Unformatted text preview: UNIVERSITY OF NORTH CAROLINA
KENAN-FLAGLER BUSINESS SCHOOL
BUSI 580: INVESTMENTS
PART I: PORTFOLIO THEORY AND ASSET PRICING
Prof. Günter Strobl Spring 2010 Problem Set 2
Note: Questions marked with an asterisk (*) are NOT required, but may be answered for
extra credit. They are typically more challenging.
A. The Capital Asset Pricing Model
1. The market price of a stock is $50. Its expected rate of return is 14%. The risk-free
rate is 6% and the market risk premium is 8.5%. What will be the market price of the
security if its correlation coefficient with the market portfolio doubles (and all other
variables remain unchanged)? Assume that the stock is expected to pay a constant
dividend in perpetuity.
2. The standard deviation of the return on stock 1, stock 2, and the market portfolio are
σ1 = 0.4, σ2 = 0.3, and σM = 0.2, respectively. The covariances between these assets
are σ1,2 = 0.02, σ1,M = 0.064, and σ2,M = 0.032. Consider a portfolio that has 75%
invested in stock 1 and 25% invested in stock 2. Call this portfolio p.
(a) What is the variance of portfolio p?
(b) What are the betas of stock 1, stock 2, and portfolio p?
(c) What are the R2 values in regressions of the return on stock 1, stock 2, and
portfolio p on the market portfolio?
3. (*) In a two-stock capital market, the capitalization of stock A is twice that of stock
B. The expected excess return on stock A is 6% and that on stock B is 8%. The
standard deviations of the excess returns are 14% and 22%, respectively.
(a) Assuming that the CAPM is correct, calculate the correlation coefficient between
the excess returns on stocks A and B.
(b) What is the beta of each stock? 1 (c) Suppose the risk-free rate is 4%. Determine the Capital Market Line (CML) and
the Security Market Line (SML).
B. Testing the CAPM
For the following questions you will need to use the returns data from Problem Set 1.
You can download the Excel spreadsheet PS1_data.xls from the course website. For a
description of the file, please refer to Problem Set 1. You also need to use the monthly
holding period returns for General Motors, IBM, Merck, Coca Cola, and Eastman Kodak
that you obtained from CRSP for the previous problem set.
4. Estimate the single-index model for each of the five stocks using monthly excess
returns over the entire sample period. Use the value-weighted index (VW) as a proxy
for the market portfolio.
(a) Are the betas of these stocks significantly different from 1 at the 5% level?
(b) Plot the average excess return for each of the five stocks as well as for the valueweighted index against their respective beta. Is it a linear relationship?
(c) Using the entire sample, estimate the historical alpha of each stock. Did any of the
five stocks significantly outperform/underperform the market over the last 50
years (significance level = 5%)? Can you reject the CAPM? Why or why not?
C. Getting Better Betas
5. (*) Consider the last 15 years of monthly excess returns on the five stocks and the
(a) Estimate the betas of the five stocks for three non-overlapping 5-year sub-periods
(i.e., for the period from Jan. 1994 to Dec. 1998, from Jan. 1999 to Dec. 2003,
and finally from Jan. 2004 to Dec. 2008). Are the betas “stable” over time? What
are the economic implications?
(b) Pretend that the current date is just before the last 5-year sub-period begins (i.e.,
end of December 2003). Pretend further that you want to come up with an
estimate of beta for the next (i.e., last) five years. Which of the following
approaches produces “better betas”? (i.e., compare the betas you get from each
method with the beta you actually estimated over the last 5-year sub-period).
i. Using the OLS estimate of beta from the middle 5-year period.
ii. Using Blume’s technique (i.e., plotting the beta estimates for the first subperiod against those for the second sub-period, determining a best-fitting
“adjustment line”, and adjusting the betas from the second sub-period to get
predicted betas for the last sub-period). 2 ...
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- Fall '09
- Capital Asset Pricing Model, Market Portfolio, betas, better betas