Question

1. Stocks A and B have the following probability distributions:

	% Returns
Probability	A	B
0.40	15	35
0.10	10	20
0.30	-5	15
0.20	-15	-5

1. If you form a 50-50 portfolio of the two stocks, calculate the expected rate of return and the standard deviation for the portfolio.      (Remember, you must calculate a new range of outcomes for the portfolio.)
2. Briefly explain why the standard deviation for the portfolio would be less than the weighted average of the standard deviations for Stocks A and B.

Answer 1

a. the expected rate of return for the portfolio = 11%

the standard deviation for the portfolio = 13.39%

b. As per modern portfolio theory. There is a Benefit of diversification of risk when non-perfectly correlated stocks are added in the portfolio.
The benefit of diversification is when non perfectly correlated stocks are added then if the stock return of stock falls then it's offset by a rise in the stock return of another stock.

P 6:40 6-10 A 15 10 35 20 PA 1 x 6 PB PCA-A)? P(B-3)? 1 1 x 3 0 -2.5) 0 (0-19.5) 0 15 6.30 0.20 - - 5 EPA-A-9.57 EPB-3-19-5. 146.25%. 222.25-12 Total EP(A-A) (8-8) = Cov(A,B) CE PCA-A)") (EP(A-8)") TA = 12-09%/3= 14.91% = 173.75% ² a) wA=0.5 i wp= 0.5 wp - WAÃ + WBO Š = 0.5(2-5) + 0.5(19.5) Tp=VwATA + wg²ro ²+2 WAWB Cov (A,B) - (0.5x12.093+ (0-5x14-9112+ 2(0.5x0-5) (173-75) = 13.39%