The journal of finance In Fama [6 the two-parameter portfolio model is generalized to a multi period decision framework Simplifying somewhat the analysis of [6],suppose the individual will cease to consume at the end of time t= T and suppose his tastes for lifetime consumption can be represented by a utility function U(C1, C2, .. Cr)that is monotone increasing and strictly concave in lifetime consumption(C1, c: Thus the individual is assumed to be with respect to lifetime consumption. Assume also that each period the prob ability distributions of one-period return on all portfolios are normal, and, for implicity that the portfolio opportunity set is expected to be the every period. Finally, assume that consumption opportunities(goods available and their relative prices) are likewise expected to be constant through time Then it is shown in [6] that although he has a multiperiod horizon, each period the individuals consumption-investment decision is in conformance with the two-period, two-parameter model. 4 That is, in making his consumption-invest- ment decision for any period t, the individual behaves as if he attempts to maximize expected utility with respect to an induced utility function U, (c Wi+1) that is monotone increasing and strictly concave in consumption for period t, Ct, health at period t+ l, w In simplest terms, the argument of the proponents of the growth-optimal model is that if the individual will not consume out of portfolio funds for many periods, then for each t and c, an appealing strategy is to choose the portfolio that maximizes E(In E(In[wt+1l)=In cr)+E[n(1+ implies higher wealth at the horizon than any alternative policy most 3 26 where R,t +1 is the one-period percentage return on portfolio p from time t to time t +1, and the tilde (" indicates that the return is a random varial The assumed appeal of this portfolio strategy arises from the fact that over an investment horizon of many periods, the policy of maximizing El Rpt+1)] period by period is growth-optimal in the sense that it"alr urely case(Fama [51). But the empirical work of this paper uses monthly returns, and for monthly ne theoretical criticism often directed at the of symmetric stable return distributions is that since they have unbounded tails, such re inconsistent with the limited ability provisions of most securities. But efficient portfol small that it has 29 this point is pre Thus the existence of limited is not an important con ideration in the choice of distribution used to approximate returns. The important consideration is descriptive valid It is well-known that the Efficient Set Theorem can be obtained with the assumption that investor utilities are well approximated by functions that are quadratic in c. But the problems with this approach are also well known. For a discussion see Fama and Miller [81, Chapter 6 4.The assumptions that consumption and investment opportunities are constant through time than required by the model of [61, but this simplified version of the model is con sufficient for our purposes. A detailed discussion of the conditions under whic behavior in a multiperiod setting is in 5. The growth-optimal model has often been criticized, most recently by Samuelson [22]. with rious examples, Samuelson shows that although over the very long run, the growth-optima policy almost surely provides higher wealth and thus higher realized utility than alternativ strategies, this does not imply that the growth-optimal policy maximizes expected utility. In