Ebook Using Yield Spreads to Estimate Expected Returns on Debt and Equity
The expected loss on corporate debt is an important input to many financial decisions, including lending, bank regulation, portfolio selection, risk management, and valuation. Starting with Altman (1968), various methods of forecasting default losses using characteristics of individual firms or rating classes have been proposed. These include discriminant analysis, approaches based on rating transitions (Elton et al., 2001), structural models of risky debt (Leland, 2002), and various proprietary models, of which the KMV model is probably the best known (Crouhy et al., 2001).
The extensive development of bond markets offers another opportunity, which we pursue in this paper: to extract the expected default loss on a corporate bond from its yield spread. We calibrate the Merton (1974) structural model of risky debt using observed bond spreads in conjunction with information on leverage, equity volatility, and equity risk premia to yield an estimate of expected future default losses incorporated in current market prices.
In contrast with commonly used estimation methods based on historical data, our forecast uses market prices and reflects current market expectations about default. Our estimates are based on an equilibrium model, and are consistent with current market yields. They provide neutral estimates of expected losses for anyone who does not believe that their forecasting ability is better than the bond market’s. Expected returns on bonds are the difference between promised returns and expected default losses. If default loss forecasts are made independently of yields, the resulting expected return estimates can have undesirable properties.
Any forecasting method that does not reflect current capital market data, such as methods based on rating transitions, will translate all short-term variation in yields into variation in expected returns. Structural models based on current capital market data, such as Leland (2002) or the KMV model (Crosbie and Bohn, 2002), will assign all variation in yields unexplained by the model to variation in expected returns. In contrast, our method produces estimates of expected returns that are neutral in the sense that, as yields vary, expected losses vary as an equilibrium fraction of the yield change. For this reason, we believe that default loss estimates produced by a procedure based on yields, such as ours, should have a central role in bank management and regulation, and the management of fixed income portfolios.
The proposed method is based on splitting the observed market spread into the part due to expected default and that due to other factors. This decomposition is achieved by first adjusting the observed spread to exclude non-default factors. The remaining spread is then calibrated to a structural model of risky debt and other capital market variables: market leverage, equity volatility and equity risk premia. Thus, the estimate of the expected default loss incorporates information contained in current bond yields, which have been shown to predict expected default. Leverage, equity prices and volatility have also been shown to contain information about future default, and form the basis of models that are widely used in practice (Crosbie and Bohn, 2002). In these methods, the Merton model is calibrated to these three variables to derive a default measure which is then used in combination with historical default and recovery data to give a forecast of expected default losses. Although our approach is similar, we calibrate the Merton model to current yield spreads and do not use historical default data.
The approach has several potential advantages over existing methods. The prediction depends on easily observable current capital market variables which should contain consensus market expectations about future default. Other estimates of future default losses are based on combinations of historical default and recovery rate data, accounting variables, and equity prices. Unlike such models, our approach does not require empirical calibration to past data or any assumptions of stability of default rates over time. It gives a direct estimate of the expected loss from default, rather than relying on separate estimation of the probability of default and the recovery rate. It is independent of accounting conventions, and thus can be used without adjustment in any country. Finally, unlike some methods, it can be applied to estimate expected default losses on individual bonds rather than on broad ratings categories. Altman and Rijken (2003) show that there is significant variation of expected default losses within ratings classes, which ratings-based approaches will fail to capture.
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