EDHEC-Risk Institute October 2016

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

Executive Summary

without the help of additional ad-hoc factors.

conditional beta and the conditional market premium (Jagannathan and Wang, 1996).

In Exhibit 5, we compare the distributions of alphas across the 30 portfolios for the four competing models. These results suggest that the parsimonious fundamental conditional CAPM with constant market premium is substantially more effective than the standard static CAPM for explaining differences in expected returns, with an average alpha that is dramatically reduced from 5.04% down to 1.69%. Remarkably, this model performs as well as the less parsimonious Fama-French-Carhart 4 factor model. The results reported in the exhibit also suggest that accounting for the covariance term between the conditional beta and the conditional market premium further improves the ability of the fundamental CAPM to explain the returns of portfolios sorted on size, book-to-market or short- term past returns with respect to the case where the premium is constant. Furthermore, the average alpha obtained with this model is almost half the value obtained with Fama-French-Carhart model, suggesting that a conditional CAPM based on fundamental betas and a time-varying risk premium can capture the size, value and momentum effects better than the Fama-French-Carhart model, and this

Parsimonious and Forward-Looking Risk Indicators for Equity Portfolios Multi-factor models are standard tools for analysing the performance and the risk of equity portfolios. In the standard Fama-French-Carhart model, size, value and momentum factors are constructed by first sorting stocks on an attribute (market capitalisation, the book-to-market ratio or past short-term return), then by taking the excess return of the long leg over the short leg. While these models are substantially more successful than the standard CAPM at explaining cross-sectional differences in expected returns, the empirical link between certain characteristics and average returns can always be accounted for by introducing new ad-hoc factors in an asset pricing model. In the end, numerous patterns have been identified in stock returns, thus raising concerns about a potential inflation in the number of long-short factors and their overlap. Our analysis suggests another meaningful approach for explaining the cross-section of expected returns, which consists in treating attributes of stocks as instrumental variables to estimate the exposure with respect to a parsimonious set of factors.

Exhibit 5: Alphas Distribution over the Cross-Section of Sorted Portfolios This exhibit provides the distribution of the estimated alphas for 30 portfolios sorted on size, book-to-market or past one-year return. These alphas are obtained by performing Fama-MacBeth regressions for three pricing models. The fourth row shows the distribution of alphas obtained in the conditional CAPM with fundamental beta and a time-varying market premium. The fundamental beta is a function of the constituents’ attributes. Regressions are done on the period 1973-2015. The last column shows the average t-statistics across alphas.

Mean Corrected T-stats

Mean

Std

1st Quartile

Median Third Quartile

Static CAPM

5.04% 2.74% 3.35% 4.95% 6.35%

1.66

Carhart Model

2.87% 1.06% 2.35% 2.66% 3.57%

0.89

Fundamental CAPM

2.86% 2.72% 1.08% 2.76% 4.19%

0.79

Fundamental CAPM with Time-Varying Market Factor

1.69% 2.70% -0.27% 1.54% 3.39%

0.71

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