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)

Figure 12: Fundamental Beta as a Function of Firm’s Attributes (Book-to-Market ratio and Market Capitalisation) Book-to-market ratio and market capitalisation 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. Attributes come from the ERI Scientific Beta US database and are updated quarterly.

Figure 13: Fundamental Beta as a Function of Stock's Past 1-Year Return Past 1-year return coefficient is 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. Attributes come from the ERI Scientific Beta US database and are updated quarterly.

of coefficients over time. To this end, we repeat the panel regression over a rolling window of a fixed size through the sample. If parameters remain constant over the entire sample, then the variation in estimates across the different windows should only reflect statistical noise. But if the parameters change at some point

can diverge trough the time as their attributes can change in different ways.

2.2.4 Stability of Model Parameters The parameters θ of the one-factor model are assumed to be constant over time. This assumption may be questioned, so it is important to assess the stability

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