The expected rate of return on a firm’s stock, the “cost of equity,” is an important input for making decisions affecting the firm. Because it affects the discount rate at which expected future cash flows are valued, the cost of equity plays a key role in the firm’s investment decisions. For a public utility, the estimated cost of equity capital has a direct impact on how the prices of the firm’s services are regulated by its state public utility commission.
The cost of equity is equal to a riskless interest rate plus the expected excess return on the firm’s stock. One approach to estimating the latter quantity uses a standard asset-pricing model, in which the expected excess return hinges on sensitivities of the firm’s stock return to market-wide factors.1 If rt denotes the stock’s excess return and ft denotes а К x 1 vector of the factors, all realized in period t, then the stock’s sensitivities, or “betas,” are the slope coefficients in the regression
where et is the mean-zero regression disturbance. When the factors appropriate to the given model are constructed as excess portfolio returns or payoffs on zero-investment positions, as will be the case in the models analyzed below, then the pricing model implies a = 0.2 That is, the pricing model implies that the stock’s expected excess return, //, is given by 13’A, wrhere A is the vector of “factor premiums,” the expected values of the factors.
The elements of /3 and A must be estimated, so the true cost of equity is uncertain. Moreover, even if (3 and A were known for certain, one might be skeptical about whether any pricing model could deliver the correct cost of equity for every stock. That is, a decision maker might be uncertain about whether the model misprices the stock in question, so that the expected excess return might actually be
where a is some unknown non-zero amount by which the model misprices the stock. This “mispricing” uncertainty about a contributes further to the uncertainty about the cost of equity. Finally, if the decision maker has any doubts about which pricing model to use, then the uncertainty about fx also includes that “model” uncertainty. This study attempts to quantify these various sources of uncertainty and gauge the relative importance of each in estimating a firm’s cost of equity.