EDHEC-Risk Institute October 2016

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

Introduction

of a firm matter to explain its exposure to market risk. For instance, Beaver, Kettler and Scholes (1970) find a high degree of contemporaneous association between the market beta and accounting measures such as the dividends-to- earnings, growth, leverage, liquidity, asset size, variability of earnings and covariability of earnings within the context of ‘intrinsic value’ analysis. By representing the beta as an explicit function of these characteristics, one is able to immediately incorporate the most recent information about a stock. If the time-varying beta was estimated through a rolling-window regression, this information would be reflected with a lag, since this type of regression by construction tends to smooth variations over time. Second, we choose characteristics that correspond to well- documented and economically grounded patterns in equity returns, namely the size, the value and the momentum effects. In particular, we are interested in testing whether variations in the fundamental beta across stocks are consistent with an expected outperformance of small, value and winner stocks. We estimate three specifications for the fundamental beta, by employing pooled regression techniques, as suggested by Hoechle, Schmidt and Zimmermann (2015). In recent work, these authors introduce a Generalised Calendar Time method, which allows them to represent alphas and betas of individual stocks as a function of discrete or continuous characteristics. With this powerful technique, it is thus possible to let the alpha and beta of each stock depend on the sector as well as the market capitalisation, the book-to- market ratio and the past recent return.

or one quarter). Ang and Chen (2007) have also no explicit model for the betas, but they treat them as latent variables to be estimated by filtering techniques. The empirical success of these models is mixed. Harvey (1989) finds that the data rejects the model’s restrictions, and Lewellen and Nagel (2006) conclude that the conditional CAPM performs no better than the unconditional one in explaining the book-to-market and the momentum effects. On the other hand, Ang and Chen (2007) report that the alpha of the long- short value-growth strategy is almost insignificant in a conditional model. The measurement of conditional betas is not only essential for researchers testing asset pricing models, but also for portfolio managers who want to implement an allocation consistent with their views on factor returns. For instance, a fund manager who anticipates a bear market will seek to decrease the beta of his or her portfolio, and one who expects temporary reversal of the momentum effect will underweight past winners. For practical applications, it is clearly useful to have an expression of the conditional beta as a function of observable variables, as opposed to having it extracted by filtering methods. The main contribution of this paper is to propose an alternative specification for the conditional market beta, as a function of the very same characteristics that define the Fama- French and Carhart factors, and we call it a “fundamental beta”. We have the same linear specification for the beta as Ferson and Schadt (1996), but we replace the macroeconomic variables by the market capitalisation, the book-to-market ratio and the past one-year return. This choice of variables is motivated by several reasons. First, it makes intuitive sense that the microeconomic characteristics

We then present three applications of the fundamental beta. In the first one we use

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