Finance Homework p. 65 (3, 4), p (1, 2, 3, 4, 5, 12, 14), p. 107 (2), p. 109 (3,4)

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1 Finance Homework p. 65 (3, 4), p (1, 2, 3, 4, 5, 12, 14), p. 107 (2), p. 109 (3,4) Julian Vu 2-3: Given: Security A Security B r = 7% r = 12% σ (standard deviation) = 35% σ (standard deviation) = 10% rxy = -0.3 rxy = -0.7 ß = -1.5 ß = 1 Which security is riskier? Why? Use standard deviation. (Tighter probability distribution is less risky): Because Security B has a smaller standard deviation ( 10% > 35%), meaning that Security B has a smaller range of variation, then security B is less risky. 2-4: You own a portfolio with $250,000 worth of long-term U.S. gov. bonds. a. Would your portfolio be riskless? In this case, we are examining default-risk. Because U.S. gov. bonds are backed by the word of the U.S. Government, they are deemed to be riskless, regardless of whether it is a 90-day T-Bill or a long-term T-Bond. b. Now suppose you hold a portfolio consisting of $250,000 worth of 30-day Treasury bills. Every 30 days your bills mature, and you reinvest the principal in a new batch of bills. Assume that you live on the investment income from your portfolio and that you want to maintain a constant standard of living. Is your portfolio truly riskless? If it is a Treasury bill, then the amount received will not variate from amount expected. Because you do not expect more every time you reinvest (fixed-income), then you theoretically do not face risk. Only in the case of treasury notes, however. c. Can you think of an asset that would be completely riskless? Could someone develop such an asset? Explain. I thought that treasury notes were completely riskless. I understand that if the U.S. Government went for broke and could not repay their debts, then the risk would be existent, however such is not generally the case.

2 2-1: A stock s return has the following distribution: Demand for the Profitability of this Rate of Return Company s Products Demand Occurring if this demand occurs Weak 0.1 (50%) Below Average 0.2 (5%) Average % Above Average % Strong % Calculate the stock s expected return, standard deviation, and coefficient of variation. r^m = 11.40%, σ = 26.69%, CV = An individual has $35,000 invested in a stock which has a ß = 0.8, and $40,000 invested in a stock with a ß of 1.4. If these are the only two investments in her portfolio, what is her portfolio s beta? 2-3 Assume that the risk-free rate (RF) is 5% and the market risk premium is 6%. What is the expected return for the overall stock market? What is the required rate of return on a stock that has a ß of 1.2? Return on market: Return on stock:

3 2-4 Assume that the risk-free rate is 6%, and the expected return on the market is 13%. What is the required rate of return on a stock that has a beta of 0.7%? 2-5 e market and Stock J have the following probability distributions: Probability rm rj % 20% 0.4 9% 5% % 12% a. Calculate the expected rates of return for the market and Stock J b. Calculate the standard deviations for the market and Stock J. Stock: probability return on market return on stock pi * ri ri - r^ (ri - r^)^2 rm - ri rm - ri^2 (ri - r^)^2 * Pi Expected return: (r^) Sum: Variance: Standard dev: Market: probability return on market return on stockpi * rm rm - r^ (rm - r^)^2 (rm - r^)^2) * Pi Expected rate: Variance: Standard dev:

4 σm = 3.85%, σj = 6.22% c. Calculate the coefficients of variation for the market and Stock J. CVM = , CVi = =========================================== 2-12 Stocks A and B have the following historical returns: Stock A Returns Stock B Returns Year ra rb 2002 (18%) (14.5%) % 21.80% % 30.50% 2005 (0.50%) (7.60%) % 26.30% a. Calculate the average rate of return for each stock during the 5-year period. b. Assume that someone held a portfolio consisting of 50 percent of Stock A and 50 percent of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average rate of returno n the portfolio during this period? c. Calculate the standard deviation of returns for each stock and for the portfolio. d. Calculate the coefficient of variation for each stock and for the portfolio. e. If you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why?

5 Security A has an expected rate of return of 6 percent, a standard deviation of returns of 30%, a correlation coefficient with the market of -0.25, and a beta coefficient of -0.5 Security B has an expected return of 11%, a standard deviation of returns of 10%, a correlation with the market of 0.75, and a ß of 0.5. Which security is more risky, why? 3-3 e beta coefficient of an asset can be expressed as a function of the asset s correlation with the market as follows: a. Substitute this expression for beta into the Security Market Line (SML), Equation 3-9. is results in an alternative form of the SML. b. Compare your answer to part a with the Capital Market Line (CML), Equation 3-6. What similarities are observed? What conclusions can be drawn? 3-4 Suppose you are given the following information. e beta of company i, bi, is 1.1, the risk-free rate, rrf, is 7%, and the expected market premium, rm - rrf, is 6.5%. (Assume that ai - 0.0). a. Use the Security Market Line (SML) of CAPM to find the required return for this company. b. Because your company is smaller than average and more successful than average (that is, it has a low book-to-market ratio), you think the Fama-French three-factor model might be more appropriate than the CAPM. You estimate the additional coefficients from the Fama-French threefactor model: e coefficient for the size effect, ci, is 0.7, and the coefficient for the book-to-market effect, di, is If the expected value of the size factor is 5%, and the expected value of the bookto-market factor is 4%, what is the required return using the Fama-French three-factor model?