Performance Evaluation and Active Portfolio Management Difficulties in adjusting average returns for risk present a host of issues, as the proper measure of risk may not be obvious, and risk levels may change along with portfolio composition. The following data is given for a particular sample period: (a) Average return Beta Standard deviation Portfolio P 35% 1.2 42% Page 6 of 8 Market M 28% 1.0 30 %
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- 28) A manager who evaluates portfolios' investment performance adjusted for market risk is most likely to rank portfolios based on their: Select one or more: Sharpe ratio Treynor measure Jensen's Alpha measure M-squared measuresProblem 2: You have access to three risky assets (Stocks A, B, and C) and ariskless asset:Expected Return, Standard DeviationStock A 8% , 35%Stock B 12% , 50%Stock C 15% , 75% Riskless Asset expected return 5%Correlation(A,B) 0.2Correlation(A,C) 0.2Correlation(B,C) -0.2 a) What are the portfolio weights of the tangency portfolio?b) What is the Sharpe ratio of the tangency portfolio?5. Portfolio risk and diversification A financial planner is examining the portfolios held by several of her clients. Which of the following portfolios is likely to have the smallest standard deviation? A portfolio consisting of about 30 energy stocks. A portfolio containing only Chevron stock. A portfolio consisting of about 30 randomly selected stocks. Portfolio managers pick stocks for their clients’ portfolios based on the investment objective of the portfolio and several other factors. One key consideration is each stock’s contribution to portfolio risk and its statistical relationship with the portfolio’s other stocks. Based on your understanding of portfolio risk, identify whether each statement is true or false. Statement True False The market risk component of the total portfolio risk can be reduced by randomly adding stocks to the portfolio. A portfolio’s risk is not equal to the weighted average of the individual…
- Problem 11-25 Portfolio Returns and Deviations [LO 1, 2] Consider the following information on a portfolio of three stocks: State of Economy Probability of State of Economy Stock A Rate of Return Stock B Rate of Return Stock C Rate of Return Boom .13 .02 .32 .50 Normal .55 .10 .22 .20 Bust .32 .16 −.21 −.35 If your portfolio is invested 40 percent each in A and B and 20 percent in C, what is the portfolio’s expected return, the variance, and the standard deviation? Note: Do not round intermediate calculations. Round your variance answer to 5 decimal places, e.g., .16161. Enter your other answers as a percent rounded to 2 decimal places, e.g., 32.16. If the expected T-bill rate is 4.25 percent, what is the expected risk premium on the portfolio? Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.Question 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?iv. Given 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 Ave. return 35 % 28 % Beta 1.2 1.0 Standard Dev 42% 30 %
- Consider the following data:Expected Return Standard DeviationRussell Fund 16% 12%Windsor Fund 14% 10%S&P 500 Fund 12% 8%The correlation between the returns on the Russell Fund and the S&P 500 Fund is 0.7. The T-Bill rate is 6%. Which of the following portfolios would you prefer to hold in combination with T-bills and why?(a) Russell Fund(b) Windsor Fund(c) S&P 500 Fund(d) A portfolio of 60% Russell Fund and 40% S&P 500 Fund.KINDLY ANSWER PART 5,6.and 7 Using the stock price data for any two companies provided below carry out the following tasks: 1.Compute, for each asset: i.Total Returns ii.Expected returns iii.standard deviation iv.Correlation Coefficient 2.Construct the variance-covariance matrix 3.Construct equally weighted portfolio and calculate Expected Return, Standard Deviation and Sharpe ratio. 4.Reconstruct equally weighted portfolio and calculate Expected Return, Standard Deviation and Sharpe ratio. 5.Use Solver to determine optimal risky portfolio. 6.Create hypothetical portfolios (commencing from Weight A=0 and weight B=100) 7.Calculate Expected return and Standard Deviation for all the above combinations 8.Graph the efficient frontier 9.Graph the optimal portfolio 10.Assuming that the investors prefers lower level of risk than what a portfolio of risky assets offer, introduce a risk free asset in the portfolio with a return of 3% 11.Using hypothetical weights (A= Portfolio of Risky…2) A risky portfolio is provided with an expected rate of return of 19.5%, standard deviation of 30% and risk free rate of 8.5%. If the client chooses to invest three different risky assets a proportion of equal investments and also in T bills. a) Determine weights of all the distributed assets. b) Determine the Sharpe ratio of the portfolio c) If the investment is done such a way that the expected return is maximized with standard deviation not exceeding 25%. Determine the investment proportion and expected return of the portfolio.
- 2 local Philippine equities have the same risk (standard deviation) and return expectations: 10 % expected return and 20 % risk in terms of standard deviation. Suppose you wish to create an equally weighted portfolio (50% in each equity) to examine the effect of correlation on standard deviation/risk. Comment on the return and risk of portfolios with different correlationsDifficulties in adjusting average returns for risk present a host of issues, as the proper measure of risk may not be obvious, and risk levels may change along with portfolio composition. The following data is given for a particular sample period: Portfolio P Market M Average return 35 % 28 % Beta 1.2 1.0 Standard deviation 42 % 30 % Calculate the following performance measures for portfolio P and the market: Sharpe, Jensen (alpha) and Treynor. The Treasury bill rate during the period was 6 %. By which measures did portfolio P outperform the market? What do these measures mean or imply? Explain.5. Portfolio risk and diversification A financial planner is examining the portfolios held by several of her clients. Which of the following portfolios is likely to have the smallest standard deviation? A portfolio with 10 randomly selected international stocks. A portfolio with 10 randomly selected stocks from U.S. and international markets. A portfolio with 10 randomly selected U.S. stocks. Portfolio managers pick stocks for their clients’ portfolios based on the investment objective of the portfolio and several other factors. One key consideration is each stock’s contribution to portfolio risk and its statistical relationship with the portfolio’s other stocks. Based on your understanding of portfolio risk, identify whether each statement is true or false. Statement True False A portfolio’s risk is likely to be smaller than the average of all stocks’ standard deviations, because diversification lowers the portfolio’s risk.…