Question

Richard has two investment opportunities. He can invest in The Sunglasses Company or The Umbrella Company. If he diversifies his investment by putting​ 60% of his money into The Sunglasses and​ 40% into The​ Umbrella, what is the expected return and standard deviation of his​ portfolio? State of the Economy Probability of the State Expected Return Sunglasses Company Expected Return Umbrella Company Sunny 0.50 ​25% ​0% Rainy 0.50 ​0% ​25%

A. The expected return for the portfolio is​ 25.00% and the standard deviation​ 25.00%.

B. The expected return for the portfolio is​ 12.50% and the standard deviation​ 2.50%.

C. The expected return for the portfolio is​ 25.00% and the standard deviation​ 0.00%.

D. The expected return for the portfolio is​ 12.50% and the standard deviation​ 25.00%.

E. The expected return for the portfolio is​ 12.50% and the standard deviation​ 12.50%

Answer 1

Expected return of Sunglasses = Probability * respective return

Expected return of Sunglasses = 0.5 * 25%

Expected return of Sunglasses = 12.50%

Expected return of Umbrella = Probability * respective return

Expected return of Umbrella = 0.5 * 25%

Expected return of Umbrella = 12.50%

1. Expected Return = Weight in Sunglasses * Return from sunglasses + Weight in Umbrella * Return from Umbrella

Expected Return = 0.60 * 12.50% + 0.40 * 12.50%

Expected Return = 12.50%

the stocks are exactly reversed in the probability states which makes correlation as -1 and SD as expected return of 12.50%

SD = sqrt(Weight in Sunglasses^2 * SD from sunglasses^2 + Weight in Umbrella^2 * SD from Umbrella^2 + 2 * Weight in Sunglasses * weight of umbrella * SD from sunglasses * SD from Umbrella * Correlation)

SD = sqrt(0.60^2 * 0.125^2 + 0.40^2 * 0.125^2 + 2 * 0.60 * 0.40 * 0.125 * 0.125 * -1)

SD = sqrt(0.000625)

SD = 2.50%

Option B. The expected return for the portfolio is​ 12.50% and the standard deviation​ 2.50%.

Please upvote