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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 1
For the following set of questions you will need to use the returns data contained in the
Excel spreadsheet PS1_data.xls. Please download this file from the course website. The
file contains monthly returns for three indexes (VW = value-weighted index of stocks
listed on the NYSE, AMEX, and NASDAQ including distributions, EW = equallyweighted index including distributions, S&P = S&P 500 index excluding dividends) and
one-month risk-free rates (RF) over the period from January 1959 to December 2008.
You also need to obtain monthly holding period returns (including dividends) for the
following five stocks from CRSP for the same 50-year period: General Motors (ticker:
GM), IBM, Merck (MRK), Coca Cola (KO), and Eastman Kodak (EK). You can access
A. Empirical Properties of Stock Returns
1. Calculate the largest and smallest returns for each of the three indexes and five stocks
over the entire period. Did anything happen on or around these dates to explain such
extreme returns? Are these clustered in time? Why or why not?
2. Compute the mean returns and standard deviations of each of the indexes and
individual stocks over the entire period. Are any of the mean returns significantly
different from 1%? Can the returns be modeled as normally distributed random
3. Compute the correlation matrix for the indexes and individual stocks for the entire
sample. Which index is most highly correlated with the S&P 500 (VW or EW) and
why? Which of the five stock returns is most highly correlated with the S&P 500 and
why? Are the correlations among the five stocks unusual in any way or are they as
you expected them to be? Why or why not? 1 B. Mean-Variance Portfolio Optimization
4. Using the entire sample of monthly returns on the 5 stocks in the data set, calculate
and plot the mean-variance efficient frontier in mean-standard deviation space. Plot
the position of each stock in mean-standard deviation space. 1
5. If you are restricted to invest in the 5 individual stocks, what is the minimum level of
risk you have to bear? How would the minimum variance portfolio look like if you
cannot sell stocks short?
6. Compute the optimal tangency portfolio using the average T-bill rate. Plot it on the
graph you created in (4). What is the Sharpe ratio of the optimal tangency portfolio?
7. Suppose your desired rate of return is 1.5% per month. Which portfolio (consisting of
the five stocks and T-bills) would you optimally choose? 1 Hint: There are several ways to determine the efficient frontier. Probably the easiest way is to use Excel’s
solver to minimize the variance at two possible values of expected portfolio returns. Then use the fact that
the entire efficient frontier can be constructed as a linear combination of any two frontier portfolios once
you know the coordinates of and covariance between these two portfolios. 2 ...
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This note was uploaded on 04/06/2010 for the course BUSI 580 taught by Professor Strobl during the Fall '09 term at UNC.
- Fall '09