A reduced form model of default spreads with Markov-switching macroeconomic factors

We examine the ability of observed macroeconomic factors and the possibility of changes in regime to explain the proportion of yield spreads caused by the risk of default in the context of a reduced form model. For this purpose, we extend the Markov-switching risk-free term structure model of Bansal and Zhou (2002) to the corporate bond setting and develop recursive formulas for default probabilities, risk-free and risky zero-coupon bond yields as well as credit default swap premia. The model is calibrated with consumption, inflation, risk-free yields and default data for Aa, A and Baa bonds from the 1987 to 2008 period. We find that our macroeconomic factors are linked with two out of three sharp increases in the spreads during this sample period, indicating that the spread variations can be related to macroeconomic undiversifiable risk.     

Estimating Risk‐Adjusted Costs of Financial Distress

The search for the optimal, or value‐maximizing, capital structure involves weighing the expected benefits of higher leverage against the expected “costs of financial distress.” These costs include not only the direct costs of reorganization, but less quantifiable effects of financial trouble such as damage to the firm's reputation, the loss of key employees and customers, and the loss of value from forgone investment opportunities. This article proposes a new method for valuing expected financial distress costs. While researchers have provided estimates of the costs associated with financial distress when it takes place, whether or when these costs will be incurred is, of course, unknown at the time the financing decision. As a result, the “correct” discount rate for valuing expected distress costs is difficult to derive. Instead of adjusting the discount rate to reflect historical default rate probabilities, the authors' method uses “risk‐neutral” probabilities of encountering distress that allow for discounting at the risk‐free rate. The risk‐neutral probabilities of default are derived by incorporating the systematic risk premia implicit in corporate bond yield spreads. This method results in a significant increase in estimates of financial distress costs. In a simple example presented by the authors, distress costs estimated at about 1.6% of firm value using the conventional method turn out to run about 5% after adjusting for the increased systematic risk associated with financial distress.     

The term structure of credit spreads with jump risk

Default risk analysis is important for valuing corporate bonds, swaps, and credit derivatives and plays a critical role in managing the credit risk of bank loan portfolios. This paper offers a theory to explain the observed empirical regularities on default probabilities, recovery rates, and credit spreads. It incorporates jump risk into the default process. With the jump risk, a firm can default instantaneously because of a sudden drop in its value. As a result, a credit model with the jump risk is able to match the size of credit spreads on corporate bonds and can generate various shapes of yield spread curves and marginal default rate curves, including upward-sloping, downward-sloping, flat, and hump-shaped, even if the firm is currently in a good financial standing. The model also links recovery rates to the firm value at default so that the variation in recovery rates is endogenously generated and the correlation between recovery rates and credit ratings before default reported in Altman [J. Finance 44 (1989) 909] can be justified.     

Corporate Yield Spreads and Bond Liquidity

We find that liquidity is priced in corporate yield spreads. Using a battery of liquidity measures covering over 4,000 corporate bonds and spanning both investment grade and speculative categories, we find that more illiquid bonds earn higher yield spreads, and an improvement in liquidity causes a significant reduction in yield spreads. These results hold after controlling for common bond‐specific, firm‐specific, and macroeconomic variables, and are robust to issuers' fixed effect and potential endogeneity bias. Our findings justify the concern in the default risk literature that neither the level nor the dynamic of yield spreads can be fully explained by default risk determinants.     

Taxes,Default Risk,and Yield Spreads

This paper develops a model of bond prices and yield spreads that incorporates the effect of both taxes and differences in default probabilities. The tax loss consequences of default are recognized. Traditionally, tax-free (municipal) bond yields have been viewed as linearly related to taxable yields with a slope coefficient equal to one minus the tax rate and the intercept representing differences in default risk. While our model supports the linearity assumption, it implies that the slope and intercept are both functions of both the break-even tax rate and the default probability(ies). Clientele effects among both municipal and taxable bonds are demonstrated. Finally, the implied marginal tax rates and the implied default probabilities are estimated for different categories of municipal bonds.     

Determinants of yield spread dynamics: Euro versus US dollar corporate bonds

This paper presents a systematic comparison between the determinants of euro and US dollar yield spread dynamics. The results show that US dollar yield spreads are significantly more affected by changes in the level and the slope of the default-free term structure and the stock market return and volatility. Surprisingly, euro yield spreads are strongly affected by the US (and not the euro) level and slope. This confirms the dominance of US interest rates in the corporate bond markets. Interestingly, I find that liquidity risk is higher for US dollar corporate bonds than euro corporate bonds. For both regions, the effect of changes in the bid-ask spread is mainly significant during periods of high liquidity risk. Finally, the results indicate that the credit cycle as measured by the region-specific default probability significantly increases US yield spreads. This is not the case for euro yield spreads.     

A Multifactor Model of Credit Spreads

We represent credit spreads across ratings as a function of common unobservable factors of the Vasicek form. Using a state-space approach we estimate the factors, their process parameters, and the exposure of each observed credit spread series to each factor. We find that most of the systematic variation across credit spreads is captured by three factors. The factors are closely related to the implied volatility index (VIX), the long bond rate, and S&P500 returns, supporting the predictions of structural models of default at an aggregate level. By making no prior assumption about the determinants of yield spread dynamics, our study provides an original and independent test of theory. The results also contribute to the current debate about the role of liquidity in corporate yield spreads. While recent empirical literature shows that the level and time-variation in corporate yield spreads is driven primarily by a systematic liquidity risk factor, we find that the three most important drivers of yield spread levels relate to macroeconomic variables. This suggests that if credit spread levels do contain a large liquidity premium, the time variation of this premium is likely driven by the same factors as default risk.     

CDOs and the financial crisis: Credit ratings and fair premia

We study risk and return characteristics of CDOs using the market standard models. We find that fair spreads on CDO tranches are much higher than fair spreads on similarly-rated corporate bonds. Our results imply that credit ratings are not sufficient for pricing, which is surprising given their central role in structured finance markets. This illustrates limitations of the rating methodologies that are solely based on real-world default probabilities or expected losses and do not capture risk premia. We also demonstrate that CDO tranches have large exposure to systematic risk and thus their ratings and prices are likely to decline substantially when credit conditions deteriorate.     

Risk-neutral and actual default probabilities with an endogenous bankruptcy jump-diffusion model

This paper focuses on historical and risk-neutral default probabilities in a structural model, when the firm assets dynamics are modeled by a double exponential jump diffusion process. Relying on the Leland [(1994a) Journal of Finance, 49, 1213–1252; (1994b) Bond prices, yield spreads, and optimal capital structure with default risk. Working paper no. 240, IBER, University of California, Berkeley] or Leland and Toft [(1996) Journal of Finance, 51(3), 987–1019] endogenous structural approaches, as formalized by Hilberink and Rogers [(2002) Finance and Stochastics, 6(2), 237–263], this article gives a coherent construction of historical default probabilities. The risk-neutral world where evolve the firm assets, modeled by a class of geometric Lévy processes, is constructed based on the Esscher measure, yielding useful and new analytical relations between historical and risk-neutral probabilities. We do a complete numerical analysis of the predictions of our framework, and compare these predictions with actual data. In particular, this new framework displays an enhanced predictive power w.r.t. current Gaussian endogenous structural models.      

The Cross‐Section of Credit Risk Premia and Equity Returns

We explore the link between a firm's stock returns and credit risk using a simple insight from structural models following Merton ( 1974 ): risk premia on equity and credit instruments are related because all claims on assets must earn the same compensation per unit of risk. Consistent with theory, we find that firms' stock returns increase with credit risk premia estimated from CDS spreads. Credit risk premia contain information not captured by physical or risk‐neutral default probabilities alone. This sheds new light on the “distress puzzle”—the lack of a positive relation between equity returns and default probabilities—reported in previous studies.     

A Simple Approach to Valuing Risky Fixed and Floating Rate Debt

We develop a simple approach to valuing risky corporate debt that incorporates both default and interest rate risk. We use this approach to derive simple closed-form valuation expressions for fixed and floating rate debt. The model provides a number of interesting new insights about pricing and hedging corporate debt securities. For example, we find that the correlation between default risk and the interest rate has a significant effect on the properties of the credit spread. Using Moody's corporate bond yield data, we find that credit spreads are negatively related to interest rates and that durations of risky bonds depend on the correlation with interest rates. This empirical evidence is consistent with the implications of the valuation model.     

SERIAL ISSUE EVIDENCE FOR THE RELATION BETWEEN THE RISK STRUCTURE AND MATURITY: A DECOMPOSITION METHODOLOGY

The risk structure of the interest rates literature shows that coupon effects can cause changes in yield spreads as maturity lengthens. These effects make it difficult to empirically isolate the default risk component of the spread for coupon-paying bonds. Attempts to calculate zero-coupon risk structures suffer from the relative scarcity of zero-coupon corporate bonds. We show that yield spreads for coupon-paying bonds that are identical except for default risk decompose into a relative duration component, a premium discount coupon component, and a default component. We present closed-form solutions for measuring the first two components so that the default risk portions can be isolated as residuals. We further present an empirical application of the decomposition metrics for sixteen exchange-traded serial issues and nonparametrically examine the relation between the default premia and maturity. We find various maturity relations.     

Market conditions,default risk and credit spreads

This study empirically examines the impact of the interaction between market and default risk on corporate credit spreads. Using credit default swap (CDS) spreads, we find that average credit spreads decrease in GDP growth rate, but increase in GDP growth volatility and jump risk in the equity market. At the market level, investor sentiment is the most important determinant of credit spreads. At the firm level, credit spreads generally rise with cash flow volatility and beta, with the effect of cash flow beta varying with market conditions. We identify implied volatility as the most significant determinant of default risk among firm-level characteristics. Overall, a major portion of individual credit spreads is accounted for by firm-level determinants of default risk, while macroeconomic variables are directly responsible for a lesser portion.     

A Note on Credit Risk of Vertical <Emphasis Type="Italic">Keiretsu</Emphasis> Firms: Preliminary Evidence from the Japanese Automobile Industry

This paper empirically examines the relationship between the credit risk of Toyota, Nissan and Honda keiretsu-affiliated firms and the credit risk of the respective parent company. As credit spread data for keiretsu-affiliated firms were not available we create a keiretsu default index, as a proxy, using expected default probabilities obtained from the KMV and Leland and Toft (J. Finance 51, 987–1019, 1996) option pricing models. We find parent credit spreads do not Granger cause our keiretsu default index and vice versa in a bivariate vector autoregressive (VAR) framework.JEL classification: G3, L62     

The effect of corporate diversification on credit risk: new evidence from European credit default swap spreads

This article investigates the impact of corporate diversification on credit risk. To our best knowledge, this is the first paper to use credit default swap (CDS) spreads instead of bond yield or revalued book values to test the risk‐reduction hypothesis. The analysis relies upon a sample of STOXX^® EUROPE 600 index members and covers the years 2010–2014. After controlling for various CDS‐ and firm‐specific variables, we find that diversification strategies do not significantly lower CDS premiums. Multilevel mediation analysis further shows that information asymmetries overcompensate the risk‐reducing effects resulting from corporate diversification.     

A jump to default extended CEV model: an application of Bessel processes

We develop a flexible and analytically tractable framework which unifies the valuation of corporate liabilities, credit derivatives, and equity derivatives. We assume that the stock price follows a diffusion, punctuated by a possible jump to zero (default). To capture the positive link between default and equity volatility, we assume that the hazard rate of default is an increasing affine function of the instantaneous variance of returns on the underlying stock. To capture the negative link between volatility and stock price, we assume a constant elasticity of variance (CEV) specification for the instantaneous stock volatility prior to default. We show that deterministic changes of time and scale reduce our stock price process to a standard Bessel process with killing. This reduction permits the development of completely explicit closed form solutions for risk-neutral survival probabilities, CDS spreads, corporate bond values, and European-style equity options. Furthermore, our valuation model is sufficiently flexible so that it can be calibrated to exactly match arbitrarily given term structures of CDS spreads, interest rates, dividend yields, and at-the-money implied volatilities.     

Modeling the evolution of implied CDO correlations

CDO tranche spreads (and prices of related portfolio-credit derivatives) depend on the market’s perception of the future loss distribution of the underlying credit portfolio. Applying Sklar’s seminal decomposition to the distribution of the vector of default times, the portfolio-loss distribution derived thereof is specified through individual default probabilities and the dependence among obligors’ default times. Moreover, the loss severity, specified via obligors’ recovery rates, is an additional determinant. Several (specifically univariate) credit derivatives are primarily driven by individual default probabilities, allowing investments in (or hedging against) default risk. However, there is no derivative that allows separately trading (or hedging) default correlations; all products exposed to correlation risk are contemporaneously also exposed to default risk. Moreover, the abstract notion of dependence among the names in a credit portfolio is not directly observable from traded assets. Inverting the classical Vasicek/Gauss copula model for the correlation parameter allows constructing time series of implied (compound and base) correlations. Based on such time series, it is possible to identify observable variables that describe implied correlations in terms of a regression model. This provides an economic model of the time evolution of the market’s view of the dependence structure. Different regression models are developed and investigated for the European CDO market. Applications and extensions to other markets are discussed.     

Corporate bond liquidity and yield spreads: A review

Secondary market illiquidity is an important non-default factor affecting yield spreads. Yet, a review of the literature suggests the findings are mixed, both regarding the relative size of the default versus non-default components as well as the relative importance of liquidity premium for investment-grade and high-yield bonds. While in theory country and currency risk might affect international bonds' yield spreads, empirical findings show that international corporate bonds pricing and liquidity are generally affected by the same factors as the U.S. market. We identify several other areas of disagreement and challenges in the literature that warrant further research.     

Underwriter reputation and the quality of certification: Evidence from high-yield bonds

This paper provides primary evidence of whether certification via reputable underwriters is beneficial to investors in the corporate bond market. We focus on the high-yield bond market in which certification of issuer quality is most valuable to investors owing to low liquidity and issuing firms’ high opacity and default risk. We find bonds underwritten by the most reputable underwriters to be associated with significantly higher downgrade and default risk. Investors seem to be aware of this relation, as we further find the private information conveyed via the issuer-reputable underwriter match to have a significantly positive effect on at-issue yield spreads. Our results are consistent with the market-power hypothesis, and contradict the traditional certification hypothesis and underlying reputation mechanism.     

“一带一路”倡议与公司债信用利差

本文以中国“一带一路”倡议的出台作为准自然实验,采用双重差分法考察国家倡议对微观企业债券信用利差的影响。研究发现:(1)相对于非支持企业,“一带一路”倡议实施能够显著降低支持企业的公司债二级市场信用利差,该结论在一系列稳健性检验之后仍然成立。(2)通过考察“一带一路”倡议的债券市场反应,我们发现相比于非支持企业,支持企业在倡议提出后有显著更高的债券累计超额回报率。(3)进一步检验后发现,“一带一路”倡议对公司债二级市场信用利差的降低作用主要通过资源效应和信息效应来实现。并且,政策影响范围主要集中在重点对接行业以及重点对接省份的企业。(4)“一带一路”倡议还对公司债一级市场的发行表现产生影响。具体表现为:在倡议实施之后,受倡议支持企业发行的公司债,其一级市场发行利差下降幅度更大,且包含的担保条款以及限制性契约条款显著更少。本研究探讨了“一带一路”倡议对公司债券市场的政策效应,对未来推进“一带一路”建设,提高资金融通效率具有参考意义。