Suppose that we have two financial assets. Asset 1 has return R1 that is normally distributed with mean and variance 2 1 . Asset 2 does not cost anything when purchased but its payoff next period, R2, is normally distributed with mean 0 and variance 2 2 . R1 and R2 are perfectly correlated. That is to say that Cov(R1, R2) = 12. Suppose that for every dollar you put in asset 1, you buy shares of asset 2 ( could be negative). is called the hedge ratio. The cost of a portfolio, consisting of $1 dollar in asset 1 and shares of asset 2, is 1, since you dont pay anything to buy asset 2 (for example futures). Define the value of such portfolio one period later as z = R1 + R2.

(a) Find an expression for the mean and variance of z.

(b)Find the hedge ratio that minimizes the variance of z.

(c) What is the minimized variance?