Default Risk in Equity Returns

Abstract

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 bookto-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.A FIRM DEFAULTS WHEN IT FAILS to service its debt obligations. Therefore, default risk induces lenders to require from borrowers a spread over the risk-free rate of interest. This spread is an increasing function of the probability of default of the individual firm.Although considerable research effort has been put toward modeling default risk for the purpose of valuing corporate debt and derivative products written on it, little attention has been paid to the effects of default risk on equity returns. 1 The effect that default risk may have on equity returns is not obvious, since equity holders are the residual claimants on a firm's cash f lows and there is no promised nominal return in equities.Previous studies that examine the effect of default risk on equities focus on the ability of the default spread to explain or predict returns. The default spread is usually defined as the yield or return differential between long-term BAA corporate bonds and long-term AAA or U.S. Treasury bonds.2 However, * Vassalou is at Columbia University and Xing is at Rice University. ton (1995, 1997), Jarrow and Turnbull (1995), Longstaff and Schwartz (1995), Zhou (1997), Lando (1998), andDuffee (1999), among others.2 For instance, many studies have shown that the yield spread between BAA and AAA corporate bond spread can predict expected returns in stocks and bonds. Such studies include those of Fama and Schwert (1977), Keim and Stambaugh (1986), Campbell (1987), and Fama and French (1989, 832The Journal of Finance as Elton et al. (2001) show, much of the information in the default spread is unrelated to default risk. In fact, as much as 85 percent of the spread can be explained as reward for bearing systematic risk, unrelated to default. Furthermore, differential taxes seem to have a more important inf luence on spreads than expected loss from default. These results lead us to conclude that, independent of whether the default spread can explain, predict, or otherwise relate to equity returns, such a relation cannot be attributed to the effects that default risk may have on equities. In other words, we still know very little about how default risk affects equity returns.The purpose of this paper is to address precisely this question. Instead of relying on information about default obtained from the bonds market, we estimate default likelihood indicators (DLI) for individual firms using equity data. These DLI are nonlinear functions of the default probabilities of the in...

Counterparty risk analysis using Merton's structural model under Solvency II

“…Nuevamente, esta alternativa implica suponer que cada activo dentro de un mismo rating tiene una probabilidad de default igual a la media histórica. Sin embargo, es habitual que una empresa experimente cambios importantes en su probabilidad de default antes de producirse un cambio en su rating (Vassalou y Xing, 2004). El modelo que se propone ha sido ampliamente utilizado para el análisis del riesgo de impago y diversos estudios indican su adecuación y superioridad frente a otras alternativas [Lau (2006), Gropp et al (2002) y Vassalou y Xing (2004], debido a su flexibilidad y capacidad para medir de forma continuada el riesgo a partir de información de mercado.…”

“…Sin embargo, es habitual que una empresa experimente cambios importantes en su probabilidad de default antes de producirse un cambio en su rating (Vassalou y Xing, 2004). El modelo que se propone ha sido ampliamente utilizado para el análisis del riesgo de impago y diversos estudios indican su adecuación y superioridad frente a otras alternativas [Lau (2006), Gropp et al (2002) y Vassalou y Xing (2004], debido a su flexibilidad y capacidad para medir de forma continuada el riesgo a partir de información de mercado. A través de este modelo podemos construir mediante simulación la distribución esperada de pérdidas asumiendo diferentes correlaciones y probabilidades de default con lo cual es una alternativa muy flexible para modelizar el riesgo de crédito de un conjunto de contrapartes.…”

Assessing bankruptcy prediction models via information content of technical inefficiency

“…can be computed using an iterative procedure suggested by Vassalou and Xing (2004) and Bharath and Shumway (2008). Here NðÁÞ is the standard normal distribution function, V the market value of the firm's assets, B the face value of the firm's debt, l the expected continuously compounded return on V, r V the volatility of firm's value, and T the maturing period of the firm's debt.…”

“…The well-known prediction models include discriminant analysis model (Altman 1968), Merton model (Merton 1974;Vassalou and Xing 2004), logit model (Ohlson 1980), and probit model (Zmijewski 1984), to name only a few. The common principal of these approaches is that the models are developed using single-period data of firms.…”

Comparing the Reliability of Accounting-Based and Market-based Prediction Models

“…Market-based models using the Black and Scholes (1973) and Merton (1974) contingent claims approach provide attractive option and several recent papers have been using this methodology to assess the likelihood of financial distress of companies such as studies by Bharath and Shumway (2004), Hillegeist et al (2004), Vassalou and Xing (2004), Reisz and Perlich (2007) and Campbell, Hilscher and Szilagyi (2008) (Bharath and Shumway 2004;Hillegeist, Keating et al 2004;Vassalou and Xing 2004;Reisz and Perlich 2007;Campbell, Hilscher et al 2008). Market-based model counters most of the criticisms on accounting-ratio-based models whereby: (i) the marketbased model provides a sound theoretical approach for distressed company, (ii) in efficient markets, stock prices will reflect all the information contains in the financial statements and will also reflect information which is not captured by financial statements, (iii) company accounting policies unable to influence market variables, (iv) future cash flow of company is reflected in the stock market price, and therefore it is a reliable variable to predict the future of the company, and (v) the market-based models is not time or sample dependent (Agarwal and Taffler 2008).…”