NOISE TRADER RISK 711 办=1+的+p-2(o (10) 1+r Inspection of(10)reveals that only the second term is variable,for y, p*,and r are all constants,and the one-step-ahead variance of is a simple unchanging function of the constant variance of a generation of noise traders'misperception Pe: 乐吸 (11) The final form of the pricing rule for u,in which the price depends only on exogenous parameters of the model and on public informa- tion about present and future misperception by noise traders,is ,=1+p,-p+p*-2Yμ2o r1+r)2 (12) 1+m C.Interpretation The last three terms that appear in(12)and(10)show the impact of noise traders on the price of asset u.As the distribution of p,con- verges to a point mass at zero,the equilibrium pricing function(12) converges to its fundamental value of one. The second term in(12)captures the fluctuations in the price of the risky asset u due to the variation of noise traders'misperceptions Even though asset u is not subject to any fundamental uncertainty and is so known by a large class of investors,its price varies substantially as noise traders'opinions shift.When a generation of noise traders is more bullish than the average generation,they bid up the price of u. When they are more bearish than average,they bid down the price. When they hold their average misperception-when pa=p*-the term is zero.As one would expect,the more numerous noise traders are relative to sophisticated investors,the more volatile asset prices are. The third term in(12)captures the deviations ofp from its funda- mental value due to the fact that the average misperception by noise traders is not zero.If noise traders are bullish on average,this "price pressure"effect makes the price of the risky asset higher than it depend on the primitive specification of noise traders'behavior.For example,if noise traders randomly pick each period the price p at which they will buy and sell unlimited quantities of the risky asset,then(trivially)there is only one equilibrium.If the noise traders randomly pick the quantitythat they purchase,then the fundamental solu- tion in whichp,is always equal to one is an equilibrium in addition to the equilibrium in which noise traders matter