Security F has an expected return of 10 percent and a standard deviation of 43 percent per year. Security G has an expected return of 15 percent and a standard deviation of 62 percent per year. a. What is the expected return on a portfolio composed of 30 percent of Security F and 70 percent of Security G? b. If the correlation between the returns of Security F and Security G is .25, what is the standard deviation of the portfolio described in part (a)?
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- Question Fourteen You are given the following data for four portfolios over a recent 10-year period: a) b) c) d) Portfolio 1 2 3 4 Risk Free Market Annual Return% Standard Deviation % 9 12 10 14 10 15 12 17 6 13 Rank these portfolios using the Sharpe Measure. Rank these portfolios using the Treynor Measure. Rank these portfolios using the Jensen Measure 11 Explain any differences that you observe in the rankings. Portfolio Beta 1.15 1.20 1.50 1.45Question 14 If the simple CAPM is valid and all portfolios are priced correctly, which of the situations below is possible? Consider each situation independently. and assume the rísk-free rate is 2.5%. A) Portfolio Expected Return Beta A 17.5% 1.5 Market 12.5% 1.0 B) Portfolio Expected Return Standard Deviation A 8.5% 18.0% Market 10.0% 24.0% Portfolio Expected Return 13.5% 10.0% Beta A 1.2 Market 1.0 D) Portfolio Expected Return Beta A 7.5% 0.6 Market 10.0% 1.0 Option D Option A Option C Option BQuestion 2 The expected returns and standard deviation of returns for two securities are as follows: Security Z Security Y Expected Return 15% 35% Standard Deviation 20% 40% The correlation between the returns is +0.25. a) Calculate the expected return and standard deviation for the following portfolios: i) All in Z ii) 0.75 in Z and 0.25 in Y iii) 0.5 in Z and 0.5 in Y iv) 0.25 in Z and 0.75 in Y v) All in Y b) Draw the mean-standard deviation frontier. c) Which portfolios might not be held by an investor who likes high expected return and low standard deviation?
- Portfolio Expected return Standard deviation Q 7.8% 10.5% R 10.0% 14.0% S 4.6% 5.0% T 11.7% 18.5% U 6.2% 7.5% What is the minimum level of risk that would be necessary for an investment to earn 7.0%? What is the composition of the portfolio along the Capital Market Line (CML) that will generate that expected return? Rf= 3%Question 3 a. According to the Capital Asset Pricing Model, what must be the beta of a portfolio with E[r] = 12%, if rf 3% and E[TM] = 8%? b. The market price of a security is $50. Its expected rate of return is 16%. The risk-free rate is 8%, and the market risk premium is 8.5%. What will be the market price of the security if its covariance with the market portfolio doubles (and all other variables remain unchanged)? Assume that the stock is expected to pay a constant dividend in perpetuity.Assume that you are given the following historical returns for the Market and Security J. Also assume that the expected risk-free rate for the coming year is 4.0 percent, while the expected market risk premium is 15.0 percent. Given this information, determine the required rate of return for Security J for the coming year, using CAPM. Year 1 2 O21.20% 3 4 5 6 O22.34% O 23.49% O24.63% O24.10% Market 10.00% 12.00% 16.00% 14.00% 12.00% 10.00% Security J 12.00% 14.00% 18.00% 22.00% 18.00% 14.00%
- Question 3 A portfolio consisting of 5 securities could have its beta factor computed Security % of portfolio Beta factor of A B с D E 20 10 15 20 35 security 0.90 1.25 1.10 1.15 0.70 as follows: Weighted beta factor 0.180 0.125 0.165 0.230 0.245 If the risk-free rate of return is 12% and the expected return on the market is 20%. Determine the expected return of this portfolio.Part B 1. What must be the beta of a portfolio with E(rp) = 18%, if rƒ= 6% and E(rm) = 14%? 2. The market price of a security is $50. Its expected rate of return is 14%. The risk-free rate is 6%, and the market risk premium is 8.5%. What will be the market price of the security if its correla- tion coefficient with the market portfolio doubles (and all other variables remain unchanged)? Assume that the stock is expected to pay a constant dividend in perpetuity.The following portfolio has an expected return of Security XYZ O 10.87; 1.08 O 10.87: 1.11 11.03; 1.07 O 11.03; 1.10 O 11.11; 1.09 Amount Invested $12,000 18,000 10,000 Expected Return 16.7% 7.8 94 percent and a beta of Beta 1.42 88 1.02
- Question 16 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 return 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 7 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 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…11.4. Consider the following information: Standard Deviation Beta Security T 30% 1.90 Security K 30% 1.20 a. Which security has more total risk? . b. Which security has more systematic risk? c. Which security should have the higher expected return' d. What does the total risk consist of? What kind of risk is eliminated with portfolio diversification? (Problem 11-27 Portfolio Standard Deviation Security F has an expected return of 11.1 percent and a standard deviation of 44.1 percent per year. Security G has an expected return of 16.1 percent and a standard deviation of 63.1 percent per year. a. What is the expected return on a portfolio composed of 29 percent of Security F and 71 percent of Security G? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. If the correlation between the returns of Security F and Security G is .24, what is the standard deviation of the portfolio described in part (a)? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a. Expected return b. Standard deviation 14.65 60.91 %