Nondefault Components of Investment-Grade Bond Spreads

Nondefault components of investment-grade bond spreads

James H Dignan

5,179 words

1 May 2003

Financial Analysts Journal

93-102,16

Volume 59, Issue 3; ISSN: 0015-198X

English

Copyright (c) 2003 ProQuest Information and Learning. All rights reserved. Copyright Association for Investment Management and Research May/Jun 2003

Traditionally, attempts at decomposing the spread between risk-free debt and corporate debt has focused exclusively on default risk. This focus continues despite the fact that the data indicate that the required spreads for higher-rated corporate bonds are normally far smaller than the spreads available in the market. This article challenges the traditional notion of an "excess spread" and, instead, attributes the additional spread to non-default-related factors, such as liquidity and spread volatility. The costs associated with both liquidity and spread volatility are examined, and a framework is provided for the investor to calculate adequate compensation for such costs.

Much has been written on the need to compensate corporate bond investors for default risk; much less has been written on the need to compensate these investors for other risks, such as illiquidity and spread volatility. This lack of attention is not surprising because default risk is the most obvious difference between risk-free U.S. Treasury debt and risky corporate debt. But although this difference may be the most obvious for investors in investment-grade bonds, it may not be the most important. I illustrate the costs associated with spread volatility and illiquidity and provide a framework for the investor to calculate adequate compensation for such costs.

Overview

Moody's Investors Service provides a default-probability matrix that contains useful insights into how much nominal yield compensation investors should require for default risk. Table 1 shows the required incremental yield (under a variety of assumptions as to holding periods and initial ratings) that Moody's transitional matrix requires.1 Table 2 shows the nominal yield spreads for the Lehman Brothers indexes at the end of February 2003.

Many people may object to looking simply at Moody's transitional matrix for default-driven yield premiums because of this approach's backward-looking nature. Critics may argue that the future now is considerably riskier than the past for issuers of corporate debt for a number of reasons and that, therefore, yield spreads should look wide on a historical basis. Others may disagree with this argument because the rating agencies take into account macroeconomic conditions when rating corporate securities and, in general, have done a fine job assessing default risk over long periods of time.

Without siding with either party in that debate, I suggest that the magnitude that separates even backward-looking yield requirements from actual spreads leaves most investors seriously questioning that default risk alone can explain yield premiums. In fact, Agrawal, Elton, Gruber, and Mann (2001) argued that differences in default rates cannot explain the differences in spreads between bonds of various rating classes. They found that, even with historically extreme default rates, required premiums, because of expected losses, are too small to account for nominal spreads.

Therefore, some may argue that the market is currently "irrational" and that "huge" opportunities to earn excess returns are available for those smarter (and braver, of course) than the market. Irrationality in the market is one possible explanation, but many market professionals are skeptical that gross market inefficiency is the answer. Given the amount of talent, transparency of market information, and financial resources devoted to the corporate bond market, such an explanation is less than satisfying.

A more likely explanation is that the so-called excess yield spread is, in fact, compensation for other risks associated with owning corporate securities-specifically, liquidity risk and the risk of spread volatility. To avoid confusion, I define "liquidity" here as a security's bid-ask spread and define "spread volatility" as the basis risk between a risky bond and a duration-equivalent Treasury security. Table 1. Required Incremental Yield per Year by Holding Period.Table 2. Nominal Yield Spreads by Maturity, 28 February 2003

Liquidity

How much yield compensation an investor requires for taking liquidity risk relates directly to the investor's time horizon. If the investor has the ability and intent to hold a security to maturity, any liquidity disadvantage vis-a-vis Treasury debt should not demand a particularly high premium, in the absence of opportunity costs. If the investor's time horizon is shorter than a bond's maturity, however, liquidity is clearly a component of the security's value. Specifically, the investor must determine the required incremental yield that compensates for illiquidity.

Given that illiquidity primarily involves execution costs, one can think of it as the inherent price underperformance of an illiquid security versus the liquid benchmark. Basically, liquidity risk involves the additional cost of buying and selling one security versus the cost of buying and selling another security.

If one could know ex ante what the price spread would be for the liquid versus the illiquid security, one could derive the required compensation for illiquidity without much difficulty. Given an assumed price loss, holding period, and terminal duration, one could easily solve for the basis points per year required to compensate investors for the illiquidity. For example, consider an investor with a 3-year holding period purchasing a 10-year corporate bond with a 10 bp bid-ask spread. Generally, the required basis points per year compensation for illiquidity in this situation can be determined by the following equation:

Required bps = {[1 + (xDur)]^sup 1/n^ - 1}100,

where

x = difference between the non-Treasury bid-ask spread and the Treasury bid-ask spread

Dur = duration of the bond at the end of the holding period

n = holding period, in years

For the sake of simplicity, assume that duration is nonstochastic.

Calculating the required basis point compensation for the example would entail x equal to 10 bps, Dur equal to 5.6 (i.e., the duration of the 10-year bond after 3 years in this example), and n equal to 3. Consequently, the required compensation in this instance would be approximately 18.63 bps per year-that is,

{[1 + (10 bps x 5.6)]^sup 1/3^ - 1} x 100 = 18.63 bps.

Figure 1 details a schedule of incremental yield requirements for the investor for various time horizons and a static 10 bp liquidity disadvantage associated with a 20-year bond. Obviously, the marginal investor's holding period can have a material impact on nominal yields.

Consider the cost one would incur in trading out of a 10-year zero-coupon Treasury and into a 10-year zero-coupon corporate bond "today" and then reversing the transaction at some point in the future. To make this example as realistic as possible, assume that the total bid-ask cost of the Treasury is 1/32 of a percent and that the cost of the corporate bond is in basis points per year. Moreover, so as not to penalize longer-duration securities unfairly, assume that the basis point bid-ask spread on the corporate security increases with the holding period (i.e., the shorter the security's duration, the higher the basis point bid-ask spread), as is empirically the case in the investment-grade bond market. Table 3 details a schedule of realized returns and the cost of liquidity for this example for a 10-year zero-coupon Treasury yielding 5 percent and a 10-year zero-coupon corporate bond yielding 6.5 percent (with semiannual compounding for both securities).

The point of this example is not to show what the "right" incremental yield should be but to illustrate that the appropriate nominal yield spread depends on the marginal investor's constraints. Therefore, this cost cannot be tested against historical data. To calculate the liquidity cost, one must know the security's beginning and terminal bid-ask spreads and the individual investor's holding period. Even if one had the necessary data, the information would reveal little other than what the required spread would have been for a particular investor. The point is to demonstrate that illiquidity is a real cost and that it varies according to the investor's individual characteristics. Figure 1. Required Spread for Liquidity.Table 3. Realized Returns and Cost of Liquidity for Example Trade

Although illiquidity is a real cost, calculating its cost is more difficult than the prior two examples suggest. Both examples were static in their treatment of liquidity: In the first example, the bid-ask spread was held constant at 10 bps; in the second, the bid-ask curve was held constant over time. Such stylized treatment of liquidity does not capture the variation in bid-ask spreads the investor must incur when investing in non-Treasury debt; for instance, bid-ask spreads will vary directly with the default risk of the corporate security, increasing when the default risk rises and falling when the default risk declines. Clearly, illiquidity involves both an expected loss and a variation around that expectation associated with the bid-ask spread's variability. To address illiquidity's true cost fully, however, requires, first, a discussion of spread volatility.

Spread Volatility

As with the liquidity component, appropriate compensation for spread volatility depends on the investor's time horizon, the investor's risk tolerance, and the bond's maturity. (Keep in mind that spread volatility is defined here as the price volatility vis-a-vis a duration-matched Treasury.) If the investor holds the security to maturity, intermediate over- or underperformance with respect to price change is, by and large, irrelevant (assuming no opportunity cost) and should not command a large premium. If the investor is not going to hold the bond to maturity, however, the spread at the time the bond is sold matters a great deal.

For example, a total-rate-of-return money manager with a three-year investment horizon must optimize between incremental yield and price volatility (given that the two attributes are normally inversely related). As all bond professionals know, the bond with the highest nominal yield does not always, irrespective of default, provide the highest total return over a three-year time horizon.

The investor whose time horizon differs from a bond's maturity must determine the best total return investment by incorporating incremental yield and the expected terminal spread. The investor must thus make some assumptions about the terminal spread. Many investors use a scenario approach, which ordinarily involves the probability weighting of different terminal spreads to determine relative value vis-a-vis a duration-matched Treasury. The strengths of this approach are that it is easy to implement and easy to understand. Its drawbacks are that it does not allow the investor to view the full range of probable outcomes and it introduces subjectivity by way of probability weights.

A Monte Carlo approach builds on the scenario analysis approach. Specifically, instead of using static scenarios to analyze terminal spreads, Monte Carlo analysis simulates terminal spreads in a fashion similar to the way one simulates equity prices to determine equity option prices. This approach assumes that spread changes are normally distributed-implying a lognormal spread distribution-and uses this distribution to calculate an expected holding-period return. In short, the Monte Carlo approach simulates a terminal spread distribution and uses this distribution to calculate expected relative return in a risk-neutral framework.

The expected relative return is calculated by weighting each terminal spread equally, which eliminates the subjectivity associated with scenario analysis. Moreover, unlike scenario analysis, the Monte Carlo approach captures the entire distribution, which shows the investor the full range of probable outcomes. Because the Monte Carlo technique is risk neutral, however, the expected terminal spread will equal the current spread. Thus, the Monte Carlo technique's added value comes not from the forecasting of terminal spreads but from the ability it gives investors to analyze an expected distribution of terminal spreads.

Monte Carlo analysis is appealing theoretically because it precludes spreads from ever being negative and practically because it conforms to practitioners' expectations about spreads-specifically, a clustered mean with an asymmetrical profile reflecting the fact that spreads can generally widen more than they can tighten.

Although obtaining a reliable time series for investment-grade bond spreads is difficult, given the over-the-counter nature of the swap market, swap spreads offer an excellent time series for diversified AA corporate spreads. Thus, swap spreads provide a highly effective tool to test the empirical distribution of investment-grade spreads. Figure 2 shows empirically a lognormal profile for 10-year (Panel A) and 30-year (Panel B) swap spreads from August 1998 to December 2000.

Spread Simulation. The equation one uses to generate a Monte Carlo simulation as described in the previous section is

Spread^sub N+T^ = Spread ^sub N^e^sup (r-1/2[sigma]^sup 2^)T+[sigma](T)^sup 1/2^z^,

where

N = current period

T = time

e = continuously compounded discount factor

r = drift term

[sigma] = spread volatility

Z = a random draw from the standard normal distribution Figure 2. Swap Spread Histograms, August 1998-December 2000

The time variable is the investor's holding period. The other two inputs are slightly more involved. With the drift variable, r, one can control the distribution's mean. Setting r equal to zero results in no change to the mean of the terminal spread from the current spread level. Conversely, a nonzero value shifts the terminal distribution to the right (or left if r is negative) by the specified percentage. The investor can use the drift term to introduce a directional bias with respect to average future spreads while simultaneously analyzing the variation of this average.

Although all these model inputs involve some subjectivity, volatility is clearly the most subjective. Given that the Monte Carlo technique's advantage lies in allowing the investor the opportunity to analyze an investment's variability, increasing an investment's yield volatility while holding everything else constant will obviously lower the attractiveness of that investment. Ex ante, the investor has no way of knowing the correct spread volatility, but that is no reason for the investor to avoid analyzing its effect: A spread-volatility bet is being made whether or not one analyzes the spread-volatility risk. Once a bond investment is made, the investor has implicitly invested in a spread distribution.

Estimating Volatility. Although gauging future volatility is difficult, a bond's credit rating does provide some information. Kao (2000) explained that the volatility of credit spreads is higher for lower-quality bonds and the volatilities of spread changes increase monotonically across the credit-rating spectrum (e.g., 9.0 bps a month for AAA rated debt and 16.6 bps for BBB rated debt in the 1984-98 period). Table 4 lists corporate credit spreads and spread changes for the 1990-98 period.2 Table 4. Yield-Spread Mean and Spread Volatility by Rating Grade, 1990-98

Example. This option-based approach can be illustrated by considering two hypothetical 10-year fixed-income securities, F and G, offered to an investor with a 3-year horizon. Assume that Bond F trades at a spread of 130 bps to the 10-year on-the-run Treasury security and has a spread volatility of 15 percent a year; assume that Bond G trades at a spread of 170 bps to the 10-year on-the-run Treasury and has a spread volatility of 20 percent a year. This illustration sets the drift component equal to zero and reinvests all the incremental yield at the zero-duration risk-free rate for both securities. (The unequal change in duration of the securities involved in this example complicates the analysis.) The expected excess return (i.e., the difference between the non-Treasury and Treasury bond returns) for Bond F is 122 bps a year, and its standard deviation of expected excess return is 56 bps a year. For Bond G, expected excess return is 159 bps a year, and standard deviation is 97 bps. The bonds' terminal spread distributions are shown in Figure 3-Bond F in Panel A and Bond G in Panel B.

Bond G has a greater expected return than the lower-yielding Bond F, but the relative advantage is 3 bps less than the difference between the two bonds' nominal yields because the reinvestment at the risk-free rate penalizes the higher-yielding Bond G. Expected total relative returns, however, are not risk adjusted; they are simply mean estimates that do not incorporate the variability around the mean that the investor must tolerate. As mentioned previously, the Monte Carlo approach allows the investor to calculate not only an expected return but also the return's standard deviation. In this example, Bond G's expected relative return is higher than Bond F's but so is the standard deviation of this relative return. In fact, based on a return per unit of variability, Bond F's ratio (i.e., 122/56 = 2.18) is significantly better than Bond G's ratio (i.e., 159/97 = 1.64).