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DCA vs. Lump Sum Investing
Old 06-17-2008, 08:22 AM   #1
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DCA vs. Lump Sum Investing

OK, I haven't checked out any of the old threads, but I am sure there are many threads out there discussing how Lump Sum beats out DCA (Using S&P returns and reinvested dividends) in the long run. To me, however, this is not good enough.

Simply because in the past 50 years or so we have averaged about 8-9% a year (reinvesting dividends), it should be obvious that at the end of the year, it will cost more to buy in on average than the beginning of the year, at a greater margin than the benefits of DCA would give. This gives a quite obvious tell that Lump Sum beats out DCA in the long run, but I think there is something missing out of the DCA calculations.

The reason I am writing this is because I need to see the calculations myself. EVERY CALCULATION I HAVE SEEN has assumed 0% return on the cash waiting for the DCA. Given a pretty modest 3% on money market/CDs, I want to do my own calculation of instead of comparing 6000 at the beginning of the year to 500 in the first month, 500 + 1 month's interest second month, 500 + 2 month's interest third month, etc.

The question I have is threefold: First, I started assuming putting in $600 a year, and obviously as I started some of the data mining, it eventually became obvious that over time you would put more money in per year. I was wondering all of your thoughts on how to model that (starting at $600 a year in 1960, maybe an increase in $120 per year??). If I do not model that, then the strategy that will matter the most is simply how well you start, and I want a realistic assumption. Secondly, how far back should I do the S&P returns and the time span I should use? I supposed I could just Monte Carlo it, but would prefer to control it in Excel. I was going to do the 27 different 25 year spans from 1957-2007 (Jan. 1957- Dec.1981 all the way to Jan. 1983 - Dec. 2007), but was wondering your thoughts on it also. Finally, a point that I think won't make too much difference. When calculating dividends would it be useful to just calculate them quarterly (March, June, Sept, Dec) or monthly?

P.S. While I am at it, if anyone else has any thoughts or inquiries about the differences, I could potentially test those out as well, so let me know!
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Old 06-17-2008, 10:18 AM   #2
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Other than 401Ks, I have NEVER DCA'd my money. I figure if I have made the decision to put it as risk, I might as well put my money where my mouth is.........
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Old 06-17-2008, 10:37 AM   #3
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In the current circumstances, after taxes and inflation, your "cash" earns a negative #...

To DCA or not is an emotional decision based on your sleep at night comfort level.

DD
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Old 06-17-2008, 10:44 AM   #4
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Other than 401Ks, I have NEVER DCA'd my money. I figure if I have made the decision to put it as risk, I might as well put my money where my mouth is.........
I agree. And since the market is "up" more than it's "down" over the long haul, it makes sense to me to get in as quickly as you can.

If I needed the money back in a couple of years I might DCA just to hedge the volatility risk a little over a short time, but not because it's the best strategy return-wise.
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Old 06-17-2008, 10:50 AM   #5
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I am not suggesting one over the other in any sense, it's just that I have seen many studies / Monte Carlo simulations which (kind of obviously as I've pointed out) that Lump sum beats DCA over the long haul, simply because the market trends upwards. Without access to tweak the simulation I am just going to do my own with my own modifications, the most important of which is changing the assumptiong of 0% interest earned on your "extra" DCA money while you are waiting to put it in. In other words, in both circumstances you will have $600 or whatever at the beginning of the year, just in one case you split it into 12 $50 payments (11 of which go into the bank to earn some interest) and the other goes right in as one payment. The simulations/studies I have seen do not incorporate that, so I am trying to find an unbiased result.

EDIT: To DblDoc, that does not affect anything at all. The inflation / taxes would also mitigate the stock market returns. Also, if it is a negative real rate of return with the interest, it would be a greater negative real rate of return if you didn't have the interest, so the interest on the money would still help out the DCA a little bit.
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Old 06-17-2008, 11:10 AM   #6
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In the current circumstances, after taxes and inflation, your "cash" earns a negative #...
In what time frame??
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Old 06-17-2008, 12:16 PM   #7
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there is an often overlooked virtue to DCA: you can put it on auto pilot. if you lump sum, you might be tempted to market time ...
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Old 06-17-2008, 12:28 PM   #8
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I am big into DRIPS so I DCA every month. I have 5 DRIPS with $100 a month going into each. Slow and steady wins the race!
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Old 06-17-2008, 12:33 PM   #9
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I am big into DRIPS so I DCA every month. I have 5 DRIPS with $100 a month going into each. Slow and steady wins the race!
Lump sum is slow and steady also (just do it once a year) and what you say above "Slow and steady wins the race!" is what I am setting out to test/prove.
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Old 06-17-2008, 02:26 PM   #10
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My only question is this... most of us have to DCA. I don't have yearly windfalls coming in, I have twice-a-month paychecks. So, 401(k) and taxables are funded on the 1st and 15th because that's when I have money, not when I want to DCA.

Since most of the time we won't have regular windfalls (I do have a bonus yearly but that's so variable as to be not worth modeling... guessing many other bonuses are similar, they always have been for me), then it seems either the exercise is academic or it should be modeled such that:

Year 0: DCA $600/month starting in January. Lump sum $0. (lump sum account collects DCA amount of $600/month plus interest)

Year 1: DCA $600/month+COLA. Lump sum $7200 in January.

Otherwise, it seems like it's just an exercise around if one should DCA or lump sum a windfall and proving that would be highly subject to data mining and more of a blue-moon event (unless you have a cadre of elderly family lined up with substantially equal estates coming to you and they're all terminal but 1 year apart). I'm sure I'm missing something though.
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Old 06-17-2008, 03:17 PM   #11
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Right. If you don't have a lump sum, then DCAing is a good way to build wealth. If you have a lump sum, then there's no need or reason to DCA it.
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Old 06-17-2008, 04:08 PM   #12
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In what time frame??

Until rates once again exceed our current rate of inflation (whatever that is ) + marginal tax rate. I see in another thread that the Fed may not be so anxious to raise rates again in the near term so we may be waiting awhile. Other then that my crystal ball just shows this big burning eye thing.

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Old 06-17-2008, 04:11 PM   #13
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Just to clarify. DCA is something you do with a lump sum. Periodic investing is what you do with your monthly or bimonthly pay check.

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Old 06-17-2008, 04:12 PM   #14
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I am not suggesting one over the other in any sense, it's just that I have seen many studies / Monte Carlo simulations which (kind of obviously as I've pointed out) that Lump sum beats DCA over the long haul, simply because the market trends upwards. Without access to tweak the simulation I am just going to do my own with my own modifications, the most important of which is changing the assumptiong of 0% interest earned on your "extra" DCA money while you are waiting to put it in. In other words, in both circumstances you will have $600 or whatever at the beginning of the year, just in one case you split it into 12 $50 payments (11 of which go into the bank to earn some interest) and the other goes right in as one payment. The simulations/studies I have seen do not incorporate that, so I am trying to find an unbiased result.

EDIT: To DblDoc, that does not affect anything at all. The inflation / taxes would also mitigate the stock market returns. Also, if it is a negative real rate of return with the interest, it would be a greater negative real rate of return if you didn't have the interest, so the interest on the money would still help out the DCA a little bit.
True but 1) you have control over when to take the tax hit and 2) for most of us the capital gains tax is lower then our marginal rate.

DD
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Old 06-18-2008, 09:43 AM   #15
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How many chances will you have to invest a similar lump sum? If this is something that that you will have several shots at, you will have a better chance at the average positive result. If it is a once in a lifetime thing, it'll be a crapshoot, and you can't really model that.

If you DCA into the market over the course of a few weeks you might have a small advantage of averaging out the day-to-day variations, which can be pretty large these days. And you won't lose too much to the average market rise.
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Old 06-18-2008, 09:43 AM   #16
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To Marquette's implication, yes this is mostly an academic exercise. I am trying to figure out if lump sum still beats DCA on average with the interest on the DCA purchases thrown in.

I also like your suggestion on indexing the deposits to inflation, is there a website I can have the historical rates of inflation (any respected inflation metric will do) from 1871 to the present? I am going to study the results after 10 year periods from 1871-2007... all 128 of them!

Edit: to Animorph, it is more of an academic study, but it will be ten straight years of lump sum vs. monthly DCA.
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Old 06-18-2008, 10:22 AM   #17
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Just to clarify. DCA is something you do with a lump sum. Periodic investing is what you do with your monthly or bimonthly pay check.

DD
Thanks for the clarification DD.

I'll be interested in the results of this for sure. I'd imagine that lump sum investing is most painful if you pick the 'wrong' day to invest it all but, academically, I can see how that bet pays off in most cases versus DCA.
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Old 06-20-2008, 08:32 AM   #18
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Alright, for anyone interested, I was a little surprised with the results. Considering the long term trend of the stock market upwards, I still expected a little better showing from DCA in my example. For the 99 10-year periods from 1900-2007, however, Dollar Cost Averaging only won 24 times. Of the last THIRTY 10 year spans using my metrics, Lump sum won every time EXCEPT ONE, which happened to be 1998-2007, the most recent one heh.

Just a recap:
Put in 600 a year (50 a month for DCA) on January of the first year and then an extra 120 on top of the 600 per year. Thus, I put in 600, then 720, then 840, then you get the idea. If you add up those 10 deposits, I put in a total of $11,400 over 10 years. For the DCA, I assumed the money was put into 3% CDs which expire at the end of every month. Dividends were calculated quarterly and reinvested. No tax considerations were taken.


Dollar Cost Averaging:
Count: 99
Average: $18,561.65
Standard Deviation: $5,180.35
Range: $8,172.40 - $32,877

Lump Sum:
Count: 99
Average: $19,061.47
Standard Deviation: $5,704.17
Range: $7,882.20 - $34,191


Some considerations:
The model seems to follow the long term trend that greater risk (higher STDev) leads to a greater return over the long run, as you can see that
Lump Sum has a greater range, STDev and return. The biggest things I noticed was that the dividend reinvestment added up substantially for the lump sum. Since they had a full year's worth of purchases for all four dividends in a year, dollar cost averaging had 3 months of purchases in for one, 6 months of purchases in for one, 9 months of purchases in for one, and only one with a full year's worth of purchases. This dividend reinvestment almost acted like a form of dollar cost averaging for the Lump Sum as it bought shares immediately.

Dividends were a surprising major factor in Lump Sum winning, but an unsurprising result is that during the huge gain years, the Lump Sum would do better as it would put in all the money when the shares were the cheapest (at the beginning of the year) and then gain the most on them. As stock market returns are very slightly negatively correlated to yield, I feel that during times of high yield, Lump Sum could win/compete and during times of low yield, Lump Sum would destroy DCA, so it could do well in most conditions (with a 10-year timespan).

Problems/Room for improvement of study:
-I used 10 year samples for the stock market, and there is a lot less deviation in returns over a ten year span as opposed to a 7-year, 5-year, 3-year or even 1-year span. I feel that if smaller spans were used, the benefits of Dollar Cost Averaging would be more pronounced compared to the compound interest on dividends of the Lump Sum.
-Tax considerations were not taken into consideration, but I feel that it would affect both similarly. The 3% interest on the money invested for the DCA would have to be taxed, but also the advantage in dividends for the lump sum would also be taxed. It would certainly have some effect on the results, but I feel it would not change the comparative results to much.
- I also assumed that the Lump Sum purchase would take place at the beginning of the year. Even though I have not run the numbers, but yearly returns could be very different for Lump Sum purchases if they started in January, February, March, etc. and there could be great variance of results in the Lump Sum returns.

All in all, if you are using a long timeframe, the study reverts back to the old risk/return argument which suffices to show Lump Sum beats out DCA over the long run. In shorter terms, however, it depends on most people's risk tolerance. Also, it is a lot more difficult to procure all that money at the beginning of every year but dare to dream .
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Old 06-20-2008, 08:46 AM   #19
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assuming 3% return for CD's during for 1900 - 2007 is pretty far off for some of those 10 year spans.

DCA of a lump sum is usually done over a much shorter period (more like 1 year).

You might try using a separate column to hold a closer estimate of safe returns for each year of data. Also, get the entire amount DCA'd in over a shorter period (1 to 3 years).
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Old 06-20-2008, 08:47 AM   #20
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3% is definitely inaccurate for many, many years in the timeframe, but used it for simplicity's sake, should put that in something that could have been improved. Also, the DCA versus Lump Sum that I was comparing was if for every year you planned on DCA or Lump sum, not just one lottery win or whatever.
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