The Search for Ralative Value in Bonds.

University Degree Business and Administrative studies

The Search for Relative Value in Bonds

Asset swaps are a seductive, but incomplete, approach.

May 2006

Abstract

Asset swap spreads are a widely used metric for identifying relative value in bonds. We document that this approach breaks down because different benchmark credit curves have different slopes and spread volatilities. If credit default swaps augment the relative value analysis, portfolios return to their original spread duration exposures. Apparently disparate portfolios are returned to an approximately equal footing.

The Search for Relative Value in Bonds

Introduction

Fixed-income investors have long sought a one-dimensional measure of bond attractiveness. With such a measure, security valuation is reduced to a single test. The highest scoring portfolio in today’s metric is likely to have the highest (risk adjusted) total rate of return over the coming periods. Yield to maturity is perhaps the most prominent example. Despite flaws that have been well known and well understood for more than 30 years, yield to maturity is still commonly employed in fixed income investors’ investment selections and their predictions for holding period returns [see, e.g., Homer and Leibowitz (1972) and Schaefer (1977)]. Potential errors from this approach can be large, especially when a mixture of coupon paying bonds and zero-coupon bonds is under consideration because the alternatives ‘roll down’ different yield curves. Bonds with embedded options realize holding period returns equal to their yields (either to maturity or to first call) only by numerical accident.

The search for single measure of bond attractiveness continues unabated today. One tool that has gained broad currency recently is to asset swap every bond in the portfolio – or at least every bond that can be swapped – and determine which portfolio maximizes the spread over a reference curve, typically Libor. The portfolio that swaps out best is deemed to be optimal.

The mechanics of an asset swap are straightforward. For simplicity, assume that an investor buys a bond that is a standard coupon paying issue that returns the principal at maturity. Assume further the bond sells at or near par such that the coupon rate should be near its yield to maturity. The investor simultaneously enters a pay-fixed swap with a tenor equal to the bond’s remaining term to maturity. The reference rate for the floating rate cashflows is 6-month Libor. On each coupon date, the investor receives a coupon, pays some portion of that coupon to the receive-fixed counterparty and receives the floating rate cashflow from same. The remainder of the bond’s coupon payment represents the expected return pick-up over 6-month Libor on average. Subsequent changes in the bond’s market value in response to changes in yields are offset by nearly equal changes in market value of the pay-fixed swap position. For example, a bond with a 6% coupon-rate and 6% yield when pay-fixed swap rates are 5% for the same term to maturity ‘swaps out’ at 100bp over Libor. This number (100 basis points over 6-monthLibor) is the asset swap spread and is used as the measure of relative value regardless of whether the cashflows are actually swapped.

If portfolio managers followed this rule literally and their security selection were otherwise unconstrained, they would be induced to buy bonds with the highest credit risk and longest maturity. Clearly, beneficiaries and plan sponsors impose constraints to avoid such an outcome.

The purpose of this paper is to show that maximizing the asset swap spread is a decision rule nearly certain to fail.

How do fixed-income portfolio managers add value?

The performance of an actively managed fixed-income portfolio is measured against a designated benchmark (e.g., an index or liability structure). Portfolio managers employ four basic strategies to add value relative to the benchmark. First, bond portfolio managers may seek to outperform by extending duration before a rally and shortening duration before a sell off. Unfortunately, nearly no manager has shown a consistent ability to get this right. Consequently, plan sponsors and other supervisors typically impose fairly tight duration targets on portfolio managers.

A second way to outperform is to put on steepening trades before the yield curve steepens and flattening trades before the yield curve flattens. Barbells and bullets are among the most commonly used vehicles. Specifically, a flattening yield curve tends to favor barbells while a steepening yield curve tends to favor bullets. Most portfolio managers have more latitude to express shaping views than directional views, but they are still constrained and, even then, they may not utilize all the leeway that they have been afforded.

Next, managers employ convexity and volatility trades to outperform benchmarks. When there is a mismatch between a manager’s view on volatility and implied volatility of bonds with embedded options, buying or selling convexity before realized volatility increases or decreases can enhance return.

Alternatively, instead of having realized volatility differing from implied vol, market participants may change their opinions about future volatility and, thereby, change implied vol (or pricing vol), which will enhance returns. The convexity and volatility trades can be through bullets and barbells, through bonds with embedded options, or through the interest rate derivatives markets.

Finally (and most frequently) portfolio managers attempt to outperform benchmarks through security selection. They attempt to overweight cheap issues and underweight rich issues to enhance total rate of return relative to their benchmark.

Security selection to enhance performance has lead to the search for effective ...

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Security selection to enhance performance has lead to the search for effective relative value tools in bond markets. As noted, one widely used metric for relative valuation is an asset swap. An asset swap transforms the cash flows of a fixed rate bond into a synthetic floating rate instrument. To convert the cash flows of fixed-rate bonds, the interest rate swap is constructed to make fixed-rate payments match the timing of the fixed-rate bond’s cash flows.

The swap’s floating rate cash flows received are determined by a reference rate (almost always LIBOR) plus a spread S, the asset swap spread. If a fixed-income investor is considering five fixed-rate bonds that differ in maturity and risk for inclusion in his or her portfolio and wants to assess their relative value, he or she would simply find the highest swap spreads (S), which represent the best relative value.

In practice, however, asset swaps are typically employed as a relative value detector in the following manner. After choosing portfolio duration (and perhaps key rate durations to control shaping risk) and after choosing a credit mix (or perhaps an average credit rating), find the constrained portfolio that swaps out best. This portfolio presumably represents the best relative value for a given duration target and credit target – with or without distributional constraints on durations and credit ratings. Unfortunately, this approach increases risk as well as increasing expected returns. We will demonstrate that utilizing asset swaps as a measure of relative value in this manner masks the attending increase in risk.

Determining the Asset Swap Spread

Before proceeding to the core of our analysis, we illustrate how an asset swap spread is calculated with a simple illustration. Consider a corporate bond issued by Ford that matures on June 16, 2008. The bond pays coupon interest semiannually at an annual rate of 6.625%. Assume the position with a par value of $1 million. Further assume, quite contrary to the facts, that this bond sells for $100 for settlement on June 16, 2006. The asset swap spread calculation is presented in Figures 1 and 2 using two Bloomberg screens created using the function ASW. As can be seen on the right hand side of the screen, the asset swap spread is 179.8 basis points. The actual asset swap spread in January 2006 was nearly 400bp. We chose to evaluate the asset swap on a coupon payment date to abstract from some of the details of swaps.

The asset swap spread is determined using the following procedure. First, assume that a $1 million par value position of the Ford coupon bond is valued at a price of 100 for settlement on June 16, 2006. The cash inferred at settlement is the flat price of $1,000,000 plus no accrued interest such that the full price is $1,000,000.00. This information is located in the bottom panel of Figure 2. Second, assume that a long position in a swap is established with a notional principal of $1,000,000. This information is also located in the bottom panel of Figure 2. Third, determine the net cash difference at settlement. This amount is simply the difference between the bond’s full price and the swap’s principal amount plus accrued interest. By construction, this amount is zero in our illustration. Fourth, determine the spread over the reference rate (i.e., LIBOR) required to equate the net present value of the swap’s floating-rate payments and the fixed-rate payments (i.e., the bond’s cash flows). In our illustration, using a swap spread of 179.8 basis points, the sum of the present values of the difference between the swap’s floating rate payments (plus the principal at maturity) and the bond’s cash flows to maturity is zero.

Our illustration is the special case for a bond selling at par and the accrued interest on both the bond and the swap are equal to zero. The asset swap spread makes the present value of a par swap’s floating payments equal the bond’s payments to maturity. This is true because the net cash at settlement is equal to zero.

The term structure of credit spreads and credit spread volatility

Term structures of credit spreads are steeper for lower rated credits than for higher rated credits [see, e.g., Helwege and Turner (1999)]. Table 1 displays credit spreads by credit rating and by tenor for 1991-2005. For the credit ratings of BB and B, yield data are only available for the years 1992-2005. The pattern is generally as we would expect with lower rated bonds trading at wider spreads and longer tenors within credit rating trading at wider spreads.

Table 1

Average credit spread of industrial bonds to equal tenor Treasuries, by credit rating, 1991-2005, (bp).

Source: Bloomberg

Tables 2 and 3 display the slopes of the credit curve for 2s-10s and 2s-30s respectively. The slopes are from a linear regression of the annual credit spreads on with term to maturity or duration. The beta coefficient is the increase in credit spread to same maturity Treasuries for each year of maturity/duration extension. The important result is that the credit curve slopes are generally increasing as credit quality declines.

Table 2

Slope of average credit spread of industrial bonds to equal tenor Treasuries from 2s to 10s, by credit rating 1991-2005 (bp/year).

Source: Bloomberg

Table 3

Slope of average credit spread of industrial bonds to equal tenor Treasuries from 2s to 30s, by credit rating 1991-2005 (bp/year).

Source: Bloomberg

Steeper credit curves for lower rated credits drive portfolio mix when the swaps criterion is used to measure relative value. Consider why this is so. The reason that the slope of the credit curves matters is that if a portfolio is constrained to hold, say 2s and 10s in equal amounts and AA and BBB in equal amounts, the swap criterion is virtually certain to put all of the BBB in 10s and all of the AA in 2s. Using the duration and credit mix measures of risk, this is exactly equivalent to putting all of the AA in 10s and BBB in 2s. They are not equivalent portfolios.

Table 4

Standard deviation of average credit of industrial bonds to equal tenor Treasuries, by credit rating, 1991-2005 (bp)

Source: Bloomberg

Table 4 shows spread standard deviations by credit quality and by maturity. For investment grade bonds through 10 years maturity, which represent a large majority of the corporate market, spreads become more volatile as maturities (and durations) extend and as credit quality declines.

We have seen that lower credit quality bonds have steeper term structures. They also have higher spread volatilities. The upshot of Table 1 through Table 4 is that the ‘optimal’ portfolios that result from the swap criterion will have the highest VaRs. An investment criterion that encourages an investor, who starts with a maturity ladder and a matching credit ladder, to move some money into the high duration/high yield volatility instruments causes him or her to increase VaR. This increase in risk is ignored by the current implementation of the swaps criterion.

The swap criterion is typically applied only to bullet bonds, i.e. bonds without embedded options. For MBSs, CMOs and callable/puttable bonds, investors use option-adjusted spread (OAS) analysis with the Libor curve as the curve to which spreads are measured. OAS analysis tries to separate the pricing spread impacts of embedded options from the pricing spread impacts of credit and liquidity differentials. These results are comparable to the swapped bullets only to the extent that one believes the stochastic process driving Libor and the prepayment/call/put rules employed. This is damning with faint praise. The implication is that the swap criterion is useful only for a subset of the portfolio.

The swap criterion can be used to optimize the holdings of only a subset of a fixed income portfolio, once duration and credit targets are chosen. The bonds that can be analyzed this way are corporate debt without embedded options. Because lower credits swap out better at longer maturities, the resulting portfolio will almost certainly be one that maximizes spread-duration-dollars. But, because longer dated/lower credit spreads are noisier, the portfolio’s VaR goes up. Investors have deluded themselves about finding increased value at constant risk. In the next section we demonstrate why this is so clearly the case.

Credit Swaps

Duffie [1999] provides a thorough analysis of credit swaps valuation, with variations. His fundamental, arbitrage-driven, result for the baseline case of the swap expiration matching the bond maturity is that the credit swap annuity that a hedger must pay is the credit spread of the instrument being hedged. If the swap expiration is shorter than the bond’s maturity, the credit spread for a shorter maturity bond is the appropriate swap spread. Of course, it is possible that no bond of that maturity exists, making it necessary to estimate the relevant credit spread, but that is a mere detail.

The most important variant of the base case is the instance when the bond to be hedged, which is the bond that the swaps writer would short, trades ‘special’ in the repo market. Traders often use the repo market to obtain specific securities to cover short positions. If a security is in short supply relative to demand, the repo rate on a specific security used as collateral in a repo transaction will be below the general (i.e., generic) collateral repo rate. When a particular security’s repo rate falls markedly, that security is said to be “on special.” Investors who own these securities are able to lend them out as collateral and borrow funds at attractive rates. Accordingly, the repo advantage is the difference between the general collateral rate and the special repo rate. In this case, the credit swap spread would be the sum of the bond’s credit spread and its repo advantage.

Additional variants that can influence swap spreads or all-in costs include transactions costs, the treatment of accrued swap spreads when a credit event occurs, accrued interest on a risk-free bond in the synthetic position, floaters trading away from par and fixed rate bonds standing in for floaters. All of these are nuances compared with the two main drivers – credit spreads and special repo rates.

Let us consider a credit swap without special repo rates, in the context of evaluating relative value. In the previous section, we examined an example of moving money from 2-year BBB to 10-year BBB and from 10-year AA to 2-year AA. Doing so creates a portfolio that swaps out better than the original maturity and credit ladder. We contended that risk is increased in a manner that is ignored. Here, we can demonstrate not only that the risk exists, but that it is traded.

Table 5 presents the spreads to Treasuries for Libor, AA rated bonds, and BB rated bonds for maturities of 6-month, 2-years and 10years. Table 6 presents the spread to Libor for the same bonds and maturities. We utilize these spreads in our demonstration that credit default swaps will unmask the risk increase encouraged by following the asset swaps criterion. Consider first the double-laddered portfolio which allocates half the portfolio to each maturity bucket and half the portfolio to each credit risk bucket. This portfolio trades at 35 basis points above 6-month Libor. That value comes from multiplying the portfolio share (0.25) times each of the swap spreads over 6-month Libor in Table 6 (= 0.25*10bp + 0.25*30bp + 0.25*30bp +0.25*70bp). Alternatively, the constrained portfolio that swaps out the best allocates half the portfolio to 2-year AAs and the balance in 10-year BBBs. This portfolio trades at 40 basis points above 6-month Libor (= 0.5*10bp + 0.5*70bp, in Table 6).

Table 5 Hypothetical Spreads (in basis points) to

Treasuries

Table 6 Hypothetical Spreads (in basis points)

to 6-month Libor

Now we introduce credit default swaps into the mix. Table 7 presents the premiums (in basis points) for credit default swaps for the AAs and BBBs for all three maturities. Suppose the investor implements the following transactions: buy a credit default swap on half of the 2-year AA position, write a credit default swap on an equal amount of 2-year BBBs, write a credit default swap on 10-year AAs equal to half of the 10-year BBB position and buy a credit default swap on half of the 10-year BBB position. The net impact of these transactions returns the maturity distribution of the credit risks to the initial double-laddered portfolio. This portfolio trades at 35 basis points above 6-month Libor (= 0.5 *10bp + 0.5*70bp – 0.25 * 0bp + 0.25* 20bp + 0.25*0bp – 0.25*40bp). Precisely all of the yield pickup (spread pickup) disappears. The portfolio possesses its initial risk position and its initial total spread. The evaluative benefit of comparing portfolios on an asset swapped basis disappears, too.

Table 7 Hypothetical Credit Default Swap

Premiums (in basis points)

Now, suppose that one or both of the underlying issues is trading at special repo rates. In this case, the asset swapping approach can identify relative value – it identifies special repo rates. But, those rates, in most instances, could be observed directly. In addition, unless the investor takes advantage of the special repo, the excess returns are purely hypothetical. No extra money will be collected over the holding period.

Consider the implications of having each of the components of the evaluation methodology trade. Indeed, it is possible to build an “optimal” portfolio synthetically. Instead of buying the portfolio of corporate bonds that swaps out best, investors could buy the synthetic. The portfolio would include the following components: (1) a long position in a risk-free floater; (2) a collection of pay floating/receive fixed swaps to match the desired maturity structure of the portfolio (e.g., ladder, barbell, etc.); and (3) writing credit default swaps with the highest premium intake subject to maximum exposure constraints. Any investor reluctant to execute the synthetic, especially the third component, should be equally reluctant of constructing a corporate bond portfolio using asset swap spreads because they are equivalent portfolios.

How is this approach useful?

If swapping every bond opens portfolio managers to the risk of increasing VaR in unrecognized ways, does that mean that the measure is without merit? Absolutely not. Suppose the portfolio manager wants to increase exposure to BBB bonds and two bonds, in particular, swap out wider than the rest of the universe. Because so many portfolio managers have observed that bond downgrades are ‘perfect trailing indicators,’ one possibility is that these two bonds are trading at wide spreads because they are about to be downgraded. Another possibility is that some investor has dumped supply and the spreads are likely to tighten back to average levels. Asset swap results will not tell you which of these cases is more likely. That will require additional analysis by skilled credit analysts. Still, the asset swap information can help set the research agenda; it can identify those cases most likely to become outperformers.

Alternatives

It is not enough to criticize an approach to portfolio management. One must discuss alternatives that are likely to be superior. Here, we consider two alternatives to choosing bonds based on asset swaps.

Choose an index. Once a plan sponsor or beneficiary chooses an index for a portfolio manager to match or beat, he or she has made a decision about risks in multiple dimensions. If one choose the Lehman Aggregate Index, the array of credits (and their spread durations), exposure to negative convexity through embedded optionality, aggregate duration, aggregate convexity and aggregate vega have all been chosen. To be sure, the plan sponsor might have preferred an index that had lower exposure to optionality, but with more exposure to credit. A large number of off-the-shelf indexes or a custom index, for that matter, allows quasi-independent choice of the risk exposures. If one asks the portfolio manager to add value relative to the index, it is paramount to ensure that the deviations from index risk are constrained or one could easily end up with the same portfolio as the asset swapping analyst would recommend – and the same unrecorded risks.
In many instances, as when the assets are chosen to fund a specific set of liabilities, portfolio managers’ choice of risk parameters comes pre-determined. Assets should match the duration, convexity, vega, spread duration, basis risk, etc. of the liabilities. Deviations in an attempt to minimize funding costs must, once again, be constrained.

Either of these alternatives allows portfolio managers to make better choices than simply maximizing the asset swap spread assuming all assets and liabilities are swapped to floating.

Conclusion

We examined a widely used approach to identifying relative value in bonds, utilizing asset swap spreads Comparing asset swap spreads has considerable appeal because it reduces the complicated question of relative value to a single dimension answer. The approach is misleading because it coaxes portfolio managers to increase spread duration risk in ways that are not readily apparent. The consideration of credit default swaps confirms this intuition. If the asset swaps criterion is augmented with credit default swaps, as well as interest rate swaps, then bond portfolios return to being equally attractive. Asset swap spreads are nevertheless useful for identifying bonds that are trading ‘special’ in repo markets and for setting a research agenda on specific credits trading away from their mean rating spread.

Bibliography

Duffie, Darrell. “Credit Swap Valuation.” Financial Analysts Journal, January/February 1999, pp. 73-87.

Helwege, Jean and Christopher M. Turner. “The Slope of the Credit Yield Curve for Speculative-Grade Issuers.” Journal of Finance, Vol. 54, No.5, October 1999, pp. 1869-1884.

Homer, Sidney and Martin Leibowitz. Inside the Yield Book, 1972, Prentice-Hall, Englewood Cliffs, NJ.

Schaefer, Stephen M. “The Problem with Redemption Yield.” Financial Analysts Journal, July/August 1977, pp. 59-67.

Figure 1

Figure 2