During the year just ended, Anna Schultz's portfolio, which has a beta of 0.96, earned a return of 8.2%. The risk-free rate is currently 3.6%, and the return on the market portfolio during the year just ended was 8.9%. a. Calculate Treynor's measure for Anna's portfolio for the year just ended. b. Compare the performance of Anna's portfolio found in part a to that of Stacey Quant's portfolio, which has a Treynor's measure of 1.25%. Which portfolio performed better? Explain. c. Calculate Treynor's measure for the market portfolio for the year just ended. d. Use your findings in parts a and c to discuss the performance of Anna's portfolio relative to the market during the year just ended. a. The Treynor's measure for Anna's portfolio is ☐ %. (Round to two decimal places.)
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- Marcus has an investment portfolio that paid the rate of return of 24.75%, -11%, - 30%, 19%, 15.5%, 12% and 20% over the last seven (7) years. Required: a) Calculate the arithmetic average return and the geometric average return of this portfolio. b) Discuss the difference between arithmetic average return and the geometric average return. When should Marcus use a specific average return? c) If the following information is available for Marcus’s portfolio in the forecast for next year, calculate the expected return and identify the risk of return by computing the variance and the standard deviation. State of economy Boom Normal Recession Question 5 Probability of the economic state 0.55 0.30 0.15 Rate of Return 25% 17% -8%A portfolio consists of 70% of investment A and 30% of investment B. The expected returnon investment A is 7% and the expected return on investment B is 9%. The standarddeviation of returns of investment A is 2.19%. The standard deviation of returns ofinvestment B is 4.1%. The correlation coefficient of the returns of investment A andinvestment B=+1. Finda. the expected return from the portfoliob. the standard deviation (risk) of the returns from the portfolioThe risk-free rate is currently 8.1%. Use the data in the accompanying table for the Fio family’s portfolio and the market portfolio during the year just ended to answer the questions that follow. Data Item Fio’s Portfolio Market Portfolio Rate of return 12.8% 11.2% Standard deviation of return 15.5% 9.6% Beta 1.10 1.00 Calculate Sharpe’s measure for the portfolio and the market. Compare the two measures, and assess the performance of the Fios’ portfolio during the year ended. Calculate Treynor’s measure for the portfolio and the market. Compare the two measures, and assess the performance of the Fios’ portfolio during the year ended. Calculate Jensen’s measure. Use it to assess the performance of the Fio’s portfolio during the just ended.
- You are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 13 percent and 16 percent, respectively. The standard deviations of the assets are 39 percent and 47 percent, respectively. The correlation between the two assets is 61 and the risk-free rate is 5.3 percent. What is the optimal Sharpe ratio in a portfolio of the two assets? What is the smallest expected loss for this portfolio over the coming year with a probability of 1 percent? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your Sharpe ratio answer to 4 decimal places and the z-score value to 3 decimal places when calculating your answer. Enter your smallest expected loss as a percent rounded to 2 decimal places.) Sharpe ratio Smallest expected loss %You are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 12 percent and 15 percent, respectively. The standard deviations of the assets are 29 percent and 48 percent, respectively. The correlation between the two assets is .25 and the risk-free rate is 5 percent. What is the optimal Sharpe ratio in a portfolio of the two assets? What is the smallest expected loss for this portfolio over the coming year with a probability of 2.5 percent?I. Consider the following information about K oll and Nell for one-time period: Suppose that the correlation coefficient between the returns for Koll and Nell is -0.40'. If you invest 30% in Koll and 70% in Nell, what are the expected return and standard deviation of the portfolio? Interpret your results. II. The investor achieved the following annual rate of returns over the last four-year period: 25% in Y1, 15% in Y2, 20% in Y3, 10% in Y4. (a) Calculate the geometric average rate of return for the whole 4 year period. (b) Calculate the logarithmic average rate of return for the whole 4 year period. III. Suppose you have a portfolio of IBM and Dell with a beta of 0.4 and 1.1, respectively. If you put 40% of your money in IBM, 55% in Dell and 5% in the risk-free asset, calculate and interpret the beta of your portfolio. IV. Suppose that the beta value for Kei is 1.5, and the risk-free rate of interest is 4%. The investor wishes to (i) have a shareholding in only one company, Kei, and…
- Your employer has asked you to investigate the firm’s portfolio risk and return. The portfolio comprises three stocks. It is invested 50 percent in stock A, 30 percent in stock B and 20 percent in stock C. You gathered the following information: a) Determine what is the portfolio’s expected return b) Determine the portfolio’s variance and standard deviation c) Assume that the expected risk-free rate is 2.75 percent. Determine the expected risk premium on the portfolio.Consider the following table which provides a comparison of the returns for a portfolio and its benchmark. Year 0 1 2 3 4 5 Return Alpha Sum Tracking Error Information Ratio Note: the numbers in red are negative b. Calculate the portfolio alpha in percentage terms c. Calculate the tracking error of the portfolio in percentage terms Portfolio Return 16% 9% -35% 22% 84% Required a. Calculate the annualised return of the portfolio and the benchmark in percentage terms d. Calculate the information ratio of the portfolio to 2 decimal places e. Determine to 2 decimal places the amount of Carhart alpha for the portfolio in percentage terms if: o the risk-free rate is 3.25%, o the return of the market is 9.20%, o the exposure to the value factor (when the premium is 3.15%) is 0.65 (ie 65%), o the exposure to the small cap factor (when the premium is 2.05%) is -0.12, and o the exposure to the momentum factor (when the premium is 46%) is 0.1. Benchmark Return 14% 7% -38% 18% 86%Two investments generated the following annual returns: % -Select- a. What is the average annual return on each investment? Round your answers to one decimal place. The average annual rate of return on X: The average annual rate of return on Y: b. What is the standard deviation of the return on investments X and Y? Round your answers to two decimal places. Standard deviation of X: % Standard deviation of Y: c. Based on the standard deviation, which investment was riskier? was riskier. 20X0 20X1 20X2 20X3 20X4 Investment X 11% 22 30 16 9 Investment Y 22% 24 10 13 12
- During a particular investment period, a wealth management company held an investment portfolio that earned an average return of 13% with standard deviation of 30% and beta of 1.5. The average risk-free rate of return during this investment period was 2%. (full process) (a) Calculate the Sharpe and Treynor measures of performance evaluation for this investment portfolio. This investment portfolio is composed of the following two asset classes: Asset Class Weight Return Equity 0.80 15% Bonds 0.20 5% During this particular investment period, the information on a benchmark portfolio is given in the following table. Asset Class Weight Return Equity (S&P500 Index) 0.50 17% Bonds (Lehman Brothers Index) 0.50 5% (b) Determine whether the investment portfolio of the wealth management company performed better than the benchmark portfolio in terms of the total…An investor has an investment that has produced the following returns: Year 1: 10%, Year 2: 5%, Year 3: -7%, Year 4: -3%, Year 5: 12%. Calculate the arithmetic mean return on this investment. O 6.75 O 17.00 3.40 8.50Given the following sample data, calculate the performance measures for portfolio P and the market (Sharpe, Jensen/Alpha and Treynor. The T-bill rate during the period was 6 %). By which measure did portfolio P outperform the market? Portfolio P Market M Average return 35 % 28 % Beta 1.2 1.0 Standard deviation 42 % 30 %