Refer the table below on the average excess return of the U.S. equity market and the standard deviation of that excess return. Suppose that the U.S. market is your risky portfolio. Period 1927-2018 1927-1949 1950-1972 1973-1995 1996-2018 Average Annual Returns 1-Month 1-Bills 3.38 T-bils Equity U.S. equity 11.77 9.40 14.00 13.38 10.10 0.92 3.14 7.26 2.21 Excess return 8.34 8.49 10.86 6.11 7.89 U.S. Equity Market Standard Deviation 20.36 26.83 17,46 18.41 18.39 Sharpe Ratio 0.41 0.32 0.62 0.33 0.43 a. If your risk-aversion coefficient is A-5.2 and you believe that the entire 1927-2018 period is representative of future expected performance, what fraction of your portfolio should be allocated to T-bills and what fraction to equity? Assume your utility function is u - E(P)-0.5 Ao². (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Refer the table below on the average excess return of the U.S. equity market and the standard deviation of that excess return. Suppose that the U.S. market is your risky portfolio. Period 1927-2018 1927-1949 1950-1972 1973-1995 1996-2018 Average Annual Returns 1-Month 1-Bills 3.38 T-bils Equity U.S. equity 11.77 9.40 14.00 13.38 10.10 0.92 3.14 7.26 2.21 Excess return 8.34 8.49 10.86 6.11 7.89 U.S. Equity Market Standard Deviation 20.36 26.83 17,46 18.41 18.39 Sharpe Ratio 0.41 0.32 0.62 0.33 0.43 a. If your risk-aversion coefficient is A-5.2 and you believe that the entire 1927-2018 period is representative of future expected performance, what fraction of your portfolio should be allocated to T-bills and what fraction to equity? Assume your utility function is u - E(P)-0.5 Ao². (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Refer the table below on the average excess return of the U.S. equity market and the standard deviation of that excess return. Suppose that the U.S. market is your risky portfolio. Average Annual Returns U.S. Equity Market U.S. 1-Month Excess Standard Sharpe Period equity T-Bills return Deviation Ratio 1927-2021 12.17 3.30 8.87 20.25 0.44 1927-1950 10.26 0.93 9.33 26.57 0.35 1951-1974 10.21 3.59 6.62 20.32 0.33 1975-1998 1999-2021 17.97 6.98 10.99 14.40 0.76 10.16 1.66 8.50 18.85 0.45 Required: a. If your risk-aversion coefficient is A = 3.7 and you believe that the entire 1927-2021 period is representative of future expected performance, what fraction of your portfolio should be allocated to T-bills and what fraction to equity? Assume your utility function is UB-0.5× Ao 2 b. What if you believe that the 1975-1998 period is representative? Complete this question by entering your answers in the tabs below. Required A Required B If your risk-aversion coefficient is A = 3.7 and you…
Year U.S. Gov’t T-Bills U.K. Common Stocks 2015 0.063 0.150 2016 0.081 0.043 2017 0.076 0.374 2018 0.090 0.192 2019 0.085 0.106 a. Compute the geometric mean rate of return for each of these investments and compare the arithmetic mean return and geometric mean return for each investment and discuss the difference between mean returns as related to the standard deviation of each series.
2. An analyst wants to evaluate Portfolio X, consisting entirely of U.S. common stocks, using both the Treynor and Sharpe measures of portfolio performance. The following table provides the average annual rate of return for Portfolio X, the market portfolio (as measured by the Standard & Poor's 500 Index), and U.S. Treasury bills (T-bills) during the past eight years. Annual Average Standard Deviation Rate of Return of Return Beta Portfolio X 10% 18% 0.60 S&P 500 13 1.00 12 n/a T-bills n/a n/a = not applicable a. Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and the S&P 500. Briefly explain whether Portfolio X underperformed, equaled, or outper- formed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe measure. b. Based on the performance of Portfolio X relative to the S&P 500 calculated in part (a), briefly explain the reason for the conflicting results when using the Treynor measure versus the Sharpe measure.
Refer the table below on the average excess return of the U.S. equity market and the standard deviation of that excess return. Suppose that the U.S. market is your risky portfolio. Period 1927-2021 1927-1950 1951-1974 1975-1998 1999-2021 Average Annual Returns U.S. equity 12.17 10.26 10.21 17.97 10.16 U.S. Equity Market Standard Deviation 20.25 26.57 20.32 14.40 18.85 1-Month T- Excess return 8.87 9.33 6.62 10.99 8.50 Bills 3.30 0.93 3.59 6.98 1.66 Sharpe Ratio 0.44 0.35 0.33 0.76 0.45 Required: a. If your risk-aversion coefficient is A = 3.5 and you believe that the entire 1927-2021 period is representative of future expected performance, what fraction of your portfolio should be allocated to T-bills and what fraction to equity? Assume your utility function is U = E(r) - 0.5 × Ag². b. What if you believe that the 1975-1998 period is representative?
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 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…
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%
Using CAPM to determine the expected rate of return for risky assets, consider the following example stocks, assuming that you have already compute the betas Stock Beta A 0.70 B 1.00 C 1.15 D 1.40 E -0.30 Assume that we expect the economy’s RFR to be 5 percent (0.05) and the expected return on the market portfolio (E(RM)) to be 9 percent (0.09), 1, what would this imply? With these inputs, what would the be the following required rate of returns for these five stocks, show the formula for each in your calculations.
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…
You are comparing Stock A to Stock B. Given the following information, what is the difference in the expected returns of these two securities? State of Economy Probability of State of Economy Rate of Return if State Occurs Stock A Stock B Normal .75 .13 .16 Recession .25 −.05 −.21
You are given the following partial covariance and correlation tables from historical data: Securities J K Market Securities J K Market 1.24 1.11 1.17 1.03 Covariance Matrix K 0.90 J 0.0020480 0.0021600 Also, you have estimated that the market's standard deviation is 4.3 percent. For the coming year, the expected return on the market is 14.0 percent and the risk-free rate is expected to be 4.0 percent. Given this information, determine the beta for Security K for the coming year, assuming CAPM is the correct model for required returns. Correlation Matrix K 0.60 1.00 0.90 1.00 0.60 0.80 Market 0.0020480 0.0021600 Market 0.80 0.90 1.00 Ston sharing Hidel lines We
An analyst wants to evaluate Portfolio X, consisting entirely of U.S. common stocks, using both the Treynor and Sharpe measures of portfolio performance. The following table provides the average annual rate of return for Portfolio X, the market portfolio (as measured by the Standard and Poor's 500 Index), and U.S. Treasury bills (T-bills) during the past eight years. Annual Average Standard Deviation Rate of Return of Return Beta Portfolio X 11% 18% 0.40 S&P 500 13 14 1.00 T-bills 6 n/a n/a n/a = not applicable a. Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and the S&P 500. Round your answers for the Treynor measure to one decimal place and for the Sharpe measure to three decimal places. Treynor measure Sharpe measure Portfolio X S&P 500 % Briefly explain whether Portfolio X underperformed, equaled, or outperformed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe measure. Based on the Treynor measure Portfolio…
SECURITY MARKET LINE You are given the following historical data on market returns, r, and the returns on Stocks A and B, r, and r: 8A-2 M' Year 1 29.00% 29.00% 20.00% 2 15.20 15.20 13.10 3 (10.00) (10.00) 0.50 4 3.30 3.30 7.15 23.00 23.00 17.00 6. 31.70 31.70 21.35 The risk-free rate, rp, is 9%. Your probability distribution for r for next year is as follows: M Probability M 0.1 (14%) 0.2 0.4 15 0.2 25 0.1 44 a. Determine graphically the beta coefficients for Stocks A and B. b. Graph the Security Market Line, and give its equation. c. Calculate the required rates of return on Stocks A and B. d. Suppose a new stock, C, with f̟ = 18% and b̟ = 2.0, becomes avail- able. Is this stock in equilibrium; that is, does the required rate of return on Stock C equal its expected return? Explain. If the stock is not in equilibrium, explain how equilibrium will be restored.

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