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- Using the following data: Scenario Probability return K1 return K2 0.2 -10% 5% W2 0.4 0% 30% W3 0.4 20% -5% compute the weights in the portfolio with minimum risk. What are the expected return and risk of this minimum risk portfolio?An investor has preferences represented by the utility function U = E(r) - 20². What is her certainty equivalent return for a portfolio with an expected return of 10% and a standard deviation of 15%? Oa. 1.0% O b. 2.5% O c. 0.5% O d. 5.5% O e. 10.0%You are given the following information concerning three portfolios, the market portfolio, and the risk-free asset: Portfolio X Y Z Market Risk-free Rp 11.0% ор 33.00% 10.0 28.00 8.1 10.4 5.2 18.00 23.00 Ө вр 1.45 1.20 0.75 1.00 Ө Assume that the correlation of returns on Portfolio Y to returns on the market is 0.66. What percentage of Portfolio Y's return is driven by the market? Note: Enter your answer as a decimal not a percentage. Round your answer to 4 decimal places. R-squared
- Portfolio Expected return Standard deviation Q 7.8% 10.5% R 10.0% 14.0% S 4.6% 5.0% T 11.7% 18.5% U 6.2% 7.5% (Q1) For each portfolio, calculate the risk premium per unit of risk (Sharpe ratio) that you expect to receive. Assume that the risk-free rate is 3.0%. (Q2) Using answers from Q1, which of these five portfolios is most likely to be the market portfolio and explain why. (200 words maximum)You are given the following information concerning three portfolios, the market portfolio, and the risk- free asset: Portfolio X Y Z Market Risk-free Rp 14.5% R-squared 13.5 9.1 10.7 5.4 op 36% 31 21 26 0 6p 1.60 1.30 .80 1.00 0 Assume that the correlation of returns on Portfolio Y to returns on the market is 72. What percentage of Portfolio Y's return is driven by the market? (Enter your answer as a decimal not a percentage. Round your answer to 4 decimal places.)You are given the following information concerning three portfolios, the market portfolio, and the risk-free asset: Portfolio Y Z Market Risk-free Rp 13.5% бр 35.00% 12.5 30.00 7.1 20.00 10.6 4.4 25.00 0 Вр 1.55 1.20 0.80 1.00 0 Assume that the correlation of returns on Portfolio Y to returns on the market is 0.70. What percentage of Portfolio Y's return is driven by the market? Note: Enter your answer as a decimal not a percentage. Round your answer to 4 decimal places. × Answer is complete but not entirely correct. R-squared 0.9785
- Problem 5 Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate (risk-free rate) is 7%. Your client chooses to invest 70% in the risky portfolio in your fund and 30% in a T-bill money market fund. We assume that investors use mean-variance utility: U = E(r) – 0.5 x Aa?, where E(r) is the expected return, A is the risk aversion coefficient and o? is the variance of returns. a) What is the expected value and standard deviation of the rate of return on your client's portfolio? b) What is the reward-to-volatility ratio (Sharpe ratio) of your risky portfolio? What is the reward-to-volatility ratio (Sharpe ratio) of your client's risky portfolio? Comment on the relationship between these two Sharpe ratio calculated and explain the intuition behind. c) Draw the Capital Allocation Line (CAL) of your portfolio on an expected return- standard deviation diagram. What is the slope of the CAL? Show the position of your…A portfolio has an expected rate of return of 0.15 and a standard deviation of 0.15. The risk-free rate is 6%. An investor has the following utility function: U = E(r) - (A/2)s2. Which value of A makes this investor indifferent between the risky portfolio and the risk-free asset? A. 5 B. 8 C. 6 D. 7Use the following CAPM equation for a portfolio to answer the questions that follow:E(RP) = RF + βP (RM – RF) = 1 + 0.8 (5 – 1) = 4.2% a) Is the portfolio defensive or aggressive. Why? b) If the actual portfolio return is 6%, what is the portfolio’s alpha?
- Question 7 The following figures show the optimal portfolio choice for two investors with different levels of risk-aversion graphically. Which statement is correct? E[R] 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 0.15 Figure 1 0.2 0.25 0.3 0.35 0.4 0.45 o(R) [a]H 0.3 0.25 0.2 0.15 0.1 0.05 0 0 Figure (2) shows an investor that borrows in risk-free rate and invests in the risky asset. Figure (1) shows an investor with a conservative investment behavior. 0.05 0.1 0.15 In the optimal point of both figures, the highest indifference curve is tangent to the efficient frontier. In Figure (1), more aggressive investment decision led to a higher Sharpe ratio. Figure 2 0.2 0.25 o (R) 0.3 0.35 0.4 0.45Which of the following portfolios should a risk averse investor choose? Portfolio Name σ(rP) Sharpe Ratio A 20% 0.45 B 25% 0.36 C 10% 0.27 D 15% 0.14 Portfolio D Portfolio A Portfolio C Portfolio B2. Assuming the following: Average Return (Risky Portfolio) 3.86% Standard Dev (Risky Portfolio) 10.56% Average Risk Free Rate 2.18% Return on Risk Free Asset Avg 4.15% Using the formula: E(rc)=rf + y* (E(rp) - rf) Solve for: 1. % of Risky Assets (y): 2. % of Risk Free Assets (1-y): Note: You wish to generate a 7% return for your complete portfolio E(rc)