Question

Stock X has an expected return of 12% and the standard deviation of the expected return is 20%. Stock Z has an expected return of 7% and the standard deviation of the expected return is 15%. The correlation between the returns of the two stocks is +0.3. These are the only two stocks in a hypothetical world. What is the expected return and the standard deviation of a portfolio consisting of 80% Stock X and 20% Stock Z?

Will any rational investor hold this portfolio (in this hypothetical two stock world)? Explain why or why not. What is the expected return and the standard deviation of a portfolio consisting of 20% Stock X and 80% 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 C first).

What is the maximum amount of Stock Z 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 1 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). Explain why different rational investors might hold different portfolios of these two stocks. Identify the range of portfolios a rational investor might hold. Your answer should take this form: A rational investor will hold a maximum of ___% in Stock X (with ___% in Z), or a minimum of _____% in Stock X (with _____ in Z). The set of feasible portfolios will fall within the range defined by these two end points.

Answer 1

Rational Investor will Invest in 80% of X and 20% of Y beacuse of Higher sharpe ratio than the Individual Securities.

Rational Investor will NOT Invest in 20% of X and 80% of Y because of Lower sharpe ratio than Stok A. So a rational Investor invest total cash in Stock X instead of Investing 80% in Y and 20% in X

Sensitivity of Sharpe W.r.t weight