LONG-TERM GROWTH IN A SHORT-TERM MARKET EUGENE F. FAMA AND JAMES D. MACBETH* L. INTRODUCTiON Two MoDELs that receive substantial attention in portfolio theory are the two- period, two-parameter model of Markowitz [17] and the long run, "growth optimal"model of Latane [15] and others. The growth-optimal model is often resented as an appealing alternative to the two-parameter model for those investors whose horizon is distant in the sense that portfolio funds are not needed for consumption for many periods. Thus the impression is left that the growth-optimal and the two-parameter models are not consistent with each other. A minor purpose of this paper is to dispel this impression. Empirical work that attempts to identify growth-optimal portfolios of New York Stock Exchange common stocks is also presented. The major goal of the paper is to examine whether the properties of observed growth-optimal portfolios are con- istent with a market dominated by investors whose primary concern is long run growth II. GRoWTH-OPTIMAL AND TWO-PARAMETER MODELS THEORY In the simplest version of the two-parameter portfolio model, an individual making a consumption- investment decision at time t= l, is assumed to have wealth wi which he must divide between current consumption C, and a port- folio investment W1-CI, the return on which provides his consumption C2 for period 2. The individual is assumed to make his consumption- investment deci sion as if he attempts to maximize expected utility with respect to a utility function for consumption U(Cu, C) that is monotone increasing and strictly concave in (Cu, C2)-in short, the investor is assumed to be risk-averse with respect to consumption uncertainty. The capital market is assumed to be per fect in the sense that investors are price-takers and there are no transactions costs or information costs. Finally, probability distributions of one-period per centage returns on all portfolios are assumed to be normal. a perfect capital arket, investor risk-aversion and normally distributed portfolio returns imply he Efficient Set Theorem: The expected utility maximizing portfolio for any investor is efficient in the sense that no portfolio with the same or higher expected one-period return has lower variance (or standard deviation) of return Graduate School of Business, y of Chicago. Research support from Science Foundation is gratefully ack The comments of F. Black and N the editional atefully acknowledged, And as w ur debt to Roll [21] should become clear 1. See, for example, williams [26 14], and Hakansson [12] 2. See, for example, Hakansson [12]