322  Estimating the Cost of Capital With the collapse of the TMT sector in 2001, TMT stocks returned to their original proportion of the overall market. Since beta is computed using 60 months of historical data, however, non-TMT betas still reflected the TMT- heavy market composition. Thus, to value future cash flows after 2001, a more appropriate beta than the 2001 beta would be the one from 1997, when the market composition last matched the post-2001 composition. Remember, the end goal is not to measure beta historically, but rather to use the historical estimate as a predictor of future value. In this case, recent history isn’t very useful, so the important lesson is not to overweight it. Alternatives to CAPM: Fama-French Three-Factor Model  In 1992, Eugene Fama and Kenneth French published a paper in the Journal of Finance that re- ceived a great deal of attention for its authors’ conclusion: “In short, our tests do not support the most basic prediction of the SLB [Sharpe-Lintner-Black] Capital Asset Pricing Model that average stock returns are positively related to market betas.”22 Based on prior research and their own comprehensive regres- sions, Fama and French concluded that equity returns are inversely related to the size of a company (as measured by market capitalization) and positively related to the ratio of a company’s book value to its market value of equity. Given the strength of Fama and French’s empirical results, the academic community now measures risk with a model commonly known as the Fama- French three-factor model. With this model, a stock’s excess returns are re- gressed on excess market returns (similar to the CAPM), the excess returns of small stocks over big stocks (commonly referred to as SMB for “small minus big”), and the excess returns of high-book-to-market stocks over low- book-to-market stocks (known as HML for “high minus low”).23 Because the risk premium is determined by a regression on the SMB and HML stock portfolios, a company does not receive a premium for being small. Instead, the company receives a risk premium if its stock returns are correlated with those of small stocks or high-book-to-market companies. The SMB and HML portfolios are meant to replicate unobservable risk factors, factors that cause small companies with high book-to-market values to outperform their CAPM expected returns. We use the Fama-French three-factor model to estimate Costco’s cost of equity in Exhibit 15.8. To determine the company’s three betas, we regress Costco’s monthly stock returns against the excess market portfolio, SMB, and HML. As the exhibit indicates, the Costco beta on the market portfolio is 21 A. Annema and M. Goedhart, “Better Betas,” McKinsey on Finance, no. 6 (Winter 2003): 10–13; and A. Annema and M. Goedhart, “Betas: Back to Normal,” McKinsey on Finance, no. 20 (Summer 2006): 14–16. 22 E. Fama and K. French, “The Cross-Section of Expected Stock Returns,” Journal of Finance (June 1992): 427–465. 23 For a complete description of the factor returns, see E. Fama and K. French, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics 33 (1993): 3–56. Estimating the Cost of Equity  323 slightly higher in the Fama-French regression than in the market regression presented in Exhibit 15.5, but its levered cost of equity is much lower because Costco is negatively correlated with small companies (remember, small com- panies outperform big companies on average) and companies with a high book-to-market ratio (high-book-to-market companies outperform low-book- to-market companies on average). While the Fama-French model outperforms the CAPM in predicting future returns, it is important to use caution when relying on regression results for one company at a point in time. As we discussed earlier in this chapter, regres- sion results for a single company are quite imprecise. To best implement the CAPM, for instance, we recommend using a peer group beta, rather than raw regression results. In the Fama-French model, three beta coefficients exist, and their estimation depends on one another. A set of industry betas cannot be cre- ated cleanly. Consequently, the Fama-French model works well for controlling the risk of large historical data sets but may not be appropriate for measuring a single company’s cost of equity. The bottom line? It takes a better theory to kill an existing theory, and we have yet to see the better theory. Therefore, we continue to use the CAPM while keeping a watchful eye on new research in the area. Alternatives to CAPM: Arbitrage Pricing Theory  Another proposed alterna- tive to the CAPM, the arbitrage pricing theory (APT), resembles a generalized version of the Fama-French three-factor model. In the APT, a security’s actual returns are generated by k factors and random noise: R F F F i k k = + + + + + α β β β ε 1 1 2 2 ... where Fi = return on factor i. Since investors can hold well-diversified factor portfolios, epsilon risk will disappear. In this case, a security’s expected return must equal the risk-free EXHIBIT 15.8  Costco: Cost of Equity Using the Fama-French Model, August 2019 Factor Average monthly premium,1 % Average annual premium, % Regression coefficient2 Contribution to expected return, % Market portfolio 5.0 0.90 4.5 Small-minus-big (SMB) portfolio 0.20 2.4 (0.33) (0.8) High-minus-low (HML) portfolio 0.35 4.3 (0.54) (2.3) Premium over risk-free rate3 1.4 Risk-free rate 4.1 Cost of equity 5.5 1 SMB and HML premiums based on average monthly returns data, 1926–2019. 2 Based on monthly returns data, 2014–2019. 3 Summation rounded to one decimal point.