Assume an economy in which there are three securities: Stock A with rA = 10% and $\sigma$A = 10%; Stock B with rB = 15% and$\sigma$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%.

Question

Quizplus · Accepted Answer

To find the expected return and standard deviation of the portfolio, we need to use the following formula: 
E(rp) = wA * rA + wB * rB + wRF * rRF 
where wA, wB, and wRF represent the weights of each security in the portfolio. 
To find the SD of the portfolio, we need to use the following formula: 
SD(rp) = sqrt(wA^2 * sigmaA^2 + wB^2 * sigmaB^2 + wRF^2 * 0^2 + 2 * wA * wB * rhoAB * sigmaA * sigmaB) 
where sigmaA, sigmaB, and rhoAB represent the standard deviations and correlation coefficient of Stocks A and B.

Assuming the investor wants to construct a portfolio with an expected return of 12%, we can solve for the portfolio weights as follows:

0.12 = wA * 0.1 + wB * 0.15 + wRF * 0.07 
1 = wA + wB + wRF 
Solving for the weights, we get: 
wA = 0.3333, wB = 0.4444, wRF = 0.2222

Using these weights in the formula for the SD, we get:

SD(rp) = sqrt(0.3333^2 * 0.1^2 + 0.4444^2 * 0.2^2 + 0.2222^2 * 0^2 + 2 * 0.3333 * 0.4444 * 0 * 0.1 * 0.2) 
= 0.118 or 11.8%

Therefore, we can conclude that the expected return on the investor's portfolio will probably have an expected return that is somewhat below 15% (since the weights of Stocks A and B are less than 1/2 each), and a standard deviation (SD) that is between 10% and 20% (since it is between the SDs of the individual stocks). Thus, choice C is the correct answer.

Assume an Economy in Which There Are Three Securities: Stock σ\sigmaσ

Assume an Economy in Which There Are Three Securities: Stock $\sigma$