The authors conduct an empirical analysis of industry costs of equity by using
the capital asset pricing model and a three-factor model and find great
uncertainty in estimates of industry costs of equity. Imprecise estimates of
risk factor sensitivities contribute to this variation, but uncertainty about
market and factor risk premiums are even more important.
Analysts typically evaluate investment projects by comparing the present value of
expected future cash flows with a project's initial outlay. In addition to deciding
which asset valuation model to use, an analyst faces a lack of precision in estimating
sensitivities to the model's risk factors and imprecision of measured factor risk
premiums. The authors statistically analyze these problems and their implications for
industry cost of equity (CE) estimates.
The authors apply the capital asset pricing model (CAPM) and their own three-factor model
to monthly data on 48 U.S. industry groups for the 1963–94 period. The CAPM
measure of an asset's risk is its beta coefficient—the slope of a regression of
the asset's excess return on the excess return of the market. In addition to the market
excess return, the three-factor model includes regression terms representing the
difference in returns between small and large stocks—small minus big
(SMB)—and between high- and low-book-to-market stocks—high minus low (HML).
Small average standard errors of regressions for the entire period indicate that both
models estimate factor sensitivities precisely. This precision is misleading, however,
because the estimates vary through time. For example, a two-standard-deviation rule
results in a current cost of capital in excess of the risk-free rate that may be
anywhere between 3.92 percent and 6.40 percent for an industry with a full-period CAPM
beta of 1.0. CAPM market slopes are more variable than those estimated by the
three-factor model, suggesting that the SMB and HML variables reduce CE variation.
Conditional regressions on these variables confirm this result.
If risk factor sensitivities wander over time, a shorter time frame provides a better
forecast estimate. If sensitivities are mean reverting, a longer time frame is better.
The authors provide estimates using full-period regressions; three-, four-, and
five-year rolling regressions; and three-factor model conditional regressions. They find
that industry CAPM betas are mean reverting. Thus, full-period slopes provide a slight
advantage in forecasting near-term and long-term CE estimates. In the three-factor
model, mean reversion exists for some industries but not for others. Conditional
estimates appear to identify permanent changes in sensitivities that are not found in
full-period regressions. Even though conditional estimates provide slightly more
accurate return forecasts, it is unclear which three-factor model regressions are
better.
The three statistical approaches produce only small differences in risk factor
sensitivities, but this finding may not be true for resulting CE estimates. CAPM CE
estimates differ among industries only moderately. The three-factor model produces
greater differences in CE estimates because the slopes of the SMB and HML variables
differ among industries. Large differences in three-factor model CE estimates also occur
between conditional and five-year rolling regressions. CAPM CE estimates may also vary
considerably relative to those of the three-factor model. In some industries, CAPM and
three-factor model differences are small. Large differences occur in growth industries,
where the three-factor model assigns relatively low CE estimates, and in industries
where returns co-vary with small-stock returns or behave like distressed stocks, where
the three-factor model assigns relatively high CE estimates.
Varying sensitivities of risk factors clearly contribute to uncertainty about risk
premiums and thus the cost of equity. If the market risk premium were known with
certainty, factor sensitivities would create substantial uncertainty in CE estimates.
Variations in the market risk premium and the three-factor model SMB and HML risk
premiums are an even greater source of variance in CE estimates. Assuming that industry
CAPM betas and three-factor SMB and HML coefficients are known with certainty, standard
errors of 3.0 percent annually are typical for estimates of CE. For example, the
two-standard-deviation bounds for the CE of a project with a true CAPM beta of 1.0 are
−0.26 percent and 10.58 percent. This uncertainty is further compounded by
uncertainty as to the correct asset pricing model. The authors conclude that estimates
of the cost of equity are “distressingly imprecise” and question whether a
superior approach exists for valuing projects.