THE TERM STRUCTURE OF DISCOUNT RATES

Although it is standard practice to use asset-pricing models such as t he CAPM and the APT to infer discount rates for the valuation of compa nies and investment projects, this practice is fraught with difficulti es that are rarely addressed. In the case of the CAPM, two problems of major importance are the choice of the risk-free interest rate and th e determination of the market-risk premium. Consider first the issue o f what proxy to use for the riskless interest rate. Both the CAPM and the APT imply that the riskless rate is the one period, or instantaneo us, riskless rate which, in applied work, is typically proxied by the rate on a one-month Treasury bill. However, it is unlikely that the ri skless rate will remain constant over the life of an investment projec t, and theories of the term structure based on the expectations hypoth esis suggest that a steeply sloping yield curve implies that the bill rate is expected to change. One ad hoc solution that is sometimes empl oyed is the use of forward rates over the life of the project to const ruct a series of implied riskless rates for each future period. An obv ious difficulty with this solution is that forward rates embody liquid ity premia as well as expected future spot rates. Of much greater sign ificance in applying the CAPM is the market-risk premium. It has becom e conventional to estimate this as the long-run-average excess of the market return over the Treasury bill return, which typically yields a figure of about 8% to 9%. The implicit assumption underlying this appr oach is that the market-risk premium has remained constant over a 60 y ear period which has seen major changes in the economy. Moreover, then is now extensive evidence that the market-risk premium varies over ti me with the level of interest rates.In this paper, I present an empiri cally based, but internally consistent, dynamic model of the behavior of interest rates and the market-risk premium, that allows for determi nation of a term structure of discount rates using the capital asset-p ricing model, when both the riskless interest rate and the market-risk premium vary over time. The approach, which is applicable with obviou s changes to multi-period applications of the APT, implies that the te rm structure of discount rates and the market-risk premium change over time as functions of a small number of state variables. The model is implemented by estimating the joint stochastic process for short- and long-term interest rates, the market dividend yield, and the return on the market portfolio. Then, given the stochastic process and the curr ent values of the two interest rates and the market dividend yield, th e expected return from investing $1 in the market portfolio for T year s can be estimated by Monte Carlo simulation of the system of interest rates, dividend yields, and market returns. It is then a simple matte r to convert this expected return into a discount rate for a T-period cash flow. The term structure of (risky) discount rates is shown to va ry considerably over time with the level of interest rates.