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Why Dollar-Cost-Averaging Works: A Look at the Numbers

Five Cent Nickel recently wrote a post about making money in a flat market by investing through the decline. Nickel shows that if you dollar-cost-average into a fund (index or otherwise) and the market declines, then returns to its original point, you will have made money.

It’s an excellent post (and quite timely), but it only looks at one of three possible “flat market” scenarios (the scenario in which the market starts at one point, declines, then comes back to where it started). If the opposite thing happens (ie, the market starts at one point, goes up, then comes back down), and you were dollar-cost-averaging into the market, you would have lost money. Why does it work that way?

Let’s Look at the Numbers.

When dollar-cost-averaging, the two things that determine whether or not you make money are:

  1. Your average cost per share.
  2. The ending price per share, and how it compares to your average cost per share.

Just by taking a quick glance at a hypothetical market chart, we can see how dollar-cost-averaging works in each scenario.

Scenario 1

This chart uses the numbers from Nickel’s original post. Even without doing any math we can see that, if purchases were made at each of the four points, the average cost per share purchased would be somewhere between the high point of $100/share and the low point of $66.5/share.

As a result, with an ending share price of $100/share, it’s obvious that the investor would have made money.

Scenario 2

This chart examines the opposite scenario: One in which the market starts at a point ($100/share), heads upward for a bit (to $150/share), then back down to its original price.

In this case, we can see that the average purchase price per share must be somewhere between $100 and $150.

With an ending price of $100/share, this investor has lost money.

Of course, real life isn’t very often like scenarios 1 or 2. That is, the market doesn’t seem to move in only one direction, then back to where it started. Typically, it’s all over the place (but slowly trending upward).

Scenario 3: Why Dollar-Cost-Averaging Really Works

Here we see a much more likely scenario, one in which the market moves both up and down over a given period. This time, we’ll actually have to do a little math to see what happens.

Let’s say our Oblivious Investor is happily dollar-cost-averaging into her index fund at a rate of $10,000 every year.

The first year, with a per share price of $100, her $10,000 buys her 100 shares.

In the second year, with a per share price of $150, her $10,000 only buys her 66.67 shares.

In the third year, with a per share price of $50, her $10,000 buys her 200 shares.

And at the end of the third year, the price returns to the original $100 per share. (So, still a “flat market.”) By this point, our Oblivious Investor has invested $30,000, and she owns 366.67 shares.

Dividing $30,000 by 366.67 shows us that her average per share price is just under $82. With a current market price of $100/share, our Oblvious Investor has made money. And this is in a flat market! It only gets better once we take into account the fact that (over time) stock market returns are positive.

Buy Low, Sell High (Without Even Trying!)

The reason dollar-cost-averaging works so well is that–if you invest steadily over a given period of time–your dollars will be able to buy more shares when the market is artificially low, and less when it is artificially high. In other words, you’ve set it up so that you’re automatically “buying low.” No need for complicated investing strategies. No need to try and time the market.

What about you? Have you had success with dollar-cost-averaging? Or if you’re new to this, do you know anyone who’s been DCA’ing into any funds for an extended period of time? If so, how’s it worked out?

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  1. DCA usually works, unless you started like September 2008

    I don’t have the chart handy, but quite certain the general trend is a downward line, where it’ll almost certainly take couple years for the indexes to get back to their “previous” levels

    Sigh, I kept buying at the bottoms, then the bottoms bottomed again, and again, and again, and not done yet 🙁

  2. Hi Jerry. Thanks for stopping by and commenting.

    I know just how you feel. I first started DCA’ing into an index fund in the Fall of 2001. I figured the market had already gone down a ton, so it must be about to head back up. Wrong! It went nowhere but down for another year.

    The good news though is that it *did* come back up. (Just as it will this time.) We just have to remember not to panic and take our money out.

    Also, Sept-Oct isn’t exactly a very long time frame. Dollar-cost-averaging is designed to work over an extended period (ie, several years). Over 2 month time periods, it’s almost impossible to predict what will happen.

  3. What about if you’ve got a lump sum of say $100,000 at the start. Is it better to Dollar-Cost Average it in over say five years, or to chuck it in at the start…? (I have my own views, but I’ll leave it as a thought for the reader/blogger… 😉 )

  4. I remain generally unmoved by DCA as an investment choice (investing every pay period is a different matter–you don’t have the money before each paycheck comes in, so you don’t have the choice to invest up front versus in bits and pieces over time). If the market average is down over your investing period, you will do better with DCA. If the market average is up over the period, you will do worse. Your example really didn’t show anything new in this sense: the three purchase periods your calculation covered average $66.66. So you DCA’d into a falling market (50 percent gain followed by a 66 percent loss), and beat the person who invested up front. The final return to 100 allows us to show a gain, rather than just less of a loss than the lump sum investor, but it doesn’t really change anything.

    If we reversed your example and considered a 66% gain (to 166) followed by a 50% loss (to 88), we’d find the DCA investor owned only 273.88 shares to the lump-summer’s 300, and so would lose to the lump-summer at any final share price–one dollar, one hundred or one thousand.

    Why is this important? If we believed that stocks were not going to appreciate in value over time, no one would buy them. If the market rises, the DCA investor always loses to the lump-sum up-front investor. If the market falls, the DCA investor “wins”–but _we_wouldn’t_invest_in_stocks_ if we believed that, over time, the market was more likely to fall than rise.

    Perhaps there is a valuable psychological function provided by DCA, because we are so risk-averse. If the market falls, we at least console ourselves that we didn’t invest everything at the peak. And if the market’s up…well, we’re still making money, right? But arithmetically, it is not a good proposition for an investment that you expect to appreciate over time.



  5. For what it’s worth, the above post is speaking specifically to investing monthly because that’s the way in which people are paid.

    For those with a lump sum to invest, I’m generally in the “put it all in now” camp.

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