(a) Let R1 and R2 be the returns from two securities with E(R1) = 3% and E(R2) = 8%, VAR(R1) = 0.02, VAR(R2) = 0.05, and COV(R1 R2) = -0.01.

Assuming that the two securities above are the only investment vehicles available:

(i) If we want to minimize risk, how much of our portfolio will we invest in Security 1?

(ii) Find the mean and standard deviation of a portfolio that is 40% in Security 1.

(b) You are given that assets X and Y are perfectly correlated such that Ry = 6 + 0.2RX and the probability distribution of X is:

What is the percentage of your wealth to put into asset X to achieve zero variance?

**ANSWER**

(a) (i) We can minimize risk setting the first derivate of expression for portfolio variance equal to as follows:

Solving for w (percentage of wealth to invest in security 1 to obtain the min-risk):

Thus –25% of wealth should be invested in asset x so as to achieve zero variance