the mathematics of financial markets
TRANSCRIPT
AC 2010-97: THE MATHEMATICS OF FINANCIAL MARKETS
Bertram Pariser, Technical Career Institute, Inc.
Cyrus Meherji, Technical Career Institute, Inc.
© American Society for Engineering Education, 2010
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THE MATHEMATICS OF FINANCIAL MARKETS
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Abstract
We are all aware of the tremendous upheaval that has taken place in the financial markets over
the last year. Well established banks and brokerage house have failed and had to be liquidated or
merged. Is it possible to model the financial markets to help understand the relationship;
between the most dynamic variables, Gold, The Dow Jones Industrial Average.
Using mathematics to look for correlations of sets of these data has been performed by
mathematicians. By using Microsoft Excel to examine Gold and the Dow Jones Industrial
Average we would like to find a method that would enable us to simplify and see the fluctuations
of the variables.
Introduction
We teach in the Electronic Engineering Technology department (“EET”), at TCI the College of
Technology a two year college located in New York City. Our 4000 + students are 50% inner
city and 50% foreign. It is one of the most diverse populations in NYC with over 100 different
languages spoken. The only place more diverse than TCI is the United Nations.
The mathematic courses concentrate on applied math which is necessary for our EET students.
Often the challenge exists of teaching students to make mathematical models of physical
systems. We feel that the value of teaching students to analyze large quantities of data is a valid
objective.
Data Sources
The two variables that we chose to start our instruction are the Dow Jones Industrial Average,
(“DJ”) and the price of gold. The first challenge is to find the data. The next step is to formulate
a model and then test it over the time periods listed above.
The source of data for the Dow Jones is located at Dow Jones, Wren Research1. We selected the
yearly closing price on the first day of each year.
We researched and found that the United States was on the Gold Standard and the price of Gold
was $20.67 until 1934. The source of data for Gold is R.W.Jastram (1977), London Bullion
Market Association2. The US dollar was backed by gold and the strongest currency in the world.
In 1934 the country was in the midst of a depression and President Roosevelt asked congress to
increase the gold assets in Fort Knox by raising the value of an ounce of gold from $20.67 to
$35. The price of gold was pegged at $35 per ounce over this period. In 1967 the United States
went off the Gold Standard and the US dollar is no longer backed by gold. The price of gold
relative to the dollar started to increase.
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Procedure
Our students are in a two year college studying Electronic Engineering Technology and our
mathematic courses are centered on applied mathematics geared to technology. The students
have not had the opportunity to use advanced mathematical software programs and have had
limited experience with Microsoft Word and Excel. To develop their proficiency with Word and
Excel focused on mathematics we developed a task which would be motivational as well as
educational
Our college is located in New York City the financial capital of the nation. Quite often students
hear about the Dow Jones Averages and the price of gold. They are inquisitive and want to
know why there is so much emphasis on these items in the news today. By combining these
factors within an Excel program we are satisfying their curiosity as well as instructing them on
finding data, acquiring the data and using the data.
Our students in mathematics courses learn about matrices, complex numbers, trigonometry and
linear algebra. They do not learn about correlation. The graphs that they generate in physics
courses showing displacement and velocity are generated using Excel.
Our first task was to plot our two variables on a set of axis to examine the patterns. Below in
Figure 4 is the data for the Dow Jones Industrial Average and the Price of Gold for the years
1896 to 2008. The data is presented in four columns and the the values of the Dow Jones
Industrial Average has been rounded to the nearest whole number.
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1896 40 20.67
1897 49 20.67
1898 61 20.67
1899 66 20.67
1900 71 20.67
1901 65 20.67
1902 64 20.67
1903 49 20.67
1904 70 20.67
1905 96 20.67
1906 94 20.67
1907 59 20.67
1908 86 20.67
1909 99 20.67
1910 81 20.67
1911 82 20.67
1912 88 20.67
1913 79 20.67
1914 55 20.67
1915 99 20.67
1916 95 20.67
1917 74 20.67
1918 82 20.67
1919 107 20.67
1920 72 20.67
1921 81 20.67
1922 99 20.67
1923 96 20.67
1924 121 20.67
1925 157 20.67
1926 157 20.67
1927 202 20.67
1928 300 20.67
1929 248 20.67
1930 165 20.67
1931 78 20.67
1932 60 20.67
1933 100 20.67
1934 104 35.00
1935 144 35.00
1936 180 35.00
1937 121 35.00
1938 155 35.00
1939 150 35.00
1940 131 35.00
1941 111 35.00
1942 119 35.00
1943 136 35.00
1944 152 35.00
1945 193 35.00
1946 177 35.00
1947 181 35.00
1948 177 35.00
1949 200 35.00
1950 235 35.00
1951 269 35.00
1952 292 35.00
1953 281 35.00
1954 404 35.00
1955 488 35.00
1956 499 35.00
1957 436 35.00
1958 584 35.00
1959 679 35.00
1960 616 35.00
1961 731 35.00
1962 652 35.00
1963 763 35.00
1964 874 35.00
1965 969 35.00
1966 786 35.00
1967 905 35.00
1968 944 41.70
1969 800 35.15
1970 839 37.40
1971 890 43.55
1972 1020 65.00
1973 851 111.75
1974 616 193.00
1975 852 140.75
1976 1005 134.63
1977 831 165.15
1978 805 226.40
1979 839 526.50
1980 964 589.50
1981 875 400.00
1982 1047 448.00
1983 1259 381.50
1984 1212 308.30
1985 1547 326.80
1986 1896 388.75
1987 1939 484.10
1988 2169 410.25
1989 2753 401.00
1990 2634 386.20
1991 3169 353.40
1992 3301 332.30
1993 3754 390.50
1994 3834 382.50
1995 5117 387.15
1996 6448 369.25
1997 7908 289.20
1998 9181 287.80
1999 11497 290.25
2000 10787 272.65
2001 10022 276.50
2002 8342 342.75
2003 10454 417.25
2004 10490 422
2005 10718 513
2006 12463 636
2007 13198 837
2008 11224 880
Figure 1 Data of the Dow Jones Averages and the Price of Gold from 1896 to 2008
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Figure 2 is a graph of the Dow Jones Industrial Average and the Price of Gold from 1896 to
2008 The price of gold increase from $37.40 to $589.50 an increase of 970% while the Dow
Jones Industrial Average increased $838.92 to $963.99 an increase of 15%.
1970 838.92 37.40
1971 890.20 43.55
1972 1020.02 65.00
1973 850.86 111.75
1974 616.24 193.00
1975 852.41 140.75
1976 1004.65 134.63
1977 831.17 165.15
1978 805.01 226.40
1979 838.74 526.50
1980 963.99 589.50
Figure 3 is the Dow Jones Industrial Average and the price of Gold from 1970 to 1980
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Figure 4 is a graph of the Dow Jones Industrial Average and the Price of Gold from 1970 to 1980
When one views the graph in Figure 4 the green line is a plot of the price of Gold from 1970 to
1980. Gold was selling for $37 an ounce and in 1980 it sold for $590! During the same period
The Dow Jones Industrial Average went from $839 to $964. Clearly the investment choice
between 1970 and 1980 of converting from the Dow Jones Industrials to Gold was the correct
decision. However, let’s look at some more time periods
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1980 964 589.50
1981 875 400.00
1982 1047 448.00
1983 1259 381.50
1984 1212 308.30
1985 1547 326.80
1986 1896 388.75
1987 1939 484.10
1988 2169 410.25
1989 2753 401.00
1990 2634 386.20
Figure 5 is the Dow Jones Industrial Average and the price of Gold from 1980 to 1990
Gold decreased 29% and the Dow Jones increased 310%.
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Figure 6 shows the Dow Jones Industrials and the price of Gold for 1980- 1990. Gold decreased
29% and the Dow Jones increased 310%.
Looking at the data from 1970 to 1980 one might have concluded that it is better to be in gold
then in the Dow Jones Industrial average. However over the next 10 years that strategy would
not be the correct one. So by examining the data and making models and testing the models over
different time periods students start to appreciate the challenge of making successful models.
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1990 2634 386.20
1991 3169 353.40
1992 3301 332.30
1993 3754 390.50
1994 3834 382.50
1995 5117 387.15
1996 6448 369.25
1997 7908 289.20
1998 9181 287.80
1999 11497 290.25
2000 10787 272.65
Figure 7 is the Dow Jones Industrial Average and the price of Gold from 1990 to 2000
the Dow Jones inceased 310% and Gold decreasesd 29%
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Figure 8 1990 to 2000 the Dow Jones inceased 310% and Gold decreasesd 29%
During this period if you chose to stay with the last model it was the corrct choice. The Dow
Jones Industrial Average increaded 310% and Gold decreaced 29%
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Figure 9
Figure 9 shows that from 1970 to 2008 the optimum strategey was to invest in Gold from 1970 to
1980 , then to switch to the Dow jones from 1980 to 2000, then to switch to gold in 2000 to
2008.
Conclusion
The objective of mathematical use of Excel has exceeeded our expectations. First the data was
selected, then the data was imported into Excel. Next the data was analyzed by generating
graphs in Excel and finally the graphs were used to analyze investment decisions. The data is
much clearer in graphical form than in tabular form. This analysis has demonstrated to students
the value of Excel for mathematical aquisition of data using graphical analysis,
Our analysis was done by selecting data for the Dow Jones Industrial Average and for Gold from
1896 to 2008. We captured the data and examined the the price fluctuations for the two
variables. The data suggested that Gold and the Dow Jones Industrial Average do not rise and
fall in phase. By examining the data our students now listen to the news with more interest.
Commercials for investing in Gold now are viewed with a knowledge of how that investment in
the past turned out by buying and holding over a long period.
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Bibliography
1 Dow Jones, Wren Research, http://www.wrenresearch.com.au/
2 R.W.Jastram (1977), London Bullion Market Association, http://www.e-nisab.com/distant
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Authors
Dr Bert Pariser is a faculty member in the Electronic Engineering Technology and the Computer
Software Technology Departments at Technical Career Institutes. His primary responsibility is
developing curriculum and teaching methodology for Physics, Thermodynamics,
Electromagnetic Field Theory, Computers and Databases. Bert prepared grant proposals to the
National Science Foundation, which produced the funding for a Fiber Optics Laboratory. He
served as faculty advisor to the IEEE and faculty advisor to Tau Alpha Pi National Honor
Society. Bert was instrumental in merging Tau Alpha Pi National Honor Society into the ASEE.
In addition, Dr. Pariser Co-Founded 5 venture companies, and as a management consultant
successfully catalyzed over $100 million of new shareholder value in client businesses. Bert led
cross-functional client teams in projects to find and capture value-creating profit and growth
opportunities. Bert received a PhD, MS from Columbia University and a BS from MIT in
Electrical Engineering. [email protected]
Cyrus Meherji is a faculty member in the Electronic Engineering Technology and the Computer
Software Technology Departments at Technical Career Institutes. Together with Dr Pariser
Cyrus prepared grant proposals to the National Science Foundation, which produced the funding
for a Fiber Optics Laboratory. [email protected]
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