Question 5. You can invest in two risky assets, r₁ and r2 and one risk-free asset, r. The two risky assets are uncorrelated, and values are E[ri] = 8%, E[r₂] = 6%, Var[r₁] = 10%,Var[r₂] = 3%, and rf = 3% If you have a mean-variance optimizer with a risk aversion A = 2, what is the optimal portfolio?
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- The market has three risky assets. The variance-covariance matrix of the risky assets are as follows: r1 r2 r3 r1 0.25 0 -0.2 r2 0 4 0.1 r3 -0.2 0.1 1 Assume the market portfolio is M = 0.2 ◦ r1 + 0.5 ◦ r2 + 0.3 ◦ r3. Further assume E(rM) = 0.08. (1) What is the variance of M?(2) What is the covariance of r2 and M?(3) What is β2?(4) If the rate of return of the risk-free asset is 0.02. Then what is the fair expected rate of return of security 2?(5) An investor wants to invest in a portfolio P = 0.4◦r1+0.6◦r3. What is its “fair” expected rate of return?a. Use the following information: E[rXOM] = 15.6%, standard deviationXOM = 15.9% E[rMS]=29.7%, standard deviationMS = 35.2% Correlation of returns: ρXOM,MS = 0.139, rf=10% If the optimal amount to invest in the first asset (w) is 0.43, what is the variance of the risky portfolio when w=0.43? (write in decimal format using 5 decimal places) b. When choosing the best point of the POS (the curved line connecting two possible assets you can invest in) you need to find the point that: 1.Has the greatest difference between it’s return and the risk free rate, thus leading to the best return 2. You must solve for the optimal y allocation in order to find the best point on the POS 3. The point with the lowest standard deviation 4. The point with the greatest Sharpe ratioCourse: FinanceAs a great investor, you are interested in 3 assets to invest: A, B and C. A financial advisor tells you that the returns on the assets are independent of each other, and you are given the following data: Asset A B C E(Ri) 0.05 0.035 0.06 Variance 0.0015 0 0.008 You have not yet analyzed what your degree of risk aversion (A) is, but you know that your utility function behaves as follows: U[ E(Rp)] = E(Rp) - 0.5 * A * Variance. (See attached image for a better understanding) You are asked to:(a) Find the optimal portfolio with these 3 assets {called wA, wB and wC}.b) Calculate the expected return and risk of the optimal portfolio for the following degrees of risk aversion (A):(i) A = 5(ii) A = 10(iii) A = 16 Please ASAP
- Asset X has an expected return of 6% and a variance of 0.001. Asset Y has an expected return of 12% and the same variance asX (i.e., 0.001). The returns of assets X and are uncorrelated, and the risk-free rate is 3%. Find the variance of the highestSharpe ratio portfolio that can be formed of the two risky assets X and Y.9. A risk averse, wealth maximising, investor is faced with a choice between four investments (P, Q, R and S) that have profiles as follows: Mean return (%) Variance (%) P 19 18 Q 16 17 R 22 16 S 20 16 Between which pair of these investments would the investor find it impossible to distinguish on the basis of the above information? A. P and Q B. R and S C. P and S D. Q and RQuestion D is required. Thank you. d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to pay returns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standard deviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also has standard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whether asset A and B are overvalued or undervalued, and explain why. (Hint: Beta of asset i ( , where are standard deviations of asset i and market portfolio, is the correlation between asset i and the market portfolio)
- Two assets have the following expected returns and standard deviations when the risk-free rate is 5%: Asset A E(rA) = 10% σA = 20% Asset B E(rB) = 15% σB = 27% An investor with a risk aversion of A = 3 would find that _________________ on a risk return basis. only Asset A is acceptable only Asset B is acceptable neither Asset A nor Asset B is acceptable both Asset A and Asset B are acceptableQuestion: Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to pay returns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standard deviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also has standard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whether asset A and B are overvalued or undervalued, and explain why? (Hint: Beta of asset i (??) = ??????? , where ??,?? are standard deviations of asset i and market portfolio, ??? is the correlation between asset i and the market portfolio)Two assets have the following expected returns and standard deviations when the risk-free rate is 5%: Asset A E(rA) = 10% σA = 20% Asset B E(rB) = 15% σB = 27% An investor with a risk aversion of A = 3 would find that _________________ on a risk-return basis.
- Part a State Pr(a) ra Pr(b) rb 1 0.2 10% 0.25 12% 2 0.6 15% 0.40 20% 3 0.2 20% 0.35 18% Given the probability distribution above, determine (Calculate) and compare the: Expected return (means) Variance Standard deviation Part b How important is risk to returns and what are the key elements that must be analyzed in this regard before an investment decision is made? Discuss in no more than 200 words.d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to pay returns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standard deviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also has standard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whether asset A and B are overvalued or undervalued, and explain why.assume that risk free rate, RF, is currently 8%, the market return, 1m, is 12%, and asset a beta ba, is 1.10. (a) Draw the SML on a set of "non-diversifiable risk Please sent me complete this question for further reliance.