- Information
- AI Chat
Tute 10 - tute
Investment And Portfolio Management (FIN3IPM)
La Trobe University
Recommended for you
Related documents
Preview text
CHAPTER 8 index Models 275 :2. Which stock has more firm-specific risk? b. Which has greater market risk? 6. For which stock does market movement explain a greater fraction of return variability? d. If i} were constant at 6% and the regression had been run using total rather than excess returns, what would have been the regression intercept for stock A? Use the following data for Problems 9 through 14. Suppose that the index model for "stocks A and B is estimated from excess returns with the following results: R, = 3%+.7RM +2, RB = —2% +1%“ + es Up, = 20%; R-squareA = .20; Iii-squares = .12 . 9, What is the standard deviation of each stock? 1t]. Break down the variance of each stock to the systematic and firm-specific components. 11. What are the covariance and correlation coefficient between the two stocks? '12. What is the covariance between each stock and the market index? ‘13, For portfolio P with investment proportions of .60 in A and .40 in B, rework Problems 9, 10, and 12. 14. Rework Problem 13 for portfolio Q with investment proportions of .50 in P, .30 in the market index, and .20 in T-bills. ’15. A stock recently has been estimated to have a beta of 1: a. What will Merrill Lynch compute as the “adjusted beta" of this stock? b. Suppose that you estimate the following regression describing the evolution of beta over time: [3, = .3 +.7B,_1 What would be your predicted beta for next year? 16. Based on current dividend yields and expected growth rates, the expected rates of return on stocks A and B are 11% and 14%, respectively. The beta of stock A is .8, while that of stock B is 1. The T—bill rate is currently 6%, while the expected rate of return on the S&P 500 index is 12%. The standard deviation of stockA is 10% annually, while that of stock B is 11%. If you currently hold a passive index portfolio, would you choose to add either of these stocks to your holdings? 17. A portfolio manager summarizes the input from the macro and micro forecasters in the follow— ing table: E x .0 "-n.._ E O ‘1‘ .QJ .C .C E. 4.; {U m :5 :'.:' .9 )- Micro Forecasts Asset Expected Return (%) Beta Residual Standard Deviation 1%) Stock A 20 1 58 Stock 3 18 1 71 Stock C 17 0 60 Stock D 12 1 55 Macro Forecasts Asset Expected Return (We) Standard Deviation (%) T-bills 8 0 Passive equity portfolio 16 23 6!. Calculate expected excess returns, alpha values, and residual variances for these stocks. in. Construct the optimal risky portfolio. 0. What is Sharpe‘s measure for the optimal portfolio and how much of it is contributed by the active portfolio? at. What should be the exact makeup of the complete portfolio for an investor with a coefficient of risk aversion of 2?276 PART II Portfolio Theory and Practice 18. Recalculate Problem 17 for a portfolio manager who is not allowed to short sell securities. a. What is the cost of the restriction in terms of Sharpe’s measure? 12. What is the utility loss to the investor (A = 2) given his new complete portfolio? 19. Suppose that based on the analyst’s past record, you estimate that the relationship betWeen fore cast and actual alpha is: Actual abnormal return 2 .3 X Forecast of alpha Use the alphas from Problem 17. How much is expected performance affected by recognizing the imprecision of alpha forecasts? Challenge 20. Suppose that the alpha forecasts in row 44 of Spreadsheet 8 are doubled. All the other data ' Probi em remain the same. Recalculate the optimal risky portfolio. Before you do any calculations, how- ever, use the Summary of Optimization Procedure to estimate a back-of—the-envelope calcula- tion of the information ratio and Sharpe ratio of the newly optimized portfolio. Then recalculate 7 the entire spreadsheet example and verify your back-of~the—envel0pe calculation. fl 1. When the annualized monthly percentage rates of return for a stock market index were regressed CFA® against the returns for ABC and XYZ stocks over a 5~year period ending in 2008, using an ordi- \EOBLEMS nary least squares regression, the following results were obtained: Statistic ABC XYZ Alpha —-3% 7% Beta 0 0 R2 0 0 Residual standard deviation 13% 21% Explain what these regression results tell the analyst about risk—return relationships for each stock over the sample period. Comment on their implications for future risk—return relation— ships, assuming both stocks were included in a diversified commOn stock portfolio, especially in view of the following additional data obtained from two brokerage houses, which are based on 2 years of weekly data ending in December 2008. Brokerage House Beta of ABC Beta of XYZ Visit us at mhhe/bkm A .62 1 B .71 1 2. Assume the correlation coefficient between Baker Fund and the S&P 500 Stock Index is .70. What percentage of Baker Fund’s total risk is specific (i., nonsystematic)? 3. The correlation between the Charlottesville International Fund and the EAFE Market Index is 1. The expected return on the EAFE Index is 11%, the expected return on Charlottesville International Fund is 9%, and the risk-free return in EAFE countries is 3%. Based on this anal?“ sis, what is the implied beta of Charlottesville International? 4. The concept of beta is most closely associated with: a. Correlation coefficients. b. Mean-variance analysis. c. Nonsystematic risk. at. Systematic risk. 5. Beta and standard deviation differ as risk measures in that beta measures: a. Only unsystematic risk, while standard deviation measures total risk. I). Only systematic risk, while standard deviation measures total risk.
