Problem 13-3 Performance Evaluation (LO1, CFA5) You are given the following information concerning three portfolios, the market portfolio, and the risk-free asset: Portfolio X Y Z Market Risk-free Rp 14.0% 13.0 8.5 12.0 7.2 бр 39% 34 24 29 0 Bp 1.50 1.15 0.90 1.00 B What are the Sharpe ratio, Treynor ratio, and Jensen's alpha for each portfolio? Note: A negative value should be indicated by a minus sign. Leave no cells blank - be certain to enter "O" wherever required. Do not round intermediate calculations. Round your ratio answers to 5 decimal places. Enter your alpha answers as a percent rounded to 2 decimal places. Portfolio X Sharpe Ratio Treynor Ratio Jensen's Alpha % Y % Z % Market %
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- Consider the following information for four portfolios, the market, and the risk-free rate (RFR): Portfolio Return Beta SD A1 0.15 1.25 0.182 A2 0.1 0.9 0.223 A3 0.12 1.1 0.138 A4 0.08 0.8 0.125 Market 0.11 1 0.2 RFR 0.03 0 0 Refer to Exhibit 18.6. Calculate the Jensen alpha Measure for each portfolio. a. A1 = 0.014, A2 = -0.002, A3 = 0.002, A4 = -0.02 b. A1 = 0.002, A2 = -0.02, A3 = 0.002, A4 = -0.014 c. A1 = 0.02, A2 = -0.002, A3 = 0.002, A4 = -0.014 d. A1 = 0.03, A2 = -0.002, A3 = 0.02, A4 = -0.14 e. A1 = 0.02, A2 = -0.002, A3 = 0.02, A4 = -0.14q5- Which of the following portfolios is most likely to provide the majority of the risk-reduction benefits of diversification without incurring excessive transaction costs? a. A portfolio consisting of 197 different shares. b. A portfolio consisting of 12 different shares. c. A portfolio consisting of 53 different shares. d. A portfolio consisting of 2 different shares.INV 1 4b You have invested in a portfolio of 60% in risky assets (Portfolio R) and 40% in T-bills. The risky portfolio is described below: E(rR)=12% σR =15% Compute the standard deviation of your overall portfolio.
- IBM AMZN E(R) 0.07 0.11 Standard Deviation0.10 0.18 Correlation0.45 Suppose you have the above data on IBM and Amazon, compute the expected return and the standard deviation of an equally weighted portfolio invested in the two securitiesis there a diversification benefit? Please show your work and round to at least 3 decimal places2. Assuming the following: Average Return (Risky Portfolio) 3.86% Standard Dev (Risky Portfolio) 10.56% Average Risk Free Rate 2.18% Return on Risk Free Asset Avg 4.15% Using the formula: E(rc)=rf + y* (E(rp) - rf) Solve for: 1. % of Risky Assets (y): 2. % of Risk Free Assets (1-y): Note: You wish to generate a 7% return for your complete portfolio E(rc)Problem 11-23 Analyzing a Portfolio You want to create a portfolio equally as risky as the market, and you have $2,400,000 to invest. Given this information, fill in the rest of the following table: (Do not round intermediate calculations and round your answers to the nearest whole number, e.g., 32.) Asset Investment Beta Stock A $360,000 1.00 Stock B $624,000 1.10 Stock C 1.20 Risk-free asset
- Data: S0 = 107; X = 110; 1+r = 1.12. The two possibilities for ST are 155 and 95. (Round to 2 decimal places). a. The range of S is 60 while that of P is 15 across the two states. What is the hedge ratio of the put? Hedge ratio ? b. Form a portfolio of one share of stock and four puts. What is the (nonrandom) payoff to this portfolio? Nonrandom payoff c. What is the present value of the portfolio? Present value d. Given that the stock is currently selling at 107, calculate the put value. Put value. E(RI) = .15(.11) + .55(.18) + .30(.08) 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 WND 0.80 STA 1.35 CTE 1.15 DUY 1.20 EVN -0.20 Stock WND the economy’s RFR to be 6 percent (0.06) and the expected return on the market portfolio (E(RM)) to be 8 percent (0.08) Stock STA, the economy’s RFR to be 5percent (0.05) and the expected return on the market portfolio (E(RM)) to be 7 percent(0.07) Assume that all the other stocks is as follows since 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),Exhibit 18.11USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM Weights Policy Actual 50% stocks 60% stocks 50% bonds 40% bonds Returns Index Actual 8% stocks 9% stocks 5% bonds 7% bonds Refer to Exhibit 18.11. Which of the following statements is TRUE? a. Sector/security selection hurt the portfolio performance; returns were 6.8% less than if the manager invested the funds in stocks and bond indexes. b. Sector/security selection improved the port-folio performance by 6.8%; each sector return was higher than for index return. c. Sector/security selection improved the port-folio performance by 1.4%; each sector return was higher than for index value. d. Sector/security selection hurt the portfolio performance; returns were 1.4% less than if the manager invested the funds in stocks and bond indexes.
- Excel Questions 1) What would happen to the contribution of asset allocation to overall performance if the actual weights had been 75/12/13 instead of 70/7/23? Explain your result. 2) What would happen to the contribution of security selection to overall performance if the actual return on the equity portfolio had been 8.28% instead of 7.28% and the return on the bond portfolio had been .89% instead of 1.89%? Explain your result.Problem 13-10 Returns and Standard Deviations [LO1] Consider the following information: State of Economy Probability of State of Economy Rate of Return if State Occurs Stock A Stock B Stock C Boom .15 .37 .47 .27 Good .45 .22 .18 .11 Poor .35 −.04 −.07 −.05 Bust .05 −.18 −.22 −.08 a. Your portfolio is invested 20 percent each in A and C, and 60 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b-1. What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., .16161.) b-2. What is the standard deviation? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)INV 1 4b You have invested in a portfolio of 60% in risky assets (Portfolio R) and 40% in T-bills. The risky portfolio is described below: E(rR)=12% σR =15% T-bill rate 3% Expected Return on Overall Portfolio is 8.4% What is the standard deviation of your overall portfolio?