FIN 4504 Homework 2: Portfolio Analysis and Capital Asset Pricing Model - Prof. Jason J. K, Assignments of Finance

Download FIN 4504 Homework 2: Portfolio Analysis and Capital Asset Pricing Model - Prof. Jason J. K and more Assignments Finance in PDF only on Docsity! Name ________________________________ Homework #2 FIN 4504 Karceski Fall 2006 Due date: November 13, 2006 at the beginning of class Answer all questions (1 through 22). Multiple choice: Please circle the best/most correct response. 1. Both portfolio X and portfolio Y are well-diversified. The risk-free rate is 5%, and the return for the market is 15%. Portfolio Expected Return Beta X 17% 1.20 Y 15% 0.20 Which of the following about portfolio X and portfolio Y is true? Portfolio X Portfolio Y (a) Overvalued Undervalued (b) Properly valued Properly valued (c) Undervalued Undervalued (d) Properly valued Overvalued (e) Properly valued Undervalued 2. According to Professor Richard Thaler at the University of Chicago, the experience of losing $X is about ____ times as acute as the experience of winning $X. (a) 0.5 (b) 0.8 (c) 1.1 (d) 2.0 (e) 5.0 3. According to Warren Buffett, probably the biggest difference between you and him is __________ . (a) he can invest in some things that you cannot invest in (b) he has access to more and better data sources than you (c) he loves his job more than you (d) he can value companies more accurately than you (e) he travels differently than you 4. For most students in FIN 4504 at UF this semester, their most valuable financial asset is their __________ . (a) car (b) parents’ financial support (c) own personal human capital (d) holdings of stocks, bonds, and real estate (e) network of UF friends and alumni 5. Which of the following information would not be enough for you to compute the beta of a stock i? (i stands for stock i, j stands for stock j, m stands for the market portfolio) (a) E(ri), E(rj), rf , βj (b) σi, σm , σ 2(ei) (c) E(ri), σi , σm , ρi,m. (d) E(ri), σi , rf , E(rm) (e) ρi,j, σi , σj , βj 2 6. According to CAPM, which of the following will not impact the risk premium that a particular investor X will require for a particular stock Y? (a) the variance of the market return (b) the beta of stock Y (c) the risk aversion of investor X (d) the risk-free rate of return (e) the correlation coefficient between stock Y and the market portfolio 7. Suppose you are comparing two asset pricing models. Model A has 3 factors, and model B has 4 factors, all of which are different from Model A’s factors. What criterion is most appropriate to decide which model is better? (a) Model A is better because it has fewer factors. (b) Model B is better because it has more factors. (c) The better model is the one where the alphas of all stocks are closer to zero. (d) The better model is the one where the betas/sensitivities of all stocks for each of the factors are closer to one. (e) CAPM is generally the best model, so it doesn’t really matter whether Model A is better than Model B or not. 8. When CAPM holds, the correlation coefficient between _________ is always equal to 1. (a) any two growth stocks (b) any two large stocks (c) two stocks in the same industry (d) a well-diversified portfolio and the market portfolio (e) a large stock and the market portfolio (f) none of the above 9. Which of the following statements about the security market line (SML) are true? I. The SML provides a benchmark for evaluating expected investment performance. II. The SML leads all investors to invest in the same portfolio of risky assets. III. The SML is a graphic representation of the relationship between expected return and beta. IV. Properly valued assets plot exactly on the SML. (a) I and III only (b) II and IV only (c) I, II, and IV only (d) I, III, and IV only (e) I, II, III, and IV 10. Which of the following phenomena have been observed in U.S. stock returns? (circle all that are valid) (a) Short-term return reversals (b) Intermediate-term return momentum (c) The overall market has unusually high returns in January months (d) growth stocks outperform value stocks on average (e) small stocks outperform large stocks on average 5 14. (a) Does finance theory (in particular, the separation theorem) support the use of the Rule of 100 when deciding how much money to put into stocks and how much to put into bonds? Why or why not? (b) Briefly explain the Grossman-Stiglitz paradox. 15. (a) Briefly describe the two types of arbitrage opportunities. (b) What is the difference between a profitable trading strategy and an arbitrage opportunity? 6 16. (a) What is behavioral finance? (b) What is the difference between a fundamental valuation approach and a "greater-fool" theory approach to investing? (c) Why are the covariance terms more important than the variance terms when computing the variance of a portfolio that is comprised of many stocks? 17. (a) What is the historical (geometric) daily average return for the U.S. stock market? (b) How much did the market fall (within 1%) on Black Monday, October 19, 1987? (c) Why do we call Bill Sharpe's model the Capital Asset Pricing Model when the main equation or the CAPM [ E(ri) = rf + βi(E(rm) - rf) ] is in terms of expected returns, not prices? 7 Problems: Please show all relevant work, and put a circle or a box around your final answers. 18. Assume that three securities, A, B and C, constitute the market portfolio (i.e., the market portfolio contains only these two stocks). The market portfolio's weight on stock A is 0.25, its weight on stock B is 0.40, and its weight on stock C is 0.35. The standard deviation of stock A is 40%, the standard deviation of stock B is 50%, and the standard deviation of stock C is 60%, and the correlation between each pair of stocks is 30%. (a) Compute the betas of stock A and B. (b) If the expected return on the market is 10% and the risk-free rate is 5%, draw the capital market line, making sure to label both X and Y-axes. 10 21. Assume the Fama-French 3-factor model holds, and that the annual expected returns of the three factors are: ( ) 5.16%, ( ) 3.24%, and ( ) 4.80% m f E r r E SMB E HML− = = = . The annualize variance covariance matrix of the three factors, in the order given above, is 2.47% 0.50% 1.00% 0.17% 0.00% 0.77% V    =    −  The results from a 3-factor model for Microsoft and are provided below. Stock i α i β i s i h 2 ( ) i eσ Microsoft 0.022 0.89 0.27 -0.65 4.60% GM 0.008 1.77 0.44 0.03 4.11% (a) Using the Fama-French 3-factor model, what is the annual expected risk premium for GM? (b) Using the Fama-French 3-factor model, and assuming that the firm-specific component between GM and Microsoft are uncorrelated, what is the expected annualized covariance between the return on GM and the return on Microsoft? (c) Using the Fama-French 3-factor model, what is the annualized variance of Microsoft? 11 22. Consider the following data for a one-factor economy. All portfolios are well diversified. Annual Portfolio Expected Return Beta A 0.16 1.15 B 0.07 0.60 C 0.09 0.80 (a) Does an arbitrage opportunity exist? How do you know? (b) What would the arbitrage strategy be?