Stocks A and B are quite similar: Each has an expected return of 12%, a beta of 1.2, and a standard deviation of 25%.The returns on the two stocks have a correlation of 0.6.Portfolio P has 50% in Stock A and 50% in Stock B.Which of the following statements is CORRECT?
A) Portfolio P has a standard deviation that is greater than 25%.
B) Portfolio P has an expected return that is less than 12%.
C) Portfolio P has a standard deviation that is less than 25%.
D) Portfolio P has a beta that is less than 1.2.
E) Portfolio P has a beta that is greater than 1.2.

Question

Quizplus · Accepted Answer

The standard deviation of a two-asset portfolio depends on the correlation between the returns of the two assets. When the correlation between returns is less than 1, the standard deviation of the portfolio is less than the weighted average of the standard deviations of the individual assets. In this case, since the correlation between the returns on stocks A and B is only 0.6, the standard deviation of the portfolio is less than 25%. Therefore, answer choice (C) is correct. Since both stocks have an expected return of 12% and the portfolio is split evenly between them, the expected return of the portfolio is also 12%. The beta of the portfolio is simply the weighted average of the betas of the individual stocks, which is 1.2 for both stocks, so answer choices (D) and (E) are both incorrect.

Stocks a and B Are Quite Similar: Each Has an Expected