Your portfolio consists of $50,000 invested in Stock X and $50,000 invested in Stock Y. Both stocks have an expected return of 15%, betas of 1.6, and standard deviations of 30%. The returns of the two stocks are independent, so the correlation coefficient between them, rXY, is zero. Which of the following statements best describes the characteristics of your two-stock portfolio?
A) Your portfolio has a standard deviation of 30%, and its expected return is 15%.
B) Your portfolio has a standard deviation less than 30%, and its beta is greater than 1.6.
C) Your portfolio has a beta equal to 1.6, and its expected return is 15%.
D) Your portfolio has a beta greater than 1.6, and its expected return is greater than 15%.

Question

Quizplus · Accepted Answer

The portfolio's beta is the weighted average of the individual betas, which is (0.5 * 1.6) + (0.5 * 1.6) = 1.6. The portfolio's expected return is the weighted average of the individual expected returns, which is (0.5 * 15%) + (0.5 * 15%) = 15%. The portfolio's standard deviation is not provided in the question, but it can be calculated using the formula: σp = √(w1^2 * σ1^2 + w2^2 * σ2^2 + 2 * w1 * w2 * σ1 * σ2 * rXY), where w1 and w2 are the weights of the two stocks in the portfolio, σ1 and σ2 are the standard deviations of the two stocks, and rXY is the correlation coefficient between the two stocks. Since the correlation coefficient is zero, the formula simplifies to: σp = √(w1^2 * σ1^2 + w2^2 * σ2^2) = √((0.5)^2 * (30%)^2 + (0.5)^2 * (30%)^2) = 21.21%.

Your Portfolio Consists of $50,000 Invested in Stock X and $50,000