Question

5. Use the following information to complete the questions: State of Economy Probability that State will Occur Return on Stock A Return on Stock B Return on Stock Recession 0.4 10% 15% 20% Boom 0.6 8% 4% 0% 8.8% 8.4% 8% Expected Return 0.20 0.50 0.30 Portfolio Weight 5a. Compute the expected return for the portfolio. 5b. Compute the variance and standard deviation for the portfolio.

Answer 1

5a. Expected Return in recession =0.20*10%+0.5*15%+0.30*20% =15.50%
Expected Return in Boom =0.20*8%+0.5*4%+0.30*0% =3.60%
Expected return for the portfolio =0.4*15.50%+0.6*3.60% =8.36%

5b. Variance =0.4*(15.50%-8.36%)^2+0.6*(3.60%-8.36%)^2 =0.339864%
Standard Deviation =Variance^0.5 =0.339864%^0.5 =5.83%