EDHEC-Risk Institute October 2016

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

Executive Summary

decomposition of the fundamental beta, and suggests that there is a substantial dispersion in the estimates across the 500 stocks.

on the sector of stock i . The method can be easily extended to handle country effects in addition to sector effects. Formally, the model reads:

Sector in Multi-Dimensional Portfolio Analysis with Fundamental Betas Risk and performance analysis for equity portfolios is most often performed according to one single dimension, typically based on sector, country or factor decompositions. In reality, risk and performance of a portfolio can be explained by a combination of several such dimensions, and the question arises to assess, for example, what the marginal contributions of various sectors are in addition to stock-specific attributes to the performance and risk of a given equity portfolio. The fundamental beta approach can be used for this purpose, provided that one introduces a sector effect in the specification of the conditional alpha and beta. This is done by replacing the stock-specific constants θ α , 0, i and θ β , 0, i by sector-specific terms, which only depend

This model can be used to decompose the expected return and the variance of a portfolio conditional on the current weights and constituents’ characteristics. In Exhibit 2, we show an application of this method to the analysis of the expected performance a broad equally-weighted portfolio of US stocks. At the first level, expected return is broken into a systematic part – which comes from the market exposure – and an abnormal part. Each of these two components is further decomposed into contributions from sectors and continuous attributes.

Exhibit 2: Absolute Performance Decomposition of the EW S&P 500 Index on Market Factor with Fundamental Alpha and Fundamental Beta 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 perform the performance attribution.

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