EDHEC-Risk Institute October 2016

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

3. Applications of Fundamental Beta

Figure 22: Largest Distance to 1 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 figure shows the largest distance to 1 computed over the 1,000 universes.

3.3 Asset Pricing with the Fundamental CAPM

3.3.1 Fundamental CAPM with Constant Market Risk Premium

The 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 ask whether the fundamental CAPM introduced in Section 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.

Unconditional Form of the Model In the conditional CAPM, the expected return of a stock i conditional on the information available at date t is a linear function of the stock’s conditional beta, the slope coefficient being the conditional market premium. Mathematically, this is written as: (3.4) In this model, expected returns can vary both in the cross-section and the time-series: cross-sectional variation is generated by the factor exposure only, while time variation results from changes in the market premium or the beta. We first consider the case where the conditional market premium is constant, and we relax this assumption in Section 3.3.2. Since conditional expected returns are not observable, we follow Jagannathan and Wang (1996) in transforming the

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