Question

Question 1: Suppose there are two risky assets, A and B. You collect the following data on probabilities of different states happening and the returns of the two risky assets in different states: State Probability Return Asset A Return Asset B State 10.3 7% 14% State 20.4 6% -4% State 30.3 -8% 8% The risk-free rate of return is 2%. (a) Calculate expected returns, variances, standard deviations, covariance, and correlation of returns of the two risky assets. (b) There are three investors. The first one wants a portfolio with standard deviation of 3%, the second one wants a portfolio with standard deviation of 5%, and the third one wants a portfolio with standard deviation of 7%. Each investor has only $1,000 to invest. Describe how much each investor should allocate to different assets to create the desired portfolios. What is the expected return of the portfolio of each investor?

Answer 1

Solution & Asset A sceneris State shability Return (1) - rx P (182) i 0.3 Stet 2 2 .4 State 3 - 2.4 Expected Return (21) & sum of weighted return "B weigure Standard deviation s q Asset AL Asset B Statel Stecte a State 3 0.3 04 4.2 2.4 Expected return (1) = sin of weighted return Standard deviation of B Actual retorn - Expected return B. Actuel - Expected Covariance of ALB 8 Probability State I 3 State a state 3 4.9 3.9 9 0.2 -10)

Page 2 Covariance a sum Correlation ALB = Coverience std. dew. Axsid. ) sid. deu. Axstd. deu.b Exfected return al = Wt. Stock A x Return stock a (+) wt. Stock B x Return stock B. + 0.5x5 0.50 2.1 13.55-10