Bond Risk and Return: A Review and Extension

Abstract

While considerable research exists on models designed to capture specific risk and return attributes of fixed income securities, general equilibrium and arbitrage asset valuation theories (e.g., CAPM, APT, Option Pricing) have been applied primarily to common stocks. Pricing models been used to empirically test risk and return relationships for fixed income securities.The purpose of this study is to review the major directions of research in bond risk and return and to analyze the use of OLS regression in determination of CAPM based market model risk estimates. Both Alexander [ l ] and Weinstein [ 2 ] have recently used OLS regression to obtain market model estimates of security betas for fixed income securities. Alexander highlights some of the violations of assumptions (e.g., autocorrelation of residuals) of the market model regression. This paper confirms his finding and uses Cochrane-Orcutt procedures to remove the effects of residual autocorrelation.Only recently have C U M , APT, and Option Statistical DesignFirst, distribution properties of the bond returns use in the analysis are reviewed. Second, market model parameters derived from the OLS and Cochrane-Orcutt regressions are used to forecast bond returns in a following prediction period. Lastly, the parameters of the market model are used as inputs to the Sharpe portfolio model to derive efficient bond portfolios. The correspondence between the return and variance of corner efficient portfolios and the actual return and risk in hold-out period i s also used as a basis for determining the usefulness of OLS determined bond betas. Summary and ConclusionsIt i s important to note that OLS estimates of beta may be systematically biased since a bond's beta i s a function of its duration, which systematically declines as the bond approaches maturity. This is also true, however, for a stock's beta. For stocks or bonds, the estimated beta is at best insignificantly different from the true average beta of the forecast o r prediction period. In addition, problems in derivation of duration based beta models are such that duration based beta models are not necessarily superior to OLS determined beta models. Given the greater familiarity and use of OLS regressiori models, this paper instead concentrates on problems and approaches to deriving OLS based bond betas. For the period analyzed the various violations of the assumptions of the linear regression model did not seriously affect estimation expected returns on risk. References[l] Alexander, Gordon, "Applying the Market Model to Long-Term Corporate

Corporate Bond Price Data Sources and Return/Risk Measurement

“…Alternatively, the infrequent trading typical of the organized exchanges may help explain why Moody's prices result in a larger standard deviation of return. 10 Despite such greater return variability, Moody's prices result in less market sensitivity (lower betas). A possible explanation for this is that Moody's prices and, therefore, returns are, in many cases, noncontemporaneous with the Merrill Lynch, Moody's, and/or the S&P 500 index.…”

“…(R 2 s for betas calculated using the S&P 500 are shown in the bottom part of Table 5. 10 The following example shows why less frequent trading may account, in part, for the greater variability of returns based on Moody's (exchange) prices: the actual trade price series of 100, 125, 150, 175, 200, representing a frequently traded security, has a return deviation of 39.5; whereas, the price series of 100, 100, 150, 150, 200, representing securities with infrequent trades, has a return standard deviation of 41.8.…”

Bond Beta and Default Risk

“…Alexander (1980) also finds serial correlation in his monthly time series data but no evidence of heteroscedasticity. Hill, Schneeweis, and Mohan (1982) conclude that the statistical problems of using OLS regression estimates of bond betas from time series data do not seriously affect the estimates.…”