Question

Question #2: Optimal Risky Portfolio [22 Points] You are trying to decide whether to buy Vanguard's Large Stock Equity Fund and/or its Treasury Bond Fund (both are risky assets). You believe that next year involves several possible scenarios to which you have assigned probabilities. You have also estimated the expected returns for each of the two funds for each scenario. Your spreadsheet looks like the following: Probability Next Year's Possibilities Large Stock Equity Fund Expected Rate of Return Bond Fund Expected Rate of Return Severe Recession 0.20 -0.30 -0.09 Mild Recession 0.30 -0.15 0.10 Normal Growth 0.45 0.12 0.06 Strong Growth 0.05 0.45 0.02 (a) Given the probabilities for the four possible economic conditions and their associated rates of return, calculate the expected return for each fund. [4 Points] (b) Given the probabilities for the four possible economic conditions and their associated rates of return, calculate the standard deviation for each fund. [6 Points] (c) Using your answers from Parts (a) and (b) calculate the covariance between the two funds, and the correlation coefficient. [6 Points] (d) Using the formulas for the expected return and risk of a portfolio, calculate the expected return and standard deviation of a portfolio that is weighted 40% in the stock equity fund and 60% in the bond fund. Show your work. [6 Points]

Answer 1

amino 0.2 Possibilities Sev. Recession Mild Recession Normal Growth Strong Growth Expected Return Standard Dev. Covariance Correlation Weights Portfolio return prob Large stock Bond Formula -0.3 -0.09 0.3 -0.15 0.1 0.45 0.12 0.06 0.05 0.45 0.02 -0.0285 0.04 D4*$C$4+D5*$C$5+D6*$C$6+D7*$C$7 0.3295451 0.081803 STDEV.S(D4:D7) 0.0085 COVARIANCE.S(D4:D7,E4:E7) 0.3153094 CORREL(D4:D7, E4:E7) 0.61 0.0126 D12*D8+E12*E8 10 11 12 0.4 13 14 15 16 Portfolio variance Portfolio Std Dev 0.019895 0.1410496 ((D12^2)*(D9^2))+((E12^2)*(E9^2))+(2*D12*E12*D10*D9*E9) SQRT(D15) 17