At this point, it is worth mentioning that the paper is solely concerned with the structure of risk in the stock market, not with the structure of expected returns. Multi-factor models of the covariance matrix can still be very useful if economic arguments tie them up to the cross-section of expected returns, as in the Arbitrage Pricing Theory of Ross (1976). Any discussion of the relationship between risk factors and expected returns is outside the scope of the paper. There should be no ambiguity over whether we define “factors” in terms of the mean vector or of the covariance matrix of stock returns: it is always.
