Long-Term Growth in a Short-Term Market In terms of the expected utility model of [6], the policy of maximizing E[In(1+Ro, t+1] period by period implies that for each t and ct, U(c, Wt+1) is well approximated by a function that is logarithmic in w+1. Since it is monotone increasing and strictly concave in wt+1, the log utility function is consistent with the two-parameter model Given normally distributed one- period percentage portfolio returns, the Efficient Set Theorem applies. The growth-optimal portfolio is just the specific mean-variance efficient portfolio that is optimal for the log utility function. Thus the two-parameter and growth optimal models are mutually consistent o The main goal henceforth is to test whether the process of price formation the New York Stock Exchange is dominated by growth-optimizers. The first step is to develop the characteristics of such a"growth-optimizers'market III. A GROWTH-OPTIMIZERS, CAPITAL MARKET: THEORY For portfolio decisions at time t, the growth-optimal portfolio maximizes [In(1+Ro,t+i)1, the expected value of the continuously compounded rate of growth of portfolio funds from t to t+ 1. If portfolio G maximizes E[ln(1+ Rp, t+1)l, then it can be shown that for all assets i and j in g R R E E 1+R (1) In mathematical terms equation (1) is just a necessary condition for a maximum of E[In(1+Ro, t+1]. But it provides a testable implication of the hypothesis that the market is dominated by growth-optimizers when that hy- pothesis is structured into a theory of market equilibrium. In particular, sup pose that all investors are growth-optimizers and that there is complete agreement among them with respect to the distribution of the return on any portfolio. Then every investor has the same view of which portfolio is growth- optimal and all will hold that portfolio, It follows that if the market is to clear the growth-optimal portfolio G must be the market portfolio, henceforth with each asset weighted in proportion to the total market value of a.x referred to as M. By definition, M is the portfolio of all assets in the mark Since M is growth-optimal, it follows from (1) that for any two asset d ) that ve strategies have higher expected utilities than the growth-optimal polio shows that any uniform policy such as maximizing E[In(1 by period is un likely to be optimal. For example, as the n he consumes from portfolio funds, long-run growth considerations are likely to become less impressive, so that the log utility function is no longer a good approximation to his taste But it is well to note that early advocates of the growth-optimal model (e. g, Williams [26] eed lata d the model as an alternative to expected utility maximization, Among later advocates, Hakansson [121 does present the growth-optimal model in an expected utility framework, and it is primarily arguments like his that Samuelsons criticisms apply 6. See Roll [21]. This development of the characteristics of a growth-optimizers'market is du 7. The " complete agreement'assumption is usually called "homogeneous expectations