Stocks A and B each have an expected return of 15%,a standard deviation of 20%,and a beta of 1.2.The returns on the two stocks have a correlation coefficient of +0.6.You have a portfolio that consists of 50% A and 50% B.Which of the following statements is CORRECT?
A) The portfolio's beta is less than 1.2.
B) The portfolio's expected return is 15%.
C) The portfolio's standard deviation is greater than 20%.
D) The portfolio's beta is greater than 1.2.
E) The portfolio's standard deviation is 20%.

Question

Quizplus · Accepted Answer

The expected return of a portfolio is a weighted average of the individual stock returns. Since the portfolio is split equally between stocks A and B, the expected return of the portfolio would be (0.5)(15%) + (0.5)(15%) = 15%.

The beta of a portfolio is also a weighted average of the individual stock betas, where the weights are the portfolio weights. Therefore, the portfolio beta would be (0.5)(1.2) + (0.5)(1.2) = 1.2.

The standard deviation of a portfolio is a function of the individual stock standard deviations, the portfolio weights, and the correlation between the stocks. Using the formula:

Portfolio standard deviation = [(0.5)^2 x (0.2)^2 + (0.5)^2 x (0.2)^2 + 2 x 0.5 x 0.5 x 0.6 x 0.2 x 0.2]^0.5 = 14.14%.

Therefore, the correct option is B.

Stocks a and B Each Have an Expected Return of 15%,a