EDHEC-Risk Institute October 2016

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

Executive Summary

deviation levels with respect to the target, with a number of dates (such as March 1996, December 2005 or March 2007) where the relative error exceeds 60%! In comparison, the fundamental method leads to much lower extreme differences between target and realised factor exposures, thus suggesting that this methodology allows for the error in the estimation of the conditional betas to be reduced versus what can be achieved with the classical rolling-window approach. Fundamental Betas and the Cross-Section of Expected Returns The main goal of an asset pricing model is to explain the differences in expected returns across assets through the differences in their exposures to a set of pricing factors. It is well known that the standard CAPM largely misses this goal, given its inability to explain effects such as size, value and momentum. In this subsection, we investigate whether the fundamental CAPM introduced in Section 2.2.3 is more successful from this perspective. To this end,

we conduct formal asset pricing tests by using Fama and MacBeth method (1973). There are two statistics of interest in the output of these tests. The first one is the average alpha of the test portfolios, which measures the fraction of the expected return that is not explained by the model. The second set of indicators is the set of factor premia estimates, which should have plausible values. More specifically, we test two versions of the conditional CAPM based on fundamental betas, one with a constant market premium and one with a time-varying market premium. The latter approach is more realistic since it is well documented that some variables, including notably the dividend yield and the default spread, have predictive power over stock returns, at least over long horizons – see Fama and French (1988, 1989), Hodrick (1992), Menzly, Santos and Veronesi (2004). Introducing a time-varying market premium implies that the unconditional expected return of a stock depends not only on its average conditional beta but also on the covariance between the

Exhibit 4: Largest Distance to 1 for the Portfolio Realised Beta across 1,000 Universes 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 71 that remained in the S&P 500 universe for the period 1970-2015, and the portfolios are rebalanced every quarter. The control regression on Ken French’s market factor is done on a 5-year rolling window of quarterly returns. For each window, the Exhibit shows the largest distance to 1 computed over the 1,000 universes.

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