Equilibrium in the model

993 deriving the equilibrium in this model, we focus on the linear equilibrium. It is well known that this equilibrium concept is the same as Kyle 1985. We then solve for the optimal investment decision by the manager. The following lemma provides the characterization of the equilibrium stock price and the demand of informed traders. Lemma 1. The unique equilibrium is given by: e s x 2 1     , and   e x u v e Y v P 2 1 2 1              , where 2 1 1 se u      , 2 2 1 se se u      － ,   2 1 2 1 se u se Ve Vs           and Ve    2 . Proof. See Appendix A. We see that the informed trader places different weights on the private and public earnings information in making a decision on his demand. Further, we also see that these two weights are in the opposite direction. The relative weight is se    －  2 1 . Therefore, the informed trader is attaching relatively greater importance to his private signal than the public earnings signal as the correlation between the two signals becomes higher. 994 Note that 1   because the second-order profit maximization condition for the informed trader requires 2 1 ＜ －  . In this model, 1  is an increasing function of the amount invested by the manager  and the volatility of the investment return or firm profitability 2  , and a decreasing function of the variance of the uninformed traders‘ order flows 2 u  . It could be viewed 2  as a value-relevant measure of the public earnings information. We see in this model that 2  is increasing in the manager‘s level of investment  , the volatility of the investment return  and the correlation between the value of the firm and the public earnings information Ve  .

3.2. Manager‟s investment

Next, let us consider the manager‘s investment policy for maximizing her expected utility with a negative exponent. To do this, we need to solve the following problem,     P U E  max subject to e Y v P 2 1       . The constraint is necessary to reflect the situation in which the manager takes into consideration how her investment will affect the stock price when the manager makes an investment decision.

3.2.1 Perfect information case first-best scenario

To start with, we consider the perfect information case in which the market maker sets the stock price equating to the realized value of the firm; that is, where v P   . We can regard this as the benchmark for evaluating the manager‘s choice of investment in the model. 995 Lemma 2. In the perfect information case in which means that v P   , the manager‘s optimal investment is given by 2   r v FB  . Proof. See Appendix A. This obviously suggests that the manager‘s investment increases with the mean of the investment return and decreases with both the variance of the investment return and the magnitude of the manager‘s risk aversion.

3.2.2 Imperfect information case second-best scenario

Now, we consider the imperfect information case in which the stock price is set by the market maker who only observes the public earnings information e~ and the total order x u Y ~ ~ ~   as a two-signal version of the model in Kyle 1985. In other words, the stock price is informationally imperfect in the sense that the market maker sets the stock price without kn owing the informed trader‘s private information s~ and the value of the firm v~  , as well as without separating the informed trader‘s order flow x ~ from the uninformed trader‘s order flow u~ . More specifically, the manager faces the following problem when she makes her choice of the investment level:      P Var r P E 2 max   subject to e Y 2 1       v P . The following proposition provides some characterizations of the optimal investment policy undertaken by the manager. Proposition 1 a In the imperfect information case, the manager‘s investment policy is given by: