When the tendency for the returns on a portfolio’s individual holdings to move together is strong, the dispersion in portfolio returns will be wide, no matter how many holdings it has. The “law of the average covariance” tells us how any reduction in dispersion that diversification can achieve is limited by this tendency.

Are risk and (expected) return adequate measures of a portfolio’s utility to its owner? Many academics have argued that they aren’t, insisting instead on a more complex measure they call “expected utility.” If so-called mean-variance analysis is not adequate, it merely gives us the wrong answer at low cost. But when the investor’s expected utility can be closely approximated by some function of his portfolio’s mean and variance, he loses little by picking his portfolio on the basis of risk and return.