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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 RSQR 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
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av: [15] 6. Application of the CAPM2 to Measuring Portfolio Performance During a recent five year period, the Blackpebble hedge fund earned an average annualized rate
of return of 14% and had an annualized standard deviation of 30%. Over the same period, the
riskfree 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
ReturnBeta space, but rather in ReturnSigma space, using what you know about twofund 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 riskfree 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 runup in 1999 and early 2000, and the REIT
(Real Estate Investment Tust) run up 2005—2007.) ...
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 Winter '08
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