Efficiency of Competitive Stock Markets Where Trades have Diverse Information575 nits of risky assets purchased in period 0, r>0 is the exogenous rate of return on the risk free asset, and P, is the(unknown) exogenous payoff per unit on the risky asset(also called the period I price of the risky asset). The budget constraint is Wor= Xa+ Pox here Po is the current price of the risky asset. Substituting(2)into(I)to eliminate Xo yields H1=(1+n)Ha+[F1-(1+)Pl]x At time zero, P, is unknown. The ith trader observes y, where P1+ and P, is a realization of the random variable PI. Thus, a fixed, but unknown, realization of P, mixes with noise, e, to produce the observed yr. Later, we shall argue that traders also get information from Po. For the present, let 1, denote the information available to the ith trader. assume that the ith trader has a utility function where a is the coefficient of absolute risk aversion Each trader is assumed to maximize the expected value of U, (W,)conditional on I;. If WI is normally distributed conditional on then where Var[ WIilL,] is the conditional variance of wu given I. It follows that to maximize E[U(W,) 1] is equivalent to maximizing E[Wn4-za[n1小 since the expression in (7) in a monotone increasing transformation of the expres sion in (6). All we have shown is that mean-variance analysis in the Normal case can be derived from the utility function in(5) E[m小]=(1+)+{E[1-(1+)Px