Durham Asset Management1
Durham Asset Management (DAM) is a small firm with 50 employees that
manages the pension funds of small to medium-sized companies. Durham was
founded in 1975 and has grown considerably throughout the years. Initially,
DAM managed the pension funds of three small companies whose asset values
totaled $30 million. By 1991 DAM's funds under management were valued at $2
billion.
James Franklin is a senior vice president at DAM, in charge of managing the
equity portion of one of its largest pension funds. Franklin meets on a quarterly
basis with company officials who supervise his decisions and oversee his
performance. His work is measured on several levels, including both subjective
and objective criteria. The subjective criteria include estimates of the quality of
research reports. The objective criteria include the actual performance of
Franklin's portfolio relative to a customized index of companies in DAM's investment universe. Franklin attempts to "beat" the index not by trying to time
market moves, but by investing more heavily in those companies he expects to
outperform the customized index and less heavily in those companies he expects
to underperform the index.
Franklin has several research analysts who are charged with following the
performance of several companies within specific industries. The research
analysts prepare reports that analyze the past performance of the companies and
prepare projections of future performance. The projections include assessments
of the "most likely" or average performance anticipated over the next month.
Franklin analyzes their findings and often asks for additional information or
suggests modifications to the analyses. After a period of careful review, the final
forecasts for the next month are assembled and summarized. Each month the
analysts' forecasts are compared to the actual results. Annual bonuses for the
analysts are based in part on the comparison of these numbers.
It is now late December 1991, and the projections for January 1992 are indicated
in Table 1.
From Practical Management Science (2nd ed., Winston and Albright, 2001 Duxbury Press, pp.
397-398).
1
The projections have been made for 15 U.S. companies divided into five industry
groups. The five industry groups are metals, retail, computer, automotive, and
aviation.
Company
Forecasted Mean Return
Aluminum Co. of America (ALCOA)
0.6%
Reynolds Metals
0.9%
Alcan Aluminum, Ltd.
0.8%
Walmart Store, Inc.
1.5%
Sears, Roebuck & Co.
0.8%
Kmart Corporation
1.3%
International Business Machines (IBM)
0.4%
Digital Equipment Corporation (DEC)
1.1%
Hewlett Packard Co. (HP)
0.7%
General Motors Corp. (GM)
1.2%
Ford Motor Co. (FORD)
0.9%
Chrysler Corp.
1.3%
Boeing Co.
0.3%
McDonnell Douglas Corp.
0.2%
United Technologies Corp.
0.7%
Table 1: Projections for January1992 for DAM Case Study
Franklin would like to use the portfolio optimization approach to see what
portfolios it would recommend. He has data containing end-of-month prices for
the last two years for each of the companies. The data are contained in the
spreadsheet dam.xls. Also included in the spreadsheet is information about
dividends and stock splits. Using these data, James constructs a history of 24
monthly returns for each of the 15 companies.
The past data provide useful information about the volatility (standard
deviation) of stock returns. They also give useful information about the degree of
association (correlation) of returns between pairs of stocks. However, average
returns from the past do not tend to be good predictors of future average returns.
Rather than using the raw historical data directly, Franklin creates 24 future
return scenarios by adjusting the 24 historical returns. The adjustments are made
so that the means of the future scenario returns are consistent with the forecasts
from Table 1. The adjustments are also made so that the volatilities and
correlations of the future scenario returns are the same as in the historical data.
The exact procedure that Franklin uses for developing future scenario returns is
described next. Let rij0 denote the historical return of security j in month i (for j =
1, ... , 15 and i = 1, ... , 24). Suppose that the average historical return of security j
is  0j . For security j, denote the forecasted mean return in Table 1 by  j . (For
example,  1  0.6% and  2  0.9% , where the index 1 refers to ALCOA and 2
refers to Reynolds Metals.) Franklin creates the future scenario return rij for
security j in scenario i using the following equation:
rij  rij0   j   0j
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(i)
Prof. Juran
Franklin assumes that any of the scenarios defined by equation (i) can occur with
equal probability. DAM's policy is never to invest more than 30% of the funds in
any one industry group. Franklin measures the risk of a portfolio by its standard
deviation of return. He then solves a portfolio optimization model for various
minimum levels of mean return to see which portfolios are recommended. After
analyzing the trade-off between risk and return, Franklin makes a judgment as to
which portfolio to hold for the coming month.
Questions
1.
Use the information in the file dam.xls to create a history of 24 monthly
returns for the 15 companies. Compute the historical average return of
each stock. In particular, what was the historical return of ALCOA
from 12/29/89 to 1/31/90? What was the historical return of Boeing
from 5/31/90 to 6/29/90? Explain how you account for dividends and
stock splits in computing monthly returns. (Note: This has already
been done for you in dam.xls. If you are interested, take a look and see
how “if” statements were used to deal with the stock splits.)
2.
Develop 24 future scenario returns for each of the 15 stocks using
equation (i). What is the explanation underlying it? In particular, what
is the return of ALCOA if scenario 1 occurs? What is the return of
Reynolds Metals if scenario 3 occurs?
3.
Compute and graph the mean-standard deviation efficient frontier,
with no shorting allowed. Compute at least six points on the efficient
frontier (including the minimum standard deviation and maximum
expected return points). Create a table of results showing the following
for each of your points on the efficient frontier: (1) the optimal
portfolio weights, (2) mean portfolio return, and (3) standard
deviation. (Briefly explain the equations and optimization model used
in the spreadsheet.)2
Acknowledgment: Thanks to Ziv Katalan and Aliza Schachter for assistance in developing this
case.
2
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Prof. Juran
Hints:
When there are no splits, the historical return for a month can be computed by
the formula:
Return = (New price + Dividend - Initial price) / Initial price.
If the stock splits 3 for 2, the return is given by:
Return = (New price + Dividend - Initial price*(2/3) / (Initial price*(2/3)), which
is equivalent to:
Return = ( (3/2)(New price + Dividend) - Initial price) / Initial price.
If the stock splits 2 for 1, the return is given by:
Return = (New price + Dividend - Initial price*(1/2) / (Initial price*(1/2)), which
is equivalent to:
Return = ( 2(New price + Dividend) - Initial price) / Initial price.
(These return formulas with splits assume that the dividend is paid after the
split, not before. However, in the data there are no cases of a split and dividend
in the same month, so this issue never arises.)
Examples:
The price of ALCOA on 90/01/31 was 61.375. Its price on 89/12/29 was 75.0. A
dividend of 1.7975 was paid between these dates. Hence, the return for the
month ending 90/01/31 was
-0.157700 = (61.375 + 1.7975 - 75.0) / 75.0 .
The price of Boeing on 90/06/29 was 58.5. The previous month's price was
82.625. There were no intervening dividends, but the stock split 3 for 2. Hence
the return was
0.062027 = ((3/2)(58.5) - 82.625) / 82.625.
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