Security A\'s expected return is 10 percent while the expected return of B is 14

Question

Security A's expected return is 10 percent while the expected return of B is 14 percent. The standard deviation of A's returns is 5 percent, and it is 9 percent for B. An investor plans to invest equal amounts in A and B. Which of the following statements is true about this portfolio consisting of stock A and stock B?

A the risk of the portfolio is equal to 7 percent
B the lower correlation of returns between two stocks, the higher the portfolio's risk
C the risk of the portfolio is PRIMARILY dependent on the utility function of the investor
D the higher the correlation of returns between the two stocks, the higher the portfolio's risk

Explanation / Answer

First of all, the risk of the portfolio depends on SD of A's return, SD of B's return and the correlation between A's and B's returns. We're given A's and B's returns in the problem, so the portfolio risk relies on the correlation. So we can eliminate answers A and C. Furthermore, the higher the correlation, the riskier the portfolio would be. Imagin a portfolio of two assets with correlation 1.0, in this case, no risk is reduced. So, the answer would be D.

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