Vanguard Lump Sum vs DCA study

[livesoft]

Carolyn T. Geer writes in the WSJ about a Vanguard study: http://online.wsj.com/article/SB1000087 ... 44512.html
The reported results are consistent with previous studies that I have read. Does anybody have a link to the Vanguard report that she writes about? I imagine that we will be citing it whenever anyone asks the question.

[ObliviousInvestor]

I believe this is it: https://pressroom.vanguard.com/nonindex ... raging.pdf

[livesoft]

Thanks, that's the study. The results are that LS is better than DCA about two-thirds of the time and "better" is not really much better. The difference is about the same amount as charged by a financial advisor for just one year.

In other words, the cost to do the non-optimal thing and DCA is actually quite small.

[livesoft]

And a link to a commentary by Larry Swedroe on a similar study:
http://www.cbsnews.com/8301-505123_162- ... er-results

The authors even took a look at how the two strategies performed during the 10-year period 2001-2010. For the 109 rolling 12-month periods, lump-sum investing outperformed in 70 (64 percent). The average outperformance was 1.3 percent.

I wonder what the amount of underperformance in the 36% of cases where LS underperformed DCA was? If the average underperformance was more than 1.3 percent, say 3 percent, would that not be interesting?

( The lengthy Boglehead thread on the subject requesting a ban of LS vs DCA threads is here: http://www.bogleheads.org/forum/viewtopic.php?t=83767 )

[rustymutt]

I personally believe that this issue resolves down to the conditions of the financial markets at the time of consideration.
For example, if you'd lumped sum into the markets in March of 2009, you'd be way ahead after 3 years of steady growth of capital markets. On the other hand, if you'd held back and DCA in, you'd be behind. So in a sense, timing of this method makes a huge difference, and can flip the returns either way.

If I was a young worker, I'd be DCA into the markets every pay day. Most of us don't start out with huge amounts of capital to do something with.

[livesoft]

If I was a young worker, I'd be DCA into the markets every pay day. Most of us don't start out with huge amounts of capital to do something with.

This comment is specifically acknowledged and addressed on the top of page 4 of the Vanguard report.

[stan1]

Fine to talk in generalities and in third person.

If you personally received a $1M inheritance in January, 2007 or September, 2000 -- would you have lump sum invested it using a 60-70% equity asset allocation? Assume you were under 50 and had under $1M in net worth (e.g. weren't already "wealthy" by any definition)

[iceport]

( The lengthy Boglehead thread on the subject requesting a ban of LS vs DCA threads is here: http://www.bogleheads.org/forum/viewtopic.php?t=83767 )

Actually, perhaps a more enlightening (and certainly less time-consuming) thread is this one:

lump sum and dollar cost averaging.

If nothing else, it's fantastic to get the perspective of Dr. William Bernstein in his 7 contributions to the thread. His first post provides a link to a most interesting article from his Efficient Frontier site.

(There are also many contributions from bob90245 a couple of months before he stopped posting here.)

--Pete

[nisiprius]

The Vanguard study is interesting, but seems to me to miss an important step in the analysis. I have always believed the lump-sum versus DCA debate is basically a risk/reward debate. Really, isn't it obvious?

It seems intuitively obvious that lump-summing would have higher return (because of longer average time in the market).

It also seems intuitively obvious that lump-summing would have higher "variability of results"/"dispersion of outcomes"/"risk," because you are staking everything on a sample size of one moment in the market, instead of averaging across many moments.

The study confirms these intuitions.

The study, to its credit, at least goes on to address the question of risk-adjusted reward, and finds higher Sharpe ratios for lump-summing. That's genuine support for lump-summing as being of more than psychological benefit. The effect is (dare I say "of course?) small.

But here's my point. Although the increased reward may more than make up for the increased risk, the increased risk is substantial, as shown by their figure 3. On a $1,000,000 investment, in the range shown by their table, you could quite conceivably end up with $200,000 less (OR $300,000 more) by lump-summing. That's a meaningful difference, and a sane person might decide that's more risk than they would care to take.

What they should have done, and I don't for the life of me understand why so few studies ever do this, is to equalize the risk between the investments being compared by adjusting their stock/bond allocation. They should have given some kind of formula for equalizing that risk. For example, they should have said, "if you want to arrive at a 60/40 portfolio, then you should either DCA with 60/40 purchases, or you should lump-sum with less than 60% stocks. If their Sharpe ratio calculations apply in the way we all expect, lump-summing should still win, but we would have a direct apples-to-apples comparison.

A Sharpe ratio of 0.81 versus 0.72? I'm not interested in debating points, and I can't spend a Sharpe ratio. Please, how much is that in dollars? (Or pounds, or Australian dollars?)

Now, I suppose if I were not lazy I could figure out a way to calculate dollars from Sharpe ratios, but I don't want to, because due to the nonlinear way assets combine it just seems more proper to me to actually present two actual portfolios, with the stocks and bonds interacting however they interact, that have the same dispersion of outcomes, and compare the returns.

I am very tired of reports that ask us to decide which is better between two courses of that have different returns and different dispersions of outcome.

[epilnk]

Fine to talk in generalities and in third person.

If you personally received a $1M inheritance in January, 2007 or September, 2000 -- would you have lump sum invested it using a 60-70% equity asset allocation? Assume you were under 50 and had under $1M in net worth (e.g. weren't already "wealthy" by any definition)

Why Jan 2007 or Sept 2000? Should we have known those were or were not times to lump sum? I don't recall having any info one way or another back then. I don't have any info now, either.

I personally match your hypothetical situation fairly well, though not at either of your proposed times. I lump sum invested about 2/3rds of it immediately. The other third I held back in a MM account on principle; the money was a major change to our financial situation so I thought it wiser to let some time pass to rethink the plan and goals. So that final third got more gradually released - not as a DCA, but as decisions were made about the mortgage, 529s, REITs, bonds in taxable, need vs ability to take risk, etc.

[livesoft]

....
But here's my point. Although the increased reward may more than make up for the increased risk, the increased risk is substantial, as shown by their figure 3. On a $1,000,000 investment, in the range shown by their table, you could quite conceivably end up with $200,000 less (OR $300,000 more) by lump-summing. That's a meaningful difference, and a sane person might decide that's more risk than they would care to take.

This is interesting to me in the context of some behavorial finance academician reports on loss aversion. I have seen reported that a chance of losing X dollars needs to be offset by a chance of gaining 2X dollars for many people. So a chance of being $300K ahead does not offset the chance of losing $200K.

Also since the average advantage of LS is no more than 2%, I wonder if one should spend 2% of a windfall on some kind of option to protect against some chance of loss? Or maybe 0.5% or 1% of the windfall?

And like epilnk wrote, many (including myself) advocate invest an amount (half, 2/3rds) now in a LS and then DCA the rest over a time frame of less than a year. (Isn't investing 2/3rds now in LS very Bayesian?). If the market drops during the DCA period, then accelerate the DCA schedule. Are there any studies of this kind of scheduling?

[epilnk]

What they should have done, and I don't for the life of me understand why so few studies ever do this, is to equalize the risk between the investments being compared by adjusting their stock/bond allocation. They should have given some kind of formula for equalizing that risk. For example, they should have said, "if you want to arrive at a 60/40 portfolio, then you should either DCA with 60/40 purchases, or you should lump-sum with less than 60% stocks. If their Sharpe ratio calculations apply in the way we all expect, lump-summing should still win, but we would have a direct apples-to-apples comparison.

I am very tired of reports that ask us to decide which is better between two courses of that have different returns and different dispersions of outcome.

I agree that a comparison that normalizes risk would be infinitely superior and much more informative. I would also argue that in the windfall case it is more important to focus on limiting downside risk. Most prudent investors would approach a sudden (and perhaps surprise) jump in their net worth with the mindset of "first, don't do anything stupid". It is one of my pet peeves that "risk of underperforming the market" and "risk of losing money" are tossed about almost interchangeably in investment discussions; those risks have extremely different behavioral outcomes.

Although I didn't do any math to work it out, I intuitively ended up doing something very similar to what you recommend. The initial lump sum was allocated much more conservatively than our normal AA, and gradually adjusted back up to where we wanted to be.

[iceport]

Some interesting points:

All of the academic research on LS vs DCA, including this one on my site by Bill Jones:

http://www.efficientfrontier.com/ef/997/dca.htm

does show that LS dominates most of the time. That's because nearly all of this work is predicated on the post-1926 Ibbotson/CRSP database, which reflects a very high equity risk premium. In a world with low equity returns, by contrast, you're almost always better off DCA/VA'ing.

For example, the person who DCA'd/value averaged over five years from 2003 to 2007 was sorry. The person who did so from 2006 to 2010 was glad to have done so.

The real question is what the long-run expected equity risk premium will be going forward. I don't think it's going to be as high as it was between 1926 and 2012.

Best,

Bill

No, you're missing a key component to the equation, which is volatility.

DCA and VA produce a returns advantage because with high volatility, the geometric advantage of buying shares very low more than outweighs the disadvantage of buying high.

In other words, it's not enough that the equity premium is always positive (which, in the long run, it should be) and therefore LS should always dominate. That is simply not true; given a high enough volatility of returns, any ERP can be overcome to produce an advantage for DCA/VA.

Rather, the question is the interaction between the volatility and ERP, and that's something that can't be solved with simple heuristic arguments; you actually have to do the math for each individual case.

Bill

--Pete

[pkcrafter]

I'm not sure now much DCA actually reduces market risk.

If you personally received a $1M inheritance in January, 2007 or September, 2000 -- would you have lump sum invested it using a 60-70% equity asset allocation? Assume you were under 50 and had under $1M in net worth (e.g. weren't already "wealthy" by any definition)

What if you dollar cost averaged for a year beginning January, 2006 or September, 1999?

Paul

[Default User BR]

As I have mentioned in the past, I got serious about investing, realigned my portfolio by moving out of bonds and cash (100k from the sidelines) to a 70/30 allocation -- in summer of 2007. That being said, I still believe in lump-sum. So to the question above, yes if presented with a large sum to invest I would do LS. I might well adjust my asset allocation to a somewhat more conservative approach based on the totals, but that has nothing to do with LS/DCA.


Brian

[Aptenodytes]

I have a kind of similar approach to Nisi, but not identical.

1) The fact that all the studies seem to focus on which approach has the highest expected return is silly, I agree. We don't need studies to tell us the answer. If we weren't sure about this question, we wouldn't be buy, hold, rebalance investors. It is a bit like doing the labs in intro physics class where you "discover" that the Earth's gravitational force is 9.8 meters/sec/sec. The exercise might be useful pedagogically, but nobody has any doubt ahead of time regarding the answer.

2) To me, there are only two questions that matter:

a) After the windfall, what is the best way to adjust your AA? I see very little discussion of this, but it seems to be overwhelmingly important. In some cases, nothing will change; in other cases the investor will be thrust into an entirely different situation. The most important question facing the investor presented with a significant new infusion of resources, is "How should I now adjust my AA?" Am I in a position to take on less risk? If so, how much less?

b) Once the target AA has been determined (whether changed or not), then the only other question is this one: "Taking into account the relevant psychological factors at work, what pathway gets me in the market as quickly as practical without incurring too much anxiety?" This question is entirely behavioral, because as we seem to all agree, we all know the financially/mathematically optimal path. But people aren't machines, and they are all different. Therefore what matters is not what a machine would do, but what is going to work for a specific person. For some it is going to be all-in; for others something like Livesoft's half-in, half DCA. Others will need to reserve the whole amount and DCA in more gradually. The goal for everyone is the same -- getting the right balance of high speed and low anxiety.

[iceport]

This question is entirely behavioral, because as we seem to all agree, we all know the financially/mathematically optimal path.

Dr. William Bernstein, it seems, disagrees with you on this.

(That's not so easy to disregard.)

--Pete

[Dale_G]

snip

This is interesting to me in the context of some behavorial finance academician reports on loss aversion. I have seen reported that a chance of losing X dollars needs to be offset by a chance of gaining 2X dollars for many people. So a chance of being $300K ahead does not offset the chance of losing $200K.

Also since the average advantage of LS is no more than 2%, I wonder if one should spend 2% of a windfall on some kind of option to protect against some chance of loss? Or maybe 0.5% or 1% of the windfall?

And like epilnk wrote, many (including myself) advocate invest an amount (half, 2/3rds) now in a LS and then DCA the rest over a time frame of less than a year. (Isn't investing 2/3rds now in LS very Bayesian?). If the market drops during the DCA period, then accelerate the DCA schedule. Are there any studies of this kind of scheduling?

my bold

Except that it may be "found money", I see no difference between an investor lump summing a million dollars into the market and an investor who already has a million dollars invested in the market. Both face the same probability of gain or loss.

I'm sure livesoft is not suggesting a permanent hedge, but the gains or losses can occur at any time. If a permanent hedge doesn't make financial sense, then a hedge on an initial investment doesn't either

Dale

[Ketawa]

Some interesting points:

All of the academic research on LS vs DCA, including this one on my site by Bill Jones:

http://www.efficientfrontier.com/ef/997/dca.htm

does show that LS dominates most of the time. That's because nearly all of this work is predicated on the post-1926 Ibbotson/CRSP database, which reflects a very high equity risk premium. In a world with low equity returns, by contrast, you're almost always better off DCA/VA'ing.

For example, the person who DCA'd/value averaged over five years from 2003 to 2007 was sorry. The person who did so from 2006 to 2010 was glad to have done so.

The real question is what the long-run expected equity risk premium will be going forward. I don't think it's going to be as high as it was between 1926 and 2012.

Best,

Bill

No, you're missing a key component to the equation, which is volatility.

DCA and VA produce a returns advantage because with high volatility, the geometric advantage of buying shares very low more than outweighs the disadvantage of buying high.

In other words, it's not enough that the equity premium is always positive (which, in the long run, it should be) and therefore LS should always dominate. That is simply not true; given a high enough volatility of returns, any ERP can be overcome to produce an advantage for DCA/VA.

Rather, the question is the interaction between the volatility and ERP, and that's something that can't be solved with simple heuristic arguments; you actually have to do the math for each individual case.

Bill

--Pete

I'm still not convinced by Dr. Bernstein's arguments in favor of DCA or VA. When he says "you actually have to do the math for each individual case", he is still looking backwards at the past. There is no way to know what volatility will be ex ante, otherwise you could successfully time the market.

[nisiprius]

Well, let me suggest this. I see almost no reason at all to put everything in as a single lump sum on a single day, as opposed to putting 1/4 of it in as four successive purchases spaced a week apart. The stock market definitely can jink around about one percent or more, day to day, even under normal circumstances. By spacing the purchases a week apart you can cut your standard deviation in half, and the cost of losing an average of a couple of weeks in the market, at, say, an assumed 10% per year return (ah, remember the days when we always assumed 10% per year returns?), isn't very high.

A meaningful reduction in "risk" at a low cost.

[Aptenodytes]

This question is entirely behavioral, because as we seem to all agree, we all know the financially/mathematically optimal path.

Dr. William Bernstein, it seems, disagrees with you on this.

(That's not so easy to disregard.)

--Pete

Bernstein is a proponent of Value Averaging, which as I understand it is counter to Boglehead principles. It is a form of market timing. Once you unmoor yourself from the Boglehead principles, anything is possible -- I will grant that readily. I've read a few of Bernstein's posts here and I have to say I find the approach unworkable in practice.

[Aptenodytes]

Well, let me suggest this. I see almost no reason at all to put everything in as a single lump sum on a single day, as opposed to putting 1/4 of it in as four successive purchases spaced a week apart. The stock market definitely can jink around about one percent or more, day to day, even under normal circumstances. By spacing the purchases a week apart you can cut your standard deviation in half, and the cost of losing an average of a couple of weeks in the market, at, say, an assumed 10% per year return (ah, remember the days when we always assumed 10% per year returns?), isn't very high.

A meaningful reduction in "risk" at a low cost.

This would be, in the terms of my earlier post here, a behavioral trick to facilitate getting quickly into the market. It can't possibly make sense on financial grounds alone. The reason is that it is unstable. If this approach made financial sense, then once you are in the market you would need to start over again, and pull the original windfall back out and start all over again. Because once you are fully invested you are in exactly the situation you feared when you contemplated going all-in. And something like Zeno's paradox sets in where you end up chasing your tail moving money in and out.

Whatever risks you are worried about that would hit your lump-sum-invested windfall, those same exact risks are facing the rest of your portfolio. So if it makes financial sense to protect your windfall by keeping it out of the market, it has to make sense to do the same to the rest of your portfolio.

Avoiding these cycles of contradiction and confusion is why I think it makes sense to separate the what-to-do-with-my-windfall question into two parts: (1) how should I change my AA? This is a question that has a coherent answer grounded strongly in finance, as well as your own attitudes and desires. The answer you get would be stable -- not flitting around endlessly day to day; and (2) how can I get in to the AA in a manner that balances the expected benefits from speed and the comfort from going slowly? This is a behavioral question -- each of us has to determine what works for us.

It seems to me that efforts to solve the 2nd question by searching for empirical proof are misguided -- they are category mistakes. And they distract attention from the 1st question, which seems to get far less attention that it should.

[iceport]

This question is entirely behavioral, because as we seem to all agree, we all know the financially/mathematically optimal path.

Dr. William Bernstein, it seems, disagrees with you on this.

(That's not so easy to disregard.)

--Pete

Bernstein is a proponent of Value Averaging, which as I understand it is counter to Boglehead principles. It is a form of market timing. Once you unmoor yourself from the Boglehead principles, anything is possible -- I will grant that readily. I've read a few of Bernstein's posts here and I have to say I find the approach unworkable in practice.

Aptenodytes,

Whether Dr. Bernstein is a proponent of VA or not is irrelevant. Bernstein's comments address both DCA and VA. So there's no need to introduce VA into the discussion, if you believe it's a form of market timing, it's unworkable, or counter to Boglehead principles.

Please consider his insights in reference to DCA.

His two main points, as I read them, are: 1) the size of the ERP is a key factor in determining which method, DCA or LS, will be better; and 2) another key factor is volatility. Some combinations of ERP and volatility favor DCA over LS. A third point is that Bernstein believes (as most experts agree) that the ERP will be lower going forward than the average over the 1926 to 2012 period.

(As an aside, I can find no part of VA that is inherently counter to Boglehead principles, or remotely similar to market timing -- unless rebalancing is also a form of market timing. It seems troublesome enough, though, that I have not attempted it.)

--Pete

[financenoob]

I haven't read through all the articles yet, but I think looking at lump sum over all data points isn't really a reasonable way to do it.

I'd be more interested to see LS vs DCA for times when:
(a) the market is at at 52 week high
(b) the market is at a 5 year high

etc...

I suspect that while the overall difference won't be THAT big, I don't think anyone can argue that making a huge investment at the present peak of market is obviously less optimal than investing on a dip. The problem, of course, is not knowing when the dip will come.

[Aptenodytes]

[quote="financenoob"]I haven't read through all the articles yet, but I think looking at lump sum over all data points isn't really a reasonable way to do it.

I'd be more interested to see LS vs DCA for times when:
(a) the market is at at 52 week high
(b) the market is at a 5 year high
[/quote
The temptation to do this is understandable. but notice that the logic applies equally to the money in your portfolio already. if you wanted to play those games you probably would not be hanging out here. That is why i think focusing on the aa is more productive than the timing.

[iceport]

I haven't read through all the articles yet, but I think looking at lump sum over all data points isn't really a reasonable way to do it.

I'd be more interested to see LS vs DCA for times when:
(a) the market is at at 52 week high
(b) the market is at a 5 year high

The temptation to do this is understandable. but notice that the logic applies equally to the money in your portfolio already. if you wanted to play those games you probably would not be hanging out here. That is why i think focusing on the aa is more productive than the timing.

Given Dr. Bernstein's comments elsewhere, that valuations matter in assessing the merit of DCA relative to LS, this is an interesting question. (Not to mention that we're in a thread started by the creator of the RBD® technique for timing purchases!)

As for the money already invested, rebalancing is the only reasonable response to inflated equity valuations, not wholesale liquidation and re-purchase. There is, after all, a difference between the risk of purchasing at an inopportune time, and the risk of purchasing at an inopportune time combined with the risk of selling at an inopportune time. Anyone worried about the former would be foolish to purposefully create the latter.

--Pete

[Aptenodytes]

... notice that the logic applies equally to the money in your portfolio already. if you wanted to play those games you probably would not be hanging out here. That is why i think focusing on the aa is more productive than the timing.

Given Dr. Bernstein's comments elsewhere, that valuations matter in assessing the merit of DCA relative to LS, this is an interesting question. (Not to mention that we're in a thread started by the creator of the RBD® technique for timing purchases!)

As for the money already invested, rebalancing is the only reasonable response to inflated equity valuations, not wholesale liquidation and re-purchase. There is, after all, a difference between the risk of purchasing at an inopportune time, and the risk of purchasing at an inopportune time combined with the risk of selling at an inopportune time. Anyone worried about the former would be foolish to purposefully create the latter.

--Pete

Your feelings are understandable, but note that they are feelings, which is what makes the timing question a behavioral one. Financially, pathway A, in which you receive a lump sum and move it in to your portfolio gradually, is absolutely identical to pathway B, in which you remove a lump sum from your portfolio and then move it back in gradually, assuming equal sums and tax-advantaged status. When many people think A is smart but B is dumb, they are expressing their emotions. Basic arithmetic makes them equal in financial terms.

These differences in how we feel about lump sums are a function of some well-understood psychological truths, which are just as valid as mathematics. Ignoring them makes no more sense than ignoring math.

For me, if I were lucky enough to receive a lump sum, I would put all my effort into thinking through the implications for my AA; I would not worry so much about the timing question. The AA question has a mixture of objective and subjective implications. The timing question is purely subjective.

[Tom_T]

Financially, pathway A, in which you receive a lump sum and move it in to your portfolio gradually, is absolutely identical to pathway B, in which you remove a lump sum from your portfolio and then move it back in gradually, assuming equal sums and tax-advantaged status.

I'm not sure I understand this.

A. I move my lump sum into the market today, with the Dow at 13K (as a benchmark for argument's sake.)
B. I remove my lump sum from the market. The Dow drops under 10K for a year or so. I move my lump sum back in gradually, at lower prices.

If the Dow then recovers, don't I have a lot more money with (B) than I would have with (A)? I certainly have more shares.

(I'm not arguing for market timing, mind you.)

[iceport]

Bernstein's assessment has nothing whatsoever to do with feelings. Period. If you don't want to address them, fine, but don't lump them in with a behavioral argument.

--Pete

[Aptenodytes]

Financially, pathway A, in which you receive a lump sum and move it in to your portfolio gradually, is absolutely identical to pathway B, in which you remove a lump sum from your portfolio and then move it back in gradually, assuming equal sums and tax-advantaged status.

I'm not sure I understand this.

A. I move my lump sum into the market today, with the Dow at 13K (as a benchmark for argument's sake.)
B. I remove my lump sum from the market. The Dow drops under 10K for a year or so. I move my lump sum back in gradually, at lower prices.

If the Dow then recovers, don't I have a lot more money with (B) than I would have with (A)? I certainly have more shares.

(I'm not arguing for market timing, mind you.)

Your two scenarios are not the same so the bottom lines are different. You didn't move the first lump sum in gradually. Here are two drastically oversimplified scenarios that are identical to make the point.

A) Day 0, you have a $90,000 portfolio.
Day 1, you receive $10,000 lump sum windfall. You keep it out of your $90,000 portfolio initially.
Day 30, you move in $5,000; portfolio is up 1% for the month. You have $5,000 out and $95,900 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982,

B) Day 0, you have a $100,000 portfolio.
Day 1, you remove $10,000. You have $10,000 out and $90,000 in.
Day 30, you move $5,000 back in; portfolio is up 1% for the month. You have $5,000 out and $95,900 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982.

Scenario A is what many people find acceptable, and scenario B everyone says is stupid. Financially they are the same. Ergo, the difference is behavioral. The properties of arithmetic will make the sums equal no matter what happens to the market. The properties of psychology will make most people anxious about what to do with the lump sum.

[Aptenodytes]

Bernstein's assessment has nothing whatsoever to do with feelings. Period. If you don't want to address them, fine, but don't lump them in with a behavioral argument.

--Pete

I realize that. I was referring to the view that removing money from a tax-advantaged portfolio is different than keeping money out -- as far as I know Bernstein didn't argue that.

[iceport]

Here are two drastically oversimplified scenarios that are identical to make the point.

A) Day 0, you have a $90,000 portfolio.
Day 1, you receive $10,000 lump sum windfall. You keep it out of your $90,000 portfolio initially.
Day 30, you move in $5,000; portfolio is up 1% for the month. You have $5,000 out and $95,900 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982,

B) Day 0, you have a $100,000 portfolio.
Day 1, you remove $10,000. You have $10,000 out and $90,000 in.
Day 30, you move $5,000 back in; portfolio is up 1% for the month. You have $5,000 out and $95,900 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982.

Scenario A is what many people find acceptable, and scenario B everyone says is stupid. Financially they are the same. Ergo, the difference is behavioral. The properties of arithmetic will make the sums equal no matter what happens to the market. The properties of psychology will make most people anxious about what to do with the lump sum.

This ignores market volatility. What if, using your own example, there was a 5% drop in prices on Day 1 that was recovered within a week?

There is, after all, a difference between the risk of purchasing at an inopportune time, and the risk of purchasing at an inopportune time combined with the risk of selling at an inopportune time.

The risks are real, with very real consequences for your portfolio.

--Pete

EDIT: Of course, the case of a 5% drop on Day 1 would certainly qualify as an RBD®, so I suppose we all know what livesoft would do...

[Tom_T]

A. My portfolio is zero. I receive a windfall of $100K. I invest it all today. Let's assume that I am buying a mythical "Dow stock" whose share price is the Dow index. $100K/13000 = 7.69 shares. That's what I own.

B. My portfolio is zero. I receive a windfall of $100K. I do nothing. Dow drops to 10K. I decide to invest half, so that's $50K/10000 = 5 shares. Dow drops another 1K, I invest the other $50K. $50K/90000 = 5.55 shares. I now own 10.55 shares.

If the Dow then returns to 13K, under (A), my portfolio is worth $100K. No change. Under (B), however, my portfolio is worth $137,150, since I bought in at much lower prices.

Alternatively, if I wait, and the market goes up, I am then faced with the choice of buying in under higher prices. I would have been better off not waiting. But there's no way to know in advance.

[iceport]

Tom_T,

The argument in favor of LS over DCA is that because the market tends to rise over time, the odds are better that a LS will come out ahead. Clearly, that doesn't always happen, as your example illustrates, but it's more likely. So people advocate relying solely on expected outcomes, not on possible negative outcomes.

(Notice how different that advice becomes when we consider essentially the same choice with respect to asset allocation.)

--Pete

[Tom_T]

Tom_T,

The argument in favor of LS over DCA is that because the market tends to rise over time, the odds are better that a LS will come out ahead. Clearly, that doesn't always happen, as your example illustrates, but it's more likely. So people advocate relying solely on expected outcomes, not on possible negative outcomes.

(Notice how different that advice becomes when we consider essentially the same choice with respect to asset allocation.)

--Pete

Agreed. I was just using an example. Market timing can be stressful and headache-inducing ("should I buy? sell? Is this a good time? Bad time?").

[tadamsmar]

The Vanguard study is interesting, but seems to me to miss an important step in the analysis. I have always believed the lump-sum versus DCA debate is basically a risk/reward debate. Really, isn't it obvious?

It seems intuitively obvious that lump-summing would have higher return (because of longer average time in the market).

It also seems intuitively obvious that lump-summing would have higher "variability of results"/"dispersion of outcomes"/"risk," because you are staking everything on a sample size of one moment in the market, instead of averaging across many moments.

The study confirms these intuitions.

The study, to its credit, at least goes on to address the question of risk-adjusted reward, and finds higher Sharpe ratios for lump-summing. That's genuine support for lump-summing as being of more than psychological benefit. The effect is (dare I say "of course?) small.

But here's my point. Although the increased reward may more than make up for the increased risk, the increased risk is substantial, as shown by their figure 3. On a $1,000,000 investment, in the range shown by their table, you could quite conceivably end up with $200,000 less (OR $300,000 more) by lump-summing. That's a meaningful difference, and a sane person might decide that's more risk than they would care to take.

What they should have done, and I don't for the life of me understand why so few studies ever do this, is to equalize the risk between the investments being compared by adjusting their stock/bond allocation. They should have given some kind of formula for equalizing that risk. For example, they should have said, "if you want to arrive at a 60/40 portfolio, then you should either DCA with 60/40 purchases, or you should lump-sum with less than 60% stocks. If their Sharpe ratio calculations apply in the way we all expect, lump-summing should still win, but we would have a direct apples-to-apples comparison.

A Sharpe ratio of 0.81 versus 0.72? I'm not interested in debating points, and I can't spend a Sharpe ratio. Please, how much is that in dollars? (Or pounds, or Australian dollars?)

Now, I suppose if I were not lazy I could figure out a way to calculate dollars from Sharpe ratios, but I don't want to, because due to the nonlinear way assets combine it just seems more proper to me to actually present two actual portfolios, with the stocks and bonds interacting however they interact, that have the same dispersion of outcomes, and compare the returns.

I am very tired of reports that ask us to decide which is better between two courses of that have different returns and different dispersions of outcome.

So, suppose you had clear proof that the risk is not worth the reward.

And, suppose some of your nest egg can be removed from the market right now and DCAed back in with no cost to you.

Would your remove said funds and DCA them back in?

This was discussed in a paper mentioned in that long thread posted earlier. This killed DCA as far as the peer-reviewed literature is concerned. Has not been a paper since (for decades) that treated LS/DCA as anything but behavioral.

I agree that the difference in DCA vs LS is too small to worry about. Another issue is that it may net benefit a financial advisor to advise DCA for a windfall in spite of the lower Sharpe Ratio because of the behavioral issues.

[Aptenodytes]

Here are two drastically oversimplified scenarios that are identical to make the point.

A) Day 0, you have a $90,000 portfolio.
Day 1, you receive $10,000 lump sum windfall. You keep it out of your $90,000 portfolio initially.
Day 30, you move in $5,000; portfolio is up 1% for the month. You have $5,000 out and $95,900 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982,

B) Day 0, you have a $100,000 portfolio.
Day 1, you remove $10,000. You have $10,000 out and $90,000 in.
Day 30, you move $5,000 back in; portfolio is up 1% for the month. You have $5,000 out and $95,900 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982.

Scenario A is what many people find acceptable, and scenario B everyone says is stupid. Financially they are the same. Ergo, the difference is behavioral. The properties of arithmetic will make the sums equal no matter what happens to the market. The properties of psychology will make most people anxious about what to do with the lump sum.

This ignores market volatility. What if, using your own example, there was a 5% drop in prices on Day 1 that was recovered within a week?

There's still no difference in the two scenarios.

[Aptenodytes]

if I wait, and the market goes up, I am then faced with the choice of buying in under higher prices. I would have been better off not waiting. But there's no way to know in advance.

That's the logic behind buy/hold/rebalance.

[tadamsmar]

Here are two drastically oversimplified scenarios that are identical to make the point.

A) Day 0, you have a $90,000 portfolio.
Day 1, you receive $10,000 lump sum windfall. You keep it out of your $90,000 portfolio initially.
Day 30, you move in $5,000; portfolio is up 1% for the month. You have $5,000 out and $95,900 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982,

B) Day 0, you have a $100,000 portfolio.
Day 1, you remove $10,000. You have $10,000 out and $90,000 in.
Day 30, you move $5,000 back in; portfolio is up 1% for the month. You have $5,000 out and $95,900 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982.

Scenario A is what many people find acceptable, and scenario B everyone says is stupid. Financially they are the same. Ergo, the difference is behavioral. The properties of arithmetic will make the sums equal no matter what happens to the market. The properties of psychology will make most people anxious about what to do with the lump sum.

This ignores market volatility. What if, using your own example, there was a 5% drop in prices on Day 1 that was recovered within a week?

There's still no difference in the two scenarios.

You are correct. This paper made the same argument 43 years ago:

http://faculty.chicagobooth.edu/george. ... A_1979.pdf

Since then, the LS vs DCA issue has been considered obviously behavioral everywhere but in newsgroups like this one and a maybe a few blogs, certainly in all the peer-reviewed literature. Constantinides, using your argument, killed off any real hope of defending DCA of a windfall with ordinary finance arguments.

The papers in this link will get you up to date on the behavioral finance theories about the DCA vs LS issue:

http://www.bogleheads.org/forum/viewtop ... &start=500

[iceport]

Here are two drastically oversimplified scenarios that are identical to make the point.

A) Day 0, you have a $90,000 portfolio.
Day 1, you receive $10,000 lump sum windfall. You keep it out of your $90,000 portfolio initially.
Day 30, you move in $5,000; portfolio is up 1% for the month. You have $5,000 out and $95,900 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982,

B) Day 0, you have a $100,000 portfolio.
Day 1, you remove $10,000. You have $10,000 out and $90,000 in.
Day 30, you move $5,000 back in; portfolio is up 1% for the month. You have $5,000 out and $95,900 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982.

Scenario A is what many people find acceptable, and scenario B everyone says is stupid. Financially they are the same. Ergo, the difference is behavioral. The properties of arithmetic will make the sums equal no matter what happens to the market. The properties of psychology will make most people anxious about what to do with the lump sum.

This ignores market volatility. What if, using your own example, there was a 5% drop in prices on Day 1 that was recovered within a week?

There's still no difference in the two scenarios.

That's odd. I come up with a different value in the modified Scenario B.

B) Day 0, you have a $100,000 portfolio.
Day 1, you remove $10,000 on a day that the market dropped 5%. You have $10,000 out and $90,000 $85,000 in.
Day 7, market recovers short term loss. You have $10,000 out and $89,474 in.
Day 30, you move $5,000 back in; portfolio is up 1% for the month. You have $5,000 out and $95,900 $95,368 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982 $98,461.

What did I do wrong?

--Pete

[Aptenodytes]

Here are two drastically oversimplified scenarios that are identical to make the point.

A) Day 0, you have a $90,000 portfolio.
Day 1, you receive $10,000 lump sum windfall. You keep it out of your $90,000 portfolio initially.
Day 30, you move in $5,000; portfolio is up 1% for the month. You have $5,000 out and $95,900 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982,

B) Day 0, you have a $100,000 portfolio.
Day 1, you remove $10,000. You have $10,000 out and $90,000 in.
Day 30, you move $5,000 back in; portfolio is up 1% for the month. You have $5,000 out and $95,900 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982.

Scenario A is what many people find acceptable, and scenario B everyone says is stupid. Financially they are the same. Ergo, the difference is behavioral. The properties of arithmetic will make the sums equal no matter what happens to the market. The properties of psychology will make most people anxious about what to do with the lump sum.

This ignores market volatility. What if, using your own example, there was a 5% drop in prices on Day 1 that was recovered within a week?

There's still no difference in the two scenarios.

That's odd. I come up with a different value in the modified Scenario B.

B) Day 0, you have a $100,000 portfolio.
Day 1, you remove $10,000 on a day that the market dropped 5%. You have $10,000 out and $90,000 $85,000 in.
Day 7, market recovers short term loss. You have $10,000 out and $89,474 in.
Day 30, you move $5,000 back in; portfolio is up 1% for the month. You have $5,000 out and $95,900 $95,368 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982 $98,461.

What did I do wrong?

--Pete

You changed the assumption regarding Day 30, which is that portfolio is up 1% for the month. You changed it to up about 0.4%. To make the scenarios comparable, you have to change that assumption in both, which of course yields identical final outcomes.

[livesoft]

I am amused by the length of this thread. I am especially amused that folks haven't proposed special ways to do DCA. It appears that the papers only test the very simplistic "invest on the first day of the month" or "invest on the last day of the month" or something like that. I guess I'm thinking that there must be some algorithm out there that is better than LS and better than straight-up DCA. And I am not talking about DCA over the next 5 years. I am talking about DCA schedules of less than 12 months.

After all, LS is only moderately better than DCA in how often it is better (that is, DCA is better quite a bit of the time). And "better" is not really significantly better ... on average only in the low single digits. If LS was better 90% of the time and was 10% better performance, then I would defect into the LS camp. As it is, I am willing to pay potentially 1% to 2% to DCA for the chance not to lose even more due to a near-future, unpredicted market drop.

Furthermore, the chance of huge market run-up in the 12 months just after a LS investment is rather remote unless there has been a huge market downdraft in the preceding few months. If one uses this knowledge, I would bet that lessens the advantage of LS even more. That is, if the market has dropped 50% in the past year, you had better LS and not DCA.

And to add to this: The idea of LS 50% now and use DCA with the other 50%, cuts the average advantage of LS-all-now from 2% to just 1%. Is that 1% lower performance worth it to some folks? I definitely think so. Indeed, if the market dropped by 2% while in the DCA part of this schedule, one could LS the rest right then and be even. If the market dropped more, then one would be ahead. Has there ever been a time in history when the market did NOT drop by 5% as some point in the following 12 months?

[iceport]

That's odd. I come up with a different value in the modified Scenario B.

B) Day 0, you have a $100,000 portfolio.
Day 1, you remove $10,000 on a day that the market dropped 5%. You have $10,000 out and $90,000 $85,000 in.
Day 7, market recovers short term loss. You have $10,000 out and $89,474 in.
Day 30, you move $5,000 back in; portfolio is up 1% for the month. You have $5,000 out and $95,900 $95,368 in.
Day 60, you move in $5,000; portfolio is down 2% for that month. You are all in, and balance is $98,982 $98,461.

What did I do wrong?

--Pete

You changed the assumption regarding Day 30, which is that portfolio is up 1% for the month. You changed it to up about 0.4%. To make the scenarios comparable, you have to change that assumption in both, which of course yields identical final outcomes.

?

Say your "portfolio" consists of 100000 shares, each worth $1.00.

On the day you sell, the share price drops to $0.95/share, so you need to sell 10526.3158 shares to raise $10,000. You have 89473.6842 shares left (worth $85,000). When they rise 1% from their original $1.00/share value on Day 0, they are only worth $90,368.42.

No change of assumptions was involved.

--Pete

(Sorry, livesoft, for cluttering up your thread.)

[Aptenodytes]

You changed the assumption regarding Day 30, which is that portfolio is up 1% for the month. You changed it to up about 0.4%. To make the scenarios comparable, you have to change that assumption in both, which of course yields identical final outcomes.

?

Say your "portfolio" consists of 100000 shares, each worth $1.00.

On the day you sell, the share price drops to $0.95/share, so you need to sell 10526.3158 shares to raise $10,000. You have 89473.6842 shares left (worth $85,000). When they rise 1% from their original $1.00/share value on Day 0, they are only worth $90,368.42.

No change of assumptions was involved.

You are right, in this case the two end points are not the same. But note that what you had to do to get different end points was make the starting points de facto different by imposing a 5% drop on day 1. And because end of day mutual fund prices are highly predictable, you would know ahead of time if the money you were pulling out was at a rising or falling price. If you wanted to pull out a bunch of money on a day of stable or rising prices, that would be very easy to do. At the very best, you've identified that on about half the days, the comparison isn't valid. That still has you pulling money out of your portfolio half the time and then immediately putting it back in.

In any event, the armchair explanations of people like me have reached their limit. The peer-reviewed publications tadamsmar posted are extremely clear on this matter.

[Ketawa]

Say your "portfolio" consists of 100000 shares, each worth $1.00.

On the day you sell, the share price drops to $0.95/share, so you need to sell 10526.3158 shares to raise $10,000. You have 89473.6842 shares left (worth $85,000). When they rise 1% from their original $1.00/share value on Day 0, they are only worth $90,368.42.

No change of assumptions was involved.

--Pete

(Sorry, livesoft, for cluttering up your thread.)

Under your scenario, the portfolios no longer have the same value on Day 1.

Original Scenario A, portfolio has $100,000 on day 1.
Original Scenario B, portfolio has $100,000 on day 1.
Modified Scenario A, portfolio has $96,500 on day 1.
Modified Scenario B, portfolio has $95,000 on day 1.

There's really no need to look at it much further, and it will just confuse the issue further to add in additional adds and drops. We really only care about what happens from Day 1 onward, since that is when you receive the lump sum. You might as well say that the 5% drop occurred on Day 0 instead of Day 1.

[iceport]

In any event, the armchair explanations of people like me have reached their limit. The peer-reviewed publications tadamsmar posted are extremely clear on this matter.

Perhaps. I still maintain that selling and subsequent DCA in series is distinctly different from DCA alone. In terms of the type of risk DCA is intended to mitigate, the combination of sell-then-buy compounds that risk.

I seriously doubt he will, but I'd be very interested to see how wbern would respond to tadamsmar in the prior thread he resurrected: Re: lump sum and dollar cost averaging

--Pete

[tadamsmar]

Perhaps there needs to be some work on behavioral finance as to why people refuse to accept that DCA of a lump sum simply has to be a behavioral finance issue. I suppose if something has utility in terms of behavioral finance, then believing that it's not just behavioral finance also has utility. That's all I can figure.

[iceport]

Looks like I was wrong -- possibly on more than one thing. A surprising response that leads to more questions: http://www.bogleheads.org/forum/viewtop ... 8#p1481938

--Pete