EDHEC-Risk Institute October 2016

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

1. Literature and Practice Reviews

Figure 9: Relative Performance Decomposition of the Equally-Weighted Portfolio of the S&P 500 Universe on Carhart Factors with Sector Decomposition Factor returns are from Ken French's library. Sector returns are equally-weighted portfolios from the S&P 500 universe. Returns are quarterly. The excess returns to each sector portfolio are regressed on Carhart factors over the period 2002-2015, in order to estimate their exposures. We then obtain the factor exposures of the equally- weighted portfolio in excess of the market factor with the portfolio sector allocation at the last rebalancing date (Q2 2015) and the factor exposures of sector portfolios. We use formula (1.13) to make the performance attribution. decomposition. The sum of all factor contributions and the alpha gives the overall performance of the portfolio conditional on the composition of the portfolio at the end of 2015. Most of the performance is explained by market exposure and the alpha. Inside theses exposures, some sectors have larger contributions, such as Information and Technology, Industrial, Health for the market exposure and Energy for the alpha. Figure 9 shows similar results in terms of factor contributions and sector decomposition for the excess return of the portfolio over the market factor: the most noticeable difference is the market exposure, which is strongly reduced.

As appears from Figure 10, most of the realised volatility of the portfolio is due to its exposure to the market and to the sectors that already had the largest contributions to performance (Information and Technology, Industrial and Healthcare). In Figure 11, where we examine the tracking error of the portfolio, it is specific risk that displays the largest contribution.

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