Assume an economy in which there are three securities: Stock A with rA = 10% and A = 10%; Stock B with rB = 15% and B = 20%; and a riskless asset with rRF = 7%. Stocks A and B are uncorrelated (rAB = 0). Which of the following statements is most CORRECT?
A) The expected return on the investor's portfolio will probably have an expected return that is somewhat above 15% and a standard deviation (SD) of approximately 20%.
B) The expected return on the investor's portfolio will probably have an expected return that is somewhat below 10% and a standard deviation (SD) of approximately 10%.
C) The expected return on the investor's portfolio will probably have an expected return that is somewhat below 15% and a standard deviation (SD) that is between 10% and 20%.
D) The investor's risk/return indifference curve will be tangent to the CML at a point where the expected return is in the range of 7% to 10%.
E) Since the two stocks have a zero correlation coefficient, the investor can form a riskless portfolio whose expected return is in the range of 10% to 15%.

Question

Quizplus · Accepted Answer

To calculate the expected return and standard deviation of the portfolio, we need to use the following formula:
E(rp) = wA × rA + wB × rB + wRF × rRF
σp = [wA^2 × σA^2 + wB^2 × σB^2 + 2 × wA × wB × σA × σB]^0.5

Assuming equal weights for Stock A and B (wA = wB = 0.5) and using the given values, we get:
E(rp) = (0.5 × 10%) + (0.5 × 15%) + (0.5 × 7%) = 11%
σp = [0.5^2 × 10%^2 + 0.5^2 × 20%^2 + 2 × 0.5 × 0.5 × 10% × 20%^0.5] ^0.5 = 14.14%

Therefore, the expected return on the portfolio will be below the expected return of Stock B (15%) but above the expected return of Stock A (10%). The standard deviation of the portfolio will be between the standard deviations of the two stocks (10% and 20%).

Option A and B are incorrect because they do not consider the correlation between the stocks and overestimate or underestimate the portfolio's volatility. Option D is not relevant to the question as we do not have any information to determine the investor's risk/return preference. Option E is incorrect because the question does not mention anything about forming a riskless portfolio.

Assume an Economy in Which There Are Three Securities: Stock