Nonpricetaking Behavior

Up to now we have assumed that individuals act as price takers in that they ignore the impact of their buying or selling behavior on the equilibrium price of securities and, hence, on their

"See Lintner [79], Sharpe [118], Fama [32], and Gonedes [41).

18Lintner assumes the negative exponential utility function given by u(w) = e~a'wi. The measure of risk aversion is given by ar optimal portfolio holdings. The obvious question to ask is what happens if there are one or more investors, such as mutual funds or large pension funds, who believe that their behavior nnpacts price. ITie method of analysis used by Lindenberg [77,78] derives equilibrium con-.litions under all possible demands by the price affector. The price affector selects her portfolio to maximize utility given the equilibrium prices that will result from her action. \ssuming that the price affector operates so as to maximize utility, we can then arrive at equilibrium conditions. Lindenberg finds that all investors, including the price taker, hold some combination of the market portfolio and the riskless asset. However, the price affector will hold less of the riskless asset (will be less of a risk avoider) than would be the case if the price ..Ifector did not recognize the fact that her actions affected price. By doing so the price affector increases utility. Because the price affector still holds a combination of the riskless asset and the market portfolio, we still get the simple form of the CAPM, but the market price of risk is lower than it would be if all investors were price takers.

Lindenberg [77] goes on to analyze collective portfolio selection and efficient allocation among groups of investors. He finds that by colluding or merging, individuals or institutions can increase their utility. This analysis provides us with one reason for the existence of large financial institutions.

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