EDHEC-Risk Institute October 2016

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

3. Applications of Fundamental Beta

one sector as a reference and letting its coefficient be equal to zero. The number of coefficients to estimate is now equal to 6 N +2 S +2 C –2. 3.1.2 Illustration with the US Equally Weighted Broad Index The model is estimated over the S&P 500 universe with N = 500 stocks and the period 2002-2015 (which corresponds to 51 quarterly returns). The stocks are classified into the 10 sectors of the TRBC list, which are Energy, Basic Materials, Industrials, Cyclical Consumer, Non Cyclical Consumer, Financials, Healthcare, Technology, Telecoms and Utilities. As in Section 1, we focus on the decomposition of expected return and volatility of the equally-weighted portfolio of the S&P 500 universe. We also perform the decomposition both for absolute return and risk and for excess return and tracking error with respect to the market factor.

geographical classification in addition to the sector and the three continuous attributes. This model can be written as:

The number of coefficients to estimate now grows to 6 N +2 S +2 C (with S sectors and C countries/regions). But the previous regression contains collinear variables because the sum of country dummies variables is constant and equal to 1 for any asset i and replicates the sum of sectors dummies variables. Therefore, one constraint must be applied to obtain a unique solution. This can be done, for instance, by choosing one country or

Figure 17: Absolute Performance Decomposition of the Equally-Weighted Portfolio of the S&P 500 Universe on the Market Factor with Fundamental and Sector Attributes The coefficients of the one-factor model are estimated with a pooled regression of the 500 stocks from the S&P 500 universe. Data is quarterly and spans the period 2002-2015, and market returns are from Ken French's library. Attributes (capitalisation, book to-market and past one-year return) and sector classification come from the ERI Scientific Beta US database and are updated quarterly. We use formula (3.2) to make the performance attribution.

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