Consider an agent who can invest in a risky asset whose payoff x is normally

distributed with mean 10 and variance 5. The price of the risky asset at t=0 is p=3.

There also exists a risk-free asset whose rate is rf = 2% (and its price at t=0 is

normalized to 1). The investor has utility given by u(w)=-exp(- w).

A) Find the optimal demand for the risky asset.

B) Suppose now that the agent is exposed to an additional source of risk y, which is

normally distributed with mean 0 and variance 1. This additional source of risk

covaries positively with the payoff x of the risky asset, with cov(x,y)=0.5.

Compute the hedging demand as well as the resulting total demand for the risky

asset. Is the optimal demand for the risky asset greater or lower than under

question A) and why is it the case?