بر روی اهمیت عوامل خطر سیستماتیک در تشریح مقطع گسترش بازدهی اوراق قرضه شرکتی

In this paper we examine the importance of systematic equity market factors in explaining the cross-sectional variation in yield spreads on corporate debt. Based on a sample of 1771 corporate bonds over the period from January 1985 to March 1998, we find that once the default-related variables are controlled for, bond betas or sensitivities to aggregate equity market risks have very limited explanatory power. This is in contrast to [Elton, E.J., Gruber, M.J., 2001. Explaining the rate spread on corporate bonds. Journal of Finance 56, 247–277] who find that market factors tied to expected returns are predominantly important, but who do not control for these variables (i.e. the relevant variables from structural models), possibly biasing their estimates. On the other hand, our finding that the systematic factors exhibit some limited explanatory power suggests that the standard contingent claims approach may not fully apply. This finding is consistent with previous research that bond betas are not completely irrelevant once market frictions are introduced. Overall, the evidence provides empirical support for the proposition that structural models capture important elements of corporate bond yield spread determination and equity market systematic factors are by no means predominant.

How important are systematic risk factors to the determination of the cross-section of corporate bond yield spreads? Structural models of corporate bond pricing imply that systematic risk factors should not play a role in the pricing of corporate bonds, while firm and issue characteristics should be among the most important factors. Yet recent empirical evidence indicates that systematic factors related to expected returns are of primary importance. Understanding the relative significance of these two influences is important for understanding how well structural models of bond pricing capture the process determining the yield spreads of corporate bonds. In a recent article, Elton et al. (2001), examine rate spreads between corporate and government bonds and suggest that systematic risk factors related to expected returns on equity are of primary importance in the determination of these spreads. In particular, they find that rate spreads on corporate bonds are largely attributable to three factors: possible loss from default (estimated within the context of a risk-neutral world), tax differential between corporate and government bonds, and systematic risk of the equity market. For example, in the case of 10-year corporate bonds, they find that only 17.8% of the rate spread between corporate and Treasuries can be explained by the expected loss from default, while 36.1% can be explained by local taxes, and 46.7% can be explained by systematic risk factors. When performing cross-sectional regressions of the average rate spread on bond return sensitivities (or betas) to systematic equity market factors, they find that the market factors can explain about 32% of the cross-sectional differences for industrial bonds and about 58% for financial bonds. Thus, they conclude that the market factors used to explain returns in the equity market are the most important determinants of yield spreads on corporate bonds. These empirical results appear largely contradictory to structural models of corporate bond pricing. In a line of research that stems from Merton (1974), structural models of corporate bond yields view corporate liabilities as contingent claims on the value of the underlying firm. As a result, contingent claims theory implies that the pricing of corporate bonds should be independent of the expected returns on the underlying asset because it is possible to hedge away the risk through replication. This implies that derivative prices (in this case, bond prices) should be unrelated to the expected return of the underlying asset and the systematic factors that affect the prices of the underlying asset, once we have controlled for all the relevant variables. 2 Various contingent claims models differ in the modeling of financial distress and/or bankruptcy. For example, Merton (1974) models financial distress as an exogenously terminal date check for default. Black and Cox (1976) extend Merton’s model to include a fixed absorbing barrier. Others have taken the approach of modeling an endogenous bankruptcy point. Anderson and Sundaresan (1996a) adopt a game-theoretic model of bankruptcy, whereas Mella-Barral and Perraudin (1997) model liquidation as an option. Leland (1994) endogenizes the decision to default. Regardless of the assumptions about the bankruptcy barrier, these structural models propose that the value of debt is a function of the coupon rate, risk-free interest rate, principal, probability of default, the recovery rate, cost of bankruptcy, and the default barrier. Note that since we are examining yields cross-sectionally, the risk-free rate, principal, and cost of bankruptcy should not be factors because they do not vary across bonds at a given point in time. Thus, once we control for the default-related variables, these models imply that the cross-section of corporate bonds should be independent of the expected returns on the underlying firms and the systematic risk factors that determine those expected returns. Empirically, however, Collin-Dufresne et al. (2001) show that most of the time-series variation in corporate bond yield spreads is related to movements in the aggregate corporate bond market. Their finding implies that corporate bonds cannot be replicated using a position in the underlying firm’s equity and risk-free bonds and therefore cannot be completely hedged. This suggests that standard contingent claims theory may not fully apply and that as a result, systematic risk factors may play a role in pricing. For example, Figlewski, 1989 and Longstaff, 1995, and Bakshi et al. (1997) recognize that expected returns may be priced into options in an imperfect market. In particular, Figlewski (1989) states “The standard arbitrage eliminates price expectations and risk aversion from option pricing in a frictionless market. However, within the wide bounds on the option prices that are all that can be established by the standard arbitrage in an actual, imperfect options market, there is certainly room for these and many other factors to have an influence.” This caveat to contingent claims pricing certainly applies in this instance and it is an empirical question as to whether systematic risk factors are important determinants of the cross-section of corporate bond yield spreads. Recent research on the performance of these structural models includes Anderson and Sundaresan (1996b) and Eom et al. (2001). Anderson and Sundaresan (1996b) empirically compare several structural models using aggregate time series data for the US bond market. They find that recent models using an endogenous bankruptcy barrier fit the data better than the Merton (1974) model. Eom et al. (2001) test another set of structural models using a cross-section of bonds in 1997. They find that the Merton (1974) and Geske (1977) models tend to underestimate corporate bond yields, whereas Longstaff and Schwartz (1995) and Leland and Toft (1996) tend to overestimate yields. In this paper we examine the importance of systematic equity market factors in explaining the cross-sectional variation in yield spreads on corporate debt, once we have controlled for those relevant variables that structural models indicate are important. Based on a sample of 1771 corporate bonds over the period from January 1985 to March 1998, we find that once the default-related variables are controlled for, bond betas or sensitivities to aggregate equity market risks have very limited explanatory power. This is in contrast to Elton et al. (2001) who use a covariance, or beta, pricing framework to price securities and find that market factors tied to expected returns are predominantly important. Our findings do not imply that the beta approach is incorrect. Rather, for derivative securities, it may be more accurate to use contingent claim analysis. One possible reason is that contingent claims theory suggests that time variation in firm leverage (or other firm characteristics) may lead to time variation in the betas, possibly biasing the Elton et al. results. We show that, based on our findings, the beta approach provides limited incremental contribution for the pricing of bonds once we control for those relevant variables such as issue and firm characteristics that contingent claims analysis suggests are important. On the other hand, our finding that the systematic factors exhibit some limited explanatory power suggests that the standard contingent claims approach may not fully apply. This finding is consistent with the discussion above that bond betas are not completely irrelevant once market frictions are introduced and provides important empirical support for the proposition that structural models capture important elements of corporate bond yield spread determination. Interestingly, Vassalou and Xing (2004) find that systematic default risk is also important in explaining the cross-section of equity returns. Our other findings include the following. First, consistent with the predictions of structural models, we find that the effect of firm leverage on credit spreads is larger for lower-rated bonds. Second, we find that bond yield spreads reflect these important issuer characteristics, both across and within rating categories. The rest of the paper is structured as follows. Section 2 describes the sample of bonds and yield spreads across rating categories and maturity groups. Section 3 presents the empirical results of our regression analysis of yield spreads on issue and issuer characteristics and systematic equity market factors. Section 4 examines robustness. Section 5 concludes the paper.

5. Conclusion In this paper we examine the importance of systematic equity market factors in explaining the cross-sectional variation of corporate bond yield spreads. In a recent article, Elton et al. (2001), examine rate spreads between corporate and government bonds and suggest that systematic risk factors related to expected returns on equity are of primary importance in the determination of these spreads. These empirical results appear to contradict structural models of corporate bond pricing. In a line of research that stems from Merton (1974), structural models of corporate bond yields view corporate liabilities as contingent claims on the value of the underlying firm. As a result, contingent claims theory implies that the pricing of corporate bonds should be independent of the expected returns on the underlying asset because it is possible to hedge away the risk through replication. This implies that systematic risk factors should not play a role in pricing once we have controlled for all the relevant variables. The structural models imply that these relevant variables are the coupon rate, risk-free interest rate, principal, and default-related variables. We examine a sample of 1771 bonds issued by 358 US corporations over the period from January 1985 to March 1998. By using cross-sectional regressions at the end of each quarter in the sample period, we control for these structural variables and find that bond betas on equity market factors provide limited explanatory power. Although the bond betas are not completely irrelevant in determining the cross-section of corporate bond prices, they are by no means predominant. The structural model variables explain a much more significant portion of the cross-sectional variation in yield spreads. This provides support for the idea that the structural models capture important features of the process determining corporate bond yield spreads and supports the proposition that the systematic factors have limited explanatory power once these relevant structural model factors are controlled for. On the other hand, our finding that the bond betas to these expected return factors are not completely irrelevant is consistent with the findings of Collin-Dufresne et al. (2001). They show that most of the time-series variation in corporate bond yield spreads is related to movements in the aggregate corporate bond market, which implies that corporate bonds cannot be replicated using a position in the underlying firm’s equity and risk-free bonds and therefore cannot be completely hedged. This suggests that standard contingent claims theory may not fully apply and that as a result, systematic risk factors may play a role in pricing.