Empirical Estimation of the Expected Rate of Return on a Portfolio of Stocks

Abstract

We invert the residual income valuation model (using current stock prices, current book value of equity and short-term forecasts of accounting earnings) to obtain an estimate of the expected rate of return for a portfolio of stocks. Our approach is analogous to the estimation of the internal rate of return on a bond using market values and coupon payments.

Estimation of the cost of equity capital by inverting the residual income valuation model requires an estimate of growth in residual income beyond the forecast horizon. The contribution of our method is that we use the stock price and accounting data to simultaneously estimate the unique implied growth rate and the internal rate of return. This growth rate provides an adjustment for the fact that our estimate of the internal rate of return is based on current book value of equity and short-term earnings forecasts.

Our analysis of DJIA firms yields estimates of expected growth that are considerably higher than those assumed by earlier studies. Our estimated market premium over the risk-free rate is closer to the historical premium than that obtained by other studies using earnings forecast data.

After completing the pro-forma forecasting of earnings (as described in, Penman [2000], for example) and/or after obtaining analysts' forecasts of earnings for a number of firms with comparable operating activities, our method may be used to estimate the market's expectation of the cost of capital and growth for these firms. These estimates for comparable firms may be used to determine the intrinsic value of an unlisted firm, a division of a firm, or a firm that is believed to be relatively over/under-valued.

Keywords: Rate of return, market premium, residual income model

JEL Classification: G12, G14, G31, M41