EDHEC-Risk Institute October 2016

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

Appendix

A.1 Sufficient Condition for Equality between Average Conditional Beta and Unconditional Beta Suppose that the conditional expected return and the conditional variance of the market are constant. Then, the unconditional moments equal the conditional ones:

Next, we take the expectation of the conditional beta and we use the fact that conditional moments are constant:

which is the unconditional beta.

A.2 Returns on Attribute-Sorted Portfolios (1973-2014) We first form decile portfolios from the S&P 500 universe by sorting stocks on the book-to-market ratio z-score, market-cap z-score and momentum z-score over the period 1973-2014 with quarterly returns. Each portfolio contains 50 stocks in each period.

Portfolio 10 (resp. 1) has the highest (resp. lowest) B/M ratio and the highest (resp. lowest) excess return over the period.

Portfolio 10 (resp. 1) has the highest (resp. lowest) Momentum price and the highest (resp. smallest) excess return over the period.

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