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 followingtable provides the average annual rate of return for Portfolio X, the market portfolio (asmeasured by the Standard & Poor's 500 Index), and U.S. Treasury bills (T-bills) duringthe past eight years.Annual AverageStandard DeviationRate of Returnof ReturnBetaPortfolio X10%18%0.60S&P 500131.0012n/aT-billsn/an/a = not applicablea. Calculate both the Treynor measure and the Sharpe measure for both Portfolio X andthe 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 theSharpe 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 measureversus the Sharpe measure.

Treynor ratio refers to the risk adjusted return based on the systematic risk or beta.Sharpe ratio…

Answered: 2. An analyst wants to evaluate…

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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Assume the return on large-company stocks is currently 11.5 percent. The risk premium on large-company stocks is 8.6 percent and the inflation rate is 2.4 percent. What is the current risk-free rate of return
Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 27% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 3%. Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with weights as shown below. Note: Round your "Expected Return" answers to 2 decimal places and "Variance" answers to 4 decimal places. WBills 0.0 0.2 0.4 0.6 0.8 1.0 WIndex 1.0 0.8 0.6 0.4 0.2 0.0 Expected Return 11.00 % % % % % % Variance 0.0729 Example
8. A portfolio consists of bonds, stocks, commodities and real estates. The portfolio weightings, expected returns, variances and correlation matrix are shown below. Bonds Stocks Commodities Real Estate Correlation Matrix Bonds Stocks Commodities Real Estate Weight 50% 10% 15% 25% Bonds 1.0 Stocks -0.2 1.0 Expected Return 8% 12% 20% 16% Commodities 0.1 0.4 1.0 Variance (%²) 10 30 15 20 Real Estate 0.3 0.6 0.2 1.0 a. Calculate the expected return and the standard deviation of the return of the portfolio.
Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 33% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 4%. Calculate the utility levels of each portfolio for an investor with A = 2. Assume the utility function is U = E(r) Note: Do not round intermediate calculations. Round your answers to 4 decimal places. Negative amounts should be indicated by a minus sign. - 0.5 × Ag². X Answer is complete but not entirely correct. WIndex U(A = 2) 0.0111 0.0504 0.0808 x 0.1026 0.1164 X 0.1200 X WBills 0.0 0.2 0.4 0.6 0.8 1.0 1.0 0.8 0.6 0.4 0.2 0.0
Data are given as follows: (all the values are in percent) Month Average portfolio return market Average Average risk-free return rate 2.464 3.360 0.090 16.130 2.348 0.090 0.771 -1.484 0.120 -6.386 -2.437 0.120 15 -2.861 1.965 0.090 16 -7.673 2.806 0.120 0.805 -5.721 0.150 -0.372 0.327 0.150 1.508 2.464 0.150 10 2.003 2.250 0.150 11 -4.723 6.639 0.210 12 Calculate Treynor measure, Sharpe ratio, tracking error, information ratio, and hit ratio. Then, evaluate the performance of this portfolio. 2.383 4.874 0.210
Expected return
8. A portfolio consists of bonds, stocks, commodities and real estates. The portfolio weightings, expected returns, variances and correlation matrix are shown below. Weight Expected Return Variance (%2) Bonds 50% 10% 15% 25% 8% 12% 20% 16% 10 30 15 20 0.1 0.3 0.4 0.6 1.0 0.2 1.0 Stocks Commodities Real Estate Correlation Matrix Bonds 1.0 -0.2 1.0 Stocks Commodities Real Estate Bonds Stocks Commodities Real Estate Calculate the standard deviation of the return of the portfolio.
The following represents the probability distribution for the rates of return for next month: Probability 1/6 2/6 2/6 1/6 Portfolio Market M P (%) (%) -20 -5 -5 +5 +10 0 +50 +10 What is the market beta of P?
Considering the attached set of securities and portfolio returns: Assume that you initially invested $1,000,000 in the portfolio and that the distribution of the annual rate of return of the portfolio is normal. What is the distribution of the return of the portfolio 20 years after its formation? Provide the graph of the distribution of the return of the portfolio.
* A nces The expected return on Big Time Toys is 12% and its standard deviation is 21.6%. The expected return on Chemical Industries is 9% and its standard deviation is 27.4%. a. Suppose the correlation coefficient for the two stocks' returns is 0.28. What are the expected return and standard deviation of a portfolio with 53% invested in Big Time Toys and the rest in Chemical Industries? (Round your answers to 2 decimal places.) Portfolio's expected return Portfolio's standard deviation b. If the correlation coefficient is 0.78, recalculate the portfolio expected return and standard deviation, assuming the portfolio weights are unchanged. (Round your answers to 2 decimal places.) Portfolio's expected return Portfolio's standard deviation c. Why is there a slight difference between the results, when the correlation coefficient was 0.28 and when it was 0.78? The higher the correlation is between the two variables, the less the potential is for diversification. V
3
3. The following table gives actual data on the U.S. CPI and the S&P 500 total return index (SPTRI). CPI SPTRI 12/3 1/2011 226 2159 12/3 1/2012 230 2504 12/3 1/2013 233 3316 12/3 1/2014 235 3769 А. Use this data to compute the average annual nominal return and real return for two consecutive 1- year holding period returns of a sto ck portfolio that matches the S&P 500 total return index. (for example you could compute 2011-12 and 2012-2013) Please use continuous compounding. Express your final answer in percentage. В. Now compute the average annual real return to a 2-year holding -period portfolio of your two consecutive years. С. You have a friend who has been studying the stock market for the last few years and is about to invest $10,000 in a highly diversified portfolio. After 10 years, your friend expects to have over $66,000 in real dollars. You recall from your favorite report in Econ 135 that the average 10 year holding period return is about 7% with a standard deviation of 6%.…

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