You are managing two mutual funds, A and B. Fund A invests in stocks and Fund B
invests in money market. Fund A’s return follows a normal distribution with a mean of
6 percent and a standard deviation of 4 percent; while Fund B’s return follows a
normal distribution with a mean of 3 percent and a standard deviation of 1 percent.
The correlation coefficient between two funds is -0.5. An investor comes to your
office and tells you that she can tolerate a maximum of 2.5 percent of likelihood that
her investment loses money (i.e., a negative return). Assume that any portfolio
constructed from funds A and B also follows a normal distribution.
a) Find the probability that Fund A generates a negative rerun.
b) Find the probability that Fund B generates a negative return.
c) What is the best expected return that you can provide if you propose an
investment portfolio to your client that satisfies her investment criterion?
