EDHEC-Risk Institute October 2016

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

2. From Historical Betas (and Alphas) to Fundamental Betas (and Alphas)

Figure 15 displays the distributions of the four coefficients that appear in the decomposition of the fundamental beta. For each coefficient, there is a substantial dispersion in the estimates across the 500 stocks, which suggests that the model with uniform coefficients imposes indeed too much structure. Even if the fundamental beta diverges from in-sample historical beta during sub-period, we expect in average over the period that the fundamental beta would be close to the historical beta. For this reason, we study the difference of the average fundamental beta over the period with the historical in-sample beta for each of the 500 stocks. Results are reported in Figure 16 for the more flexible model and for the constrained version. Specific coefficients from model of formula 2.4 lead to a fundamental beta closer to the in-sample historical beta. Indeed, Figure 16 shows that the “Flexible Fundamental Beta” is less dispersed around the in-sample historical beta.

Figure 16: Temporal Mean of Fundamental Beta and “Flexible” Fundamental Beta Minus Historical Beta The coefficients are estimated with the GCT-regression model for the Fundamental Beta and with time-series regressions for the Flexible Fundamental Beta on the 500 stocks from the S&P 500 universe with quarterly stock returns. We use z-score attributes from the ERI Scientific Beta US universe and market returns come from Ken French's library over the period 2002-2015. We represent for the 500 stocks, the difference between the average over the period of the fundamental and Flexible Fundamental Beta and the in-sample historical beta. We obtain two distributions of 500 stocks for each estimation method.

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