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20. You have been given this probability distribution for the return of Apple (AAPL). Probability Rate of Return 0.5 30% 0.5b. Suppose the expected return and standard deviation of Amazon (AMZN) is 10% and 5%. The correlation between AAPL and AMZN ic. Assume that you have a risk aversion parameter A = 4 and the risk-free rate is 8%. What is your optimal investment in P*?

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Answer #1

1.
Expected return=0.5*30%+0.5*10%=20%

Standard deviation=sqrt(0.5*(30%-20%)^2+0.5*(10%-20%)^2)=10.00%

2.
Expected return=0.5*10%+0.5*20%=15%

Standard deviation=sqrt((0.5*10%)^2+(0.5*5%)^2+2*0.5*10%*0.5*5%*0.71)=7.00%

3.
Optimal investment=(return of optimal risky portfolio-risk free rate)/(A*standard deviation of optimal risky portfolio^2)=(15%-8%)/(4*7%*7%)=3.571428571

Borrow 257.14 Invest 357.14 (257.14 from borrowed amount and 100 from own money) in optimal risky portfolio

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