Corporate bond default risk: A 150-year perspective

We study corporate bond default rates using an extensive new data set spanning the 1866-2008 period. We find that the corporate bond market has repeatedly suffered clustered default events much worse than those experienced during the Great Depression. For example, during the railroad crisis of 1873-1875, total defaults amounted to 36% of the par value of the entire corporate bond market. Using a regime-switching model, we examine the extent to which default rates can be forecast by financial and macroeconomic variables. We find that stock returns, stock return volatility, and changes in GDP are strong predictors of default rates. Surprisingly, however, credit spreads are not. Over the long term, credit spreads are roughly twice as large as default losses, resulting in an average credit risk premium of about 80 basis points. We also find that credit spreads do not adjust in response to realized default rates.     

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.     

Exploring the components of credit risk in credit default swaps

In this paper, we test the influence of various fundamental variables on the pricing of credit default swaps. The theoretical determinants that are important for pricing credit default swaps include the risk-free rate, industry sector, credit rating, and liquidity factors. We suggest a linear regression model containing these different variables, especially focusing on liquidity factors. Unlike bond spreads which have been shown to be inversely related to liquidity (i.e., the greater the liquidity, the lower the spread), there is no a priori reason that the credit default swap spread should exhibit the same relationship. This is due to the economic characteristics of a credit default swap compared to a bond. Our empirical result shows that all the fundamental variables investigated have a significant effect on the credit default swap spread. Moreover, our findings suggest that credit default swaps that trade with greater liquidity have a wider credit default swap spread.     

Credit risk measurement: Developments over the last 20 years

This paper traces developments in the credit risk measurement literature over the last 20 years. The paper is essentially divided into two parts. In the first part the evolution of the literature on the credit-risk measurement of individual loans and portfolios of loans is traced by way of reference to articles appearing in relevant issues of the Journal of Banking and Finance and other publications. In the second part, a new approach built around a mortality risk framework to measuring the risk and returns on loans and bonds is presented. This model is shown to offer some promise in analyzing the risk-return structures of portfolios of credit-risk exposed debt instruments.     

Common risk factors in the cross-section of corporate bond returns

We investigate the cross-sectional determinants of corporate bond returns and find that downside risk is the strongest predictor of future bond returns. We also introduce common risk factors based on the prevalent risk characteristics of corporate bonds—downside risk, credit risk, and liquidity risk—and find that these novel bond factors have economically and statistically significant risk premiums that cannot be explained by long-established stock and bond market factors. We show that the newly proposed risk factors outperform all other models considered in the literature in explaining the returns of the industry- and size/maturity-sorted portfolios of corporate bonds.     

Credit risk and bond pricing of local government in China

The relationship between credit risk and the pricing of local government bonds in China is explored in this paper. The pricing of local government bonds was found to reflect credit risk, but the risk premium was small. The type of bond (‘directional’ or ‘non-directional’) significantly affected pricing. Repayment source had no effect. The authors make recommendations for the central government, local governments and investors.     

Modeling CDS spreads: A comparison of some hybrid approaches

According to the credit risk model proposed by Cathcart and El-Jahel (2006), default can occur either expectedly, when a certain signaling variable breaches a lower barrier, or unexpectedly, as the first jump of a Poisson process, whose intensity depends on the signaling variable itself and on the interest rate. In the present paper we test the performances of such a model and of other three models generalized by it in fitting the term structure of credit default swap (CDS) spreads. In order to do so, we derive a semi-analytical formula for pricing CDSs and we use it to fit the observed term structures of 65 different CDSs. The analysis reveals that all the model parameters yield a relevant contribution to credit spreads. Moreover, if the dependence of the default intensity on both the signaling variable and the interest rate is removed, the pricing of CDSs becomes very simple, from both the analytical and the computational standpoint, while the goodness-of-fit is reduced by only a few percentage points. Therefore, when using the credit risk model proposed by Cathcart and El-Jahel (2006), assuming a constant default intensity provides an interesting and efficient compromise between parsimony and goodness-of-fit. Furthermore, by fitting the term structure of CDS spreads on a period of about twelve years, we find that the parameters of the model with constant default are rather stable over time, and the goodness-of-fit is maintained high.     

Probability weighting and default risk: a possible explanation for distressed stock puzzles

This paper suggests incorporating investor probability weighting and the default risk of individual firms into a consumption-based asset pricing model. The extended model provides a unified explanation for several anomalous patterns observed in financial markets. The analysis addresses not only widely recognized asset pricing puzzles, such as the equity premium puzzle, but also less-studied anomalies on financially distressed stocks. The simulation, under which the model is calibrated according to U.S. historical data, shows that a combination of mild overweighting of probability on tail events and nonlinearity of equity values caused by default risk has the potential to resolve these patterns.     

A new approach for option pricing under stochastic volatility

We develop a new approach for pricing European-style contingent claims written on the time T spot price of an underlying asset whose volatility is stochastic. Like most of the stochastic volatility literature, we assume continuous dynamics for the price of the underlying asset. In contrast to most of the stochastic volatility literature, we do not directly model the dynamics of the instantaneous volatility. Instead, taking advantage of the recent rise of the variance swap market, we directly assume continuous dynamics for the time T variance swap rate. The initial value of this variance swap rate can either be directly observed, or inferred from option prices. We make no assumption concerning the real world drift of this process. We assume that the ratio of the volatility of the variance swap rate to the instantaneous volatility of the underlying asset just depends on the variance swap rate and on the variance swap maturity. Since this ratio is assumed to be independent of calendar time, we term this key assumption the stationary volatility ratio hypothesis (SVRH). The instantaneous volatility of the futures follows an unspecified stochastic process, so both the underlying futures price and the variance swap rate have unspecified stochastic volatility. Despite this, we show that the payoff to a path-independent contingent claim can be perfectly replicated by dynamic trading in futures contracts and variance swaps of the same maturity. As a result, the contingent claim is uniquely valued relative to its underlying’s futures price and the assumed observable variance swap rate. In contrast to standard models of stochastic volatility, our approach does not require specifying the market price of volatility risk or observing the initial level of instantaneous volatility. As a consequence of our SVRH, the partial differential equation (PDE) governing the arbitrage-free value of the contingent claim just depends on two state variables rather than the usual three. We then focus on the consistency of our SVRH with the standard assumption that the risk-neutral process for the instantaneous variance is a diffusion whose coefficients are independent of the variance swap maturity. We show that the combination of this maturity independent diffusion hypothesis (MIDH) and our SVRH implies a very special form of the risk-neutral diffusion process for the instantaneous variance. Fortunately, this process is tractable, well-behaved, and enjoys empirical support. Finally, we show that our model can also be used to robustly price and hedge volatility derivatives.     

A comprehensive structural model for defaultable fixed-income bonds

An exact valuation formula for defaultable corporate coupon bonds is proved. The model incorporates discrete coupons, bankruptcy costs, taxes and the market risk generated by a stochastic risk-free structure. The aim of this paper is twofold: first, we generalise previous pricing models for corporate bonds; second, we provide a comprehensive formula in order to properly disentangle the contribution of several risk factors to credit spreads.     

Bankruptcy probability changes and the differential informativeness of bond upgrades and downgrades

Prior studies have found that stock returns around announcements of bond upgrades are insignificant, but that stock prices respond negatively to announcements of bond downgrades. This asymmetric stock market reaction suggests either that bond downgrades are timelier than upgrades, or that voluntary disclosures by managers preempt upgrades but not downgrades. This study investigates these conjectures by examining changes in firms’ probabilities of bankruptcy (assessed using bankruptcy prediction models) and voluntary disclosure activity around rating change announcements. The results indicate that the assessed probability of bankruptcy decreases before bond upgrades, but not after. By contrast, the assessed probability of bankruptcy increases both before and after bond downgrades. We also find that controlling for potential wealth-transfer related rating actions, which can impact stock returns differently, does not alter our results. Tests of press releases and earnings forecasts issued by firms suggest that the differential informativeness of upgrades and downgrades is not caused by differences in pre-rating change voluntary disclosures by upgraded and downgraded firms. The results support the hypothesis that downgrades are timelier than upgrades.     

Bond yields and debt supply: new evidence through the lens of a preferred-habitat model

This paper examines the responsiveness of bond yields to changes in debt supply. The preferred-habitat theory predicts a positive relation between the term spread and relative supply of longer term debt, and that this relation is stronger when risk aversion is high. To capture this effect, a time-varying coefficient model is introduced and applied to German bond data. The results support the theoretical predictions and indicate substantial time variation: under high risk aversion, yield spreads react about three times more strongly than when risk aversion is low. The accumulated response of term spreads to a one standard deviation change in debt supply ranges between 4 and 46 basis points.     

The Basel Committee proposals for a new capital accord: implications for Italian banks

Following a few general considerations on the recently proposed revision of the Basel Agreement on capital adequacy, this paper focuses on the first pillar of the Basel Committee proposals, the handling of capital requirements for credit risk in the banking book. The Basel Committee envisages an approach alternatively based on external ratings or on internal rating systems for the determination of the minimum capital requirement related to bank loan portfolios. This approach supports a system of capital requirements that is more sensitive to credit risk. On the basis of specific assumptions, these requirements provide a measure of the value at risk (VaR) produced by models used by major international banks. We first address the impact of the standardised and (internal ratings-based) IRB foundation approach using general data on Italian banks loans' portfolios default rates. We then simulate the impact of the proposed new rules on the corporate loan portfolios of Italian banks, using the unique data set of mortality rates recently published by the Bank of Italy. Three main conclusions emerge from the analysis: (i) the standardised approach implicitly penalizes Italian banks in their interbank funding as their rating is generally below AA/Aa, (ii) the average default rate experienced by Italian banks is higher than the one implied in the benchmark risk weight (BRW) proposed by the Basel Committee for the IRB foundation approach, thereby potentially leading to an increase in the regulatory risk weights, and (iii) the risk-weight is based on an average asset correlation that is significantly higher than the one historically recorded within the Italian banks' corporate borrowers. These findings support the need for a significant revision of the basic inputs and assumptions of the Basel proposals. Finally, in relation to the conditions that allow the capital market to effectively discipline banks, we comment on the proposals advanced in relation to the third pillar of the new capital adequacy scheme.     

Calendar effects and the pricing of risk: the UK evidence

For some time there has been a puzzle surrounding the seasonal behaviour of stock returns. This paper demonstrates that there is an asymmetric relationship between risk and return across the different months of the year. The paper finds that systematic risk is only priced during the months of January, April and July. Variance risk and firm size are priced during several months of the year including January. An analysis of the relative behaviour of size based securities reveals that firm capitalization makes a valuable contribution to the magnitude of risk premiums.     

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.     

Assessing business risk: The case of Premier Punch, Inc

The recently issued Statement on Auditing Standards No. 109, Understanding the Entity and Its Environment and Assessing the Risks of Material Misstatement, emphasizes the need for auditors to understand the client’s business and environment, particularly the client’s business risk [American Institute of Certified Public Accountants (AICPA) (2006a), understanding the entity and its environment and assessing the risks of material misstatement, Statement on Auditing Standards No. 109. New York, NY: AICPA]. However, the manner in which auditors obtain such an understanding, especially an auditor’s assessment of a client’s business risk, is often challenging for students because they lack the business experience necessary to perform such an assessment. This case provides students with an opportunity to assess business risk in a realistic context that includes evidence beyond the content of the financial statements. Company information is provided via a webpage (www.premierpunch.com) with content similar to that of an actual investor relations site. Students must evaluate the information presented in the company’s annual report, press releases and other sources, and consider the impact of that information on several facets of business risk. Students also perform an analytical review of the company’s financial statements and synthesize the case information into a professional memo containing their assessment of business risk.     

Liquidity risk of corporate bond returns: conditional approach

We study the exposure of the US corporate bond returns to liquidity shocks of stocks and Treasury bonds over the period 1973–2007 in a regime-switching model. In one regime, liquidity shocks have mostly insignificant effects on bond prices, whereas in another regime, a rise in illiquidity produces significant but conflicting effects: Prices of investment-grade bonds rise while prices of speculative-grade (junk) bonds fall substantially (relative to the market). Relating the probability of these regimes to macroeconomic conditions we find that the second regime can be predicted by economic conditions that are characterized as “stress.” These effects, which are robust to controlling for other systematic risks (term and default), suggest the existence of time-varying liquidity risk of corporate bond returns conditional on episodes of flight to liquidity. Our model can predict the out-of-sample bond returns for the stress years 2008–2009. We find a similar pattern for stocks classified by high or low book-to-market ratio, where again, liquidity shocks play a special role in periods characterized by adverse economic conditions.     

On the way to recovery: A nonparametric bias free estimation of recovery rate densities

In this paper we analyse recovery rates on defaulted bonds using the Standard & Poor's/PMD database for the years 1981–1999. Due to the specific nature of the data (observations lie within 0 and 1), we must rely on nonstandard econometric techniques. The recovery rate density is estimated nonparametrically using a beta kernel method. This method is free of boundary bias, and Monte Carlo comparison with competing nonparametric estimators show that the beta kernel density estimator is particularly well suited for density estimation on the unit interval. We challenge the usual market practice to model parametrically recovery rates using a beta distribution calibrated on the empirical mean and variance. This assumption is unable to replicate multimodal distributions or concentration of data at total recovery and total loss. We evaluate the impact of choosing the beta distribution on the estimation of credit Value-at-Risk.     

Evaluating the sovereign and household credit risk in Singapore: A contingent claims approach

This study evaluates the credit risk of the household and government (sovereign) sectors in Singapore using the contingent claims approach (CCA). The CCA model estimates the default probability of both sectors based on the market value of the assets and liabilities of the sectors. Compared to the traditional credit rating system, this model is able to provide numerical estimates of the exposures and default probabilities. We find that from the year 2000 to 2013, variations in the credit risk measures correspond to the economic growth of Singapore. In addition, we suggest that the main factor affecting the credit risks in the government and household sectors in Singapore is the volatility of the assets held by both sectors, given that the asset-to-distress barrier ratios are relatively stable over the past 14 years for both sectors.