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# Math in the News: Issue 93

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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.

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### Math in the News: Issue 93

1. 1. Saving for College Math in the News Issue 93
2. 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. 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. 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. 5. Dollar Cost Averaging As the price of Google’s stock changes, the value of your shares changes, too.
6. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 20. Dollar Cost Averaging