EDHEC-Risk Institute October 2016

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

3. Applications of Fundamental Beta

5-year rolling window. The first five years of the sample are used to calibrate the initial betas. Thus, the first beta is available in December 1979, that is ten years after the beginning of the sample. Over the 44-year sample, both betas move around their means, as shown in Figure 21. The average beta of the portfolios constructed with the fundamental approach is not systematically closer to 1 than that of the portfolios based on the traditional historical approach, but it exhibits less time variation. In particular, the average beta of the latter portfolios over the period March 1991-March 1996 is as low as 0.37, a number that indicates a severe deviation from neutrality. In September 2008, the ex-post average is at 1.18, which means that on average, the historical method led to portfolios that were more aggressive than expected between 2003 and 2008. With the fundamental betas, the range of ex-post betas is narrower, between 0.74 and 1.15.

13-year period. The resulting out-of- sample market beta is taken as a measure of the ex-post market neutrality. We complete this indicator with the market correlation computed over the period 2002-2015. Table 3 shows that portfolios based on fundamental beta achieve, on average, better market neutrality than those based on time-varying historical beta, with an in-sample beta of 0.925 versus 0.869, on average, across the 1,000 universes. We observe the same phenomenon in term of correlation with an average market correlation of 0.914 for portfolios based on fundamental betas, versus 0.862 for the portfolios based on historical time-varying beta. Since these numbers are only averages across the 1,000 universes, we also compute the standard deviations of the 1,000 out-of- sample betas or correlations around their respective means. The dispersion levels are close for both methods. To check whether these results are robust to the choice of the sample period, we perform again the comparison between the two methods on a longer sample, which spans the period 1970-2015. The results from Table 4 are clear: the portfolios constructed with the fundamental method are ex-post closer to neutrality than those that rely on rolling-window betas. We take advantage of the longer sample size to compute the out-of-sample beta on a

Table 3: Targeting Beta Neutrality for Maximum Deconcentration Portfolios Based on Fundamental and Time-Varying Historical Betas (2002-2015) 1,000 maximum deconcentration portfolios of 30 random stocks subject to a beta neutrality constraint are constructed by using the rolling-window or the fundamental betas. The 30 stocks are picked among the 218 that remained in the S&P 500 universe for the period 2002-2015, and the portfolios are rebalanced every quarter. The control regression on Ken French’s market factor is done using quarterly returns over the period 2002-2015. The market beta and the market correlation are computed for each portfolio over the period 2002-2015 and are averaged across the 1,000 universes. Also reported are the standard deviations of the beta and the correlation over the 1,000 universes. Out-of-Sample Market beta Out-of-Sample Market correlation Mean Standard Deviation Mean Standard Deviation Historical 0.869 0.032 0.862 0.025 Fundamental 0.925 0.035 0.914 0.020

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