Assume that you manage a risky portfolio with an expected rate of return of 14% and a standard deviation of 46%. The T-bill rate is 4%. Your client chooses to invest 85% of a portfolio in your fund and 15% in a T-bill money market fund. Required: a. What are the expected return and standard deviation of your client's portfolio? (Round your answers to 1 decimal place.) Expected return Standard deviation b. Suppose your risky portfolio includes the following investments in the given proportions: Stock A Stock B Stock C 30% 30 40 Security T-Bills Stock A Stock B Stock C What are the investment proportions of your client's overall portfolio, including the position in T-bills? (Round your answers to 1 decimal place.) % per year % per year Investment Proportions % % % %
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- You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 29%. The T-bill rate is 5%. Suppose that your client prefers to invest in your fund a proportion y that maximizes the expected return on the complete portfolio subject to the constraint that the complete portfolio's standard deviation will not exceed 18%. a. What is the investment proportion, y? (Round your answer to 2 decimal places.) Investment proportion y % b. What is the expected rate of return on the complete portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Rate of return %You manage a risky portfolio with an expected rate of return of 19% and a standard deviation of 31%. The T-bill rate is 5%. Suppose that your client prefers to invest in your fund a proportion y that maximizes the expected return on the complete portfolio subject to the constraint that the complete portfolio’s standard deviation will not exceed 19%. a. What is the investment proportion, y? (Round your answer to 2 decimal places.) b. What is the expected rate of return on the complete portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 28%. The T-bill rate is 7%. Your client's degree of risk aversion is A = 2.0, assuming a utility function u E(r) = A0². a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Investment proportion y Expected return Standard deviation - % b. What are the expected value and standard deviation of the rate of return on your client's optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.) % %
- You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 36%. The T-bill rate is 6%. Your client's degree of risk aversion is A = 3.1, assuming a utility function u = E(r) A02. a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Investment proportion y % b. What are the expected value and standard deviation of the rate of return on your client's optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected return % Standard deviation %You manage a risky portfolio with an expected rate of return of 19% and a standard deviation of 32%. The T-bill rate is 7%. Your client’s degree of risk aversion is A = 3.3, assuming a utility function U = E(r) - ½Aσ². a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the expected value and standard deviation of the rate of return on your client’s optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)You manage a risky portfolio with an expected rate of return of 22% and a standard deviation of 34%. The T-bill rate is 6%. Your client's degree of risk aversion is A = 1.7. Required: a. What proportion, y, of the total investment should be invested in your fund? b. What are the expected value and standard deviation of the rate of return on your client's optimized portfolio? Complete this question by entering your answers in the tabs below. Required A Required B What proportion, y, of the total investment should be invested in your fund? Note: Round your answer to 2 decimal places. Investment proportion y %
- You manage a risky portfolio with an expected rate of return of 10% and a standard deviation of 34%. The T-bill rate is 4%. Suppose that your client prefers to invest in your fund a proportion y that maximizes the expected return on the complete portfolio subject to the constraint that the complete portfolio's standard deviation will not exceed 10%. Required: a. What is the investment proportion, y? b. What is the expected rate of return on the complete portfolio?Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 42%. The T-bill rate is 6%. Your client chooses to invest 85% of a portfolio in your fund and 15% in a T-bill money market fund. Required: a. What are the expected return and standard deviation of your client's portfolio (Round your answers to 1 decimal place.) Expected return Standard deviation b. Suppose your risky portfolio includes the following investments in the given proportions: 26% 35 39 Stock A Stock B Stock C What are the investment proportions of your client's overall portfolio, including the position in T-bills? (Round your answers to 1 decimal place.) Security T-Bills Stock A Stock B Stock C % per year % per year Investment Proportions % % % %. Assume that you manage a risky portfolio with an expected rate ofreturn of 18% and a standard deviation of 28%. The T-bill rate (risk-free rate) is 7%. Yourclient chooses to invest 70% in the risky portfolio in your fund and 30% in a T-bill moneymarket fund. We assume that investors use mean-variance utility: U = E(r) − 0.5 × Aσ2,where E(r) is the expected return, A is the risk aversion coefficient and σ2is the variance ofreturns.a) What is the expected value and standard deviation of the rate of return on your client’sportfolio? b) What is the reward-to-volatility ratio (Sharpe ratio) of your risky portfolio? What isthe reward-to-volatility ratio (Sharpe ratio) of your client’s risky portfolio? Commenton the relationship between these two Sharpe ratio calculated and explain the intuitionbehind. c) Draw the Capital Allocation Line (CAL) of your portfolio on an expected returnstandard deviation diagram. What is the slope of the CAL? Show the position ofyour client on your fund’s CAL.…
- If your portfolio includes 35 percent of X, 40 percent of Y and 25 percent of Z, answer the following questions: (a) Calculate the portfolio expected return. (b) Calculate the variance and the standard deviation of the portfolio. (c) If the expected T-bill rate is 3.80 percent, calculate the expected risk premium on the portfolio. (d) If the market index fund has the same expected return as your portfolio, without considering any transaction cost, would you consider selling your portfolio and investing the market index fund instead? Explain your thoughts.You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate is 8%. Your client’s degree of risk aversion is A = 3.5.a. What proportion, y, of the total investment should be invested in your fund?b. What is the expected value and standard deviation of the rate of return on your client’s optimized portfolio?f. Assume a Portfolio of two assets A and B whose standard deviations of their returns are 8.6% and 10.8% respectively, while their correlation coefficient of returns is Pas = - 0.61. You are given the right to do portfolio optimization without restrictions. What proportions would you choose and why?