In this issue of Math in the News we look at the investment strategy known as Dollar Cost Averaging. We explore several simulated scenarios and look at the pros and cons of this strategy.

1. Saving for College
Math in the News
Issue 93

2. Dollar Cost Averaging
Lately, the stock market
has been doing well, but
is it necessary for the
stock market to soar in
order for your portfolio
to grow? In this issue
we look at a strategy
called Dollar Cost
Averaging, which can
be used to build a
college fund
portfolio, or any longterm investment.

3. Dollar Cost Averaging
When you purchase stock, your money is used
to purchase shares in the company, based on
the current stock price.

4. Dollar Cost Averaging
For example, suppose you purchase $1000 of
Google stock (GOOG) on January 2, 2014. This
is the number of shares you purchased
(source: Yahoo Finance).
GOOG Price/Share: $1,180.97
$1000
Number of shares purchased =
$1,180.97
» 0.846

5. Dollar Cost Averaging
As the price of Google’s stock changes, the
value of your shares changes, too.

6. Dollar Cost Averaging
Dollar Cost Averaging is a method of
purchasing stocks over a long period of time,
allowing you to increase your investment with
a low-risk investment strategy.

7. Dollar Cost Averaging
Here’s how Dollar Cost Averaging works:
• Purchase a set amount of a certain stock
every month. This can be set up as an
automatic payment from a bank account.
• Regardless of price fluctuations in the
stock, continue purchasing the set amount
each month.

8. Dollar Cost Averaging
Over time, in spite of the ups and downs in the
stock, the value of your stock holdings will
continue to grow. The key is to identify a stock
of a company that will continue to grow over
the period of your investment. The safest
strategy is to pick companies with long track
records of growth (Coke, IBM, etc.).

9. Dollar Cost Averaging
Let’s look at an example:
IBM. Suppose you started
purchasing $50 in stock
every month starting
January 2000 and ending
December 2013. During
this 168-month period you
invested $8400. How much
would you have ended up
with?

10. Dollar Cost Averaging
We’ll run a simulation
showing Dollar Cost
Averaging purchases of
stocks over this 168month periods. Most
stock Web sites have
historical data on the
price of a stock. We’ll be
using data from Yahoo
Finance, part of which is
shown in this
spreadsheet. (The data
can be downloaded as a
spreadsheet from Yahoo
Finance.)
Date
1/3/00
2/1/00
3/1/00
4/3/00
5/1/00
6/1/00
7/3/00
8/1/00
9/1/00
10/2/00
11/1/00
Price
$93.47
$85.65
$98.67
$92.95
$89.56
$91.44
$93.69
$110.31
$94.10
$82.30
$78.22

11. Dollar Cost Averaging
Create a line graph of the stock price data.
Notice that although there are a lot of
fluctuations, the stock price grew during the
investment period.

12. Dollar Cost Averaging
Add a column that
shows the number
of shares
purchased each
month. Simply
divide the $50 by
the share price for
that month. Here
is some of the
data.
Date
Price
1/3/00 $93.47
2/1/00 $85.65
3/1/00 $98.67
4/3/00 $92.95
5/1/00 $89.56
6/1/00 $91.44
7/3/00 $93.69
8/1/00 $110.31
Shares
Purchased
0.5349
0.5838
0.5067
0.5379
0.5583
0.5468
0.5337
0.4533

13. Dollar Cost Averaging
Create a line graph of the share purchase data.
Notice that as the stock price increases, fewer
shares are purchased. Also, when the stock
dips in price, more shares are purchased.

14. Dollar Cost Averaging
Now add a fourth column to find the cumulative
value of your stock month in and month out.
Note the type of formula you should use in this
column. After the 168-month period, the stock
value is over $16,000.
Date
Price
1/3/00
$93.47
2/1/00
$85.65
3/1/00
$98.67
4/3/00
$92.95
5/1/00
$89.56
6/1/00
$91.44
7/3/00
$93.69
8/1/00 $110.31
Shares
Cumulative
Purchased Value
0.5349
$50.00
0.5838
$95.82
0.5067
$160.38
0.5379
$201.08
0.5583
$243.75
0.5468
$298.87
0.5337
$356.22
0.4533
$469.41
Spreadsheet Formula
=SUM($D$2:D3)*C3

15. Dollar Cost Averaging
Here is a graph of the cumulative value of your
stock purchases. It’s similar to the stock price
graph shown earlier. The Dollar Cost Averaging
strategy aligns itself with the overall
performance of the stock.

16. Dollar Cost Averaging
Save your spreadsheet and try a different data
set for a company that didn’t grow during this
period: JC Penney. Simply replace the data in
column B with the new data.

17. Dollar Cost Averaging
Here is the stock performance graph. As you
can see, this stock went into a decline that it
still hasn’t emerged from.

18. Dollar Cost Averaging
As a result a Dollar Cost Averaging approach
with this stock would have resulted in less
value after 168 months.

19. Dollar Cost Averaging
The key with Dollar Cost Averaging is to find
companies that will continue to show
growth, or to know when it’s time to divest
from a company that is losing stock value.

20. Dollar Cost Averaging