b) Scarlett has a mean-variance utility function: U = E(r) – Ao², where A stands for her risk-aversion parameter. Scarlett can invest in a portfolio with an expected return of 9% and a standard deviation of 14%, or she can be T-Bills which have a risk-free 5% rate of return. What is the maximum level of risk aversion for which the risky portfolio is preferred to T-Bills?
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- Assume an investor with the coefficient of risk aversion A=5.5. To maximize her expected utility, she would choose the asset with an expected rate of return of _______ and a standard deviation of ________, respectively." a. 21%; 16% b. 24%; 21% c. 12%; 30% d. 15%; 5%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%The risky portfolio expected return and standard deviation is 14% and 20%, respectively. The risk free rate is 5%. The risk aversion coefficient A is 2.5 and 4 for Mary and Kim, respectively. Answer the following questions: A. Who is more risk averse? B. What is the capital allocation y to the risky portfolio for each investor? C. Suppose investors have the following utility function: U = E(R) - ¹2 Ao² Calculate the Utility level for each investor's optimal complete portfolio.
- Mean-variance expected utility is given by Eu = e-, where e is expected return, v is the variance of the portfolio and tis risk tolerance. Suppose an investor has risk-loving preferences. What can we say about the value of t? Select one: Ot1 O. t>0 O t=0On the basis of the utility formula below, which investment would you select if you were risk averse with A = 4? Investment Expected return E(r) Standard deviation σ 1 0.12 0.30 2 0.15 0.50 3 0.21 0.16 4 0.24 0.21a. 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 ratio
- An investor is considering two possible investment alternatives, Portfolio A and Portfolio B. The expected returns for each are shown in the table below under two different market conditions, along with the investors prediction for the probability of each market condition. The investor's prediction for the probability of each market condition. The investor's utility function can be represented as U(w) - square root (w). If the investor maximises their expected utility, which alternative would they choose? Portfolio A Portfolio B Bull Market Bear Market Portfolio A 16% Portfolio B 4% Probability 0.75 3% 2% 0.25Suppose the utility function is U = E(r) - 0.5Ao2. Draw the indifference curve corresponding to a utility level of 0.2 for an investor with a risk aversion coefficient of 3. Please note the vertical line indicates expected return, and plot standard deviation on the horizontal line.Supposing the return from an investment has the following probability distribution Return Probability R (%) 8 0.2 10 0.2 12 0.5 14 0.1 Required: What is the expected return of the investment? What is the risk as measured by the standard deviation of expected returns?
- c. Suppose the risk-free rate is 4.2 percent and the market portfolio has an expected return of 10.9 percent. The market portfolio has a variance of .0382. Portfolio Z has a correlation coefficient with the market of .28 and a variance of .3285. According to the capital asset pricing model, what is the expected return on Portfolio Z?The risk free rate is 3%. The optimal risky portfolio has an expected return of 9% and standarddeviation of 20%. Answer the following questions.a) Assume the utility function of an investor is U = E(r) − 0.5Aσ2. What is condition ofA to make the investors prefer the optimal risky portfolio than the risk free asset? b) Assume the utility function of an investor is U = E(r) − 2.5σ2. What is the expectedreturn and standard deviation of the investor’s optimal complete portfolio?he risk free rate is 3%. The optimal risky portfolio has an expected return of 9% and standarddeviation of 20%. (a) Assume the utility function of an investor is U = E(r) − 0.5Aσ2. What is condition ofA to make the investors prefer the optimal risky portfolio than the risk free asset? (b) Assume the utility function of an investor is U = E(r) − 2.5σ2. What is the expectedreturn and standard deviation of the investor’s optimal complete portfolio?