On The Direction of Preference for Moments of Higher Order Than The Variance

EMPIRICAL AND THEORETICAL ATTACKS on the Markowitz mean-variance, portfolio theory have given impetus to the investigation of moments of higher order than the variance. Denoting w as an investor's wealth, and i his incomes (a random variable), if the investors utility function, U, is solely dependent on the sum of his wealth and income we can define his utility as U = U(i + w). The investor's rate of return on investment of w is defined as f = i/w and his utility may be given by U = U(rw + w). Letting jt = E(w + rw), representing the expected value on investment, expanding U in the familiar Taylor series, and taking the expected value of both sides gives: