOR and LIBID. In addition, we wish to examine the ability of estimated LIBOR par bond yields to track swap rates. We present these results later in the paper. To better assess these results, we analyze below the data set from the interbank market. In table 2 we present the summary statistics for the differences between DRI LIBOR and Data Stream LIBOR for all available maturities, and in fig. 4 the frequencies of differences. Though most of the differences are within 10 basis points, the average differences are significant in the two-year and five-year rates. The joint hypothesis that the differences at all maturities are zero is also rejected at the 1% significance level. Thus, the LIBOR data in these two series appear to
86
T.-s. Sun et al., Interest rate swaps
1
Table
Summary statistics for the spreads and the term premiums of spreads between swap offer rates quoted by an AAA-rated swap dealer and Treasury yields, for 605 daily observations in the period October 11, 1988 to April 15, 1991. The spreads and term premiums are measured in basis points. The term premiums of the spread is defined as the difference between the spread concerned and the corresponding two-year spread. Spread Maturity Statistic
2-yr
4-yr
3-yr Full sample
Mean Std. t-value
64.33 12.35 128.05b
Mean Std. t-value”
74.89 13.25 19.71b
70.84 7.65 221.74b Inverted
5-yr
____.
7-yr
10-yr
77.49 8.20 232.38”
81.60 9.10 220.27h
77.34 8.78 124.30b
79.87 8.91 126.53b
7-yr
I 0-yr
13.16 14.29 22.63b
17.27 16.44 25.81b
2.45 16.87 2.05b
4.98 17.85 3.94h
period (N = 605) 72.78 6.84 261.5Sb
76.54 8.32 226.16b
yield curve sample period” (IV = 200)
15.56 1.78 137.00b
74.15 7.51 139.22b
76.59 9.23 117.10b
Term premium
of spread
Maturity Statistic
3-yr Full sample
Mean Std. f-value T2 (Fs,w,~)
6.52 6.74 23.75b Inverted
Mean Std. f-value T* (F5.195)
4-yr
period (N = 605) 8.45 11.76 17.66b 1605.25
yield curve sample 0.67 1.29 1.30
5-yr
- 0.74 14.56 - 0.72 318.19
12.21 14.18 21.16b (318.92b) period” (N = 200) 1.70 16.77 1.43 (62.36b)
“The inverted sample period is from December 14, 1988 to October 11, 1989, with 200 daily observations. The yield curve is defined as inverted when the ten-year Treasury yield is less than the two-year Treasury yield. ‘Rejections at the 1% significance level.
be statistically different. Are these differences economically significant? Table 3 provides the bid-offer spreads between LIBID and LIBOR from Data Stream. The spreads are consistently around 12.5 basis points and relatively more volatile in the longer maturities. There are three observations with a zero bid-offer spread, which could be due to data entry errors. Given the size of the spreads, the two sets of data do not seem to differ significantly from an economic
T.-s. Sun
et al.. Interestrate
swaps
87
Table 2 Summary statistics for differences observations in the period October
between DRI and Data Stream LIBOR data, for 605 daily 11. 1988 to April 15, 1991. The differences are measured in basis points. Maturity
3-y’
Statistic Max. Min. Mean Std. t-value T2(F6.s~~) “Rejections
50.00 - 43.15 - 0.11 5.64 ~ 0.47
I-yr 56.30 - 31.25 - 0.09 5.95 ~ 0.38
at the 1 “/o significance
2-yr 31.30 - 37.50 0.87 7.48 2.88” 26.57
3-yr 25.00 - 43.75 0.33 7.61 I .05 (4.39”)
4-yr 43.80 - 31.20 - 0.01 1.65 - 0.02
5-yr 25.00 - 24.95 ~ 0.81 8.01 - 2.47
level
Maturity
below-10
-1Oto-S
-5toO Difference
Oto5 (in basis points)
5tolO
above10
Fig. 4. The frequencies of differences between DRI and Data Stream LlBOR data, observations in the period October I I, 1988 to April 15, 1991.
standpoint. Also, the differences verified from fig. 5, where we plot rates. Can the rates from one data set plus white noise? We certainly
for 605 daily
vary randomly through time: this is easily the path of the differences for the two-year set be equal to the rates from the other data cannot rule out this possibility, considering
88
T.-s. Sun et al., Interest rate swaps Table 3
Summary statistics for bid-offer spreads daily observations in the period October
between Data Stream LlBlD and LIBOR data, for 605 II, 1988 to April 15, 1991. The spreads are measured in basis points. Maturity
Statistic
f-yr
I-yr
2-yr
3-yr
4-yr
5-yr
Max. Min. Mean Std.
18.70 0.00 12.44 0.95
18.75 6.25 12.49 0.57
25.00 12.50 12.52 0.51
50.00 0.00 12.64 1.97
50.00 12.50 12.58 1.61
50.00 6.25 12.50 1.65
1”
I 30
20
H
10
i. 6 B 5 g -10
vI
-
1 I
u II
-20
I
I
i
I
30
40 ( 10/11/88
I
I
05/29/89
I
I 01/14/w Time
I
I 09/01/90
Fig. 5. The differences between DRI and Data Stream data of the two-year LIBOR, observations in the period October I I, 1988 to April 15, 1991.
I
I 04/19/91
for 605 daily
the original sources. Data Stream’s LIBOR and LIBID data are taken from The Financial Times, which compiles the rates from five banks: National Westminister, Bank of Tokyo, Deutsche Bank, Bank of National de Paris, and Morgan Guaranty. On the other hand, DRI’s data are taken from Reuters, which compiles the rates from four banks: National Westminister, Bank of Tokyo,
T.-s. Sun et al., Interest rate swaps
89
Bankers Trust, and Barclays Bank. Our empirical results on the relationship between swap rates and par bond yields show that using DRI’s data or Data Stream’s data makes little difference, confirming that they are not economically significant from each other.
4. Empirical evidence We first examine the effect of the dealers’ credit spreads of swap quotations. Then we describe how in the interbank market, and compare the swap LIBID par bond yields. We also explore how well Treasury yields and the LIBOR par bond yields.
reputations on the bid-offer to construct par bond yields rates with the LIBOR and the swap offer rates track the
4.1. Impact of swap dealer’s credit rating on swap rates
Suppose that the credit quality of the counterparties is the same for different swap dealers, and that the swap contracts do not differ in other characteristics such as the up-front fee and collaterals. In section 2, we argue that the swap offer rates of AAA-rated dealers should be higher than those of A-rated dealers, and the swap bid rates of AAA-rated dealers should be lower than those of A-rated dealers. With these observations, we examine this issue in tables 4 and 5. The top panel of table 4 reports the summary statistics for AAA and A swap offer rates and associated bid-offer spreads. The bid-offer spreads for the AAA swap dealer are always 10 basis points, whereas the bid-offer spreads for the A dealer vary slightly around 4.75 basis points. The lower panel of table 4 presents the differences between AAA and A swap rates in three ways: (i) the AAA offer rates minus the A offer rates, (ii) the A bid rates minus the AAA bid rates, and (iii) the AAA mid-market rates minus the A mid-market rates. The A dealer’s swap rates are bracketed by the AAA dealer’s swap rates. That is, the AAA offer rates are significantly higher than the A offer rates, and the AAA bid rates are significantly lower than the A bid rates. The breakdown of the differences given in table 5 reinforces this result. Of 605 observations, 89 to 96% of the AAA offer rates are higher than the A offer rates, and 59 to 93% of the AAA bid rates are less than the A bid rates. Finally, table 4 indicates that results based on mid-points of swap quotations can be misleading for issues related to dealers’ credit risk. The mid-point swap rates for the AAA and A dealers are not significantly different for swaps with a life of four or more years. Although the AAA swap rates bracket the A swap rates, we lose much of the critical differences when using the mid-market rates. We should qualify our results by noting that there are other aspects of the swap on which we do not have any data. These aspects might depend on the credit standing of the client, although most swap dealers indicate that the swap quotations are the same irrespective of clients’ credit ratings. Dealers assess an
90
T.-s. Sun et al., Interrst rate swaps Table 4
Summary
statistics for swap offer rates, bid-ask daily observations in the period
spreads, dctober
and differences between swap rates for 605 11, 1988 to April 15, 1991.
Maturity _ Statistic
2-yr
4-yr
3-yr
5-yr
7-yr
lo-yr
9.140% 0.517%
9.251% 0.450%
9.316% 0.416%
1Obp
1Obp
1Obp
9.114% 0.518%
9.221% 0.455%
9.290% 0.42 I %
4.67bp 0.90bp
4.79bp 1.05bp
4.77bp 0.93bp
2.68bp 4.09bp 16.10b
2.62bp 4.74bp 13.5gb
2.54bp 4.12bp 15.17b
2.62bp 4.77bp 13.50b
AAA offer rates Mean Std.
8.881% 0.790%
9.004% 0.670%
9.082% 0.580%
AAA bid-offer Mean
1Obp
1Obp
spreads”
1Obp A offer rates
Mean Std.
8.837% 0.778%
8.955% 0.659%
Mean Std.
4.73bp 1.19bp
4.14bp 1.12bp
Mean Std. t-value
4.33bp 5.84bp 18.22b
9.052% 0.585%
A bid-offer
spreads
4.65bp 1.06bp
AAA offer rates minus A offer rates 4.96bp 3.63bp 33.57b
3.03bp 2.59bp 6.34bp 4.21bp 11.77b 15.13b 1497.66 (247.54b)
A bid rates minus AAA bid rates Mean Std. f-value
0.94bp 6.03bp 3.83b
0.31bp 3.91bp 1.94’
T2 (F,,,,,) AAA mid-market Mean Std. t-value TZ(F,,,,,)
1.69bp 5.91bp 7.05b
2.32bp 3.73bp 15.33h
2.3 1bp 2.75bp 6.34bp 4.21 bp 8.96b 16.06b 482.56 (79.76b) rates minus A mid-market
rates
0.36bp ~ 0.08bp 6.32bp 4.18bp 1.41 - 0.47 240.53 (39.76b)
0.07bp 4.07bp 0.42
O.OObp 4.73bp 0.00
“Bid-offer spreads are always 10 basis points for the AAA swap dealer. “Rejections at 1% significance level. “Rejection at 5% significance level.
up-front fee that depends on the maturity and the notional amount of the swap contract. This fee might vary with the client’s credit standing. Markingto-market and the posting of marketable collateral may be required of clients with poor credit quality. These provisions are integral parts of swap contracts, but we simply do not have access to such data to pursue a more detailed investigation. The net effect of such provisions is that the quoted swap offer rate underestimates the true cash flows to the swap dealer.
T.-s. Sun et al., Interest rate swaps
91
Table 5 Frequencies
_
(in percentage) of the spreads between AAA and A swap rates for 605 daily observations jn the period October 11, 1988 to April i5, 1991 Maturity
Basis points
3-yr
2-yr
4-yr
5-yr
7-yr
lo-yr
AAA offer rates over A offer rates Above 10 5 to 10 0 to 5 -5to0 -1oto -5 Below - 10
7.11% 34.21% 52.89% 4.79% 0.33% 0.66%
Above 10 5to 10 0 to 5 -5too -1oto -5 Below - 10
1.16% 6.45% 58.86% 26.61% 7.93% 0.99%
5.45% 45.29% 45.29% 3.47% 0.17% 0.33%
1.65% 21.49% 67.77% 8.10% 0.50% 0.50%
1.16% 11.90% 77.85% 8.10% 0.33% 0.66%
0.99% 12.89% 75.21% 9.59% 0.83% 0.50%
0.99% 6.94% 82.81% 9.09% 0.17% 0.00%
1.16% 10.08% 76.36% 10.74% 1.49 % 0.17%
0.00% 10.41% 82.31% 6.12% 0.83% 0.33%
A bid rates over AAA bid rates 0.66% 3.97% 54.05% 33.22% 6.78% 1.32%
0.99% 9.42% 72.07% 15.37% I .49 % 0.66%
0.99% 10.91% 78.02% 8.76% 0.83% 0.50%
In this context it is useful to note that a swap dealer tends to work with only an ‘approved list of clients’ who have been cleared by the dealer’s credit committee. For example, the AAA dealer requires that the average credit rating of counterparties must be AA or better, and the minimum acceptable rating is A. In this case, it seems reasonable to assume that the credit quality of counterparties is relatively better for the AAA dealer, which will counteract the AAA dealer’s ability to charge higher bid-offer spreads. Hence, the empirical finding that the AAA swap rates bracket the A swap rates lends stronger support to our hypothesis about the impact of dealers’ credit ratings on bid-offer spreads.
4.2. Par bond yields To construct par bond yields, we need to estimate the zeros (or pure discount functions) in the interbank market. To clarify matters, it is useful to describe briefly the Eurodollar time deposits market. Eurodollar time deposits are dollar deposits with a bank or bank branch outside the U.S. or with an international banking facility (IBF) located in the U.S.3 Deposit maturities range from overnight to ten years. They settle by add-on convention as opposed to the
3A clear description (1991, ch. 2).
of this market
is contained
in Burghardt,
Belton,
Lane, Lute, and McVey
92
T.-s.
Sun et al..
Interestrate swaps
discount convention in the Treasury-bill market. Interest rates for time deposits are quoted on the basis of money-market conventions. For deposits with maturities of one year or less, interest is paid at the maturity date. For deposits with maturities longer than one year, interest is paid annually. It is simple to calculate the par bond yield once we have the LIBOR zeroes for all half-year and yearly intervals. Nevertheless, two things must be considered in the derivation of LIBOR zeroes. First, we have the LIBOR data only for six months, one year, two years, three years, four years, and five years, and not for the intermediate maturities of 1.5, 2.5, 3.5, and 4.5 years. Second, the LIBOR deposits with maturities in excess of one year pay coupons, which are disbursed according to money-market conventions. These factors are taken into account in the estimation procedure described in the appendix. The estimated par bond yields are then used with the actual AAA and A swap offer rates in our empirical work. To check the robustness of our conclusions, we estimate the par bond curve using four procedures: (i) arithmetic interpolation of discount functions, (ii) geometric interpolation of discount functions, (iii) arithmetic interpolation of spot rates, and (iv) geometric interpolation of spot rates. Regardless of the procedure and data used, our findings are virtually identical. For the sake of brevity, we report only the results based on Data Stream data with arithmetic interpolation of discount functions.
4.3. Swap rate versus par bond yields As noted in section 1, to investigate the implications of swap pricing theory, we can either compare the par bond yield of the counterparty with the swap offer rate or the par bond yield of the swap dealer with the swap bid rate. On the swap offer side, the relevant benchmark is the par bond yield based on LIBOR. This follows from our assumption that the counterparty participates in the interbank market and must issue a par bond in that market as an alternative to paying the swap offer rate. Hence, the comparison of swap offer rates with the LIBOR par bond yields makes most sense. To make our study complete, in table 6 we present the comparisons of (a) swap offer rates with LIBOR par bond yields, (b) swap midpoints with the par bond yields estimated from the midpoints in the interbank market, and (c) swap bid rates with LIBID par bond yields. As shown in panel A, both the AAA and the A swap offer rates are significantly lower than the LIBOR par bond yields. The differences are on average from 7.8 to 12 basis points for the AAA swap offer rates and from 12.1 to 14.6 basis points for the A rates. Note that the bid-offer spreads are around 12.5 basis points for all maturities in the interbank market, 10 and 4.75 basis points for the AAA and the A swap rates. When swap midpoints are compared with the par bond yields estimated using the midpoints of the quotes from the interbank market, as in panel B of table 6, the differences are on average from 6.6 to 10.9
T.-s. Sun et al., Interesi rate swaps
93
Table 6 Summary
statistics for par bond yields” over swap rates, for 605 daily observations in the period October 11, 1988 to April 15, 1991. The spreads are measured in basis points. Maturity
Credit
rating
_
Statistic
2-yr Panel A: LIBOR
_
3-yr
4-yr
_
S-yr
par bond - swap offer
AAA
Mean Std. t-value T2(F+.6~,)
7.11 8.75 21.83b
10.37 8.44 8.25 8.23 25.23b 30.87b 1158.94 (288.30b)
12.00 8.75 33.70b
A
Mean Std. f-value T2 (F4.60,)
12.10 10.14 29.34b
13.40 13.40 9.90 8.49 38.81b 33.27b 1820.57 (452.88b)
14.58 9.60 37.35b
_
Panel B: Midpoint
par bond - swap midpoint 9.18 8.27 27.28b 940.43 (233.94”)
10.86 8.74 30.54b
9.54 9.89 23.71b 962.23 (239.36b) .._
10.78 9.57 27.68b
AAA
Mean Std. t-value T* (F4.601
A
Mean Std. f-value TZ (F,,,,,)
AAA
Mean Std. r-value T*(F,,,,,)
5.45 8.76 15.28b
6.01 8.19 18.02b
8.00 8.37 23.50b 740.88 (1 84.30b)
9.72 8.80 27.1Sb
A
Mean Std. r-value TZ (F,,,oi
4.51 10.25 10.80b
5.70 8.62 16.25b
5.69 9.97 14.01b 372.45 (92.65 b,
6.97 9.62 17.81”
6.61 8.75 18.56b
7.22 8.15 21.78b
8.30 10.17 20.06b
9.55 8.48 27.68b
1
Panel C: LIBID
1 Panel D: LIBID
AAA
Mean Std. t-value T2 (F4.60,)
A
Mean Std. f-value T* (Fuo,)
par bond - swap bid
par bond - swap offer
- 4.45 8.76 - 12.78b
- 4.00 8.19 - 1 1.99b
- 2.00 8.37 - 5.88b 261.09 (64.95b)
- 0.23 10.18 - 0.51b
0.96 8.51 2.78b
1.03 9.96 2.55” 60.18 (14.97b)
“The data are from Data Stream. The discount interpolated from the two adjacent yearly discount quoted two-year to five-year LIBOR rates. ‘Rejections at the 1% significance level.
J.F.E.- D
- 0.28 8.80 - 0.79 2.31 9.62 5.89b
function for LIBOR in mid-year is linearly functions, which can be calculated from the
94
T.-s. Sun et al., Interest rate swaps
basis points for the AAA swap midpoints and from 8.3 to 10.8 basis points for the A midpoints. The comparison of swap bid rates with the par bond yields estimated from LIBID quotes, shown in panel C, also indicates that the par bond yields are higher than the swap bid rates. The differences are on average from 5.5 to 9.7 basis points for the AAA swap bid rates and from 4.5 to 7 basis points for the A rates. As we noted earlier, this analysis assumes that the credit quality of the swap counterparties is identical or similar to that of participants in the interbank market. We are also interested in whether the comparison of swap offer rates and LIBID par bond yields any insight. In the absence of asynchronous observations and default risk, swap offer rates and par bond yields cannot differ by more than bid-offer spreads in the interbank market. This is a no-arbitrage requirement. To see why this must be so, we provide a simple arbitrage recipe: suppose that the swap offer rate is less than the corresponding LIBID par bond yield. The counterparty obliged to pay a fixed swap offer rate can borrow the notional amount in a floating load and deposit it in the interbank market. The fixed interest received from the interbank market should at a minimum be equal to the LIBID par bond yield. Hence, the floating proceeds from the swap should exactly cover the interest payment on the floating loan, while the fixed proceeds from the interbank market are more than the fixed swap offer rate. Thus swap pricing theory also implies that the offer rates can be less than the LIBID par bond yields when there is default risk. In other words, barring the problem caused by possible asynchronous quotations, observation of swap offer rates less than LIBID par bond yields is consistent with the presence of default risk in swaps. In panel D of table 6, we compare LIBID par bond yields with the swap offer rates. The swap offer rates for the A dealer are lower than the LIBID par bond yields for all swap maturities except the two-year, where the deviation is insignificantly different from zero. In contrast, the swap offer rates of the AAA dealer are higher than the LIBID par bond yields for all swap maturities except the five-year, where the deviations are not significantly different from zero. These results are based on averages. The proposition that swap offer rates should be below the LIBID par bond yields is based not on averages but on the principle of no arbitrage. To get a perspective on this issue, we report in table 7 how often swap offer rates differ from LIBID par bond yields. Of 605 observations, 28 to 5 1% of the AAA swap offer rates are lower than the LIBID par bond yields. Roughly 4 to 12% of the differences are more than 10 basis points, the bid-offer spreads of the AAA swap rates. The deviations are much more significant for the A offer rates, which are less than the LIBID par bond yields between 48 and 61% of the time. The comparison of swap offer rates and LIBID par bond yields, subject to the qualifications described earlier, indicates that swap rates reflect default risk. Since our tests are based on interbank LIBID data from London and swap quotes from the U.S., the results are potentially subject to the problem of asynchronous observations.
T.-s. Sun ef al., Interest rate swaps
95
Table I Frequencies
in percentage of swap offer rates minus LIBID par bond yields,” observations in the period October 11, 1988 to April 15, 1991.
for 605 daily
Maturity Basis points
2-yr
3-yr
4-yr
5-yr
AAA swap offered rates minus LIBID Below - 20 - 10to -20 oto -10 Subtotal
0.99% 4.46% 22.31% 27.71%
0.50% 3.80% 25.45% 29.75%
0.66% 6.78% 33.39% 40.83%
0.66% 11.24% 39.17% 51.07%
1.49% 13.55% 39.50% 54.55%
1.98% 19.83% 39.67% 61.49%
A swap offered rates minus LIBID below - 20 - 10 to - 20 oto -10 Subtotal
1.82% 9.75% 36.03% 47.60%
1.65% 11.57% 41.49% 54.71%
“The LIBID data are from Data Stream. The discount function for LIBID in mid-year interpolated from the two adjacent yearly discount functions, which can be calculated quoted two-year to five-year LIBID rates.
is linearly from the
The comparison of average swap offer rates and LIBOR par bond yields in panel A of table 6 conveys little information about how well the swap offer rates track LIBOR par bond yields through time. To shed light on this issue, in table 8 we examine the correlations of AAA swap offer rates with Treasury yields and LIBOR par bond yields. Although not reported here, Treasury yields, par bond yields, and swap rates are all highly correlated. The ‘level’ correlations, however, are misleading. While these rates and yields can be stationary in a long interval, they are probably approximated by integrated processes over a period of two and a half years. As in Nelson and Plosser (1982) correlations of the changes in rates and yields are more appropriate. Pane1 A of table 8 indicates that the daily changes in swap rates are tracked by the daily changes in Treasury yields very well, but not by the daily changes in LIBOR par bond yields. To examine whether asynchronous quotes might contribute to the low correlations between the changes in swap rates and in LIBOR par bond yields, we compute the correlations using weekly changes. As reported in panel B of table 8, the correlations are much higher at all maturities with the weekly data. To examine this issue, we plot in fig. 6 the daily movements of the two-year LIBOR of Data Stream and the two-year Treasury yield. The sporadic flat parts in the two-year LIBOR curve indicate that the quotes in the interbank market do not change as much as the quotes in the Treasury market. Since swap quotes are expressed as a spread to the benchmark Treasuries, they change more frequently than the interbank rates. We also note that the bid-offer
96
T.-s. Sun et al., Interest
rate swaps
Table 8 Correlations of changes in AAA swap offer rates with changes in Treasury yields and LIBOR par bond yields,” for 605 daily and 131 weekly observations in the period October 11, 1988 to April 15, 1991. ~.____ Maturity 2-yr
4-yr
3-yr
S-yr
7-yr
10-yr
0.98 0.35
0.98
0.99
0.98 0.64
0.97
0.98
Panel A: Daily data (N = 605) Treasury yields LIBOR par bond yields
0.91 0.44
0.97 0.33
0.93 0.40
Panel B: Weekly data (N = 131) Treasury yields LIBOR par bond yields
0.94 0.71
0.97 0.65
0.95 0.68
“The data from Data Stream. The discount function for LABOR in mid-year is linearly interpolated from the two adjacent yearly discount functions, which can be calculated from the quoted two-year to five-year LIBOR rates.
7.5 I 7 12yearTreasury 6.5 1o/t1/9a
I 05/29/59
01/14/90
09/01/90
I
04
Time Fig. 6. The two-year LIBOR observations
of Data Stream and in the period October
the two-year Treasury yield, for 605 daily 11, 1988 to April 15, 1991.
T.-s. Sun et al., Interest
rate
swaps
97
spreads in the interbank market are large, at around 12.5 basis points. In sharp contrast, the spreads in the Treasury market are around one to two basis points. The low to moderate correlations of changes in swap rates and LIBOR par bond yields also raise the possibility that the LIBOR data do not correspond to rates at which actual transactions occur. Differences in default risk and transactions costs can account for differences in rates. It seems unlikely that they can explain the low to moderate correlations, however, because default risk and transactions costs are unlikely to change daily or weekly. Without actual transactions data, we cannot answer the question, so we must interpret with caution the tracking of swap offer rates with par bond yields constructed from LIBOR.
5. Conclusions Using daily swap quotations, we provide an empirical investigation of the interest rate swap markets. We document that the spreads between swap rates and Treasury yields generally increase significantly with maturities, whereas the increase is much smaller when the Treasury yield curve is inverted. Explaining this pattern of swap premiums is an interesting topic for future work. We find that the bid-offer spreads of swap dealers are sensitive to their credit reputations. The swap bid and offer rates of an A-rated dealer are bracketed by the rates of an AAA-rated dealer. It is interesting to note that Merrill Lynch has formed a new subsidiary to engage in swap business with large clients. This separately capitalized, credit-enhanced subsidiary has been structured to get an AAA rating. Several other investment banks, including Lehman Brothers, Salomon Brothers, and Citicorp, are exploring the launch of such credit-enhanced subsidiaries. In the equity derivatives market, a self-funded, AAA-rated subsidiary has been formed by Goldman Sachs.4 Our paper sheds some preliminary light on some of the possible advantages of higher reputation in the interest rate swap market. We also present evidence that interbank par bond yields are generally larger than swap rates. When the credit reputation of the swap dealer is lower, the swap offer rates deviate more from LIBOR par bond yields, whereas the swap bid rates deviate less from LIBID par bond yields. Our analysis points to some significant problems in testing swap pricing theory. First, the par bonds yields of counterparties are difficult to estimate. This problem is compounded by the fact that counterparties differ in credit reputation. We approach this issue by estimating the par bond yields using the interbank data on LIBOR and LIBID. Our study also highlights the illiquidity of the interbank market, with wide bid-offer spreads and infrequent changes in quotes. Transactions data on swap rates and interbank rates are critical in %ee Derivatives
Week, October
19, 1992.
98
T.-s. Sun et al., Interest rate swaps
examining the implications of swap pricing theory. Finally, data on other aspects of swap contracts, such as up-front fees and collaterals, will enable us to better assess the implications of swap pricing theory.
Appendix:
Par bond yield estimation
For LIBOR deposits with maturities coupons), the zero function is
of one year or less (which do not pay
1
b(t, t) =
r=+,l
Actual days ’ 1 + Y(4 4’
year,
360
where b(t, 7) is the price at time t of a discount bond paying $1 at time t + z in the interbank market, and y(t, T) is the corresponding LIBOR rate. For LIBOR deposits with maturities longer than one year (which pay annual coupons), the zero function is solved recursively from the following formula: r-l
c
b(t, k).
y(t, z) - 365 360
1 + Y(t’;;;365]
= 1,
k=l
z = 2,3,4,
5 years .
The equation says that the sum of the present values of coupons and the face amount equal par on the settlement date. Notice that (actual days/360) and (365/360) are money-market coupon adjustments. Hence the yearly zero function is 1b (t, z) =
r-l 1
b(t, k).
y(t, z) - 365
k=l
l+
360
y(t, z) - 365
,
z = 2, 3,4, 5 years
360
The LIBOR mid-year discount functions are estimated by the geometric or arithmetic average of their corresponding two adjacent yearly discount functions. Finally, the r-year LIBOR par bond yield c is calculated as follows:
c=
1 - b(t, z) 2r 1
b(t, 0.5 k) ’
k=l
In our empirical investigation, money-market and the bond-yield
we incorporate the difference between the conventions. In a generic swap, where the
T.-s. Sun el al., Interest rate swaps
99
six-month LIBOR is exchanged for a fixed rate every six months, the fixed-rate payments are typically set according to the bond-yield convention, whereas the LIBOR payments are subject to the money-market convention. Clearly, this implies that we have to compare the swap rate with the adjusted LIBOR par bond yield, c( 182.5/180).
References Amihud, Yakov and Haim Mendelson, 1986, Asset pricing and the bid-ask spread, Journal of Financial Economics 17, 2233249. Anderson, Theodore W., 1984, Introduction to multivariate statistical analysis, 2nd ed. (Wiley, New York, NY). Bicksler, James and Andrew H. Chen, 1986, An economic analysis of interest rate swaps, Journal of Finance 41, 645-655. Burghardt, Galen, Terry Belton, Morton Lane, Geoffrey Lute, and Richard McVey, 1991, Eurodollar futures and options: Controlling money market risk (Probus, Chicago, IL). Cooper, Ian and Antonio S. Mello, 1991, The default risk of swaps, Journal of Finance 48,597-620. Cox, John C., Jonathan E. Ingersoll, Jr., and Stephen A. Ross, 1980, An analysis of variable rate loan contracts, Journal of Finance 35, 389403. Fama, Eugene F., 1984, Term premiums in bond returns, Journal of Financial Economics 13, 529-546. French, Kenneth, 1983, A comparison of futures and forward Prices, Journal of Financial Economics 12, 311-342. Hull, John, 1989, Assessing credit risk in a financial institution’s off-balance sheet commitments, Journal of Financial and Quantitative Analysis 24, 489-501. Nelson, Charles R. and Charles I. Plosser, 1982, Trends and random walks in macroeconomic time series: Some evidence and implications, Journal of Monetary Economics IO, 1399167. Ramaswamy, Krishna and Suresh M. Sundaresan, 1986, The valuation of floating-rate instruments: Theory and evidence, Journal of Financial Economics 17.251-272. Smith, Clifford W., Charles W. Smithson, and Lee Macdonald Wakeman, 1986, The evolving market for swaps, Midland Corporate Finance Journal 3, 20-32. Smith, Clifford W., Charles W. Smithson, and Lee Macdonald Wakeman, 1988, The market for interest rate swaps, Financial Management 17, 3444. Smith, Clifford W., Charles W. Smithson, and D.S. Wilford, 1990, Managing financial risk (Harper and Row, New York, NY). Sundaresan, Suresh M., 1991, Valuation of swaps, in: Sarkis J. Khoury, ed., Recent developments in international banking and finance. Vol. 5 (Elsevier Science Publishers. New York. NY ). Turnbull, Stuart M., 1987, Swaps: Zero sum game?, Financial Management 16, 15-21. Whittaker, J. Gregg, 1987, Interest rate swaps: Risk and regulation, Economic Review of the Federal Reserve Bank of Kansas City, March, 3-13.
of Financial
Interest
Economics
rate swaps
An empirical Tong-sheng Columhiu
Received
investigation
Sun, Suresh Sundaresan,
Unirrrsii~~,
November
34 (1993) 77-99. North-Holland
New
York. NY
and Ching Wang*
10027, USA
1991. final version
received
December
1992
Using quotations from two interest rate swap dealers with different credit ratings (AAA and A), we examine the effect of dealers’ credit reputations on swap quotations and bid-offer spreads. The AAA offer rates are significantly higher than the A offer rates, and the AAA bid rates are significantly lower than the A bid rates. We also document the relation between swap rates and par bond yields estimated from London interbank offered rate (LIBOR) and bid rate (LIBID) data. We identify some of the problems in testing the implications of swap pricing theory.
1. Introduction Interest rate swaps are agreements between two institutions in which each commits to make periodic payments to the other based on a predetermined amount of notional principal for a predetermined life, called the maturity. The periodic payments may either be fixed or may float with an agreed-upon floating index such as the six-month London interbank offered rate (LIBOR). The two institutions engaging in the swap transaction are called counterparties. In most cases, transactions are arranged and intermediated by swap dealers, which are typically investment or commercial banks. Swap dealers that act as intermediaries absorb the counterparties’ credit risks and receive the bid-offer spread. Dealers may also receive up-front fees for arranging swap transactions. The
Correspondencr to: Suresh York, NY 10027, USA.
Sundaresan,
Graduate
School
of Business, Columbia
University,
New
*We thank John Breit, William Broeksmit, and Brian Herring for providing us with the swap data and for their comments and suggestions. We have also benefited from the comments and suggestions of participants in the faculty workshops at Baruch College, the University ofToronto, the Universite Catholique de Louvain, and the Hebrew University. Special thanks go to John Hull and Alan White for their suggestions. Comments and suggestions made by Clifford Smith and an anonymous referee significantly improved the paper. 0304-405X/93/$06.00
:i
1993-E]
sevier Science Publishers
B.V. All rights
reserved
78
T.-s. Sun et al., Intrrest
rate swaps
credit reputations of swap dealers differ widely, with some dealers enjoying an AAA credit rating and others a rating of A or less. In interest rate swaps no principal amounts change hands. In so-called generic interest rate swaps one counterparty pays a fixed and the other a floating rate, with the payment frequency coinciding with the term of the floating index. To illustrate the market conventions, we provide in fig. 1 an example of an intermediated swap transaction. The dealer that makes fixed payments and receives floating payments is said to be on the bid side of the transaction. Thus, in fig. 1, the swap dealer has a bid rate of Treasury plus 15 basis points. If the swap has a term of five years, the five-year Treasury yield will be used as the benchmark. Conversely, the dealer that pays a floating rate and receives a fixed rate is said to be on the offer side of the transaction. In the example in fig. 1, the dealer has an offer rate of the five-year Treasury yield plus 25 basis points. Swap dealers charge bid-offer spreads for their services: they pay less on the bid side and receive more on the offer side. It is intuitive to expect that, all else being equal, the bid-offer spreads depend on the swap dealers’ credit reputations. The interest rate swaps market is now estimated at about $3 trillion in notional principal amount outstanding and thus represents one of the major segments of the capital market.’ The significance of this growth is perhaps best understood in the context that this market did not exist before 1980. The importance of the swap market in managing risk is now well recognized in the academic literature, as evidenced by the extensive treatment of swaps in a recent text by Smith, Smithson, and Wilford (1990).
Offer
Bid Side
Fig. I. A five-year
Intermediated
interest
Side
rate swap
Interest rate swaps are agreements between two institutions, called counterparties, in which one counterparty pays a fixed and the other a floating rate based on a predetermined notional principal for a predetermined maturity. The most common index for the floating rate is the six-month London interbank offered rate (LIBOR). Most swaps are arranged and intermediated by swap dealers. The dealer that pays a fixed rate and receives a floating rate is on the bid side of the transaction, and the dealer that pays a floating rate and receives a fixed rate is on the offer side. In this five-year swap, on the bid side the dealer receives the six-month LIBOR and pays a swap bid rate equal to the five-year Treasury yield plus I5 basis points. On the offer side the dealer pays the six-month LIBOR and receives a swap offer rate equal to the five-year Treasury yield plus 25 basis points.
‘InternatIonal
Swap Dealers’ Association
(ISDA) survey
1990.
T.-s. Sun ei al.. Inreresi rate .wups
79
To our knowledge, no empirical investigation of interest rate swaps has appeared in the literature. This is the principal motivation for our paper. Using daily interest rate swap quotations from a swap dealer with a credit rating of AAA and another dealer with a credit rating of A, we provide some stylized facts about the behavior of swap rates. We also describe how the swap rates and their biddoffer spreads are related to the swap dealers’ credit reputations. The bid-offer spreads of the A dealer are much smaller than those of the AAA dealer, and the A swap rates are typically bracketed by the AAA rates. Interestingly, the midpoints (or the average of bid and offer) of swap quotations for the two dealers are not statistically significantly different from each other for swaps with a life of four or more years. A second motivation for our paper is that swap pricing theory offers potentially testable implications. For example, under simplifying assumptions (no transactions costs or default), swap pricing theory implies that the arbitrage-free rate for a generic interest rate swap should equal the yield on a par bond with the same maturity. This proposition assumes away the risk of default. When there is a default risk, swap pricing theory implies that the par bond yield is greater than the swap rate. The par bond yields are therefore either greater than or equal to the swap rates. Since default risk and transactions costs are unlikely to change daily, the changes in swap rates should be closely related to (or tracked by) the changes in par bond yields. We investigate the presence of default risk in swaps. This investigation turns out to be considerably more difficult, because of data limitations and the nature of swap and interbank markets. The data limitations are easily understood in the context of fig. 1. To investigate the implications of default risk in swaps, we can compare either the par bond yield of counterparty Y (in fig. 1) with the swap offer rate or the par bond yield of the swap dealer with the swap bid rate. Data on the par bond yields of various counterparties, however, are simply unavailable. We are thus forced to pursue this inquiry indirectly by examining the relation between the swap rates and the estimated par bond yields in the interbank market. Specifically, the counterparties of the swap dealers are assumed to be represented by the participants in the interbank market whose LIBOR and LIBID (London interbank bid rate) are used to estimate the par bond yields. The swap and interbank markets also differ in liquidity. Swap quotes are typically keyed off respective benchmark Treasury yields. as illustrated in fig. 1. Since the Treasury benchmark issues are very actively traded, swap quotes change frequently. The interbank market, on the other hand, is relatively thin. The bid-offer spreads in the interbank market, as measured by the difference between LIBOR and LIBID, are around 12.5 basis points for all maturities and the quotes tend to change less frequently. The implications of these data problems for our study are addressed later in the paper. To mitigate this difficulty at least partially, we conduct our empirical work using LIBOR data from two sources, Data Research Incorporated (DRI)
80
T.-s. Sun et al.. Interest rate swaps
and Data Stream. We also obtain data on LIBID from Data Stream. Later in the paper we discuss in detail these data sets and the inferences one can draw from them. Our empirical evidence shows that the swap offer rates of both dealers are significantly less than the LIBOR par bond yields. The deviations of AAA swap offer rates from the par bond yields vary on average from about 8 to 12 basis points, and the deviations of A swap offer rates vary from about 12 to 15 basis points. The average deviations for each dealer are, for most part, within the bid-offer spread in the interbank market, which is about 12.5 basis points. Comparisons of (a) swap bid rates with LIBID par bond yields and (b) swap midpoints with the par bond yields estimated from the midpoints in the interbank market also show that the par bond yields on average are greater than swap rates, albeit the differences are less pronounced. A comparison of swap offer rates with LIBID par bond yields indicates a sharp contrast between AAA and A swap quotes. The AAA swap offer rates exceed LIBID par bond yields in three out of four swap maturities, whereas the A swap offer rates are below the LIBID par bond yields in three out of four swap maturities. We further examine the extent to which the par bond yields are able to track swap quotes by regressing the changes in the par bond yields with the changes in swap quotes. Regressions based on weekly changes perform much better than regressions based on daily changes. This points to the presence of asynchronicity in quotes. We view our results in this context as an attempt to highlight some regularities and alert researchers to potential problems in testing the implications of swap pricing theory. Clearly, it is desirable to use transactions data on swaps and actual par bond yields of counterparties to examine the implications of swap pricing theory. The paper is organized as follows. Section 2 briefly reviews the literature and swap pricing theory. In section 3 we provide summary information on swap rates of the two dealers, and discuss the LIBOR and LIBID data. Section 4 presents the empirical evidence. We first examine the effect of the dealers’ credit reputations on the bid-offer spreads of swap quotations. Then we compare the swap rates with the LIBOR and LIBID par bond yields. We also explore how well the Treasury yields and the LIBOR par bond yields track swap rates. Section 5 concludes and discusses the directions for future research in the light of our evidence.
2. Swap pricing theory Academic research in swap markets focuses on many papers explore the economic rationale for the of interest rate swap markets, principles of swap interest rates and credit risks on the structure and
three distinct issues. First, existence and the evolution pricing, and the impact of valuation of swaps. Papers
in this category include Bicksler and Chen (1986) Smith, Smithson, and Wakeman (1986, 1988) and Turnbull (1987). Second, a number of papers examine how swap contracts can be valued in an arbitrage-free setting. The groundwork for pricing swaps is laid in the valuation of floating-rate instruments by Cox, Ingersoll, and Ross (1980) and Ramaswamy and Sundaresan (1986). Interest rate swaps can be valued by finding the level of fixed payments that will have the same present value as the floating payments. Smith, Smithson, and Wakeman (1986) also suggest a valuation procedure. Papers by Hull (1989) Sundaresan (1991) and Cooper and Mello (199 1) provide approaches to pricing interest rate and currency swaps that are subject to either interest rate or default risk or both. Finally, a number of papers explore the regulatory framework for swaps and capital adequacy for swap market makers. Hull (1989) discusses the issue of capital determination for off-balance-sheet commitments using contingentclaims valuation principles, and Whittaker (1987) examines the regulatory aspects of swap markets. The issue of capital adequacy is addressed by Smith, Smithson, and Wilford (1990). For our empirical work, the key insight from swap pricing theory is the implication that, under certain assumptions to be discussed, the rate for a generic interest rate swap must equal the yield on a par bond issued by the counterparty that is making the fixed payments. This insight follows readily from the work of Smith, Smithson, and Wakeman (1986, 1988) and Sundaresan (1991). We establish the swap pricing proposition under the following assumptions: (A.l)
Reset index (A.2) There (A.3) There (A.4) There
dates precede the payment dates with a lag equal maturity. are no transactions costs, taxes, or other frictions. are no arbitrage opportunities. is no default risk.
to the floating
Generic interest rate swaps satisfy assumption (A.1). Assumption (A.2) implies perfect market conditions, and assumption (A.3) implies that the swaps are priced identically to a replicating portfolio that duplicates the cash flows of the swap. Assumption (A.4) which ignores default risk, is clearly restrictive: we examine whether the major pricing implication derived under this assumption is broadly consistent with the data on swap quotes. We also explore the directional bias introduced when this assumption is relaxed. Swap Pricing Proposition. Under ussumptions (A.I)-(A.4), the arbitrage-free swap rate on the settlement date should equal the yield on a par bond that makes 0 fixed payments on the sume dates as thejloating leg of the swap. The intuition generic interest
behind this result is easy to understand. Consider the five-year rate swap in fig. I between the swap dealer and counterparty Y.
Counterparty Y is long in the floating leg and short in the fixed leg. On the settlement date, the position of counterparty Y can be replicated as follows: issue at par a five-year fixed-rate note with a principal amount equal to the notional principal and invest the notional principal in the LIBOR maturing on the next reset date. The interest to be received on the next reset date equals the principal amount times LIBOR. The interest is withdrawn and the principal is rolled into the LIBOR that matures on the next reset date and so on. On the last date, the maturing notional amount is used to cover the balloon payment of the fixedrate note. This strategy replicates all the cash flows of the generic swap. Therefore the swap rate on the settlement date must be the yield (or the coupon) on the fixed-rate note issued at par. A fuller discussion of this result appears in Smith, Smithson, and Wakeman (1986). It is instructive to examine this proposition further. The proposition ignores default risk, but clearly, both the swap dealer and the counterparties carry such risk. The par bond issued by the counterparty is riskier than the swap, since it has a balloon payment at maturity that is also subject to default risk. In addition, with a par bond only the issuer (in fig. 1, counterparty Y) can default. In swaps, both parties to the transaction can default. As pointed out by Smith, Smithson, and Wakeman (1988), in swaps it is the joint probability that counterparty Y is in financial distress and the value of the swap is negative to counterparty Y that defines default. This risk is smaller than the default risk associated with a loan. Most swap structures also provide for netting arrangements whereby only the difference between the fixed rate and the floating rate is paid by the counterparties. In addition, swaps typically provide for ‘offsets’ whereby the solvent counterparty is relieved of its obligations if the other counterparty defaults. Hence the default risk is likely to have a smaller impact in swap transactions. The swap pricing proposition also assumes away transactions costs and bidoffer spreads. The swaps we study are intermediated by dealers who absorb the credit risk and guarantee performance. For this service, they typically charge a fee that is embodied in the swap bid-offer spreads. Swap markets tend to have narrower bidoffer spreads than the interbank market, however. As argued by Amihud and Mendelson (1986), higher transactions costs lead to higher quoted yields. Both these factors (transactions costs and default risk) introduce the same directional bias in the basic pricing proposition: the par bond yields of counterparties will be higher than the swap rate to reflect higher transactions costs and higher default risk. So, we regard the basic proposition that equates swap rates with par bond yields as the null hypothesis. The alternative hypothesis is that the par bond yields will exceed the swap rates when default risk is important.’ In addition, default risk has a significant impact on the bid-offer spreads of swap dealers with different credit ratings. Suppose that the credit quality of the ‘A
proof of the alternative
hypothesis
will be made available
to interested
readers
upon request.
T.-s. Sun
et ul., Interestrate swups
83
counterparties is the same for different swap dealers, and that the swap contracts do not differ in other characteristics such as the up-front fee and collateral. Then the swap bid rates of AAA-rated dealers should be lower than those of A-rated dealers. For a swap dealer, swap bid rates pertain to obligations to make fixed payments in the future. Other things being equal, the present value of fixed payments from a dealer with better credit is higher. Swap dealers with a credit rating of AAA are therefore able to pay lower fixed rates. On the other hand, the swap offer rates of AAA-rated dealers should be higher than those of A-rated dealers. For a swap dealer, swap offer rates pertain to obligations to make floating payments in the future. Payments from a dealer with better credit have a higher present value, which implies that AAA swap dealers can demand higher fixed rates. The requirement that the credit quality of the counterparties is the same is only a sufficient condition and is not necessary. As long as the credit quality of the counterparties of an AAA-rated dealer is not significantly better than that of the counterparties of an A-rated dealer, our arguments will hold. In our empirical investigation, we examine the relationship between the bid-offer spreads of the two swap dealers.
3. Data description and diagnostics We obtain swap quotations from AIG Financial Products and Merrill Lynch. The short-term debt (commercial paper) is rated PI+ for AIG and Pl for Merrill Lynch, whereas the long-term debt is rated AAA for AIG and A for Merrill Lynch. We refer to the AIG swap quotes as AAA quotes and the Merrill Lynch quotes as A quotes. Our data set contains 605 daily swap bid and offer rates from October 11, 1988 to April 15, 1991. These rates apply to interest rate swaps in which fixed U.S. dollar rates are exchanged for the six-month LIBOR. The swap rates are available for two-, three-, four-, five-, seven-, and ten-year maturities. AIG also provided us with the corresponding Treasury benchmark yields. To estimate the par bond yields, we obtain LIBOR quotes from DRI for the same sample period for the following maturities: six months, one year, two years, three years, four years, and five years. The data for intermediate maturities and extended maturities are unavailable. To assess the quality of LIBOR quotations from DRI, we also obtain LIBOR and LIBID data from Data Stream for the same sample period. In the rest of this section we first describe the swap rates and the Treasury yields. Then we discuss the LIBOR and LIBID data and examine the quality of the data sets. 3. I. Swaps und Treasuries Figs. 2 and 3 provide the surfaces of the Treasury yield curves and the AAA swap offer rates for the entire sample period. The sample period includes periods
T.-s. Sun
et cd.. Interestrute swaps
Maturity lo-year -year
Fig. 2. U.S. Treasury
yield curve.
MawritY
10-w
Fig. 3. AAA
swap offer rates.
T.-s. Sun et
al.. Intere.s~ rate
swaps
85
of upward-sloping Treasury yield curve as well as inverted yield curve. Of 605 daily yield curve observations, 405 pertain to an upward-sloping Treasury yield curve and the remaining 200 (from December 14, 1988 to October 11, 1989) correspond to an inverted Treasury yield curve. The yield curve is defined as inverted when the ten-year Treasury yield is less than the two-year yield. The close association between swap quotes and the respective Treasury benchmark yields is evident from these figures. The two figures also indicate that inversions in the Treasury yield curve are accompanied by inversions in the swap curve. The average Treasury yields for the overall sample increase from 8.24% for a maturitiy of two years to 8.5% for a maturity of ten years, implying a term premium of 26 basis points. The corresponding AAA swap offer rates rise from 8.88% to about 9.32%, with a term premium of 44 basis points. The top panel of table 1 provides the summary statistics for the spreads between AAA swap offer rates and Treasury yields. The spreads are significantly positive at all maturities irrespective of the shape of the Treasury yield curve. The lower panel describes the corresponding term premiums of swap spreads _ the differences between the spread concerned and the two-year spread. The results here are striking: the term premiums are significantly positive for the overall sample, whereas most of the premiums are not significantly different from zero when the yield curve is inverted. Following Fama (1984), we use Hotelling T2 statistics to test the hypothesis that all premiums are zero. [See Fama (1984) or Anderson (1984) for more details of the statistics.] The joint hypothesis that the term premiums at all maturities are the same is decisively rejected for both the whole sample period and the subperiod when the yield curve is inverted. The behavior of the A swap rates is similar (and therefore not reported here). The term premiums of swap spreads for the overall sample increase significantly with maturities; the increase is much smaller when the Treasury yield curve is inverted.
3.2. LIBOR
and LIBID
As pointed out earlier, one of our goals is to compare the swap quotes with the estimated par bond yields based on LIBOR and LIBID. In addition, we wish to examine the ability of estimated LIBOR par bond yields to track swap rates. We present these results later in the paper. To better assess these results, we analyze below the data set from the interbank market. In table 2 we present the summary statistics for the differences between DRI LIBOR and Data Stream LIBOR for all available maturities, and in fig. 4 the frequencies of differences. Though most of the differences are within 10 basis points, the average differences are significant in the two-year and five-year rates. The joint hypothesis that the differences at all maturities are zero is also rejected at the 1% significance level. Thus, the LIBOR data in these two series appear to
86
T.-s. Sun et al., Interest rate swaps
1
Table
Summary statistics for the spreads and the term premiums of spreads between swap offer rates quoted by an AAA-rated swap dealer and Treasury yields, for 605 daily observations in the period October 11, 1988 to April 15, 1991. The spreads and term premiums are measured in basis points. The term premiums of the spread is defined as the difference between the spread concerned and the corresponding two-year spread. Spread Maturity Statistic
2-yr
4-yr
3-yr Full sample
Mean Std. t-value
64.33 12.35 128.05b
Mean Std. t-value”
74.89 13.25 19.71b
70.84 7.65 221.74b Inverted
5-yr
____.
7-yr
10-yr
77.49 8.20 232.38”
81.60 9.10 220.27h
77.34 8.78 124.30b
79.87 8.91 126.53b
7-yr
I 0-yr
13.16 14.29 22.63b
17.27 16.44 25.81b
2.45 16.87 2.05b
4.98 17.85 3.94h
period (N = 605) 72.78 6.84 261.5Sb
76.54 8.32 226.16b
yield curve sample period” (IV = 200)
15.56 1.78 137.00b
74.15 7.51 139.22b
76.59 9.23 117.10b
Term premium
of spread
Maturity Statistic
3-yr Full sample
Mean Std. f-value T2 (Fs,w,~)
6.52 6.74 23.75b Inverted
Mean Std. f-value T* (F5.195)
4-yr
period (N = 605) 8.45 11.76 17.66b 1605.25
yield curve sample 0.67 1.29 1.30
5-yr
- 0.74 14.56 - 0.72 318.19
12.21 14.18 21.16b (318.92b) period” (N = 200) 1.70 16.77 1.43 (62.36b)
“The inverted sample period is from December 14, 1988 to October 11, 1989, with 200 daily observations. The yield curve is defined as inverted when the ten-year Treasury yield is less than the two-year Treasury yield. ‘Rejections at the 1% significance level.
be statistically different. Are these differences economically significant? Table 3 provides the bid-offer spreads between LIBID and LIBOR from Data Stream. The spreads are consistently around 12.5 basis points and relatively more volatile in the longer maturities. There are three observations with a zero bid-offer spread, which could be due to data entry errors. Given the size of the spreads, the two sets of data do not seem to differ significantly from an economic
T.-s. Sun
et al.. Interestrate
swaps
87
Table 2 Summary statistics for differences observations in the period October
between DRI and Data Stream LIBOR data, for 605 daily 11. 1988 to April 15, 1991. The differences are measured in basis points. Maturity
3-y’
Statistic Max. Min. Mean Std. t-value T2(F6.s~~) “Rejections
50.00 - 43.15 - 0.11 5.64 ~ 0.47
I-yr 56.30 - 31.25 - 0.09 5.95 ~ 0.38
at the 1 “/o significance
2-yr 31.30 - 37.50 0.87 7.48 2.88” 26.57
3-yr 25.00 - 43.75 0.33 7.61 I .05 (4.39”)
4-yr 43.80 - 31.20 - 0.01 1.65 - 0.02
5-yr 25.00 - 24.95 ~ 0.81 8.01 - 2.47
level
Maturity
below-10
-1Oto-S
-5toO Difference
Oto5 (in basis points)
5tolO
above10
Fig. 4. The frequencies of differences between DRI and Data Stream LlBOR data, observations in the period October I I, 1988 to April 15, 1991.
standpoint. Also, the differences verified from fig. 5, where we plot rates. Can the rates from one data set plus white noise? We certainly
for 605 daily
vary randomly through time: this is easily the path of the differences for the two-year set be equal to the rates from the other data cannot rule out this possibility, considering
88
T.-s. Sun et al., Interest rate swaps Table 3
Summary statistics for bid-offer spreads daily observations in the period October
between Data Stream LlBlD and LIBOR data, for 605 II, 1988 to April 15, 1991. The spreads are measured in basis points. Maturity
Statistic
f-yr
I-yr
2-yr
3-yr
4-yr
5-yr
Max. Min. Mean Std.
18.70 0.00 12.44 0.95
18.75 6.25 12.49 0.57
25.00 12.50 12.52 0.51
50.00 0.00 12.64 1.97
50.00 12.50 12.58 1.61
50.00 6.25 12.50 1.65
1”
I 30
20
H
10
i. 6 B 5 g -10
vI
-
1 I
u II
-20
I
I
i
I
30
40 ( 10/11/88
I
I
05/29/89
I
I 01/14/w Time
I
I 09/01/90
Fig. 5. The differences between DRI and Data Stream data of the two-year LIBOR, observations in the period October I I, 1988 to April 15, 1991.
I
I 04/19/91
for 605 daily
the original sources. Data Stream’s LIBOR and LIBID data are taken from The Financial Times, which compiles the rates from five banks: National Westminister, Bank of Tokyo, Deutsche Bank, Bank of National de Paris, and Morgan Guaranty. On the other hand, DRI’s data are taken from Reuters, which compiles the rates from four banks: National Westminister, Bank of Tokyo,
T.-s. Sun et al., Interest rate swaps
89
Bankers Trust, and Barclays Bank. Our empirical results on the relationship between swap rates and par bond yields show that using DRI’s data or Data Stream’s data makes little difference, confirming that they are not economically significant from each other.
4. Empirical evidence We first examine the effect of the dealers’ credit spreads of swap quotations. Then we describe how in the interbank market, and compare the swap LIBID par bond yields. We also explore how well Treasury yields and the LIBOR par bond yields.
reputations on the bid-offer to construct par bond yields rates with the LIBOR and the swap offer rates track the
4.1. Impact of swap dealer’s credit rating on swap rates
Suppose that the credit quality of the counterparties is the same for different swap dealers, and that the swap contracts do not differ in other characteristics such as the up-front fee and collaterals. In section 2, we argue that the swap offer rates of AAA-rated dealers should be higher than those of A-rated dealers, and the swap bid rates of AAA-rated dealers should be lower than those of A-rated dealers. With these observations, we examine this issue in tables 4 and 5. The top panel of table 4 reports the summary statistics for AAA and A swap offer rates and associated bid-offer spreads. The bid-offer spreads for the AAA swap dealer are always 10 basis points, whereas the bid-offer spreads for the A dealer vary slightly around 4.75 basis points. The lower panel of table 4 presents the differences between AAA and A swap rates in three ways: (i) the AAA offer rates minus the A offer rates, (ii) the A bid rates minus the AAA bid rates, and (iii) the AAA mid-market rates minus the A mid-market rates. The A dealer’s swap rates are bracketed by the AAA dealer’s swap rates. That is, the AAA offer rates are significantly higher than the A offer rates, and the AAA bid rates are significantly lower than the A bid rates. The breakdown of the differences given in table 5 reinforces this result. Of 605 observations, 89 to 96% of the AAA offer rates are higher than the A offer rates, and 59 to 93% of the AAA bid rates are less than the A bid rates. Finally, table 4 indicates that results based on mid-points of swap quotations can be misleading for issues related to dealers’ credit risk. The mid-point swap rates for the AAA and A dealers are not significantly different for swaps with a life of four or more years. Although the AAA swap rates bracket the A swap rates, we lose much of the critical differences when using the mid-market rates. We should qualify our results by noting that there are other aspects of the swap on which we do not have any data. These aspects might depend on the credit standing of the client, although most swap dealers indicate that the swap quotations are the same irrespective of clients’ credit ratings. Dealers assess an
90
T.-s. Sun et al., Interrst rate swaps Table 4
Summary
statistics for swap offer rates, bid-ask daily observations in the period
spreads, dctober
and differences between swap rates for 605 11, 1988 to April 15, 1991.
Maturity _ Statistic
2-yr
4-yr
3-yr
5-yr
7-yr
lo-yr
9.140% 0.517%
9.251% 0.450%
9.316% 0.416%
1Obp
1Obp
1Obp
9.114% 0.518%
9.221% 0.455%
9.290% 0.42 I %
4.67bp 0.90bp
4.79bp 1.05bp
4.77bp 0.93bp
2.68bp 4.09bp 16.10b
2.62bp 4.74bp 13.5gb
2.54bp 4.12bp 15.17b
2.62bp 4.77bp 13.50b
AAA offer rates Mean Std.
8.881% 0.790%
9.004% 0.670%
9.082% 0.580%
AAA bid-offer Mean
1Obp
1Obp
spreads”
1Obp A offer rates
Mean Std.
8.837% 0.778%
8.955% 0.659%
Mean Std.
4.73bp 1.19bp
4.14bp 1.12bp
Mean Std. t-value
4.33bp 5.84bp 18.22b
9.052% 0.585%
A bid-offer
spreads
4.65bp 1.06bp
AAA offer rates minus A offer rates 4.96bp 3.63bp 33.57b
3.03bp 2.59bp 6.34bp 4.21bp 11.77b 15.13b 1497.66 (247.54b)
A bid rates minus AAA bid rates Mean Std. f-value
0.94bp 6.03bp 3.83b
0.31bp 3.91bp 1.94’
T2 (F,,,,,) AAA mid-market Mean Std. t-value TZ(F,,,,,)
1.69bp 5.91bp 7.05b
2.32bp 3.73bp 15.33h
2.3 1bp 2.75bp 6.34bp 4.21 bp 8.96b 16.06b 482.56 (79.76b) rates minus A mid-market
rates
0.36bp ~ 0.08bp 6.32bp 4.18bp 1.41 - 0.47 240.53 (39.76b)
0.07bp 4.07bp 0.42
O.OObp 4.73bp 0.00
“Bid-offer spreads are always 10 basis points for the AAA swap dealer. “Rejections at 1% significance level. “Rejection at 5% significance level.
up-front fee that depends on the maturity and the notional amount of the swap contract. This fee might vary with the client’s credit standing. Markingto-market and the posting of marketable collateral may be required of clients with poor credit quality. These provisions are integral parts of swap contracts, but we simply do not have access to such data to pursue a more detailed investigation. The net effect of such provisions is that the quoted swap offer rate underestimates the true cash flows to the swap dealer.
T.-s. Sun et al., Interest rate swaps
91
Table 5 Frequencies
_
(in percentage) of the spreads between AAA and A swap rates for 605 daily observations jn the period October 11, 1988 to April i5, 1991 Maturity
Basis points
3-yr
2-yr
4-yr
5-yr
7-yr
lo-yr
AAA offer rates over A offer rates Above 10 5 to 10 0 to 5 -5to0 -1oto -5 Below - 10
7.11% 34.21% 52.89% 4.79% 0.33% 0.66%
Above 10 5to 10 0 to 5 -5too -1oto -5 Below - 10
1.16% 6.45% 58.86% 26.61% 7.93% 0.99%
5.45% 45.29% 45.29% 3.47% 0.17% 0.33%
1.65% 21.49% 67.77% 8.10% 0.50% 0.50%
1.16% 11.90% 77.85% 8.10% 0.33% 0.66%
0.99% 12.89% 75.21% 9.59% 0.83% 0.50%
0.99% 6.94% 82.81% 9.09% 0.17% 0.00%
1.16% 10.08% 76.36% 10.74% 1.49 % 0.17%
0.00% 10.41% 82.31% 6.12% 0.83% 0.33%
A bid rates over AAA bid rates 0.66% 3.97% 54.05% 33.22% 6.78% 1.32%
0.99% 9.42% 72.07% 15.37% I .49 % 0.66%
0.99% 10.91% 78.02% 8.76% 0.83% 0.50%
In this context it is useful to note that a swap dealer tends to work with only an ‘approved list of clients’ who have been cleared by the dealer’s credit committee. For example, the AAA dealer requires that the average credit rating of counterparties must be AA or better, and the minimum acceptable rating is A. In this case, it seems reasonable to assume that the credit quality of counterparties is relatively better for the AAA dealer, which will counteract the AAA dealer’s ability to charge higher bid-offer spreads. Hence, the empirical finding that the AAA swap rates bracket the A swap rates lends stronger support to our hypothesis about the impact of dealers’ credit ratings on bid-offer spreads.
4.2. Par bond yields To construct par bond yields, we need to estimate the zeros (or pure discount functions) in the interbank market. To clarify matters, it is useful to describe briefly the Eurodollar time deposits market. Eurodollar time deposits are dollar deposits with a bank or bank branch outside the U.S. or with an international banking facility (IBF) located in the U.S.3 Deposit maturities range from overnight to ten years. They settle by add-on convention as opposed to the
3A clear description (1991, ch. 2).
of this market
is contained
in Burghardt,
Belton,
Lane, Lute, and McVey
92
T.-s.
Sun et al..
Interestrate swaps
discount convention in the Treasury-bill market. Interest rates for time deposits are quoted on the basis of money-market conventions. For deposits with maturities of one year or less, interest is paid at the maturity date. For deposits with maturities longer than one year, interest is paid annually. It is simple to calculate the par bond yield once we have the LIBOR zeroes for all half-year and yearly intervals. Nevertheless, two things must be considered in the derivation of LIBOR zeroes. First, we have the LIBOR data only for six months, one year, two years, three years, four years, and five years, and not for the intermediate maturities of 1.5, 2.5, 3.5, and 4.5 years. Second, the LIBOR deposits with maturities in excess of one year pay coupons, which are disbursed according to money-market conventions. These factors are taken into account in the estimation procedure described in the appendix. The estimated par bond yields are then used with the actual AAA and A swap offer rates in our empirical work. To check the robustness of our conclusions, we estimate the par bond curve using four procedures: (i) arithmetic interpolation of discount functions, (ii) geometric interpolation of discount functions, (iii) arithmetic interpolation of spot rates, and (iv) geometric interpolation of spot rates. Regardless of the procedure and data used, our findings are virtually identical. For the sake of brevity, we report only the results based on Data Stream data with arithmetic interpolation of discount functions.
4.3. Swap rate versus par bond yields As noted in section 1, to investigate the implications of swap pricing theory, we can either compare the par bond yield of the counterparty with the swap offer rate or the par bond yield of the swap dealer with the swap bid rate. On the swap offer side, the relevant benchmark is the par bond yield based on LIBOR. This follows from our assumption that the counterparty participates in the interbank market and must issue a par bond in that market as an alternative to paying the swap offer rate. Hence, the comparison of swap offer rates with the LIBOR par bond yields makes most sense. To make our study complete, in table 6 we present the comparisons of (a) swap offer rates with LIBOR par bond yields, (b) swap midpoints with the par bond yields estimated from the midpoints in the interbank market, and (c) swap bid rates with LIBID par bond yields. As shown in panel A, both the AAA and the A swap offer rates are significantly lower than the LIBOR par bond yields. The differences are on average from 7.8 to 12 basis points for the AAA swap offer rates and from 12.1 to 14.6 basis points for the A rates. Note that the bid-offer spreads are around 12.5 basis points for all maturities in the interbank market, 10 and 4.75 basis points for the AAA and the A swap rates. When swap midpoints are compared with the par bond yields estimated using the midpoints of the quotes from the interbank market, as in panel B of table 6, the differences are on average from 6.6 to 10.9
T.-s. Sun et al., Interesi rate swaps
93
Table 6 Summary
statistics for par bond yields” over swap rates, for 605 daily observations in the period October 11, 1988 to April 15, 1991. The spreads are measured in basis points. Maturity
Credit
rating
_
Statistic
2-yr Panel A: LIBOR
_
3-yr
4-yr
_
S-yr
par bond - swap offer
AAA
Mean Std. t-value T2(F+.6~,)
7.11 8.75 21.83b
10.37 8.44 8.25 8.23 25.23b 30.87b 1158.94 (288.30b)
12.00 8.75 33.70b
A
Mean Std. f-value T2 (F4.60,)
12.10 10.14 29.34b
13.40 13.40 9.90 8.49 38.81b 33.27b 1820.57 (452.88b)
14.58 9.60 37.35b
_
Panel B: Midpoint
par bond - swap midpoint 9.18 8.27 27.28b 940.43 (233.94”)
10.86 8.74 30.54b
9.54 9.89 23.71b 962.23 (239.36b) .._
10.78 9.57 27.68b
AAA
Mean Std. t-value T* (F4.601
A
Mean Std. f-value TZ (F,,,,,)
AAA
Mean Std. r-value T*(F,,,,,)
5.45 8.76 15.28b
6.01 8.19 18.02b
8.00 8.37 23.50b 740.88 (1 84.30b)
9.72 8.80 27.1Sb
A
Mean Std. r-value TZ (F,,,oi
4.51 10.25 10.80b
5.70 8.62 16.25b
5.69 9.97 14.01b 372.45 (92.65 b,
6.97 9.62 17.81”
6.61 8.75 18.56b
7.22 8.15 21.78b
8.30 10.17 20.06b
9.55 8.48 27.68b
1
Panel C: LIBID
1 Panel D: LIBID
AAA
Mean Std. t-value T2 (F4.60,)
A
Mean Std. f-value T* (Fuo,)
par bond - swap bid
par bond - swap offer
- 4.45 8.76 - 12.78b
- 4.00 8.19 - 1 1.99b
- 2.00 8.37 - 5.88b 261.09 (64.95b)
- 0.23 10.18 - 0.51b
0.96 8.51 2.78b
1.03 9.96 2.55” 60.18 (14.97b)
“The data are from Data Stream. The discount interpolated from the two adjacent yearly discount quoted two-year to five-year LIBOR rates. ‘Rejections at the 1% significance level.
J.F.E.- D
- 0.28 8.80 - 0.79 2.31 9.62 5.89b
function for LIBOR in mid-year is linearly functions, which can be calculated from the
94
T.-s. Sun et al., Interest rate swaps
basis points for the AAA swap midpoints and from 8.3 to 10.8 basis points for the A midpoints. The comparison of swap bid rates with the par bond yields estimated from LIBID quotes, shown in panel C, also indicates that the par bond yields are higher than the swap bid rates. The differences are on average from 5.5 to 9.7 basis points for the AAA swap bid rates and from 4.5 to 7 basis points for the A rates. As we noted earlier, this analysis assumes that the credit quality of the swap counterparties is identical or similar to that of participants in the interbank market. We are also interested in whether the comparison of swap offer rates and LIBID par bond yields any insight. In the absence of asynchronous observations and default risk, swap offer rates and par bond yields cannot differ by more than bid-offer spreads in the interbank market. This is a no-arbitrage requirement. To see why this must be so, we provide a simple arbitrage recipe: suppose that the swap offer rate is less than the corresponding LIBID par bond yield. The counterparty obliged to pay a fixed swap offer rate can borrow the notional amount in a floating load and deposit it in the interbank market. The fixed interest received from the interbank market should at a minimum be equal to the LIBID par bond yield. Hence, the floating proceeds from the swap should exactly cover the interest payment on the floating loan, while the fixed proceeds from the interbank market are more than the fixed swap offer rate. Thus swap pricing theory also implies that the offer rates can be less than the LIBID par bond yields when there is default risk. In other words, barring the problem caused by possible asynchronous quotations, observation of swap offer rates less than LIBID par bond yields is consistent with the presence of default risk in swaps. In panel D of table 6, we compare LIBID par bond yields with the swap offer rates. The swap offer rates for the A dealer are lower than the LIBID par bond yields for all swap maturities except the two-year, where the deviation is insignificantly different from zero. In contrast, the swap offer rates of the AAA dealer are higher than the LIBID par bond yields for all swap maturities except the five-year, where the deviations are not significantly different from zero. These results are based on averages. The proposition that swap offer rates should be below the LIBID par bond yields is based not on averages but on the principle of no arbitrage. To get a perspective on this issue, we report in table 7 how often swap offer rates differ from LIBID par bond yields. Of 605 observations, 28 to 5 1% of the AAA swap offer rates are lower than the LIBID par bond yields. Roughly 4 to 12% of the differences are more than 10 basis points, the bid-offer spreads of the AAA swap rates. The deviations are much more significant for the A offer rates, which are less than the LIBID par bond yields between 48 and 61% of the time. The comparison of swap offer rates and LIBID par bond yields, subject to the qualifications described earlier, indicates that swap rates reflect default risk. Since our tests are based on interbank LIBID data from London and swap quotes from the U.S., the results are potentially subject to the problem of asynchronous observations.
T.-s. Sun ef al., Interest rate swaps
95
Table I Frequencies
in percentage of swap offer rates minus LIBID par bond yields,” observations in the period October 11, 1988 to April 15, 1991.
for 605 daily
Maturity Basis points
2-yr
3-yr
4-yr
5-yr
AAA swap offered rates minus LIBID Below - 20 - 10to -20 oto -10 Subtotal
0.99% 4.46% 22.31% 27.71%
0.50% 3.80% 25.45% 29.75%
0.66% 6.78% 33.39% 40.83%
0.66% 11.24% 39.17% 51.07%
1.49% 13.55% 39.50% 54.55%
1.98% 19.83% 39.67% 61.49%
A swap offered rates minus LIBID below - 20 - 10 to - 20 oto -10 Subtotal
1.82% 9.75% 36.03% 47.60%
1.65% 11.57% 41.49% 54.71%
“The LIBID data are from Data Stream. The discount function for LIBID in mid-year interpolated from the two adjacent yearly discount functions, which can be calculated quoted two-year to five-year LIBID rates.
is linearly from the
The comparison of average swap offer rates and LIBOR par bond yields in panel A of table 6 conveys little information about how well the swap offer rates track LIBOR par bond yields through time. To shed light on this issue, in table 8 we examine the correlations of AAA swap offer rates with Treasury yields and LIBOR par bond yields. Although not reported here, Treasury yields, par bond yields, and swap rates are all highly correlated. The ‘level’ correlations, however, are misleading. While these rates and yields can be stationary in a long interval, they are probably approximated by integrated processes over a period of two and a half years. As in Nelson and Plosser (1982) correlations of the changes in rates and yields are more appropriate. Pane1 A of table 8 indicates that the daily changes in swap rates are tracked by the daily changes in Treasury yields very well, but not by the daily changes in LIBOR par bond yields. To examine whether asynchronous quotes might contribute to the low correlations between the changes in swap rates and in LIBOR par bond yields, we compute the correlations using weekly changes. As reported in panel B of table 8, the correlations are much higher at all maturities with the weekly data. To examine this issue, we plot in fig. 6 the daily movements of the two-year LIBOR of Data Stream and the two-year Treasury yield. The sporadic flat parts in the two-year LIBOR curve indicate that the quotes in the interbank market do not change as much as the quotes in the Treasury market. Since swap quotes are expressed as a spread to the benchmark Treasuries, they change more frequently than the interbank rates. We also note that the bid-offer
96
T.-s. Sun et al., Interest
rate swaps
Table 8 Correlations of changes in AAA swap offer rates with changes in Treasury yields and LIBOR par bond yields,” for 605 daily and 131 weekly observations in the period October 11, 1988 to April 15, 1991. ~.____ Maturity 2-yr
4-yr
3-yr
S-yr
7-yr
10-yr
0.98 0.35
0.98
0.99
0.98 0.64
0.97
0.98
Panel A: Daily data (N = 605) Treasury yields LIBOR par bond yields
0.91 0.44
0.97 0.33
0.93 0.40
Panel B: Weekly data (N = 131) Treasury yields LIBOR par bond yields
0.94 0.71
0.97 0.65
0.95 0.68
“The data from Data Stream. The discount function for LABOR in mid-year is linearly interpolated from the two adjacent yearly discount functions, which can be calculated from the quoted two-year to five-year LIBOR rates.
7.5 I 7 12yearTreasury 6.5 1o/t1/9a
I 05/29/59
01/14/90
09/01/90
I
04
Time Fig. 6. The two-year LIBOR observations
of Data Stream and in the period October
the two-year Treasury yield, for 605 daily 11, 1988 to April 15, 1991.
T.-s. Sun et al., Interest
rate
swaps
97
spreads in the interbank market are large, at around 12.5 basis points. In sharp contrast, the spreads in the Treasury market are around one to two basis points. The low to moderate correlations of changes in swap rates and LIBOR par bond yields also raise the possibility that the LIBOR data do not correspond to rates at which actual transactions occur. Differences in default risk and transactions costs can account for differences in rates. It seems unlikely that they can explain the low to moderate correlations, however, because default risk and transactions costs are unlikely to change daily or weekly. Without actual transactions data, we cannot answer the question, so we must interpret with caution the tracking of swap offer rates with par bond yields constructed from LIBOR.
5. Conclusions Using daily swap quotations, we provide an empirical investigation of the interest rate swap markets. We document that the spreads between swap rates and Treasury yields generally increase significantly with maturities, whereas the increase is much smaller when the Treasury yield curve is inverted. Explaining this pattern of swap premiums is an interesting topic for future work. We find that the bid-offer spreads of swap dealers are sensitive to their credit reputations. The swap bid and offer rates of an A-rated dealer are bracketed by the rates of an AAA-rated dealer. It is interesting to note that Merrill Lynch has formed a new subsidiary to engage in swap business with large clients. This separately capitalized, credit-enhanced subsidiary has been structured to get an AAA rating. Several other investment banks, including Lehman Brothers, Salomon Brothers, and Citicorp, are exploring the launch of such credit-enhanced subsidiaries. In the equity derivatives market, a self-funded, AAA-rated subsidiary has been formed by Goldman Sachs.4 Our paper sheds some preliminary light on some of the possible advantages of higher reputation in the interest rate swap market. We also present evidence that interbank par bond yields are generally larger than swap rates. When the credit reputation of the swap dealer is lower, the swap offer rates deviate more from LIBOR par bond yields, whereas the swap bid rates deviate less from LIBID par bond yields. Our analysis points to some significant problems in testing swap pricing theory. First, the par bonds yields of counterparties are difficult to estimate. This problem is compounded by the fact that counterparties differ in credit reputation. We approach this issue by estimating the par bond yields using the interbank data on LIBOR and LIBID. Our study also highlights the illiquidity of the interbank market, with wide bid-offer spreads and infrequent changes in quotes. Transactions data on swap rates and interbank rates are critical in %ee Derivatives
Week, October
19, 1992.
98
T.-s. Sun et al., Interest rate swaps
examining the implications of swap pricing theory. Finally, data on other aspects of swap contracts, such as up-front fees and collaterals, will enable us to better assess the implications of swap pricing theory.
Appendix:
Par bond yield estimation
For LIBOR deposits with maturities coupons), the zero function is
of one year or less (which do not pay
1
b(t, t) =
r=+,l
Actual days ’ 1 + Y(4 4’
year,
360
where b(t, 7) is the price at time t of a discount bond paying $1 at time t + z in the interbank market, and y(t, T) is the corresponding LIBOR rate. For LIBOR deposits with maturities longer than one year (which pay annual coupons), the zero function is solved recursively from the following formula: r-l
c
b(t, k).
y(t, z) - 365 360
1 + Y(t’;;;365]
= 1,
k=l
z = 2,3,4,
5 years .
The equation says that the sum of the present values of coupons and the face amount equal par on the settlement date. Notice that (actual days/360) and (365/360) are money-market coupon adjustments. Hence the yearly zero function is 1b (t, z) =
r-l 1
b(t, k).
y(t, z) - 365
k=l
l+
360
y(t, z) - 365
,
z = 2, 3,4, 5 years
360
The LIBOR mid-year discount functions are estimated by the geometric or arithmetic average of their corresponding two adjacent yearly discount functions. Finally, the r-year LIBOR par bond yield c is calculated as follows:
c=
1 - b(t, z) 2r 1
b(t, 0.5 k) ’
k=l
In our empirical investigation, money-market and the bond-yield
we incorporate the difference between the conventions. In a generic swap, where the
T.-s. Sun el al., Interest rate swaps
99
six-month LIBOR is exchanged for a fixed rate every six months, the fixed-rate payments are typically set according to the bond-yield convention, whereas the LIBOR payments are subject to the money-market convention. Clearly, this implies that we have to compare the swap rate with the adjusted LIBOR par bond yield, c( 182.5/180).
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