Required: 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 overall portfolio? (Do not round intermediate calculations and round your answer to 2 decimal places.)
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- 2) A risky portfolio is provided with an expected rate of return of 19.5%, standard deviation of 30% and risk free rate of 8.5%. If the client chooses to invest three different risky assets a proportion of equal investments and also in T bills. a) Determine weights of all the distributed assets. b) Determine the Sharpe ratio of the portfolio c) If the investment is done such a way that the expected return is maximized with standard deviation not exceeding 25%. Determine the investment proportion and expected return of the portfolio.Problem 11-25 Portfolio Returns and Deviations [LO 1, 2] Consider the following information on a portfolio of three stocks: State of Economy Probability of State of Economy Stock A Rate of Return Stock B Rate of Return Stock C Rate of Return Boom .13 .02 .32 .50 Normal .55 .10 .22 .20 Bust .32 .16 −.21 −.35 If your portfolio is invested 40 percent each in A and B and 20 percent in C, what is the portfolio’s expected return, the variance, and the standard deviation? Note: Do not round intermediate calculations. Round your variance answer to 5 decimal places, e.g., .16161. Enter your other answers as a percent rounded to 2 decimal places, e.g., 32.16. If the expected T-bill rate is 4.25 percent, what is the expected risk premium on the portfolio? Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.INV 2 -1 You are considering an investment in a portfolio P with the following expected returns in three different states of nature: Recession Steady Expansion Probability 0.10 0.55 0.35 Return on P -15% 20% 40% The risk-free rate is currently 4%, and the market portfolio M has an expected return of 16% and standard deviation of 20%, and its correlation with P is .7. Is P an efficient portfolio relative to the market?
- Subject: Finacial stratgy & policy 8-4: Is it possible to construct a portfolio of real-world stocks that has an expected return equal to the risk-free rate? 8-5: Stock A has an expected return of 7%, a standard deviation of expected returns of 35%, a correlation coefficient with the market of –0.3, and a beta coefficient of –0.5. Stock B has an expected return of 12%, a standard deviation of returns of 10%, a 0.7 correlation with themarket, and a beta coefficient of 1.0. Which security is riskier? Why?Problem 2: You have access to three risky assets (Stocks A, B, and C) and ariskless asset:Expected Return, Standard DeviationStock A 8% , 35%Stock B 12% , 50%Stock C 15% , 75% Riskless Asset expected return 5%Correlation(A,B) 0.2Correlation(A,C) 0.2Correlation(B,C) -0.2 a) What are the portfolio weights of the tangency portfolio?b) What is the Sharpe ratio of the tangency portfolio?Problem 3: You have access to two investment opportunities. Mutual Fund A, which promises 20% expected return with a variance of 0.36, and Mutual Fund B, which promises 15% expected return with a variance 0f 0.12. The covariance between the two is 0.084. 1. Suppose that you seek to construct a portfolio with an expected return equal to 18%. What proportions of your wealth should you invest in A and B? What is the standard deviation of such portfolio? 2. In addition to the funds A and B in the previous question, now you decide to include fund C to your portfolio. Its expected return is 10, its variance 0.0625, its correlation with A is 0.1050 and its correlation with B is 0.07. You want to achieve an expected return of 16% on your portfolio, with the minimum possible risk (measured by the standard deviation). Derive analytically (that is, without the help of solver, but trough calculus) the weights of such desired portfolio, and its standard deviation.
- 3.1 Problem 3: You have access to two investment opportunities. Mutual Fund A, which promises 20% expected return with a variance of 0.36, and Mutual Fund B, which promises 15% expected return with a variance 0f 0.12. The covariance between the two is 0.084. Suppose that you seek to construct a portfolio with an expected return equal to 18%. What proportions of your wealth should you invest in A and B? What is the standard deviation of such portfolio?QUESTION 7 An investor wishes to construct a portfolio consisting of a 70 percent allocation to a stock index and a 30 percent allocation to a risk-free asset. The return on the risk-free asset is 4.5 percent, and the expected return on the stock index is 12 percent. Calculate the expected return on the portfolio. a. 16.50 percent b. 17.50 percent c. 14.38 percent d. 9.75 percent e. 8.25 percentIn-class Example 4: Portfolio Risk Return Suppose that a portfolio of stocks has an expected return E(rS) = 12% and a standard deviation of returns sS = 20%. A portfolio of corporate bonds has an expected return E(rB) = 6% and a standard deviation sB = 9%. a) What is the expected portfolio return and portfolio standard deviation for an equally weighted combination of the stock and bond portfolio if the correlation between stock and bond portfolio returns, rSB, is -0.5? b) Suppose you require a portfolio expected return of 15% per year. What weights must you assign to the stock and bond portfolios to achieve this expected return? What is the standard deviation of returns for this combination portfolio if the correlation between stock and bond returns is -0.5? C) Suppose that the standard deviation of the market (sM) is 15% and the correlation between the stock portfolio and the market is 0.7. What is the beta of the stock portfolio?
- (corrected problem) NEW Problem 3: You have access to two investment opportunities. Mutual Fund A, which promises 20% expected return with a variance of 0.36, and Mutual Fund B, which promises 15% expected return with a variance 0f 0.12. The CORRELATION COEFFICIENT between the two is 0.084. Suppose that you seek to construct a portfolio with an expected return equal to 18%. What proportions of your wealth should you invest in A and B? What is the standard deviation of such portfolio?7.a. You manage a risky portfolio with E(r) =18% and σ = 28%. The T-Bill rate is 8%. Your client chooses to invest 70% of a portfolio in your funds and 30% in T-Bill funds. Calculate the Expected return and standard deviation of your client’s portfolio.b. Suppose that your risky portfolio includes the following investments in the given proportions:Stock AStock BStock C25%32%43%c. What is the Sharpe ratio of your risky portfolio? Your client’s?d. Draw the CAL of your portfolio. What is the slope of the CAL? Show the position of your client on your fund’s CAL