EDHEC-Risk Institute October 2016

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

Executive Summary

As an illustration, we have focused on the conditional CAPM one-factor model, and we estimate a time-varying beta that is explicitly given by a linear function of the very same characteristics that define the three Fama-French-Carhart factors. We show that a conditional CAPM based on this fundamental beta can capture the size, value and momentum effects as well as the Fama-French-Carhart model, but without the help of additional factors. The pricing errors are further reduced by introducing a time-varying market premium, which introduces the cyclical covariation between fundamental betas and the market risk premium as a driver of expected returns. The fundamental beta also provides an alternative measure for the true unknown value of the conditional beta. This estimate is a function of observable variables and is not subject to the artificial smoothing effect that impacts betas estimated by a rolling window regression analysis. Since the fundamental beta immediately responds to changes in the value of a stock's attributes, they can be used to more effectively assess the impact of a change in the portfolio composition on the factor exposure. We illustrate these benefits by constructing market-neutral portfolios based on the fundamental and the rolling-window methods, and we show that the former approach achieves better out-of-sample neutrality. Interestingly, this approach can be extended in a straightforward manner from a single-factor model to a multi-factor model, thus allowing exposure to a variety of underlying systematic macro factors to depend upon the micro characteristics of the firm.

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An EDHEC-Risk Institute Publication