Question

Use the following scenario analysis for stocks X and Y to answer the questions.

	Bear	Normal	Bull
	Market	Market	Market
Probability	25.00%	45.00%	30.00%
Stock X	-40.00%	13.00%	55.00%
Stock Y	-22.00%	8.00%	29.00%

Assume you have a $200,000 portfolio and you invest $80,000 in stock X and the remainder in stock Y. If the risk–free rate of return is 3.75%, and we assume that the standard deviation of the excess returns on the portfolio is 15%, what is the Sharpe Ratio for this portfolio formed from stocks X and Y?  

b) What is the expected rate of return for stock Y?

Enter your answer rounded to two decimal places. For example, if your answer is 123.45% or 1.2345 then enter as 1.23 in the answer box.

Answer 1

The expected retrun is the sum of the return of each probabiity with its return at that probability level Stock Y return (%) Return (Y) Stock X return (%) Return (X) Probability Bear 0.25 -40 -10 -22 -5.5 Normal 0.45 13 5.85 8. 3.6 Bull 0.30 55 16.5 29 8.7 Expected return 12.35 6,80 Expected retrun from the portfolio expected return X * weight of X + Expected return Y * weight of Y Since of 200000, 8000 is being invested in X, so the weight of X 8000/20000 Weight of X 0.4 Weight of Y 1-0.4 0.6 Expected retrun from the portfolio 0.4*12.35 +0.6*6.8 9.02 (expected return from the portfolio - risk free rate )/standard deviation of the portfolio excess return Sharpe ratio = (9.02-3.75)/15 0.351 The expected rate of retrun from the stock Y as calculated above is = 6.80%