Security F has an expected return of 11.70 percent and a standard deviation of 4

Question

Security F has an expected return of 11.70 percent and a standard deviation of 44.70 percent per year. Security G has an expected return of 16.70 percent and a standard deviation of 63.70 percent per year.

What is the expected return on a portfolio composed of 23 percent of Security F and 77 percent of Security G? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

If the correlation between the returns of Security F and Security G is .18, what is the standard deviation of the portfolio described in part (a)? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Security F has an expected return of 11.70 percent and a standard deviation of 44.70 percent per year. Security G has an expected return of 16.70 percent and a standard deviation of 63.70 percent per year.

Explanation / Answer

a.What is the expected return on a portfolio composed of 23 percent of Security F and 77 percent of Security G? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

    Expected return on a portfolio  = Weight of Security F * Expected return of Security F+ Weight of Security G * Expected return of Security G

    Expected return on a portfolio  = 23%*11.70 + 77%*16.70

    Expected return on a portfolio  = 15.55%

Answer

  Expected return 15.55%

b.If the correlation between the returns of Security F and Security G is .18, what is the standard deviation of the portfolio described in part (a)? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Standard deviation of the portfolio = (Weight of Security F^2* SD of Security F^2 + Weight of Security G^2 * SD of Security G^2 + 2*Weight of Security F*Weight of Security G*SD of Security F*SD of Security G*correlation)^(1/2)

Standard deviation of the portfolio = (23%^2*44.70%^2 + 77%^2*63.70%^2 + 2*23%*77%*44.70%*63.70%*0.18)^(1/2)

Standard deviation of the portfolio = 51.89%

Answer

  Standard deviation 51.89%

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