Stock A has a beta of 1.2 and a standard deviation of 20%.Stock B has a beta of 0.8 and a standard deviation of 25%.Portfolio P has $200,000 consisting of $100,000 invested in Stock A and $100,000 in Stock B.Which of the following statements is correct? (Assume that stocks are in equilibrium.)
A)Stock A's returns are less highly correlated with the returns on most other stocks than are B's returns.
B)Stock B has a higher required rate of return than Stock A.
C)Portfolio P has a standard deviation of 22.5%.
D)Portfolio P has a beta equal to 1.0.

Question

Quizplus · Accepted Answer

To find the standard deviation of the portfolio, we use the formula:
σp = √(wA²σA² + wB²σB² + 2wAwBσAσBρAB)
where wA and wB are the weights of Stock A and Stock B in the portfolio, respectively, σA and σB are the standard deviations of Stock A and Stock B, respectively, and ρAB is the correlation coefficient between the returns on Stock A and Stock B. Since the question does not provide the correlation coefficient, we assume it to be zero (i.e., the returns on Stock A and Stock B are uncorrelated) to obtain:
σp = √(0.5²×0.2² + 0.5²×0.25²) = 0.225 or 22.5%
To find the beta of the portfolio, we use the formula:
βp = wAβA + wBβB
where βA and βB are the betas of Stock A and Stock B, respectively. Substituting the given values, we get:
βp = 0.5×1.2 + 0.5×0.8 = 1.0
Therefore, statement D is correct. Statements A and B cannot be determined from the given information.

Stock a Has a Beta of 1