Answer the 4th question plz. Thank you very much! An investor put money into a b

Question

Answer the 4th question plz. Thank you very much!

An investor put money into a bond fund and a stock fund and expects the following returns depending upon the economic states: State Recession Normal Growth Probability Bond Return Stock Return 10% 6% 5% 35% 50% 15% -20% 5% 30% ! If the investor allocated 75% of his funds to the stock investment and 25% to the bond investment, compute the portfolios expected return and risk. 3. 4. Compute the covariance and correlation between the bond fund and the stock fund

Explanation / Answer

Step 1: Calculation of SD 1) Bond Return State Probability P (%) Bond Return(%) Deviation (D1) PD^2 Recession 35 10 2.75 2.65 Normal 50 6 -1.25 0.78 Growth 15 5 -2.25 0.76 7.25 4.19 Standard Deviation 2.05 2)Stock Return State Probability(%) Stock Return(%) Deviation (D2) PD^2 Recession 35 -20 -20 140 Normal 50 5 5 12.5 Growth 15 30 30 135 0 287.5 Standard Deviation 16.96 Step 2: Calculation of Co variance Probability(%) Deviation (D1) Deviation (D2) 35 2.75 -20 -19.25 50 -1.25 5 -3.125 15 -2.25 30 -10.125 -32.5 Step 3: Calculation of Correlation Correlation = Covariance/(SD of stock*SD of bond) -0.93 Step 4: Calculation of Portfolio Return Item Expected Value Weight Expected Value*Weight Bond 7.25 0.25 1.81 Stock 0 0.75 0 1.81 Portfolio Return 1.81% Step 5: Calculation of Portfolio Risk Square root of [(Ws*SDs)^2+(Wb*SDb)^2+(2*Ws*Wb*SDs*SDb*correlation)] Where Ws Weight of stock investment Wb Weight of bond investment SDs Standard Deviation of stock investment SDb Standard Deviation of bond investment Square root of [(.75*16.96)+(.25*2.05)+(2*.75*.25*16.96*2.05*-.93)] 12.24%

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