5. You are considering investing $1,000 in a complete portfolio. The complete po

Question

5. You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of treasury bills that pay 4% and a risky portfolio, P, constructed with 2 risky securities X and Y. The optimal weights of X and Y in P are 40% and 60% respectively. X has an expected rate of return of 18% and Y has an expected rate of return of 10%. To form a complete portfolio with an expected rate of return of 10%, what percentage of your complete portfolio should you invest in treasury bills?

6. Using the data from problem 5, if the risky portfolio, P, has a standard deviation of 25%, what is the standard deviation of the complete portfolio that you formed in problem 5?

7. Using the data from problems 5 and 6, what is the 5% Value at Risk (VaR) for the expected return on the risky portfolio P?

Explanation / Answer

5. You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of treasury bills that pay 4% and a risky portfolio, P, constructed with 2 risky securities X and Y. The optimal weights of X and Y in P are 40% and 60% respectively. X has an expected rate of return of 18% and Y has an expected rate of return of 10%. To form a complete portfolio with an expected rate of return of 10%, what percentage of your complete portfolio should you invest in treasury bills?

Expected return from risky portfolio = 40%*18 + 60%*10

Expected return from risky portfolio = 13.20%

Expected Return of your portfolio = Weight of treasury stock * Return on Treasury Stock + (1-Weight of treasury stock)*Expected return from risky portfolio

10% =  Weight of treasury stock *4% + (1- Weight of treasury stock )13.20%

10% = 4% Weight of treasury stock + 13.20% - 13.20% Weight of treasury stock

9.20% Weight of treasury stock = 13.20%-10%

Weight of treasury stock = 3.20%/9.20%

Weight of treasury stock = 34.78%

6. Using the data from problem 5, if the risky portfolio, P, has a standard deviation of 25%, what is the standard deviation of the complete portfolio that you formed in problem 5?

standard deviation of the complete portfolio = (1-Weight of treasury stock)*standard deviation of risky portfolio

standard deviation of the complete portfolio = (1-34.78%)*25%

standard deviation of the complete portfolio = 16.31%

7. Using the data from problems 5 and 6, what is the 5% Value at Risk (VaR) for the expected return on the risky portfolio P?

at 95% confidendce , Expected Worst case = -1.65*SD

Expected Worst case = -1.65*16.31

Expected Worst case = -26.91%

Value at Risk (VaR) = 1000*26.91% = $ 269.10

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