EDHEC-Risk Institute October 2016

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

1. Literature and Practice Reviews

or factor/country). But when the number of dimension grows (e.g. by adding country dimension), this method cannot be applied to perform a joint decomposition of return and risk on sectors and countries. Indeed, one has to make a choice in a first stage between projecting the return on sector or on country returns. One solution might be to project the portfolio return on sector country classes gathering all stocks from a given sector-country pair, but this would severely increase the number of regressors to handle in the first step. In Section 3.1, we will introduce an alternative approach that can accommodate both dimensions simultaneously, by representing alphas and betas as functions of the stock’s characteristics. We illustrate this method by decomposing the expected return and risk of the equally weighted portfolio of the S&P 500 universe on 20 March 2015. Decompositions are performed for both absolute return and risk. Figure 8 shows the absolute performance

(1.14)

Again, time-varying volatilities for factors and specific risk is straightforward. Overall, this method starts by decomposing portfolio performance and risk in factors contributions and then disentangles the factors contributions into sectors contributions. It is a convenient approach for decomposing portfolio performance and risk through two dimensions (factor/sector introducing

Figure 8: Absolute 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. We regress for each sector portfolios their excess returns on Carhart factor returns for the period 2002-2015 and use OLS to estimate the factors exposures of each portfolios. We then recompose the factors exposures of the equally-weighted portfolio with the portfolio sector allocation at the last rebalancing date (Q1 2015) and the factors exposures of sector portfolios. We use formula (1.13) to make the performance attribution.

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