Time‐Varying Asset Volatility and the Credit Spread Puzzle

Most extant structural credit risk models underestimate credit spreads—a shortcoming known as the credit spread puzzle. We consider a model with priced stochastic asset risk that is able to fit medium‐ to long‐term spreads. The model, augmented by jumps to help explain short‐term spreads, is estimated on firm‐level data and identifies significant asset variance risk premia. An important feature of the model is the significant time variation in risk premia induced by the uncertainty about asset risk. Various extensions are considered, among them optimal leverage and endogenous default.     

DURATION,DEFAULT RISK,AND THE TERM STRUCTURE OF INTEREST RATES

We examine the interactive effect of default and interest rate risk on duration of defaultable bonds. We show that duration for defaultable bonds can be longer or shorter than default‐free bonds depending on the relation between default intensity and interest rates. Empirical evidence indicates that in most cases duration for defaultable bonds is much shorter than for their default‐free counterparts because of the negative relation between default risk and interest rates. Results suggest that the duration measure must be adjusted for the effects of default risk and stochastic interest rates to achieve an effective bond portfolio immunization.     

Do U.S. Insurance Firms Offer the “Wrong” Incentives to Their Executives?

We examine the relation between executive compensation and market‐implied default risk for listed insurance firms from 1992 to 2007. Shareholders are expected to encourage managerial risk sharing through equity‐based incentive compensation. We find that long‐term incentives and other share‐based plans do not affect the default risk faced by firms. However, the extensive use of stock options leads to higher future default risk for insurance firms. We argue that this is because option‐based incentives induce managerial risk‐taking behavior, which seeks to maximize managerial payoff through equity volatility. This could be detrimental to the interests of shareholders, especially during a financial crisis.     

A mean/variance approach to long-term fixed-income portfolio allocation

Abstract

Long-term investments in bonds offer known returns, but with risks corresponding to defaults of the underwriters. The excess return for a risky bond is measured by the spread between the expected yield and the risk-free rate. Similarly, the risk can be expressed in the form of a default spread, measuring the difference between the yield when no default occurs and the expected yield. For zero-coupon bonds and for actual market data, the default spread is proportional to the probability of default per year. The analysis of market data shows that the yield spread scales as the square root of the default spread. This relation expresses the risk premium over the risk-free rate that the bond market offers, similarly to the risk premium for equities. With these measures for risk and return, an optimal bond allocation scheme can be built following a mean/variance utility function. Straightforward computations allow us to obtain the optimal portfolio, depending on a pre-set risk-aversion level. As for equities, the optimal portfolio is a linear combination of one risk-free bond and a risky portfolio. Using the scaling law for the default spread allows us to obtain simple expressions for the value, yield and risk of the optimal portfolio.     

Municipal Bond Liquidity and Default Risk

This paper examines the pricing of municipal bonds. I use three distinct, complementary approaches to decompose municipal bond spreads into default and liquidity components, and find that default risk accounts for 74% to 84% of the average spread after adjusting for tax‐exempt status. The first approach estimates the liquidity component using transaction data, the second measures the default component with credit default swap data, and the third is a quasi‐natural experiment that estimates changes in default risk around pre‐refunding events. The price of default risk is high given the rare incidence of municipal default and implies a high risk premium.     

More on Properness: The Case of Mean-Variance Preferences

This paper focuses on the situations where individuals with mean-variance preferences add independent risks to an already risky situation. Pratt and Zeckhauser (Econometrica, 55, 143–154, 1987) define a concept called proper risk aversion in the expected utility framework to describe the situation where an undesirable risk can never be made desirable by the presence of an independent undesirable risk. The assumption of mean-variance preferences allows us to study proper risk aversion in an intuitive manner. The paper presents an economic interpretation for the quasi-concavity of a utility function derived over mean and variance. The main result of the paper says that quasi-concavity plus decreasing risk aversion is equivalent to proper risk aversion.     

Dynamic credit default swap curves in a network topology

Systemically important banks are connected and their default probabilities have dynamic dependencies. An extraction of default factors from cross-sectional credit default swap (CDS) curves allows us to analyze the shape and the dynamics of default probabilities. In extending the Dynamic Nelson Siegel (DNS) model to an across firm multivariate setting, and employing the generalized variance decomposition of Diebold and Yilmaz [On the network topology of variance decompositions: Measuring the connectedness of financial firms. J. Econom., 2014, 182(1), 119–134], we are able to establish a DNS network topology. Its geometry yields a platform to analyze the interconnectedness of long-, middle- and short-term default factors in a dynamic fashion and to forecast the CDS curves. Our analysis concentrates on 10 financial institutions with CDS curves comprising of a wide range of time-to-maturities. The extracted level factor representing long-term default risk shows a higher level of total connectedness than those derived for short-term and middle-term default risk, respectively. US banks contributed more to the long-term default spillover before 2012, whereas European banks were major default transmitters during and after the European debt crisis, both in the long-term and short-term. The comparison of the network DNS model with alternatives proposed in the literature indicates that our approach yields superior forecast properties of CDS curves.     

Default Risk in Equity Returns

This is the first study that uses Merton's (1974) option pricing model to compute default measures for individual firms and assess the effect of default risk on equity returns. The size effect is a default effect, and this is also largely true for the book‐to‐market (BM) effect. Both exist only in segments of the market with high default risk. Default risk is systematic risk. The Fama–French (FF) factors SMB and HML contain some default‐related information, but this is not the main reason that the FF model can explain the cross section of equity returns.     

Theory and evidence on the dynamic interactions between sovereign credit default swaps and currency options

Using sovereign CDS spreads and currency option data for Mexico and Brazil, we document that CDS spreads covary with both the currency option implied volatility and the slope of the implied volatility curve in moneyness. We propose a joint valuation framework, in which currency return variance and sovereign default intensity follow a bivariate diffusion with contemporaneous correlation. Estimation shows that default intensity is much more persistent than currency return variance. The market price estimates on the two risk factors also explain the well-documented evidence that historical average default probabilities are lower than those implied from credit spreads.     

Controlling Risk in Accounts Receivable Management

In granting trade credit, the credit manager must weigh the expected profit from a sale against the risk of customer default. A common procedure is to sell on credit only to those customers whose risk of default is below some critical level. This procedure does not effectively control a firm's ratio of bad debt to sales. In this paper, formulas are derived for the variance of this ratio under various assumptions regarding the number and size distribution of customers. Knowledge of this variance enables the credit manager to more accurately control his credit losses.     

Original-Issue Systematic and Default Risk Pricing Efficiency of Speculative-Grade Bonds

We investigate whether primary market, original‐issue risk premiums on speculative‐grade debt are justified solely by expected defaults or whether these risk premiums also include other orthogonal risk components. Studies of secondary‐market holding period risk and return have hypothesized that risk premiums on speculative‐grade debt may be explained by bond‐ and equity‐related systematic risk and possibly other types of risk. Using an actuarial approach that considers contemporaneous correlation between default frequency and severity and first‐order serial correlation, we cannot reject the hypothesis that the entire original‐issue risk premium can be explained by expected default losses. This suggests that speculative‐grade bond primary markets efficiently price default risk and that other types of risk are priced as coincident as opposed to orthogonal risks.     

The “forward premium puzzle” and the sovereign default risk

Carry-trade strategies which consist of buying forward high-yield currencies tend to yield positive excess returns when global financial markets are booming, whereas they generate losses during crises. Firstly, we show that the sovereign default risk, which is taken on by investing in high-yield currencies, may increase the magnitude of the gains during the boom periods and the losses during crises. We empirically test for this hypothesis on a sample of 18 emerging currencies over the period from June 2005 to September 2010, the default risk being proxied by the sovereign credit default swap spread. Relying on smooth transition regression (STR) models, we show that default risk contributes to the carry-trade gains during booms, and worsens the losses during busts. Secondly, we turn to the “Fama regression” linking the exchange-rate depreciation to the interest-rate differential. We propose a nonlinear estimation of this equation, explaining the puzzling evolution of its coefficient by the change in the market volatility along the financial cycle. Then, we introduce the default risk into this equation and show that the “forward bias”, usually evidenced by a coefficient smaller than unity in this regression, is somewhat alleviated, as the default risk is significant to explain the exchange-rate change.     

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.     

A Duration Model For Defaultable Bonds

I extend recent theoretical work on duration and derive an improved model for the risk‐adjusted duration of corporate bonds. My ex‐ante risk‐adjusted duration is the sum of the bond's Fisher‐Weil duration and the duration of the potential expected delay in recovery caused by the default option. My main conclusion is that failing to adjust duration for default is costly for high‐yield bonds, especially those with a shorter time to maturity. For investment‐grade bonds, this cost is trivial for all maturities.     

Systemic Bank Risk in Brazil: A Comprehensive Simulation of Correlated Market, Credit, Sovereign and Inter-Bank Risks

In this study we present a comprehensive forward‐looking portfolio simulation methodology for assessing the correlated impacts of market risk, private sector and Sovereign credit risk, and inter‐bank default risk. In order to produce better integrated risk assessment for banks and systemic risk assessments for financial systems, we argue that reasonably detailed modeling of bank asset and liability structures, loan portfolio credit quality, and loan concentrations by sector, region and type, as well as a number of financial and economic environment risk drivers, is required. Sovereign and inter‐bank default risks are increasingly important in the current economic environment and their inclusion is an important model extension. This extended model is demonstrated through an application to both individual Brazilian banks (i.e., 28 of the largest banks) and groups of banks (i.e., the Brazilian banking system) as of December 2004. When omitting Sovereign risk, our analysis indicates that none of the banks face significant default risk over a 1‐year horizon. This low default risk stems primarily from the large amount of government securities held by Brazilian banks, but also reflects the banks' adequate capitalizations and extraordinarily high interest rate spreads. We note that none of the banks which we modeled failed during the very stressful 2007‐2008 period, consistent with our results. Our results also show that a commonly used approach of aggregating all banks into one single bank, for purposes of undertaking a systemic banking system risk assessment, results in a misestimate of both the probability and the cost of systemic banking system failures. Once Sovereign risk is considered and losses in the market value of government securities reach 10% (or higher), we find that several banks could fail during the same time period. These results demonstrate the well known risk of concentrated lending to a borrower, or type of borrower, which has a non‐zero probability of default (e.g., the Government of Brazil). Our analysis also indicates that, in the event of a Sovereign default, the Government of Brazil would face constrained debt management alternatives. To the best of our knowledge no one else has put forward a systematic methodology for assessing bank asset, liability, loan portfolio structure and correlated market and credit (private sector, Sovereign, and inter‐bank) default risk for banks and banking systems. We conclude that such forward‐looking risk assessment methodologies for assessing multiple correlated risks, combined with the targeted collection of specific types of data on bank portfolios, have the potential to better quantify overall bank and banking system risk levels, which can assist bank management, bank regulators, Sovereigns, rating agencies, and investors to make better informed and proactive risk management and investment decisions.     

Default and Recovery Risk Dependencies in a Simple Credit Risk Model

This paper provides evidence for the relationship between credit quality, recovery rate, and correlation. The paper finds that rating grade, rating shift, and macroeconomic factors provide a highly significant explanation for default risk and recovery risk of US bond issues. The empirical data suggest that default and recovery processes are highly correlated. Therefore, a joint approach is required for estimating time‐varying default probabilities and recovery rates that are conditional on default. This paper develops and applies such a model.     

Granularity adjustment for default risk factor model with cohorts

This paper examines granularity adjustments to parameter estimators in a default risk model with cohorts. The model is an extension of the Vasicek model (Vasicek, 1991) and includes a general factor and cohort specific factors. The granularity adjustments derived in the paper concern the mean and/or the variance of observed default frequencies and are easy to implement in practice. For illustration, the method is applied to the S&P corporate ratings. The Granularity Adjusted (GA) estimators are compared to the unadjusted estimators in terms of their asymptotic properties and in finite sample.     

Distance to default,subordinated debt,and distress indicators in the banking industry*

The recent financial crisis has highlighted the inadequacy of present supervisory arrangements to identify reliable ex‐ante indicators of banking distress. For a sample of US bank holding companies, we analyse the extent to which distance to default based on market data can be explained using accounting‐based indicators of risk. We show that a larger number of bank fundamentals help predict default for institutions that issue subordinated debt. For banks that issue sub‐debt, we find that higher charter values and low bank capitalizations further increase the power of bank fundamentals to predict default risk.     

Toward a Bottom‐Up Approach to Assessing Sovereign Default Risk

The authors propose a new approach to assessing sovereign risk that focuses on the underlying profitability and financial condition of a nations private corporate sector. More specifically, the authors show how their new Z‐Metrics™ approach—an updated and expanded version of the Alt‐man Z‐score methodology—can be used to measure the (cumulative) median probability of default of the non‐financial sector for the next five years, both as an absolute measure of corporate vulnerability and a relative measure that can be compared to the risk of other sovereigns and to the market's assessment as reflected in the prices of credit default swaps. In testing their approach, the authors measure the default probabilities of listed corporate entities in nine European countries, as well as the U.S., at two different points in time: the start of 2009 (and thus prior to the recognition of the Euro crisis by markets and most credit professionals) and for the first four months in 2010 (essentially, the beginning of the recognition of the crisis). Based on these two observations, the authors suggest that their corporate health index of the private sector would not only have served as an effective early warning indicator, but provided a (mostly) useful hierarchy of relative sovereign risks. In addition to predicting sovereign default risk, another potentially valuable use of the authors' model is to remind policy makers of the importance of a profitable private sector to the financial health of sovereign governments.     

An Empirical Analysis of the Pricing of Collateralized Debt Obligations

We use the information in collateralized debt obligations (CDO) prices to study market expectations about how corporate defaults cluster. A three‐factor portfolio credit model explains virtually all of the time‐series and cross‐sectional variation in an extensive data set of CDX index tranche prices. Tranches are priced as if losses of 0.4%, 6%, and 35% of the portfolio occur with expected frequencies of 1.2, 41.5, and 763 years, respectively. On average, 65% of the CDX spread is due to firm‐specific default risk, 27% to clustered industry or sector default risk, and 8% to catastrophic or systemic default risk.