How to Discount Cashflows with Time-Varying Expected Returns

While many studies document that the market risk premium is predictable and that betas are not constant, the dividend discount model ignores time-varying risk premiums and betas. We develop a model to consistently value cashflows with changing risk-free rates, predictable risk premiums, and conditional betas in the context of a conditional CAPM. Practical valuation is accomplished with an analytic term structure of discount rates, with different discount rates applied to expected cashflows at different horizons. Using constant discount rates can produce large misvaluations, which, in portfolio data, are mostly driven at short horizons by market risk premiums and at long horizons by time variation in risk-free rates and factor loadings. TO DETERMINE AN APPROPRIATE DISCOUNT RATE for valuing cashflows, a manager is confronted by three major problems: the market risk premium must be estimated, an appropriate risk-free rate must be chosen, and the beta of the project or company must be determined. All three of these inputs into a standard CAPM are not constant. Furthermore, cashflows may covary with the risk premium, betas, or other predictive state variables. A standard Dividend Discount Model (DDM) cannot handle dynamic betas, risk premiums, or risk-free rates because in this valuation method, future expected cashflows are valued at constant discount rates. In this paper, we present an analytical methodology for valuing stochastic cashflows that are correlated with risk premiums, risk-free rates, and timevarying betas. All these effects are important. First, the market risk premium is not constant. Fama and French (2002) argue that the risk premium moved to around 2% at the turn of the century from 7% to 8% 20 years earlier. Jagannathan, McGratten, and Scherbina (2001) also argue that the market ex ante risk premium is time varying and fell during the late 1990s. Furthermore, a large literature claims that a number of predictor variables, including ∗Ang is with Columbia University and NBER. Jun Liu is at UCLA. We would like to thank Michael Brandt, Michael Brennan, Bob Dittmar, John Graham, Bruce Grundy, Ravi Jagannathan, and seminar participants at the Australian Graduate School of Management, Columbia University, the Board of Governors of the Federal Reserve, and Melbourne Business School for comments. We also thank Geert Bekaert and Zhenyu Wang for helpful suggestions and especially thank Yuhang Xing for constructing some of the data. We also thank Rick Green (the former editor), and we are grateful to an anonymous referee for helpful comments that greatly improved the paper. The authors acknowledge funding from an INQUIRE UK grant. This paper represents the views of the authors and not of INQUIRE. All errors are our own.