Hallett explains volatility drag as follows:

“You’ve no doubt scratched your head at why a portfolio’s long-term performance hasn’t quite lived up to expectations. It’s likely that volatility drag is one of the big culprits. ... If a mutual fund reports a 7 percent 10-year rate of return, for example, the only way to have achieved that precise result was to invest at the beginning of that period, hold for the full decade and have no buys or sells in between. ... The investment industry has long preached the benefits of investing a regular dollar amount so that you buy more units of a fund when the price goes down and fewer when it’s up. This intuitive argument just doesn’t hold. ... Stock fund investors, however, might see returns that are 150 basis points (or 1.5 percentage points) less than published performance just from the fact that there are regular transactions over time.”This contradicted my understanding of the effect of dollar-cost averaging (DCA), but Hallett is a smart guy, and so I set out to investigate. I started with investment return data from a spreadsheet provided by Libra Investments. I focused on the real returns of the TSX from 1970 to 2010.

**Experiment 1**

In the first experiment, I looked at rolling 15-year periods. For each period, I calculated the average compound return from investing a lump sum at the beginning of the period and holding it for the full 15 years. The average compound return across all periods was 6.19%.

Then for each period, I considered the case where an investor makes an equal size investment at the start of each year for 15 years. For each period I calculated the internal rate of return (IRR). With this method of calculating return, we don’t penalize DCA for having less money invested in the early years. Across all of the 15-year periods, the average return was 6.52%, which is more than the average lump-sum return.

Of course, this victory for DCA may be just a quirk of the particular set of returns I used. While the DCA approach edged out the lump-sum approach on average, the results for individual 15-year periods varied. The full range was from DCA winning by 3.07% from 1973 to 1987 (inclusive) to DCA losing by 2.38% from 1978 to 1992 (inclusive).

The reason why DCA performs differently from lump-sum investing is that with DCA there isn’t much money invested in the early years. If the early years have better returns than later years, then lump-sum investing will win, and if the early years have lower returns than later years, then DCA will win. The fact that the TSX was down nearly 40% in 1973-74 and up nearly 60% in 1978-79 tells us why DCA beat lump-sum starting in 1973, but lost starting in 1978.

**Experiment 2**

To factor out this dependence on the order of returns, I did a second experiment. I used 12 years of TSX return data from 1999 to 2010 inclusive. For every possible reordering of the 12 years of returns I calculated the DCA return. (There are nearly half a billion cases and it took a program 12 minutes to check them all. To do the same for 15 years of returns would have taken about 3 weeks, and I’m not that patient.)

The DCA return results ranged from -1.81% to 15.82% with an average of 6.55%. The lump sum compound return is the same in every case: 6.27% per year. So we see that DCA returns can differ from lump-sum returns by quite a bit, but on average, the DCA returns are slightly better. In fact, the DCA return was higher than the lump-sum return in 52.3% of the cases.

**Conclusion**

I can’t find any evidence that Hallett’s volatility drag exists. Either one of us is wrong, or we are calculating different things. There is another type of volatility drag that comes from compounding, but this applies to both lump-sum investing and dollar-cost averaging.

For investors who are enthusiastic about dollar-cost averaging, these results do not apply to the case where you have a lump sum and choose to invest it slowly over a period of time. This is because of the opportunity cost of the lost returns on money waiting to be invested.

If dollar-cost averaging into a specific investment was consistently creating drag, that would have to be because the returns of that investment decline over time or alternately decline whenever there is more money invested in it. That means those who get in earlier (or when it's unpopular) always have better results and most investors don't get the reported return of that investment. Much like a successful actively-managed fund being bought by an average investor :)

ReplyDeleteThe thing that would really complete this experiment would be a statistical test of the means you observed. Given those variations, I'd guess that there is no statistically significant difference between the performance of DCA and lump-sum.

ReplyDelete@Value Indexer: There is an effect where mutual funds have worse performance as they grow, but this is mainly due to investors chasing performance by piling money into last year's winner. Fund incubation is a factor as well.

ReplyDelete@Jak: I agree that the difference in returns between lump sum and DCA is small. However, I didn't generate the data with statistical methods in the second experiment. I looked at all possible reorderings of the returns. This is different from choosing many reorderings at random. So, tests of statistical significance aren't relevant here.

I find the wording in Dan's article very confusing. For one moment, I thought Dan is talking about the well-documented effect where investor returns trail fund returns due to performance chasing. Is it possible that Dan is actually referring to that?

ReplyDelete@CC: I thought this at first as well, but if you read through the extended exchange I had with Dan in the comments on his post, he was very clear that this is not what he meant.

ReplyDeleteI realized the other day I typically only leave comments with I quibble with something in an article, so instead I'm just posting to say I find your blog very insightful and always with a different perspective than the typical financial blog. I especially like today where you put claims to an empirical test. Thanks! :)

ReplyDelete@Lewin: I'm happy to hear you found it useful. I'd like to hear your quibbles too. I'm in this to learn new things as well.

ReplyDeleteOh, I didn't have any with this analysis, completely agree. Though I don't think I'm following Hallett's argument about why "volatility drag" is a problem. Random variation in price will sometimes hurt you and sometimes harm you, but it should even out over time.

ReplyDeleteThe other issue is that the DCA vs. lump sum question is moot for many people because they invest regularly whenever they get paid, outside of unusual events like an inheritance or tax return. And I think many people mix up the more general concept of periodic investments with the more narrow term DCA.

@Lewin: It seemed clear to me that Hallett was saying that the volatility drag is persistent, but I agree with you that it mostly evens out over time. I don't believe that it contributes to the reason why people see lower performance in their own portfolios than they see in the reported returns of the mutual funds they own.

ReplyDeleteWow, you really worked hard on this experiment. It's interesting that in experiment 2, analysing the 12 years of data takes minutes of calculations while 15 years would take three weeks. Reminds me of a podcast I heard that says a five character password can be cracked in minutes while a seven character password would require years, or some such thing. I'm sure YOU know more accurate figures!

ReplyDelete@Gene: Yup. There are 12! permutations for 12 years and this increases by a factor of 13*14*15=2730 for 15 years. It's a little simpler for password crackers if you assume they are trying all possibilities. For each extra character, you multiply the time by the number of possible characters to choose from. In reality, though, clever password searchers are able to guess the kinds of passwords that people actually pick.

ReplyDeleteWorking hard indeed - great stuff Michael.

ReplyDeleteI guess the time window one uses for analyses (like Dan H. did) makes all the difference in the world, since the difference in returns between lump sum and DCA is small over time, the variation becomes marginal. Good to know.

I like these details, like Lewin, very insightful.