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)

2.3 A More Flexible Specification for the Fundamental Beta Theone-factormodel introduced inSection 2.2 has exactly eight parameters: four of them tie the alpha to the characteristics, and the other four correspond to the beta. As a result, the sensitivities of the fundamental alpha and beta with respect to the characteristics are identical for all stocks. This can be regarded as a strong restriction, so we now present a more flexible version of the model in which these effects can be different from one stock to the other. The model is written as follows:

during the sample, then the rolling- window estimates should capture this instability. We check the stability of the coefficients from the GCT-regression model by using 5-year rolling windows of quarterly data. From Figure 14, the coefficients appear to be stable during the whole period except during the sub-period going from end of 2007 to 2009, in which the book-to-market ratio and the one-year price return coefficients change sign and the intercept coefficient increases from 0.8 to 1.3. This instability can be related to the rise in uncertainty caused by the subprime mortgage crisis of 2007. Except for this sub-period and the year 2014, the coefficients remain approximately constant over the entire period. At least, no trend is visible that would suggest that a permanent change in the model occurred in this sample. Overall, the model coefficients are relatively stable over time. In the next section, we show however that the assumption of uniform coefficients across stocks is questionable.

Figure 14: One-Factor Model Coefficients Estimated With a Panel Regression on 5-Year Rolling Windows With Quarterly Step The coefficients are estimated with the GCT-regression model on the 500 stocks from the S&P 500 universe with quarterly stock returns, quarterly z-scores attributes and quarterly market returns from Ken French's library over the period 2002-2015. We use 5-year rolling windows of quarterly data to obtain time-varying coefficients each quarter. Attributes come from the ERI Scientific Beta US database and are updated quarterly.

55

An EDHEC-Risk Institute Publication

Made with FlippingBook flipbook maker