Positive Feedback Investment Strategies 387 of the subsequent value of is /2;when the speculators'signal e is-,the expectation of the subsequent value of is -/2.In period 1,informed rational speculators choose their demand Di to maximize the same mean-variance utility function as in period 2 over the distribution they face as of period 1 of their certain-equivalent wealth in period 2.8 Passive investors'demand in period 1 takes the same form as in period 2.They buy low and sell high,and their demand is given by D1=-ap1· (6) Positive feedback traders'demand in period 1 is equal to zero: D=0. (7) Since the form of positive feedback behavior we study reacts to past price movements but not to current price changes,positive feedback traders do not trade in period 1. Period 0 Period 0 is a reference period.No signals are received.As a result,the price is set at its initial fundamental value of zero,and there is no trading.Period 0 provides a benchmark against which the positive feedback traders can measure the appreciation or depreciation of stock from period 0 to periods 1 and 2 and so form their positive feedback demands in periods 1 and 2. Since there is no trading in periods 0 or 3,the market clearing conditions are automatically satisfied in those periods.For periods 1 and 2,since there are u informed rational speculators and 1-g passive investors,the market clearing conditions are,respectively, 0=D+uD+(1-4)D, (8) 0=D%+uD5+(1-)D5. (9) Solution with a Noiseless Signal We consider the case of a positive demand shock,=+.The argument is symmetric in the case of a negative demand shock.If the rational speculators signal e is perfectly correlated with the period 2 demand shock then from their point of view there is no uncertainty in period 1 about the period 2 stock price. As long as informed rational speculators are present in positive measure (u>0) arbitrage guarantees the equality of prices in periods 1 and 2.If no informed rational speculators are present (=0),then the period 1 price equals zero,for no one has any information about the period 3 value of +6. p1=P2ifμ>0， (10) P1=0 if4=0. Imposing market clearing in period 2,and substituting in the period 2 demands These preferences are time consistent up to the approximation error from using the mean- variance formulation. Copyright 2001 All Riahts Reserved