1. Stock X has an expected return of 8% and the standard deviation of the expected return is 9%. Stock Z has an expected return of 10% and the standard deviation of the expected return is 7%. The correlation between the returns of the two stocks is +0.5. These are the only two stocks in a hypothetical world.
A. What is the expected return and the standard deviation of a portfolio consisting of 100% Stock X? Will any rational investor hold this portfolio (in this hypothetical two stock world)? Explain why or why not.
B. What is the expected return and the standard deviation of a portfolio consisting of 75% Stock Z and 25% Stock X? Will any rational investor hold this portfolio (in this hypothetical two stock world)? Explain why or why not. (You might want to do Part D first).
C. What is the expected return and the standard deviation of a portfolio consisting of 25% Stock Z and 75% Stock X? Will any rational investor hold this portfolio (in this hypothetical two stock world)? Explain why or why not.
D. What is the maximum amount of Stock X a rational investor will hold in his or her portfolio? What is the expected return and the standard deviation of this portfolio? The maximum amount is a percentage between 0% and 100%, and to receive full credit your answer should be within 2 percentage points of the correct answer. (Hint: Set up Excel to calculate the portfolio expected return and standard deviation as a function of the portfolio weights, which must sum to 100%. You can find the correct answer to this part by manually changing the portfolio weights, or by using the Solver function on Excel).