6. The table below provides returns on a portfolio along with returns for the corresponding benchmark index for the past eight quarters. The table also provides the difference between portfolio returns and the benchmark index. What is the annualized tracking error of the portfolio?
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- 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 0.210Compute the annual tracking error from the following information: Quarter Portfolio B's 1 2 3 4 O 1.06% O 2.12% O 3.67% O 4.25% O None Portfolio A's Return (%) 1.15 1.89 1.15 -0.47 Return (%) 1.65 -0.10 0.52 -0.60Consider 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%
- 1.2. Refer to the following observations for stock A and the market portfolio in the table: Month Rate of return Stock A Market portfolio 1 0.30 0,12 0.24 0,08 3 -0,04 -0,10 -0,02 0,08 0,07 4 0,10 5 0,06 6 0,10 a) Calculate the main statistic measures to explain the relationship between stock A and the market portfolio: i) The sample covariance between rate of return for the stock A and the market. ii) The sample Beta factor of stock A. iii) The sample correlation coefficient between the rates of return of the stock A and the market. iv) The sample coefficient of determination associated with the stock A and the mar- ket. b) Draw in the characteristic line of the stock A and give the interpretation - what does it show for the investor? c) Calculate the sample residual variance associated with stock's A characteristic line and explain how the investor would interpret the number of this statistic. d) Do you recommend this stock for the investor with the lower tolerance of risk?Question 1 Refer to the following observations for stock A and the market portfolio in the table:Month Stock A Market portfolio1 0.30 0.122 0.24 0.083 -0.04 -0.104 0.10 -0.025 0.06 0.086 0.10 0.07 a) Calculate the main statistic measures to explain the relationship between stock A and the market portfolio:• The sample covariance between rate of return for the stock A and the market;• The sample Beta factor of stock A;• The sample correlation coefficient between the rates of return of the stock A and the marketBelow are the annual returns of the stock A, B, C and D and the market portfolio for the period 2018-2022. Find the expected return and standard deviation of the stock A, B, C, D and the market portfolio. Asset A Asset D | 15,00 13,00 | 10,00 13,00 Prob. Asset B 9,00 Year 2018 2019 2020 2021 2022 Asset C 12,00 Market 14,00 12,00 |11,00 0,20 0,25 | 13,00 9,00 | 11,00 8,00 0,10 0,20 0,25 15,00 | 11,00 11,00 | 9,00 12,00 12,00 9,00 12,00 15,00 10,00 12,00 13,00
- Compute the appraisal ratio for portfolio A. Round off your final answer to three digits after the decimal point.The following portfolios are being considered for investment. During the period under consideration, RFR = 0.07. Portfolio Return Beta P 0.15 1.00 0.05 Q 0.09 0.50 0.03 R. 0.21 1.30 0.10 0.18 1.20 0.06 Market 0.12 1.00 0.04 a. Compute the Sharpe measure for each portfolio and the market portfolio. Round your answers to three decimal places. Portfolio Sharpe measure P Q R Market b. Compute the Treynor measure for each portfolio and the market portfolio. Round your answers to three decimal places. Portfolio Treynor measure P Q R Market c. Rank the portfolios using each measure, explaining the cause for any differences you find in the rankings. Portfolio Rank (Sharpe measure) Rank (Treynor measure) P |-Select- v |-Select- v Q -Select- v -Select- V R. -Select- V -Select- v -Select- v -Select- v Market -Select- v -Select- v -Select- v is poorly diversified since it has a high ranking based on the -Select- but a much lower ranking with the -Select-uppose the average return on Asset A is 7.1 percent and the standard deviation is 8.3 percent, and the average return and standard deviation on Asset B are 4.2 percent and 3.6 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions. a. What is the probability that in any given year, the return on Asset A will be greater than 12 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the probability that in any given year, the return on Asset B will be greater than 12 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c-1. In a particular year, the return on Asset A was −4.38 percent. How likely is it that such a low return will recur at some point in the future? (Do not round…
- Compute the mean return, variance, and standard deviation of returns, and the coefficient variation of Stock y based on the returns of the 5-year period below: Stock Q Year Stock Z Year 2016 2.60% 2016 0.60% 2017 -1.50% 2017 2.50% 2018 4.20% 2018 -1.20% 2019 3.60% 2019 3.60% 2020 0.50% 2020 0.90% 1. Based on your computation, which stock are you going to choose if you have the money to invest? 2. Why did choose it?The following portfolios are being considered for investment. During the period under consideration, RFR = 0.08. Portfolio Return Beta σi P 0.14 1.00 0.05 Q 0.20 1.30 0.11 R 0.10 0.60 0.03 S 0.17 1.20 0.06 Market 0.12 1.00 0.04 Compute the Sharpe measure for each portfolio and the market portfolio. Round your answers to three decimal places. Portfolio Sharpe measure P Q R S Market Compute the Treynor measure for each portfolio and the market portfolio. Round your answers to three decimal places. Portfolio Treynor measure P Q R S MarketSuppose the average return on Asset A is 6.6 percent and the standard deviation is 8.6 percent and the average return and standard deviation on Asset B are 3.8 percent and 3.2 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions. a. What is the probability that in any given year, the return on Asset A will be greater than 11 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the probability that in any given year, the return on Asset B will be greater than 11 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c-1. In a particular year, the return on Asset A was −4.25 percent. How likely is it that such a low return will recur at some point in the future? (Do…