CAPM and DCF: Does SML Relationship Gives Cost of Equity? – Ex-Ante Stock Returns are Not Same as Implied Discount Rates

Abstract

When Capital Asset pricing Model (CAPM) is considered as valid asset pricing theory, Security Market Line (SML) is supposed to give ex-ante returns for the single period investment horizon. Since the required returns should be same as the cost of equity (discount rates) in efficient markets, SML relationship is used for deriving cost of equity. Similarly, SML derived returns are used as parameter for performance evaluation like ascertaining alpha.This paper shows that the SML derived returns need not be same as implied discount rates even when CAPM is applicable and markets are efficient. This is because the stock returns and discount rates will be same mathematically only when the discount rates are expected to remain constant over the forecast period. The single period return of CAPM changes every year as the market changes with economic conditions implying that the market discount rates are changing. When the implied discount rates are varying, the ex-ante returns will have no resemblance to the implied discount rate for the year in consideration. This paper shows that the SML derived ex-ante returns may, if at all, only represent a geometric mean of the discount rates over a several investment periods into future. Similarly, the ex-ante returns can not be used for performance evaluation for single period investment horizon as it would only give the expected geometric mean of returns for the future periods making the concept of alpha evaluation erroneous.Similarly, when we extend this concept to equity risk premiums for the market, any historical risk premium can only be applicable for a similar period into the future. It is not possible to predict the equity risk premium for any individual year which again has implication for the surveys on equity risk premiums.The paper illustrates these ideas using two illustrations: Valuation of a firm using DCF Model with time-varying discount rates and Past Valuation data of S&P 500 using DDM Model.