Understanding the Mathematics of Personal Finance


Figure 13.8 shows the daily price of three obviously fictitious stocks for about a year’s trading. The stock labeled “going nowhere” starts at 100, then periodically cycles between 75 and 125, ending up at 100. The stocks labeled “climbing” and “falling” also start at 100 and cycle up and down, but end up at 120 and 80, respectively.

Table 13.2 shows the average price for these three fictional stocks and the average purchase cost per share if you bought the same dollar amount (this is not the same number of shares) every day for the year. On days when the stock price is higher than average, a dollar spent buys you comparatively less. On days when the


Day number

Figure 13.8 Dollar cost averaging example.

Table 13.2 Dollar Cost Averaging Examples


Average price ($)

Average purchase cost per share for $1.00 daily purchase ($)

Going nowhere









stock price is lower than average, it buys you comparatively more. At the end of the year, the amount of stock you own is more than you would own if you had spent all of your money buying stock at the average price. This conclusion holds for stocks going nowhere, stocks that are climbing, and stocks that are falling. In the case of stocks that are falling, of course, you might wonder why you’re buying them at all. In general, we invest in stocks because we believe that in the long run, values will grow and prices will climb. A healthy combination of purchase diversification and dollar cost averaging is perhaps an unexciting investment plan—but probably a very good one. In practice, dollar cost averaging usually means purchasing weekly or monthly or at your job’s pay periods rather than the daily purchases shown in this example.

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Understanding the Mathematics of Personal Finance


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