An Empirical Comparison of Bond Return Forecast Methods

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An Empirical Comparison of Bond Return Forecast Methods

The forecasting of corporate bond returns has had varying degrees of interest in the academic literature. The greater variability in interest rates over the past ten to fifteen years has highlighted the need for the evaluation of competing methodologies. Forecasting of bond returns is an important issue since the nature of a bond is much different from that of equity. The return of a bond consists of both interest and price change over the holding period, with a maximum holding period equal to its finite maturity. Whereas common stocks also have dividends and price change for their return, stocks theoretically have an infinite life.

The purpose of this research is to deal specifically with the issue of different bond return estimation techniques and evaluate their forecast performance. Although this study is not an exercise in forecasting interest rates, there is naturally a relationship to returns and thus performance. If one could forecast interest rates perfectly, including unexpected events, then different methods of bond return forecasting would hardly be needed. This study will use a standard interest rate forecast throughout. The methodologies employed are not all concerned with the finite life of the bonds, while some do make adjustment for this so-called "maturity effect or bias." The methods to be evaluated are variations of five different techniques used in the past. These are (1) the historical average, (2) the prior period return, (3) a bond index model with and without autocorrelation adjustments, (4) duration models based on price change and index durations, and (5) autoregressive procedures using Box-Jenkins[5] ARIMA. These are not exhaustive of all available methods but do consider the more common and popular techniques.

PREVIOUS RESEARCH

Even though much research has been done on bonds and their returns, little has been done on a comparative basis. Bond returns have been investigated for their time series properties[4, 17] and were shown to have a bias due to their declining time to maturity. Brennan and Schwartz[6] note that there is "a strong relation between price prediction errors and subsequent bond returns." The results of prior empirical research on both bonds and equities suggest that a comparative investigation be carried out to assess the relative performance of various competing forecasting methods.

Fama[10], although showing that there is a significant relationship in daily equity returns, notes that there is not in weekly and monthly price changes. Research on bonds by Barnes[2] and Hill, Schneeweiss, and Mohan[12] on bond portfolios estimation notes that there is significant autocorrelation in their data. Alexander [1], McEnally and Ferri[14], and Weinstein[19] show that there is autocorrelation in bonds returns and that the magnitude of risk changes as the indices are changed. The degree of risk also declines over time. Consequently, forecasts may be highly dependent on the index inputs.

Duration and bond betas are two measures of risk that are highly related and considered to be the most descriptive of how bond returns change. The Macauley[13] or the Fisher-Weil[11] definition of duration measures how the price of a bond changes given a change in the (flat) term structure of interest rates. Other duration measures by Cox, Ingersoll, and Ross[8] and Bierwag, Kaufman, and Toevs[3] incorporate different stochastic processes. Duvall and Cheney[9] suggest two risk measures, [Beta] from yields as measures of market reinvestment risk and duration as a measurement of price volatility. Indicative of prior research is the lack of comparability across various techniques. The performance of many has shown small errors independently for each method but not for the methods collectively (i.e., in comparison).

The comparison of these methods is useful for investors in selecting and evaluating their bond investments. …