What Range of Outcomes has the Saver Experienced?
In a previous article I described how forecasting long-term market returns may be worthwhile for the lump-sum investor, but is of little or no use to the saver. Short-term market fluctuations and the order of returns overwhelm the accuracy of any predictions for somebody engaged in long-term Dollar Cost Averaging (DCA). The expected return at the start of the period has had no correlation to the final accumulation at the end of it.
What is more useful for the saver is to remain aware of the range of possible outcomes from an extended DCA program. Many people comment on historic market returns, and the dispersion of those returns, but is the dispersion the same for DCA? What can the saver expect or plan on? Does a DCA program increase your chances for a good internal rate of return (IRR) as compared to the market returns?
Using Robert Schiller’s data dating back to 1871, I compared 30-year market returns to the IRR of a person making equal, annual contributions to their account.  Below is a graph of how the saver’s IRR compared to the market returns for those periods.
In some periods the market beat DCA, and in some DCA beat the market. On average the DCA IRR beat the market returns by less than two tenths of a percent- an amount that is insignificant. In short, they produce similar returns on average, but not in each period. As if the market returns are not uncertain enough, your DCA program will provide market returns +/- 3%, which does not seem comforting.
The next question we can ask is when does DCA under or over-perform the market returns? Does DCA compound good and bad market returns, leading to brutal bad years and glorious good ones? Or does it smooth out market returns leading to a narrower range of possible outcomes?
I calculated the average 30-year market return over the period as 6.4%. Below I have graphed how the DCA advantage lines up with periods that are above and below this market average.
On this next graph I have added the two sets of bars together to show their compounding effect by year. In my opinion, the good news is that we rarely move past the -4% range. In other words, we don’t have periods of very poor market returns negatively compounded by periods of severe DCA underperformance. This means we haven’t seen 30-year DCA periods with truly terrible returns. The same is true in the positive.
Somebody with a higher level of statistical training might be able to analyze this graph in more detail, but I am inclined to conclude that the pattern is fairly random. DCA is probably not more likely to help our to hurt during periods with either above or below average returns. And in theory, I see no reason why a long-term market trend would be more likely to be concave (which would help DCA), convex (which would hurt DCA), or anything in between.
In this figure I have graphed the actual dispersion of returns for both the 30-year DCA saver and 30-year market returns. In a sense it is encouraging that the two bar patterns are similar. As a DCA saver we were historically not likely to receive a return vastly different from what the market was likely to provide.
And just in case it isn’t obvious, the difference in the final outcomes between the high and low returns is very large. This is demonstrated in the graph below.
I have been influenced by the writings of William Bernstein, who advocates the position that one of the most important things an investor can do is try to limit the possibility of very bad outcomes. Increasing your chances of good outcomes is a good goal, but it is not always the same thing as eliminating the worst possibilities. Eliminating very bad outcomes is one reason we index, diversify, and rebalance.
However, in his recent book, The Ages of the Investor, Bernstein champions the DCA process as less risky from the perspective of trying to eliminate very bad outcomes. Compared to lump-sum investing, he calls DCA “nearly bulletproof” and uses the 12 year period from 2000 to 2011 as an example when it excelled compared to the market returns.
As we can see from the figure above, and as we will see in subsequent graphs for shorter timescales, Bernstein is incorrect. The DCA investor has historically faced the possibility of an IRR that is either above or below the range of normal market returns. The chance has remained for the DCA program to have had a worse outcome over 30 years (and other periods as well). Consider the pitiful period starting in 1891. After putting $5000 per year into the S+P 500, the saver, hoping to retire after 30 years, had only $177,802 to show for it. Yes, they had only $27,802 of capital gains on top of the $150,000 they contributed, and their IRR was only 1.075%. (Just for comparison, the market return over the same period was about 3.2%.) I know what you’re thinking, that was ages ago in a period of unregulated markets, what about in more recent times? Sure, take the period starting in 1952, where the saver faced the unfortunate reality that their 30-year DCA program chalked up an IRR of only about 2.2%. Ouch. Sequence risk is some serious stuff.
Below is a table listing the historic probability of achieving an IRR over a 30-year DCA program.
Here you need to start asking yourself what is an acceptable level of return, and if you can really afford to bet on it.
And what about for shorter investing periods? Here are the dispersion graphs and probabilities for rolling 25, 20, 25, 10, and 5 year periods.
Again, notice that the graphs demonstrate that DCA has always provided a greater range of returns. The saver faced the possibility of both superior and inferior results compared to the market returns.
What does all this mean? Consider the fact that a DCA investor has had the possibility of realizing negative real returns for periods of 25 years! That result was not likely, and over the better periods the returns were fantastic, but very bad outcomes have existed even over extended periods for the saver who turns to the stock market.
Will these patterns hold in the future? I have no idea. It seems possible that we have entered, and may continue to live in a period of higher stock valuations and lower expected returns than anything seen in the long-term data I presented above. Could that shift the dispersion of returns to lower ranges? Again, it’s anybody’s guess.
In a coming article I will dig a little bit deeper into this data and try to draw some conclusions in regards to what I believe the saver can and should expect, and discuss life-cycle investing. A common approach is to create your stock/bond split based on your timeframe. I will try to argue that this is a flawed approach. In my opinion, a much more important questions is- how flexible is the savings timeframe?
 Annual data comes from using January numbers only. All values in real (inflation adjusted), 2012 dollars. Dividends are reinvested.
 Throughout this article I am referring only to the S+P 500. These returns may be quite different from those experienced by a person with a portfolio that is diversified with international stocks, bonds, etc.
 Page 23. Do we need the Chicago Manual of Style in the age of Hyperlinks? Maybe I’m wrong, if so direct hate mail to comment section.
 Just to be clear, I am not making an argument as to whether DCA or lump-sum investing is “superior.” I am talking about a long-term savings program where the saver would have no option of lump-sum investing. A 30-year DCA program as used to invest an already held lump-sum would be pointless.
 Is the bell curve for the DCA program stretched out, or are the tails fattened? I have no idea.
 I also have a theory that lower expected returns may bring with them higher volatility and more opportunity to buy at depressed prices, leading to less damage for the DCA investor. Do I have a shred of evidence for this idea? No. I’m not even sure I believe it.
Malcolm Lewis, December, 2012