D. S. Prasada Rao, E. Anthony Selvanathan, Dirk Pilat, Generalized Theil-Tornqvist Indices with Applications to International Comparisons of Prices and Real Output, The Review of Economics and Statistics, Vol. 77, No. 2 (May, 1995), pp. 352-360

ABSTRACT 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.

Our examination of the cross-section of expected returns reveals economically and statistically significant compensation (about 6 to 9% per annum) for beta risk when betas are estimated from time-series regressions of annual portfolio returns on the annual return on the equal-weighted market index. The relation between book-to-market equity and returns is weaker than that in Fama and French (1992a). We conjecture that book-to-market results using COMPUSTAT data are affected by a selection bias and provide indirect evidence.

ABSTRACT Our examination of the cross‐section of expected returns reveals economically and statistically significant compensation (about 6 to 9 percent per annum) for beta risk when betas are estimated from time‐series regressions of annual portfolio returns on the annual return on the equally weighted market index. The relation between book‐to‐market equity and returns is weaker and less consistent than that in Fama and French (1992). We conjecture that past book‐to‐market results using COMPUS‐TAT data are affected by a selection bias and provide indirect evidence.