Consider the following information: Probability of State of Economy 0.45 Economy Bust Rate of Return if State Occurs Stock A Stock B Stock C 0.06 0.14 0.34 0.10 0.02 -0.07 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediat Round the final answer to 2 decimal places.) Expected return 10.65% b. What is the variance of a portfolio invested 25% each in A and B and 50% in C? (Do not round intermediate calc the final answer to 6 decimal places.) Variance
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- Two-Asset Portfolio Stock A has an expected return of 12% and a standard deviation of 40%. Stock B has an expected return of 18% and a standard deviation of 60%. The correlation coefficient between Stocks A and B is 0.2. What are the expected return and standard deviation of a portfolio invested 30% in Stock A and 70% in Stock B?You have observed the following returns over time: Assume that the risk-free rate is 6% and the market risk premium is 5%. What are the betas of Stocks X and Y? What are the required rates of return on Stocks X and Y? What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?A person is interested in constructing a portfolio. Two stocks are being considered. Letx = percent return for an investment in stock 1, and y = percent return for an investment instock 2. The expected return and variance for stock 1 are e(x) = 8.45% and Var(x) = 25.The expected return and variance for stock 2 are e(y) = 3.20% and Var(y) = 1. Thecovariance between the returns is sxy = −3.a. what is the standard deviation for an investment in stock 1 and for an investment instock 2? Using the standard deviation as a measure of risk, which of these stocks isthe riskier investment?
- Assume that the covariance between Stock A and Stock B is -28%^2 (0.0028). Compute the expected rate of return and variance of rate of return of Donald’s portfolio.Assume the risk-free rate is r = 3%. Consider the data below:Stock(stock 1, stock 2)Expected Return(15%,7%)Volatility(40%,30%)a) Find the What the minimum variance portfolio when ρ12 = 0? and then computeits expected return and volatility?b) Find the minimum variance portfolio when ρ12= =0.4? and then compute itsexpected return and volatility?c) Determine the tangent portfolios & their respective mean returns and volatilities.If a given stock in the portfolio had established 1.23 beta; the related expected return is at 11.7percent, and 3.5percent is the current earning of a risk-free asset; a. Determine the expected return on a portfolio that is equally invested in the two assets? b. If a portfolio of the two assets has a beta of 0.7, what are the portfolio weights? c. If a portfolio of the two assets has an expected return of 9%, what is its beta? d. If a portfolio of the two assets has a beta of 2.46, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Discuss.
- Given the following information on three stocks assuming: Stock Expected Return A 0.06 0.1 0.267 Assume further the following portfolio co-variances: AB = 0, AC = 0 and BC -0.05333. Now suppose you diversify into two securities. Given the three choices of possible portfolio combinations, can any portfolio be eliminated because it is dominated by at least one of the other portfolio combinations? Assume equal weights. Select one: B с Standard Deviation a. Portfolio (A,B) should be eliminated b. Portfolio (A,C) should be eliminated c. Portfolio (B,C) should be eliminated d. Portfolio (A,B) and Portfolio (A,C) should be eliminated e. Portfolio (A,B) and Portfolio (B,C) should be eliminated f. Portfolio (A,C) and Portfolio (B,C) should be eliminated No Portfolio dominates the others. 0 0.25 0.375a. Based on the following information, calculate the expected return and standard deviation for each of the following stocks. What are the covariance and correlation between the returns of the two stocks? Calculate the portfolio return and portfolio standard deviation if you invest equally in each asset. Returns State of Economy Prob K Recession 0.25 -0.02 0.034 Normal 0.6 0.138 0.062 Boom 0.15 0.218 0.092 b. A portfolio that combines the risk-free asset and the market portfolio has an expected return of 7 percent and a standard deviation of 10 percent. The risk-free rate is 4 percent, and the expected return on the market portfolio is 12 percent. Assume the capital asset pricing model holds. What expected rate of return would a security earn if it had a .45 correlation with the market portfolio and a standard deviation of 55 percent? 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…Consider the following Information: Rate of Return If State Occurs State of Economy Probability of State of Economy Boom .58 Stock A .08 Stock B .17 Stock C .37 Bust .42 14 .06 -.04 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round Intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the variance of a portfolio Invested 20 percent each in A and B and 60 percent in C? (Do not round Intermediate calculations and round your answer to 6 decimal places, e.g., .161616.) a. Expected return b. Variance %
- a. Based on the following information, calculate the expected return and standard deviation for each of the following stocks. What are the covariance and correlation between the returns of the two stocks? Calculate the portfolio returm and portfolio standard deviation if you invest equally in each asset. Returns State of Economy Prob J K Recession 0.25 -0.02 0.034 Normal 0.6 0.138 0.062 Boom 0.15 0.218 0.092 b. A portfolio that combines the risk-free asset and the market portfolio has an expected return of percent and a standard deviation of 10 percent. The risk-free rate is 4 percent, and the Page 7 of 33 expected return on the market portfolio is 12 percent. Assume the capital asset pricing model holds. What expected rate of return would a security earn if it had a 45 corelation with the market portfolio and a standard deviation of 55 percent? C. Suppose the risk-free rate is 4.2 percent and the market portfolıo has an expected return of 10.9 mercent Tibemadkat normfeliobasiabiamance…Following is the portfolio weights, w, percentage expected return in (%), R, vectors and variance-covariance matrix, VC, for a three-asset portfolio: 0.4 12 100 -45 10 w = [0.3], R = [10] and VC = [-45 64 10] 0.3 8 10 10 36 a. Calculate the expected return and standard deviation of the portfolio. b. Suppose an investor requires a target standard deviation of 4% for the portfolio; using the solver function in Excel, find the portfolio weights w to maximise the expected return subject to the constraints Op = 4 and wi + w2 + w3 = 1|The following portfolios are being considered for investment. During the period under consideration, RFR = 0.07.Portfolio Return Beta σiA 0.15 1.0 0.05B 0.20 1.5 0.10C 0.10 0.6 0.03D 0.17 1.1 0.06Market 0.13 1.0 0.04 a. Compute the Sharpe measure for each portfolio and the market portfolio. b. Compute the Treynor measure for each portfolio and the market portfolio. c. Rank the portfolios using each measure, explaining the cause for any differences you find in the rankings.