Consider the following information for three stocks,A,B,and C.The stocks' returns are positively but not perfectly positively correlated with one another,i.e. ,the correlations are all between 0 and 1. Portfolio AB has half of its funds invested in Stock A and half in Stock B.Portfolio ABC has one third of its funds invested in each of the three stocks.The risk-free rate is 5%,and the market is in equilibrium,so required returns equal expected returns.Which of the following statements is CORRECT?
A) Portfolio AB has a standard deviation of 20%.
B) Portfolio AB's coefficient of variation is greater than 2.0.
C) Portfolio AB's required return is greater than the required return on Stock A.
D) Portfolio ABC's expected return is 10.66667%.
E) Portfolio ABC has a standard deviation of 20%.

Question

Consider the following information for three stocks,A,B,and C.The stocks' returns are positively but not perfectly positively correlated with one another,i.e. ,the correlations are all between 0 and 1.  Portfolio AB has half of its funds invested in Stock A and half in Stock B.Portfolio ABC has one third of its funds invested in each of the three stocks.The risk-free rate is 5%,and the market is in equilibrium,so required returns equal expected returns.Which of the following statements is CORRECT?
A) Portfolio AB has a standard deviation of 20%. 
B) Portfolio AB's coefficient of variation is greater than 2.0. 
C) Portfolio AB's required return is greater than the required return on Stock A. 
D) Portfolio ABC's expected return is 10.66667%. 
E) Portfolio ABC has a standard deviation of 20%.

Quizplus · Accepted Answer

- We cannot determine the standard deviation of Portfolio AB without knowing the correlations between Stock A and Stock B. 
- The coefficient of variation of Portfolio AB cannot be determined without knowing the standard deviation of Portfolio AB and its expected return. 
- The required return of Portfolio AB is simply the weighted average of the required returns of Stock A and Stock B. We cannot determine if it is greater than the required return on Stock A without knowing the required returns of the individual stocks. 
- The expected return of Portfolio ABC is the weighted average of the expected returns of Stock A, Stock B, and Stock C. Since we are given that the required returns equal expected returns in equilibrium, and the risk-free rate is 5%, we know that the expected return on each stock is equal to the sum of the risk-free rate and a risk premium that depends on the stock's systematic risk. Therefore, we can calculate the expected return of each stock and of Portfolio ABC. Expected return of Stock A = 5% + beta of Stock A * (expected return of market - risk-free rate) = 5% + beta of Stock A * (15% - 5%) = 5% + 0.5 * 10% = 10%. Similarly, expected return of Stock B = 5% + 0.8 * 10% = 13%, and expected return of Stock C = 5% + 1.2 * 10% = 17%. Therefore, expected return of Portfolio ABC = (1/3)*(10% + 13% + 17%) = 40%/3 = 13.33333%. 
- We cannot determine the standard deviation of Portfolio ABC without knowing the correlations between the three stocks.

Consider the Following Information for Three Stocks,A,B,and C