are171a-homework-6

are171a-homework-6 - Finance Homework 6 ARE 171A Winter...

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Unformatted text preview: Finance Homework 6 ARE 171A Winter 2010 A. Havenner The first four questions use the Merrill Lynch "beta book" table. The data are up to 60 monthly observations on price changes of various stocks and the S&P 500. For each stock, a straight line was fitted by a least squares regression of the monthly stock price changes on the S&P 500 price changes, resulting in an intercept alpha and a slope beta. Beta you should already know. The intercept alpha can be interpreted as the percent change per period (here per month) that would be expected for the stock if the market didn’t change at all (if the S&P 500 remained constant that month). For example, MMM stock appreciated by +.22 percent per month (about 12 x .22 = 2.6 percent per year, or more precisely, 1.002212 — 1 = 2.67 percent per year) after correcting for the market movements. The column R-SQR gives the proportion of the total variance of the MMM price changes than can be explained by market movements, i. e., 37% of the MMM risk is market (undiversifiable) risk, and 63% is idiosyncratic (unique, diversifiable) risk. The next column measures the unique risk as a standard deviation, the standard deviation of the estimated regression error term (the residual). The next two columns give the standard errors (standard deviations) of the estimates of beta and alpha. These can be used to set up confidence intervals for the estimates of beta and alpha. For example, assuming normality and rounding the statistical table value (from your stat book) of 1.96 to 2, the MMM standard error of beta (0.12) implies that the 95% confidence interval for the true beta is bounded by .71 — 2 x .12 and .71+ 2 x .12, i. e., the true beta is expected to lie between .47 and .95 with a 95% probability. A similar confidence interval can be calculated for alpha. Ignore the adjusted beta1 column, and use "raw" betas for all calculations. 1. From the Beta Book [5] i) How can betas be negative? [4] ii) How much did Minuteman International’s stock price tend to change in an unchanged market? [6] iii) Which stock had price changes that were most closely related to the market? What proportion of the stock’s risk was market risk, and what proportion was unique risk? [5] iv) Construct the 95% confidence interval (use 1.96 rather than 2) for MOB’s beta. Construct the 95% confidence interval (use 1.96 rather than 2) for MOB’s alpha. Draw any conclusions you can. [10] 2. Sampling Error "The errors in estimating beta are so great that you might just as well assume that all betas are 1.0." Do you agree? Briefly, why or why not, with reference to the beta book table? 1 Bayesian statistical methods are used to estimate adjusted betas; they push all betas toward 1.0 (low betas are pushed up, and high betas are pushed down). 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Over the same period, the risk-free rate was 4% and the expected market return was 13 %, with a market standard deviation of 25%. How well did the Blackpebble fund perform on a risk—adjusted basis? 7. Application of the CAPM to Assets Other Than Stocks You have 25% of your wealth in a fully diversified market fund, 25% in risk—free Treasury bills, and 50% in a house with twice as much systematic risk as the market. The risk—free rate is 4% and the market risk premium E (Rm) — RF is 6%. [5] i) What is the beta of this portfolio? [10] ii) What rate of return would you expect to earn from this portfolio? Individual and Equilibrium Portfolio Management Do you know what the implications of Harry Markowitz’s efficient frontier are for choosing a portfolio of assets? Do you know what the implications are when we add the pos- sibility of borrowing and lending at the riskless rate (without homogeneous expectations)? Do you know what the result is when we add the equilibrium CAPM under homogenous expectations? NOT A QUESTION FOR THIS HOMEWORK -- DO NOT ANSWER, JUST THINK ABOUT IT. 2 Here we use the CAPM’s equilibrium characteristics but not the SML, i.e., the problem is to be solved not in Return-Beta space, but rather in Return-Sigma space, using what you know about two-fund separation. [10] 3. Additive Risk in the CAPM How would you measure the quantity of risk relative to holding the full S&P 500 of a portfolio of stocks made up of the following shares: Portfolio Share Stock 0. 15 MNES 0. 10 MIR 0. 18 MTX 0.25 MNTX 0.20 MOB 0.12 MBK [15] 4. Application of the CAPM to Project Evaluation and Risk Adjustment Suppose the risk free rate is 4% per year and the expected market return is 12%. MITEK SURGICAL PRODS, INC (MYTK) is currently considering an expansion project that will yield the following net cash flows: Xe__ Net Cash Flow -$1,200,000 $700,000 $810,000 $860,000 $920,000 $940,000 The project is expected to have the same risk structure as MYTK. What is the net present value of the expansion project? Should MYTK undertake the project? mAwNHO [15] 5. Application of the CAPM to Assessing Market Expectations The risk-free rate is 3.91% and the expected market return is 13%. You are considering purchasing Keba.com stock, which currently sells for $100 a share and will pay its next annual dividend of $1.20 exactly a year from today. Keba.com is considered to be 40% more volatile than the market as a whole, i. e., its beta is 1.4. If dividends are expected to grow at a constant rate, g% per year, into the future, then what is the implied growth rate for this stock? (This question is motivated by two periods when there was a lot of interest in what growth rates were implied by booming prices: the fast tech stock run-up in 1999 and early 2000, and the REIT (Real Estate Investment Tust) run up 2005—2007.) ...
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