EDHEC-Risk Institute October 2016

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

3. Applications of Fundamental Beta

Sector coefficients in Equation (3.1) decompose the intercept coefficients θ α , 0 ,i and θ β , 0 ,i from Equation (2.5). The largest sector contributions within the market component are those of Financials, Industrial and Cyclical Consumer, and Healthcare stands out among the contributions of the various sectors to the abnormal performance. Figure 19 shows that most of the ex-post risk of portfolio arises from the market risk while the relative risk decomposition in Figure 20 highlights the role of specific risk as being the main contributor to portfolio volatility. For both absolute risk and performance decomposition, Financials, Cyclical consumers and Industrials still appear to be the sectors that contribute most to market exposure.

At the first level, there are two components in the expected return: the contribution from the market factor and the alpha. At the second level, we split each of these two elements into fundamental and sector attributes according to the previous model. Figure 17 shows the results. Book- to-market ratio has a positive impact on market exposure and alpha, so that a higher book-to-market ratio implies higher abnormal performance and market exposure. In contrast, the past one-year return has a positive impact on the alpha but a negative impact on the market exposure. Finally the market capitalisation has a negative impact on both alpha and market exposure: the model predicts that other things being equal, large stocks will have smaller abnormal performance and market exposure. In Figure 18, we focus on the excess return, which, as usual, shows a lower market contribution than the absolute performance.

Figure 18: Relative Performance Decomposition of the Equally-Weighted Portfolio of the S&P 500 Universe on the Market Factor with Fundamental and Sector Attributes (Method 3) The coefficients of the one-factor model are estimated with a pooled regression of the 500 stocks from the S&P 500 universe. Stocks’ returns are in excess of market portfolios returns. 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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