professor of management science has decided to build an equity portfolio made up of common shares
of General Motors.
“Active equity portfolio construction is about thoroughly understanding the return objectives
of a portfolio, as well as its acceptable risk levels, and then finding the right mix of securities
that balances predicted returns against risk and other impediments that can interfere with
realizing these returns.”
He has to decide what fraction of the portfolio should be devoted to each of these four issues.
DATA COLLECTION
collect some data and obtained first day of the month closing prices for General Motors
Oracle and Microsoft common shares for the period May 1, 1997 through June 1, 2000 from
Datastream.
The values of the Dow-Jones Industrial Average for the same dates and dividend payment information
for General Motors and General Electric were also obtained. Oracle and Microsoft shares did not pay
any dividends during this period.
The yield (as a percentage) on each share issue for each month was computed using:
Yield month t = 100 [Price month t – Price month (t-1) + dividends paid in month t]/ [Price month (t-
1)]
The return on a hypothetical portfolio matching the Dow-Jones Industrial Average was computed
using the same calculation applied to the Dow average.
FORMING THE PORTFOLIO
Maximizing return alone generally produced a very risky portfolio, while minimizing risk could lead to
low returns.
suggested that it might be important to add one or more constraints into the optimization.
One measure of the risk of a portfolio is variance of the portfolio’s return.
Another approach might be to look at the efficient frontier.
Other objectives were also possible. Perhaps he should minimize the probability of loss, subject to
achieving a given return? Another approach would be to maximize the probability that the return on
the portfolio would exceed the return of the market.
HOW TO PROCEED
A difficult issue in portfolio selection is the fact that shares generally move together.
That is, if the market has a “good day,” shares of a great many companies will move up together,
conversely, on a “bad day,” the majority of the issues will trade at lower prices.
The result of this covariation of share prices is that the risk of a given portfolio cannot be found by
summing the risks of the individual shares that make up the portfolio.
professor knew of an approach for estimating portfolio risk, based on the covariance matrix for all stocks
included in the portfolio
An alternate approach would be to simulate future returns using a technique called “bootstrapping.” A
12- month sequence of returns on four stocks can be created by randomly selecting 12 months of
historical stock returns.
For each month selected, the returns of all four stocks are used, so that “good” and “bad” months will
be “good” or “bad” for all four stocks.
By simulating many 12-month returns, one can obtain a distribution of future performance on the four
stocks together.
This distribution can be used to calculate the risk of any portfolio.
then the professor thought that optimization could be used to select the proportions of the various
issues to be included in the portfolio
Assignment: Provide a quick rundown of the issues that the professor face while
creating his portfolio. Discuss what your goals and objective would be if you were
creating this portfolio, how can you “add value”. Think about issues such as efficiency,
risk-return, and how to add value. Include a recommendation of a portfolio make-up
(weights, or even suggestions of other stocks).
1. Estimate and compare the monthly returns and variability (standard deviation)
of each stock with that of the DJIA Index.
a. Which stock appears to be riskiest? Less risky?
b. How might the expected return of each stock relate to its riskiness?
2. Suppose the professor decides to make the portfolio with equal weight of stock
holding (each stock holds 25% weight in the portfolio). Estimate the resulting
portfolio position.
a. How does each stock affect the variability of the equity investment?
b. What is the correlation between the stocks?
c. How does this relate to your answer in question 1 above?
3. Compute the “beta” for each stock (Use DJIA as the market return).
a. What does beta measure?
b. How does this relate to your previous answers?
4. What is the required rate of return for each stock (CAPM)? Explain the number
and put it into context? (Use the RF rate given in the second page)
5. Make a recommendation of what you would do if you were professor. Would
you try something different?
a. What would be your main objective?
b. How would you weigh each stock in the portfolio? Why? What would be the resulting
risk and return?
Please type in your email address. I will send you the spreadsheet for this problem.
Monthly Risk-Free rate (in percentages)
1997-06-01 4.93
1997-07-01 5.05
1997-08-01 5.14
1997-09-01 4.95
1997-10-01 4.97
1997-11-01 5.14
1997-12-01 5.16
1998-01-01 5.04
1998-02-01 5.09
1998-03-01 5.03
1998-04-01 4.95
1998-05-01 5.00
1998-06-01 4.98
1998-07-01 4.96
1998-08-01 4.90
1998-09-01 4.61
1998-10-01 3.96
1998-11-01 4.41
1998-12-01 4.39
1999-01-01 4.34
1999-02-01 4.44
1999-03-01 4.44
1999-04-01 4.29
1999-05-01 4.50
1999-06-01 4.57
1999-07-01 4.55
1999-08-01 4.72
1999-09-01 4.68
1999-10-01 4.86
1999-11-01 5.07
1999-12-01 5.20
2000-01-01 5.32
2000-02-01 5.55
2000-03-01 5.69
2000-04-01 5.66
2000-05-01 5.79
2000-06-01 5.69
Exhibit 1 MONTHLY RETURN DATA
Month Sale date GM GE Oracle Microsoft DJIA
1 1-Jun-97 –0.86995 10.49754 21.13459 2.77686 4.485357
2 1-Jul-97 1.710171 9.648689 –0.91827 0.450306 5.939172
3 1-Aug-97 14.31172 5.415162 13.06766 12.58405 6.10839
4 1-Sep-97 –2.62739 –9.50521 4.180328 –6.00114 –6.97605
5 1-Oct-97 10.83401 9.592326 –5.58615 1.270802 5.156892
6 1-Nov-97 –1.20823 –0.70022 –0.33333 0.179265 –4.25563
7 1-Dec-97 –8.00688 10.23692 –11.1204 7.217417 4.413641
8 1-Jan-98 6.896552 –0.81103 –30.0094 –10.1252 –1.30861
9 1-Feb-98 –0.41824 8.503679 10.34946 19.83906 2.523061
10 1-Mar-98 17.14 –2.52101 –2.07065 7.592975 5.459818
11 1-Apr-98 –2.11712 12.89185 30.0995 8.473356 3.717582
12 1-May-98 1.760057 –0.41652 –18.5468 –0.84089 3.143211
13 1-Jun-98 3.741617 –2.50618 –10.7981 –6.56104 –2.45652
14 1-Jul-98 –0.88465 10.02896 5.526316 30.61858 1.415543
15 1-Aug-98 3.833245 –0.65811 10.72319 –0.85939 –2.89468
16 1-Sep-98 –17.0466 –7.60979 –22.8604 –6.63962 –10.9177
17 1-Oct-98 –4.77851 –8.6357 31.38686 2.78546 –2.48996
18 1-Nov-98 20.29924 17.07705 10.88889 1.691332 14.06637
19 1-Dec-98 10.07982 4.292582 23.34669 22.37762 4.909059
20 1-Jan-99 2.512648 11.95258 16.8156 7.088803 0.524331
21 1-Feb-99 30.48698 1.411765 37.06537 24.70436 1.789155
22 1-Mar-99 –10.9758 –1.23312 –7.10299 –12.2586 –0.22385
23 1-Apr-99 5.181951 10.58264 –29.4921 22.1695 5.444954
24 1-May-99 9.7295 –4.24731 0.929512 –13.8203 12.02318
25 1-Jun-99 –8.76355 –2.89773 –2.14889 –1.72759 –3.79884
26 1-Jul-99 –1.99462 8.718549 48.07843 16.16561 4.437037
27 1-Aug-99 –8.50214 –2.12594 0.95339 –6.99638 –3.79942
28 1-Sep-99 7.967033 5.396384 –1.15425 8.925834 2.742073
29 1-Oct-99 –4.35564 3.246239 20.11677 –2.59796 –6.07869
30 1-Nov-99 10.44177 11.29857 13.07998 2.667259 3.655407
31 1-Dec-99 5.367273 4.012059 38.10082 0.876813 3.285621
32 1-Jan-00 5.300939 11.46042 67.11941 25.0778 3.265296
33 1-Feb-00 14.2302 –8.34167 –8.56756 –11.685 –2.78644
34 1-Mar-00 –12.9032 –3.39731 32.40741 –11.7836 –8.17975
35 1-Apr-00 16.44444 20.82667 7.524476 0.077084 10.69253
36 1-May-00 9.291357 1.323001 3.655047 –19.1901 –3.65481
37 1-Jun-00 –24.6844 –1.39307 –2.2713 –12.0915 –1.47598
