EDHEC-Risk Institute October 2016

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

Executive Summary

As we can see, the book-to-market ratio has a positive impact both on market exposure and alpha, suggesting that a higher book-to-market ratio implies higher abnormal performance and market exposure, while the past one-year return has a positive impact on alpha but a negative impact on market exposure. Finally market capitalisation has a negative impact on both alpha and market exposure, confirming that large caps tend to have smaller abnormal performance and market exposure. Within market factor exposure and alpha contributions, some sectors have larger contributions, such as Financials, Industrials and Cyclical Consumer for market exposure and Healthcare for abnormal performance. We then compare the fundamental and the rolling-window betas as estimators of the conditional beta by constructing market-neutral portfolios based on the two methods. We show that the fundamental method results in more accurate estimates of market exposures, since the portfolios constructed in this way achieve better ex-post market neutrality compared to those in which the beta was estimated by running rolling-window regressions, which tend to smooth variations over time thereby slowing down the diffusion of new information Targeting Market Neutrality with Fundamental Betas

in the beta. In contrast, the fundamental beta is an explicit function of the most recent values of the stock’s characteristics, and as such is more forward-looking in nature. In order to achieve more robustness in the results, we do not conduct the comparison for a single universe, but we repeat it for 1,000 random universes of 30 stocks picked among the 218 that remained in the S&P 500 universe between 2002 and 2015. Hence we have 1,000 random baskets of 30 stocks, and, for each basket, we compute the two market-neutral portfolios. Exhibit 3 shows that portfolios based on fundamental beta achieve, on average, better market neutrality (corresponding to a target beta equal to 1) 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 terms 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. At each date, we also compute the 1,000 absolute differences between the 5-year rolling-window beta and the target of, and the results are reported in Exhibit 4. The historical method exhibits the largest

Exhibit 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. Market betas and correlations with the market return 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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