EDHEC-Risk Institute October 2016

Multi-Dimensional Risk and Performance Analysis for Equity Portfolios — October 2016

3. Applications of Fundamental Beta

Table 9: Estimated Expected Market Risk Premia and Average Estimated Alphas over the Cross-Section of Stocks (1973-2015) We first estimate the fundamental betas of 30 equally-weighted portfolios sorted on size, book-to-market or past one-year return. The constituents of these portfolios are picked from the S&P 500 universe, and the fundamental beta of a portfolio is a function of the constituents’ attributes. Second, we estimate the beta of each fundamental beta with respect to the yield spread between BAA- and AAA-rated Barclays US bonds, downloaded from Datastream Regressions are done with quarterly observations over the period 1973-2015. Third, we perform at each date a cross-sectional regression of returns on the average fundamental betas and the yield spread beta, to obtain an estimate for the alpha, the market premium estimate and the coefficient c sp at each date. The first column in the table reports the average alpha from these regressions, across all dates and test portfolios. The second and the third columns are the average market premium estimate and the average c sp across all dates. Average Alpha Average Market Premium Table 11: Alphas Distribution over the Cross-Section of Sorted Portfolios The first three rows of the table are a reminder of Table 7. They summarise the distribution of the estimated alphas for 30 portfolios sorted on size, book-to-market or past one-year return. These alphas are obtained by performing Fama-MacBeth regressions for three pricing models. The fourth row shows the distribution of alphas obtained in the conditional CAPM with fundamental beta and a time-varying market premium. The fundamental beta is a function of the constituents’ attributes. Regressions are done on the period 1973-2015. The last column shows the average t-statistics across alphas. Mean Std 1st Quartile Median Third Quartile Mean Corrected T-stats Static CAPM 5.04% 2.74% 3.35% 4.95% 6.35% 1.66 Carhart Model 2.87% 1.06% 2.35% 2.66% 3.57% 0.89 Fundamental CAPM 2.86% 2.72% 1.08% 2.76% 4.19% 0.79 Fundamental CAPM With Time-Varying Market Premium 1.69% (0.71) 8.59% (1.60) -8.33% (-0.36)

Fundamental CAPM with Time-Varying Market Factor

1.69% 2.70% -0.27% 1.54%

3.39%

0.71

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