Stocks A and B have a correlation coefficient of 0.8. The stocks expected return
ID: 2665112 • Letter: S
Question
Stocks A and B have a correlation coefficient of 0.8. The stocks expected returns and standard deviations are in the table below. A portfolio consisting of 40% of stock A and 60% of stock B is created.Stock Expected Return Standard Deviation
A 20% 25%
B 15% 19%
i. What is the expected return of the stock A and B portfolio?
ii. What is the standard deviation of the stock A and B portfolio?
iii. What percentage of stock A should be invested to obtain the minimum risk portfolio that contains stock A and B?
Explanation / Answer
a.Expected Return = E(R)*Weight of Stock A + E(R) * Weight of Stock B
E(R) of portfolio = 20% * .40 + 15% * .60 = 17%
b. Standard deviation of portfolio =.40(20-17)^2 + .60(15-17)^2 = 3.6+ 2.4 =6 =sqrt(6) = 2.45
c. Covariance AB = s.d A * s.d. B * correalation AB
Covariance AB = 25 * 19 * 0.8 =380
Weights of stock A =( Var B - Covab)/Var A +Var B - 2COVab
Weights of stock A = (19^2 -380)/(25^2 + 19^2 - 2 *380 )= 0.084 or 8.4%