EDHEC-Risk Institute October 2016

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

3. Applications of Fundamental Beta

3.2 Targeting Market Neutrality with Fundamental versus Historical Betas The construction of a market-neutral portfolio, that is a portfolio with a beta of one, depends inherently on the ability of the portfolio manager to accurately measure the exposure of his portfolio conditional on the current information. 9 The traditional approach to estimating a time-varying beta is to run rolling window regressions, but it tends to smooth variations over time, thereby slowing down the diffusion of new information in the beta. In contrast, the fundamental beta is an explicit function of the most recent values of the stock’s characteristics, and is thus not subject to the same delay issue as the rolling window one. Our goal in this subsection is to test whether the fundamental beta is a better estimate of the conditional beta by comparing market-neutral portfolios constructed with the two methods. We focus on the more flexible version of the fundamental beta (see Section 2.3). Each portfolio is a maximum deconcentration subject to the constraint β portfolio = 1. Mathematically, the weights are the solution to the optimisation program:

the closest approximation, to a naively diversified equally-weighted portfolio that satisfies the target factor exposure constraint. The portfolio is rebalanced every quarter, with revised estimates for the betas. It is important to note that the portfolio has by construction a beta of 1 within the estimation period but not necessarily in the backtesting period since realised out-of-sample betas of the constituents are different from the estimated betas. If the true conditional betas were known, the out-of-sample beta of the portfolio measured over a very long period would be equal to 1, because there would be no systematic prediction error, either positive or negative. In reality, the true conditional betas are not observable and are only estimated. The purpose of our comparison is precisely to find which of the two estimation methods yields the best approximation for these unknown parameters. To avoid look-ahead bias, the coefficients θ that relate the fundamental beta to the characteristics are estimated at each rebalancing date over a 5-year rolling window of quarterly data. Historical beta is estimated over the same sample. In order to achieve more robustness in the results, we do not conduct the comparison for a single universe, but we instead 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. In order to test whether the two portfolios achieve the neutrality target, we regress their returns against the market on the

9 - In a long-short context, market neutrality rather refers to a portfolio with a beta of 0. Here we focus on a long-only context, where beta neutrality is used to refer to a portfolio with a beta of 1.

subject to

and

,

where the β i are the constituents’ betas, estimated either by the statistical or the fundamental approach. In the absence of beta neutrality constraints, the solution to the optimisation program is an equally-weighted portfolio. Thus, the optimisation program generates

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