Question

Question 1

Consider two risky assets A and B with E(rA)= 15%, Sigma_A= 32%, E(rB)= 0.09, Sigma_B= 23%, corrA,B= 0.2. The risk free rate is 5%. The optimal risky portfolio of comprised of the two risky assets is to allocate 64% to A and the rest to B. What is the standard deviation of the optimal risky portfolio ?

Select one:

a. 20.75%

b. 23.61%

c. 22.86%

d. 23.00%

Question 2

Continued with previous question. What is the Sharpe ratio of the optimal risky portfolio?

Select one:

a. 0.33

b. 0.35

c. 0.31

d. 0.29

Question 3

Continue to use the information given in previous two questions.

If your target expected return is 12%, lower than the expected return of the optimal risky portfolio, which is comprised of 64% risky asset A and 36% risky asset B, which of the following statements is not correct?

Select one:

a. invest 89.16% of your capital in this optimal risky portfolio and the rest in the risk-free asset

b. The asset allocation is 57.06% in A, 32.10% in B and 10.84% in the risk-free.

c. The sigma of your complete portfolio is 21%

d. not invest in the optimal risky portfolio but choose another portfolio on the investment opportunity set that has expected return of 12%.

Question 4

Continue to use the information from previous questions.

If you only invest in the two risky assets A and B, not the risk-free asset and your target expected return is still 12%, what should be the portfolio composition ?

Select one:

a. 50% in A and 50% in B

b. 60% in A and 40% in B

c. 64% in A and 36% in B

d. 65% in A and 35% in B

Question 5

Compare the previous two portfolios with the same expected return of 12%, one with investment in the risk-free asset and another one without investment in the risk-free asset. Which of the following statements is NOT correct?

Select one:

a. The portfolio without investment in the risk-free asset situates to the left of the optimal risky portfolio on the same capital allocation line.

b. The portfolio without investment in the risk-free asset sits on the investment opportunity set comprised of the two risky assets A and B.

c. The portfolio without investment in the risk-free asset has higher standard deviation than the portfolio with investment in the risk-free asset.

d. The portfolio without investment in the risk-free asset locates below the optimal capital allocation line.

Answer 1

Answer RA= Expected Return on Assot D = 157 GA- Std. Deviation on Asset 'À 2 38 R = Expected Retom on Asset B gr. OB = Std. Deviation on Asset 'B' = 23% Correlebon (A,B) = 0.2 WA weight of Investment in Asset A = 0.64 WB : weight of Investment in Asset B = 0.36 ① Std. Deviation of portfolio wA G & who +2 WAWB GAEB Cor (A,B) 2 x 0.36x0.64 x 32 x 23 x 0.2 √ 419.4304 + 68.5584 + 67.89 976 = √555.8186 = 23.5758 Accurate Answer: 23.5758 closest Answer (as per choice) = 23.61% ie. (b). 2. Sharpe's Rotio = Rp - Rf) ; Rp = Return on portfolio - (15x0.64) + (9x0.36) & 12.841 Rf = Risk free Return op Ston dord Deviation ou portfolio Las Colcelled above] (12.84-5) 23.5758 FINAL ANS: (A) 0.33 0.33

FINAL ANS (c) INCORRECT STATEMENT : Sigma of your complete portfolio is also As Sigma (volability of Portfolio is 23.61% as in portii) ( Portfolio Composition if Target Return is 12%. investment in the Risk free Asset. without ANSWER: (a) 50% in A and so % in B Portfolio Return with so-so Composition = (WARRA) + (WB x RB) = o.sxis) + (o.sx g) - 12% The Requisite No. of ports are done as per the HomeworkLib policy