Liquidity and Arbitrage in the Market for Credit Risk

The recent credit crisis has highlighted the importance of market liquidity and its interaction with the price of credit risk. We investigate this interaction by relating the liquidity of corporate bonds to the basis between the credit default swap (CDS) spread of the issuer and the par-equivalent bond yield spread. The liquidity of a bond is measured using a recently developed measure called latent liquidity, which is defined as the weighted average turnover of funds holding the bond, where the weights are their fractional holdings of the bond. We find that bonds with higher latent liquidity are more expensive relative to their CDS contracts after controlling for other realized measures of liquidity. Analysis of interaction effects shows that highly illiquid bonds of firms with a greater degree of uncertainty are also expensive, consistent with limits to arbitrage between CDS and bond markets, due to the higher costs of “shorting” illiquid bonds. Additionally, we document the positive effects of liquidity in the CDS market on the CDS-bond basis. We also find that several firm- and bond-level variables related to credit risk affect the basis, indicating that the CDS spread does not fully capture the credit risk of the bond.

Introduction

Corporate bonds are among the least understood instruments in the U.S. financial markets. This is surprising given the sheer size of the U.S. corporate  bond market, about $6.8 trillion outstanding as of June 2009, which makes such

bonds an important source of capital for U.S. firms.1 These bonds carry a risk of default, and hence command a yield premium or spread relative to their risk free counterparts. However, the academic literature in finance has been unable to explain a significant component of corporate bond yields/prices in relation to their Treasury counterparts, despite using a range of structural and reduced-form credit risk models.

Prior studies have noted that although default risk is an important determinant of the yield spread, other factors such as liquidity, taxes, and aggregate market risk variables (other than credit risk) may also play a significant role in

determining the spread. Of these other factors, it has been conjectured that liquidity effects play an important role in the pricing of corporate bonds, and are reflected in the non default component of their yields (i.e., the portion of the corporate bond yield that cannot be explained by factors related to default risk). Since illiquid instruments are difficult to trade, investors holding them demand a risk premium that is related to the level of liquidity in the instrument. In the context of corporate bonds, this premium increases the expected return of the bond in a way that is not directly related to the credit risk embedded in the instrument. In other words, a premium for liquidity can be thought of as a non default-related component of the yield spread.

Unfortunately, the non default component of corporate bond yields has been inadequately studied, largely due to the paucity of data. In particular, the absence of frequent trades in corporate bonds makes it difficult to compute trade-based measures of liquidity relying on quoted/traded prices or yields to measure liquidity, as has been done in the equity markets. It is difficult, therefore, to measure the liquidity of corporate bonds directly. Consequently, it is a challenge to directly study the impact of liquidity on corporate bond yields and prices, thus leaving the discussion of corporate bond spreads somewhat incomplete. An important development during this decade has been the credit default swap (CDS) market, which has emerged as the barometer of the market’s collective judgment of the credit risk of the bonds issued by an obligor. The CDS contract is a derivative in which the underlying instruments are corporate bonds.

Financial theory tells us that a strong economic relationship should exist between the CDS and its underlying instruments. The CDS spread is thus a proxy for the premium attached to credit risk, which, in a world without frictions, would be exactly equivalent to the credit risk in the underlying corporate bonds. In practice, however, it may itself be affected by market frictions, as discussed later on in the paper. In this paper, we study the CDS-bond basis, the difference between the  CDS spread of the issuer and the par-equivalent CDS spread of the bond, as a (somewhat imperfect) measure of the non default component of the bond yield. 

We relate the CDS-bond basis to bond liquidity and other variables such as the bond characteristics, firm-level credit risk effects, and liquidity in the CDS market itself. We make several significant contributions in this study.

First, we use and further validate a new measure of bond liquidity, called latent liquidity, proposed by Mahanti, Nashikkar, Subrahmanyam, Chacko, and Mallik (2008), which is based on the holdings of bonds by investors, and thus does not require a large number of observed trades for its computation. This measure weights the turnover of the funds that own the bond by their fractional holdings; thus, it is a measure of the accessibility of a bond to market participants. The attractive feature of this measure is that it circumvents the problem of non availability of transaction data for corporate bonds and yet provides a reasonable proxy for liquidity. We show that our measure has explanatory power for the liquidity component of the CDS-bond basis, even after controlling for trading volume and other bond characteristics such as age, coupon, and issue size, which have been associated with bond liquidity.

Second, we show that even after controlling for credit risk using the price of the CDS contract, corporate bond prices are still affected by factors related to the default risk in the firm. We also find that the effect is one-sided: When firms are riskier, their corporate bonds tend to be relatively expensive. Furthermore, it is the illiquid bonds of firms with more uncertainty that are more expensive relative to their CDS contracts. Our interpretation is that this conclusion is due to the effects of frictions in the arbitrage mechanism. Agents participating in the CDS market and the corporate bond market may have different valuations for the credit risk of the obligor. However, arbitrageurs who try to profit from this difference may find it difficult to sell corporate bonds short because of limited supply in the borrowing and lending markets for corporate bonds. Thus, illiquid corporate bonds of firms with greater uncertainty are more likely to be expensive relative to their CDS contracts.

Third, we show that the liquidity of the CDS contract itself influences both the liquidity of the bond and the bond price itself. Bonds of issuers whose CDS contracts enjoy greater liquidity tend to be more expensive (have lower yields) in the cross section compared with their less liquid counterparts after adjusting for various bond characteristics. This is evidence of liquidity spillover effects from the CDS market to the corporate bond market.

Fourth, we demonstrate the effect of individual bond characteristics, such as the presence or absence of covenants and differences in tax status, on bond prices.

To our knowledge, this is the first paper that studies the effect of bond covenants on bond valuation, using the CDS spread as a control for credit risk. The novel bond-liquidity measure that we use in this paper is related to the theory proposed by Amihud and Mendelson (1986) according to which, in equilibrium, assets with the lowest transaction costs are held by investors with the shortest trading horizon, and have higher prices. Our metric, proposed by  Mahanti et al. (2008), can thus be thought of as a direct measure of the activity of funds holding a particular bond. It is also related to the literature on liquidity and asset prices, most notably Vayanos andWang (2007), who use a search-based model to provide for an endogenous concentration of liquidity in particular assets.

This concentration leads to active investors participating in these assets, thus lowering transaction costs and leading to higher prices at the same time. In this sense, our measure can be thought of as directly measuring the extent of search frictions when the marginal holders of a particular bond wish to trade.