Question

Security F has an expected return of 11.6 percent and a standard deviation of 44.6 percent per year. Security G has an expected return of 16.6 percent and a standard deviation of 63.6 percent per year. a. What is the expected return on a portfolio composed of 24 percent of Security F and 76 percent of Security G? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return 15.40 15.40 Correct % b. If the correlation between the returns of Security F and Security G is .19, what is the standard deviation of the portfolio described in part (a)? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation 51.45 51.45 Correct %

Answer 1

A.Expected return on a portfolio = 15.40%

B.Standard deviation of the portfolio=51.45%

Step-by-step explanation:

A.Calculation for the expected return on a portfolio

Using this formula

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

Let plug in the formula

Expected return on a portfolio = 24%×11.60 + 76%×16.60

Expected return on a portfolio =2.784+12.616

Expected return on a portfolio = 15.40%

Therefore the Expected return will be 15.40%

b. Calculation for the standard deviation of the portfolio described in part (a)

Using this formula

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

Let plug in the formula

Standard deviation of the portfolio = (24%^2×44.60%^2 + 76%^2×63.60%^2 + 2×24%×76%×44.60%×63.60%×0.19)^(1/2)

Standard deviation of the portfolio = (0.0576×0.198916+0.5776×0.404496+0.0196607)^(1/2)

Standard deviation of the portfolio =

(0.0114575+0.2336368+0.0196607)^(1/2)

Standard deviation of the portfolio=(0.264755)^(1/2)

Standard deviation of the portfolio=0.5145×100

Standard deviation of the portfolio=51.45%

Therefore Standard deviation of the portfolio will be 51.45%