4 Pricing an uncorrelated asset An individual with utility function U(u, o) = -a, o has current wealth W. Each dollar invested in the riskless asset yields 1+ R. There is also a risky asset with price P, and payoff distribution p. dan expression for his expected wealth and variance of wealth in terms of (A) If the individual purchases q units of the risky asset, write down an (B) Hence show that his optimal holding of the risky asset is: 79 antbrogas Doups (C) If differences in tastes can be represented by differences only in the parameter x,, show that the equilibrium price of the risky asset is: 9; Pr = = PA M-(1+R) PA %0% where a = J/(E, 1/a,) is the harmonic mean of the taste parameters. (D) Show also that the equilibrium price of risk reduction is: 1+R (4-70%) J ==0F J (E) By appealing to the asset pricing equation (4.3.8), show that, if F is the market portfolio, the price of asset a satisfies: = Pa-(1+R) PA = ap J (F) Suppose asset a is uncorrelated with all the other assets. Show that the