Portfolio Design: A Modern Approach to Asset Allocation

APPENDIX: ALTERNATIVE ESTIMATES OF STOCK RETURNS

To understand alternative approaches to estimating equity returns, we need to begin with the basic components of a stock return. The stock return in any given year is equal to the dividend yield plus the capital gain:

where Pt is the stock price at the end of year t and Dt is the dividend paid in year t. Estimates of future expected returns based on past historical data implicitly assume that capital gains in the past will repeat themselves. If past capital gains have been inflated as P-Es have risen, however, then past data may not be a good basis for future expectations. For that reason, some experts reject the use of past returns to predict future returns, and turn instead to more fundamental measures of corporate performance.

According to Fama and French (2002), the average return on equity can be estimated in three alternative ways. The first method simply measures the arithmetic average return over the sample period.

where GPt = (Pt − Pt − 1) / Pt − 1, the capital gain on the stock. If there is a rise in P-Es during the sample period, then the average capital gain will reflect this rise in P-Es, thereby inflating the estimate of future equity returns.

According to finance theory, the value of a stock should be based on expected ...