EDHEC-Risk Institute October 2016

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

2. From Historical Betas (and Alphas) to Fundamental Betas (and Alphas)

The two main steps for building conditional models are the identification of the information vector Z t and the estimation of the response coefficients of the conditional beta to the information variables Z t . In this process, one has to take care of the risks of data mining and spurious regression, as Ferson, Sarkissian and Simin (2006) demonstrate. Data mining refers to the practice of searching through the data to find predictor variables, and spurious regression arises with the persistence of high autocorrelation of a predictor variable, which creates artificially significant relationships. 2.1.3 Using Microeconomic Variables In this paper, we follow the linear model for the beta introduced by Ferson and Schadt (1996), but we replace the macroeconomic content by microeconomic variables, that are variables specific to each stock. Specifically, we choose, for the information vector Z t , the following firm’s attributes: Cap i,t (market capitalisation of firm i ), Bmk i,t (the book-to-market ratio of firm i ) and Ret i,t (past 1-year return of firm i ) in direct line with the construction of Fama and French (1993) factors augmented by the momentum factor (Carhart, 1997). This makes the conditional beta a function of several stock’s characteristics, as in Wang and Menchero (2014). A difference between their approach and ours is that we have only three characteristics while the Barra-type model on which they rely requires a substantial amount of additional information such as geographical and industry classification, liquidity, volatility and dividend yield. Moreover, we do not rely on a multi-factor model to estimate the market beta.

conditional moments, as opposed to being true unconditionally:

(2.2)

The authors find evidence that alpha is closer to zero in a conditional model than in an unconditional model, which suggests that the conditional CAPM does a better job of explaining average abnormal returns. For the predetermined state vector, the authors use economic variables with a one-month lag: the Treasury bill yield, the dividend yield of the CRSP value-weighted New York Stock Exchange (NYSE) and American Stock Exchange (AMEX) stock index, the slope of the term structure, the quality spread in the corporate bond market, and a dummy variable for the month of January. By using a sample of 67 open-end mutual funds over 23 years, they show that traditional measures of average performance (Jensen's alpha) are more often negative than positive for mutual funds, which has been interpreted as inferior performance. Both a simple CAPM and a four-factor model produce this result in their sample, but with the conditional model, the distribution of alphas shifts to the right and is centred around zero. Shanken (1990) uses one- month bill rate and its volatility as characteristics for the public information vector. The author estimates parameters with OLS regression and tests if any of the beta decomposition coefficients is non-zero. He insists on using corrected standard errors because of the presence of conditional heteroskedasticity and use White estimator 7 (corrected standard errors are larger than usual OLS standard errors).

7 - White estimator provides heteroskedasticity consistent standard errors that are robust to general forms of temporal dependence but not to spatial dependence, unlike the estimator of Driscoll and Kraay (1998).

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