Sorry for the deliberately provocative title, I could not resist.
I felt like wasting some time, so I decided to download the November 1978--July 2021 data about the MSCI World Index and compare the performance of Lump Sum Investing versus doing Dollar Cost Averaging over 12 months.
As you all probably know, a famous Vanguard paper did about the same, using a much greater amount of data (United States market 1926-2011, United Kingdom market 1976-2011, Australian market 1984--2011) and concluded, that, on average, LSI outperformed 12-month DCA (in terms of the ending portfolio value after 10 years) by 2.3%, 2.2% and 1.3% respectively.
Aside from verifying the results of people way more expert than me and wasting my own time, my purpose here was to consider two questions:
- Did the relative performance of LSI/DCA change in recent times? Is there any particular reason to think that "this time it is different"?
- Sometimes people suggest that DCA might be preferable to LSI because "the market is very high" or because "there has been a lot of volatility". Do these arguments make any sense? (I was pretty sure that the answer was no, for reasons I will explain in a moment, but people often say that so I might as well check that out. In the unlikely event that some criterion along these lines worked, obviously I wouldn't even think about posting this here before double-checking it on new data for one year or two and then exploiting it for a while to make ridiculous amounts of money, so if this has been published sometime around late September 2021 you already know the answers).
A hopefully unnecessary warning
I am writing this partly for my personal amusement and partly to see if anyone here finds something wrong with my analysis or some obvious error (there might well be!). If you base your financial decisions on the advice of some random redditor... well, I would like to strongly advise you not to do that, but that would lead to an interesting paradox.
Still, if you decide to do/not do something -- anything -- because of what I write here and it turns out that it was a terrible mistake that's not my fault, alright?
Why LSI should usually beat DCA, and why I don't think you can predict much more
Very briefly, if you do DCA over 12 months, investing 1/12 of what you have every months, you are buying your shares at (an approximation of) the average price they'll have over the next 12 months rather than at the current price. Thus,
- If the average price over the next 12 months is higher than the current price, which it should usually be as long as the market mostly goes up in the long term, then LSI will be more convenient than DCA, and if it is lower (which should not happen as often) DCA will be more convenient instead;
- If there existed some simple criterion (like volatility or the market being "high") that could let you predict whether DCA might be more convenient than LSI, the same criterion could let you predict if the market will mostly increase or mostly decrease over the next year. If this existed, professional investing firms would likely be aware of it already and would use it for buying shares when the market is likely to rise/sell them when it is likely to fall, thus making that very criterion obsolete at once.
Still, arguments are one thing, data is another. Let's have a look anyway.
Methods
For this analysis, I will ignore issues related to fractional shares and fees.
-
To compute the performance of LSI, I will do the following: I will assume I bought $1000 worth of shares at a certain time and I will look at their value after 12 months. That's it.
-
To compute the performance of DCA, I will assume I bought $1000 worth of shares every month, for 12 months, then I will compute the total value of my shares after 12 months. Then I will divide this value by 12, so that I can compare my investment of $12000 with the $1000 LSI investment.
Differently from the Vanguard paper, I will compare the LSI/DCA investments immediately after these 12 months instead of looking at their values after ten years from the beginning of the investment. The reason for this is that, after 12 months, all shares that could be bought have been bought one way or another and the relative performance of LSI and DCA will not change. Also, unfortunately I could not find the full data about the values of the MSCI World Index during the 2021-2031 decade, which I would need to do that. If anyone has access to that data, I would be very interested in having a look.
The two criteria I will consider and see if they have any effect on whether LSI is better or worse than DCA are
-
Is the market "high"? To estimate this, I will look at the current price divided by the average price over the last 12 months. If this rate is much higher than 1, the market has "risen rapidly"; if it is much smaller than 1, the market has "fallen rapidly".
-
Has the market been volatile lately? For this I will use the normalized standard deviation over the last 12 months -- that is, the standard deviation of the price over the last twelve months divided by the average price over the last twelve months. Using the non-normalized standard deviation would be a mistake here: the market is much higher than it once was, and a 1% fluctuation today would be far greater than a 1% fluctuation twenty years ago.
In order to evaluate LSI and DCA, I need at least 11 months of data after the current month, and in order to compute the above parameters I need at least 11 months of past data. Therefore, I will be able to compare LSI and DCA with respect to these parameters only over the Oct 1979-Aug 2020 period.
Some numbers and pretty graphs
The average return of LSI was $1113.67, with standard deviation 180.86; The average return of DCA was $1055.71, with standard deviation 97.32. On average, the difference between LSI return and DCA return was $57.96 over the initial $1000 investment, and LSI beat DCA by 4.9% (in the sense that, on average, the return of LSI was 104.9% of that of DCA, not that the return of DCA was 95.1% of that of LSI - I state the obvious, but that's not the same thing).
The 5th, 25th, 50th, 75th and 95th percentiles for LSI and DCA returns are ($771.67, $1013.49, $1127.49, $1234.04, $1395.76) and ($861.83, $1004.16, $1063.83, $1121.20, $1207.23) respectively.
These results are roughly in line with those of the Vanguard paper, if a perhaps little more favorable to LSI, and confirm what should intuitively be true: investing via DCA in general is less advantageous, but it is "safer" in the sense that it leads to somewhat more consistent outcomes. Whether that is worth it, of course, is up to personal preference.
Let us now visualize what investing $1000 using LSI/DCA would have gained (or lost) us during this period:
One thing that I think is noteworthy here is that, in recent years, the relative performance of LSI and DCA appears to have been fairly typical. Sometimes it is argued that the market is now behaving in a very different way in which it was behaving in the past, and this may well be correct; but insofar as comparing the performance of LSI and DCA is concerned, the recent times do not appear to have been particularly unusual.
Another thing that is clearly visible from this graph (and that was pretty predictable) is that the performances of LSI and DCA are highly correlated: when LSI does well, DCA usually also does (but not as well), and when LSI does badly, DCA also does badly (but not as badly).
Let's throw a quick linear regression (not the fanciest approach, I know, but there seems to be no need to get fancy here) to confirm this:
LSI vs DCA: linear regression.
The correlation coefficient is 0.9, expectedly high.
At this point, one might wonder why this graph and the linear regression suggest that, generally, DCA will gain/lose you about half than what LSI would, when we computed before that over our data LSI beat DCA by 3.8%. The answer to this is that in this graph we are looking at gains/losses, not at total returns: if, after investing $1000, you'd get $1100 if using LSI and $1050 using DCA, you'd have gained half as much using DCA as using LSI, but LSI would have beat DCA by 4.8% ((1100 - 1050)/1050 = 0.048). Also, linear regression attempts to find the linear function that minimizes quadratic error, which is also an issue when making this type of comparison (this means that linear regression tends to weigh outliers more - there are ways around it, but I don't see the point of overcomplicating our approach here).
Still, the overall message of this image is clear: over the considered data, investing via a 12-months DCA usually led to profits/losses about half as big (both in positive and in negative) than investing via LSI. Will it be the same in the future? I don't know! Perhaps! Perhaps not! The correlation seems pretty solid; but all of this is descriptive, not predictive.
And on the topic of prediction, let us see our cherished parameters -- that describe if the market has been "high" or "volatile" lately -- are of any use for deciding if DCA is better than LSI or vice versa:
Advantage of LSI vs DCA when market has been "high" or "low" recently
Yeah, not seeing much of a correlation here - in fact, this graph is a pretty clear violation of the Randall Munroe regression test.
What I think is interesting, however, is that the ratio between the current price and the previous 12-months average is not that high in recent data (the yellow dots) compared to other times in the past: in fact, it seems pretty typical. If I made no mistakes, this would seem to suggest that "the market has risen too quickly, so you should do DCA instead of LSI / you should wait to invest"-style arguments are not only incorrect in that the conclusion does not follow from the premise, but also in that the premise itself is false: the market has been rising lately, yes, but it has not been rising unusually quickly.
Let's throw a linear regression anyway, just to see what happens:
LSI vs DCA when market is high - regression
For the record, this is the linear regression algorithm throwing up its hands and going "What? No, you silly person, no".
Let's see if "volatility" -- as measured by normalized standard deviation -- fares any better as a predictor of LSI/DCA performance:
LSI vs DCA: looking at normalized standard deviation
Yeah, no. As a criterion on whether in the next 12 months the market will on the average go "up" or "down", i.e., whether it would be better to do LSI or DCA, past normalized standard deviation is useless. Perhaps less expected than this is that, it would appear (if I have not made mistakes somewhere, which might well be the case), the market has not been particularly volatile lately - quite the opposite, if anything!
Some conclusions
Is it better to use LSI or DCA? This is up to the individual investor, I think. Neither choice seems inherently unreasonable: with DCA, you will probably reduce the impact on future profits, if they happen, and losses, if they happen. If you are investing to begin with, you likely think that there is a decent probability that the price will go up; and if this is true, then by using DCA you will effectively pay part of your potential profits (in the past, about half or a little less) in exchange for diminishing the potential losses in case you are wrong (again, by about half if the past is any indication, which might or might not be the case). Also, DCA has psychological advantages that are not to be ignored - if going lump sum and seeing the value of your investment fluctuate wildly from month to month would make you miserable and worried, you might well decide that you are willing to "leave money on the table" for the sake of your own mental well-being.
What is unreasonable, however, is to try to use criteria such as "has the market been rising very quickly lately?" or "has the market been fluctuating a lot?" to decide whether DCA would be preferable to LSI or vice versa. The are simple reasons why these should not be useful indicators, and a quick-and-dirty experimental test seems to confirm this.
Also, there is often the feeling that lately the market has been "going crazy" or behaving in ways very different from what it used to be like. This might be true in some respects, but it does not seem to be true in all respects: in particular, the market has not been fluctuating more than it used to, and it has not been rising faster than it used to in proportion to its current prices (this can also be confirmed by looking at a log-scale plot of the evolution of the prices), and the relative advantage of LSI compared to DCA seems not to have been changing either.
So, this is it. I'm curious if someone here has comments or criticisms about this analysis (I repeat myself, there could easily be mistakes here!) I can also share the code somehow, if people are interested, but honestly it is nothing sophisticated (if you can do a little scripting, you can probably replicate it in maybe half an hour or so) and it could be more interesting to try to replicate/falsify my tentative conclusions independently.
Anyway, thanks for taking the time for this monster post!
Submitted September 25, 2021 at 08:32AM by Lyrolepis https://ift.tt/2Znel1O
