EDHEC-Risk Institute October 2016

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

1. Literature and Practice Reviews

Figure 10: Absolute Risk Decomposition Using Euler 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 with the portfolio sector allocation at the last rebalancing date (Q2 2015) and the factor exposures of sector portfolios. We use formula (1.14) to make the risk attribution.

Figure 11: Relative Risk Decomposition Using Euler Decomposition for 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. We regress for each sector portfolios their returns in excess of the market portfolio on Carhart factor returns for the period 2002-2015 and use OLS to estimate the factors exposures of each portfolio. We then recompose the factors exposures of the equally-weighted portfolio in excess of market factor with the portfolio sector allocation at the last rebalancing date (Q2 2015) and the factors exposures of sector portfolios in excess of market portfolio. We use formula (1.14) to make the risk attribution.

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An EDHEC-Risk Institute Publication