Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

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RonSwanson
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by RonSwanson »

With both LS and DCA, you must decide the time to put the money in the market.

For LS, do you do it this second or finish your sandwich first and have the order go in after close so that it happens the next day?

When the market is moving 2000 points in a day or 1000 points in seemingly minutes, that could be a *very* expensive sandwich if you are about to put millions of dollars into the market. I don't care how irrational it is, you will probably remember it.

So one thing you are trying to do is minimize regrets. One way to do this is to give up some control with the timing. I can think of a couple of ways to do this:

1) Have a financial advisor decide
2) Pick randomly with some dice on the day you are going to do a lump sum and just do it then.
3) Pick a time period and fixed interval and DCA the money in according to those rules. Don't change your strategy based on what the market is up to. If the market only goes up, well I guess you are happy that you have even more money now. If the market only goes down, you are happy that you are buying at lower prices. If the market is up and down, you win some and lose some.

Although deciding to DCA a windfall might technically be the same as selling everything and DCA that back in (besides taxes), they are different mental experiences.
RonSwanson
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by RonSwanson »

Also I think there is some mental benefit with moving money in gradually in that you get used to large market swings over time.

With a $1M portfolio, you might be used to seeing $20K daily swings. Switching to a $10M portfolio overnight it might not feel great at first to go through $200K daily swings in portfolio value. However after a few months, they might not even be noticeable.

When I started investing I would cringe at just a few hundred dollar swings. If I were still like that, my AA would have to be 0/100. However over time it is easier to stomach the larger numbers changing.
ValuationsMatter
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

adherenceEnergy wrote: Mon Jun 15, 2020 7:12 pm Dca is only a useful strategy to spare the emotions of a drop when you first get your feet wet investing. But that's not really the basis of a rational strategy, imo.
This right here is why I know the point I made in my first post hasn't hit you conceptually. Ok, bear with me until my next post.
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adherenceEnergy
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by adherenceEnergy »

ValuationsMatter wrote: Mon Jun 15, 2020 8:40 pm This right here is why I know the point I made in my first post hasn't hit you conceptually. Ok, bear with me until my next post.
I still am pretty sure I understand your post but don't think you understand my point. I can try to explain in gambling terms as I suspect you are a gambler. Let's say, each day you are offered a bet with a +0.03% EV with a 0.98% SD and you can bet once per day. If you have 1000 units to bet, why would your strategy be to start betting 100 units for the first week (+/- daily winnings or losings), then 200 units for the second week, etc, then on week 10, betting the full 1000 units and every day from there on out betting the full amount (+/- previous winnings/losing)? How does this strategy make any sense? If anything, shouldn't the results of earlier rounds effect how much you'd bet in later rounds? What changed that you are suddenly comfortable risking the full amount on the daily wager after week 10 regardless of the results of prior weeks? Lump sum or being invested for years is just taking the +0.03% EV with 0.98% SD daily wager everyday. On your whole portfolio, Dca just takes daily wagers of +0.003% EV with 0.098% SD on week 1, +0.006% EV with 0.196% SD on week 2, etc, up until week 10 where your betting strategy now mirrors the allin everyday strategy (aka lump sum or being invested for years). That's also why dca is repeatable. After week 20, you can sell and go back to doing 100 units on week 20, 200 units on week 21, etc. This would lower the EV and lower the SD just like it did on week 1.
Last edited by adherenceEnergy on Mon Jun 15, 2020 10:52 pm, edited 19 times in total.
Shael_AT
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by Shael_AT »

Chiming in with my 2 cents...

I get paid every 2 weeks.

Every time I get paid, I put money into 401k, roth ira, hsa, and taxable. It's all automated.

It's incredible how little I think about money, yet how much of it I have. I'm 100% sure that automating it in cycle with my paystubs over the last 10+ years has been more effective in building wealth than not. Could I lump sum once a month? Sure. But I sleep better at night knowing that if I need to get some extra cash by mid or end of month, that it's there.

If I'm wrong, I don't want to feel right. :sharebeer
Beehave
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by Beehave »

absolute zero wrote: Fri Jun 12, 2020 11:57 pm Didn’t read the whole thread, but the OP’s argument sounds like a variant of the concept of the sunk cost fallacy. Costs already incurred in the past should have zero bearing on investment decisions made in the present.

In the same way, whether a person inherited $100k in cash or built up $100k worth of stocks over the years, should not influence their decision for how to invest the $100k. The past is irrelevant. What matters now is the present state, and in both scenarios a person has $100k of investable dollars. Rationally, the decision for what to do with that money should be the same for those two scenarios.
In the sunk cost case there is one party involved.

In the inherit a windfall case there are two different parties. One has a sudden, large, unexpected cash infusion. The other has a steadily built-up stock asset. One's assets are out of balance (if they even know what balance they now wish to have) while the other is (presumably proceeding normally, no need to rebalance.

OP would have it that the windfall recipient DCA'ing the cash (or bonds) in is irrational, because it is identical to the person with the stocks dumping a bunch and then DCA'ing the money back in. But it is anything but identical. The windfall recipient is rationally rebalancing. The stock-seller is irrationally unbalancing her/his asset allocation.

If the windfall person is behaving irrationally, then so do all bogleheads who rebalance once a year rather than more frequently. That's obvious because someone who DCAs in over a year does "a better job" according to the OP's reasoning, than the once-a-year rebalancer. And for the rebalancers who trigger immediately when limit bands are exceeded, the ones with narrower bands are obviously (per OP's reasoning) behaving much more rationally than the ones with wider bands.
Beehave
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by Beehave »

adherenceEnergy wrote: Sat Jun 13, 2020 11:57 am
EnjoyIt wrote: Sat Jun 13, 2020 11:33 am Don’t bother. OP on multiple occasions fully ignores the argument regarding adjusting AA over time giving the investor time to accommodate the massive new windfall psychologically.
No, I've explained it multiple times, but if you can't understand what mental account bias is, there's no hope to keep re-explaining the application of it on glide path. I'll try again because I'm a masochist. If you want to try different different allocations, you'd start with like 25% stocks / 75% bonds / plus $x cash, then go 35% stocks / 65% bonds / plus $x cash etc. Holding specific percentages of cash is not part of a reasonable asset allocation. Go read up on asset allocation and explain why none of the model portfolios give a fixed percent for cash: https://www.bogleheads.org/wiki/Asset_allocation

They don't give fixed percent of cash, because it makes no sense to hold a fixed percentage of cash. You generally hold a specific amount of cash relative to your monthly expenditures, then as your portfolio grows and expenses stay the same, your cash pile doesn't need to grow in tandem, which is why no model portfolio gives a % cash. The percent cash you hold is mostly relative to your net worth and expenses. If you want an efund of 6 months and spend 2k/mo, you hold 12k cash. So if your net worth was 12k, you have 100% cash allocation, or if that same person has a net worth of 120k, you have a 10% cash allocation. If you chose a static 10% cash allocation, your efund would only be $1200 if your net worth was $12k, which is less than 1 month which isn't typically a good idea.

The fact that it makes no sense to hold specific percentages of cash should clue you in that if you were trying different asset allocations and trying different stock / bond ratios, you wouldn't be changing your percent of cash, as cash is not thought of as % of your portfolio, since literally no model portfolio I've ever seen gives cash as a %. Cash has a negative expected return and stocks and bonds have a positive expected return, so you want to minimize cash holdings to what's necessary for spending. You don't put depreciating assets as a percentage of your optimal portfolio. You minimize holding them to what you need them for, which is an efund. When you dca, your portfolio now contains a very large percent of cash, as opposed to a fixed increment relative to your expenses, so it's temporarily not a rational portfolio until it's invested.
Cash, bonds, and stocks behave differently. There are times (a good chunk of 2018 is a recent example) during which cash outperforms both stocks and bonds by several percentage points. For someone with adequate monthly income (annuity, pension, Social Security) it can be absolutely perfectly rational to barbell low risk cash and high risk stock and not worry about missing out on the income delta between bonds and cash when setting their target allocation. They can figure that the liquidity of cash and its greater resiliency to inflation compared to bonds are worthwhile for them, especially since deflation (where bonds shine) is ALSO where their pension and annuity and Social Security shine. They may also decide that with the safety and liquidity of cash, they can keep more stock in the ratio than they'd be willing with bonds which they consider riskier. So I disagree with the premise that cash is obviously irrational to hold. It really depends.

But there are other problems with the argument that DCA is mental accounting bias:
Consider three bogleheads; B1, B2, and B3. Each has a 60/40 allocation target they maintain faithfully according to strict rebalancing rules that they do not break. Each inherits a $1 million windfall in cash (or in bonds - - doesn't matter), and it comes in (totally unexpected) the day after they just rebalanced.
B1 rebalances whenever their ratio changes outside the 55/45 to 65/35 range. So B1 rebalances by LS immediately.
B2 rebalances every 6 months. Therefore, B2 LS's in after a 6 month wait (B2's next rebalance window).
B3 rebalances every year. So B3 LS's all-in after a 12 month wait.

Are B2 and B3 irrational? They've followed their strict rebalancing rules (which I've seen advocated here many times with no one's hair on fire about it).

Now comes irrational B4 who in a fit of mental accounting bias DCA's their million dollar windfall in over a 12 month period.

Now, if you think about it, from a results perspective, B4 has obviously done a better job than B3 and arguably about as well at B2. After all, OP's ground rule is that we only look at results, not intentions and motivation. B4 got more money in faster than B3. As for B3 vs. B2, who did a better job is a horse race - mixed bag. So I'm guessing on those grounds both B2 and B3 are at least as irrational as B4, or maybe worse.

Or is the irrationality only because it's a large sum? If that's the issue, let's suppose the windfall is a smaller sum. But if it were a small sum, nothing changes. B4 still does better than B3 and about as well as B2. And since all that matters, so OP has said, is the dollar-for-dollar end result (not the intention or meta-rule or ...) it follows that B3 and B2 are behaving irrationally even with small sums of money.

The upshot is that the hypothesis that DCA is mental accounting bias is either wrong, or else it does not go far enough. If DCA is wrong, then we need to add that rebalancing by fixed periods is mental accounting bias too. And I wonder whether we should expand that hypothesis having rebalancing band limits is not the answer, because a wider rebalancing trigger band than a narrower retriggering band is another form of emotional bias sneaking in to inhibit rationality.

I'll just mention that the many bogleheads who choose to rebalance with wider rather then narrower bands, or only once or twice a year (or longer!), are actually adhering exactly to the metarule I proposed way above. That rule says - pace your moves and avoid making sudden, unplanned moves.

All that DCA is, if you think about it, is rebalancing. And there are lots of rational ways to rebalance. Not just immediate lump sum.
absolute zero
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by absolute zero »

Beehave wrote: Mon Jun 15, 2020 11:22 pm
absolute zero wrote: Fri Jun 12, 2020 11:57 pm Didn’t read the whole thread, but the OP’s argument sounds like a variant of the concept of the sunk cost fallacy. Costs already incurred in the past should have zero bearing on investment decisions made in the present.

In the same way, whether a person inherited $100k in cash or built up $100k worth of stocks over the years, should not influence their decision for how to invest the $100k. The past is irrelevant. What matters now is the present state, and in both scenarios a person has $100k of investable dollars. Rationally, the decision for what to do with that money should be the same for those two scenarios.
In the sunk cost case there is one party involved.

In the inherit a windfall case there are two different parties. One has a sudden, large, unexpected cash infusion. The other has a steadily built-up stock asset. One's assets are out of balance (if they even know what balance they now wish to have) while the other is (presumably proceeding normally, no need to rebalance.

OP would have it that the windfall recipient DCA'ing the cash (or bonds) in is irrational, because it is identical to the person with the stocks dumping a bunch and then DCA'ing the money back in. But it is anything but identical. The windfall recipient is rationally rebalancing. The stock-seller is irrationally unbalancing her/his asset allocation.

If the windfall person is behaving irrationally, then so do all bogleheads who rebalance once a year rather than more frequently. That's obvious because someone who DCAs in over a year does "a better job" according to the OP's reasoning, than the once-a-year rebalancer. And for the rebalancers who trigger immediately when limit bands are exceeded, the ones with narrower bands are obviously (per OP's reasoning) behaving much more rationally than the ones with wider bands.
There are two “parties” in my sunk cost example. The person who has incurred a (sunk) cost and now has an investment opportunity before them. And the person who has the exact same investment opportunity, but was fortunate to avoid having to incur the same cost to get there. They should both treat the investment opportunity the same.
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adherenceEnergy
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by adherenceEnergy »

Beehave wrote: Mon Jun 15, 2020 11:37 pm
But there are other problems with the argument that DCA is mental accounting bias:
Consider three bogleheads; B1, B2, and B3. Each has a 60/40 allocation target they maintain faithfully according to strict rebalancing rules that they do not break. Each inherits a $1 million windfall in cash (or in bonds - - doesn't matter), and it comes in (totally unexpected) the day after they just rebalanced.
B1 rebalances whenever their ratio changes outside the 55/45 to 65/35 range. So B1 rebalances by LS immediately.
B2 rebalances every 6 months. Therefore, B2 LS's in after a 6 month wait (B2's next rebalance window).
B3 rebalances every year. So B3 LS's all-in after a 12 month wait.

Are B2 and B3 irrational? They've followed their strict rebalancing rules (which I've seen advocated here many times with no one's hair on fire about it).

Now comes irrational B4 who in a fit of mental accounting bias DCA's their million dollar windfall in over a 12 month period.

Now, if you think about it, from a results perspective, B4 has obviously done a better job than B3 and arguably about as well at B2. After all, OP's ground rule is that we only look at results, not intentions and motivation. B4 got more money in faster than B3. As for B3 vs. B2, who did a better job is a horse race - mixed bag. So I'm guessing on those grounds both B2 and B3 are at least as irrational as B4, or maybe worse.
This is a goofy example that falls under the meta rule argument. Yes technically B4 did a better job of rebalancing than B2 and B3, but only because they did it faster, but lump sum rebalancing when the windfall received would have been best like B1. The rebalancing meta rule of every X months is to minimize time spent doing it and for tax reasons. Almost any investor getting a large cash/bond windfall would probably revisit their rebalancing "rule" after receiving a large windfall. The reason people don't question the rebalancing rules of doing it every X months is that it assumes no random large cash windfall, and typical performance of it only falling out of your target allocation by a few %. But just because b2 and b3 didn't revisit their Metarule doesn't mean b4 acted rationally either.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by nigel_ht »

adherenceEnergy wrote: Mon Jun 15, 2020 9:32 pm
ValuationsMatter wrote: Mon Jun 15, 2020 8:40 pm This right here is why I know the point I made in my first post hasn't hit you conceptually. Ok, bear with me until my next post.
I still am pretty sure I understand your post but don't think you understand my point. I can try to explain in gambling terms as I suspect you are a gambler. Let's say, each day you are offered a bet with a +0.03% EV with a 0.98% SD and you can bet once per day. If you have 1000 units to bet, why would your strategy be to start betting 100 units for the first week (+/- daily winnings or losings), then 200 units for the second week, etc, then on week 10, betting the full 1000 units and every day from there on out betting the full amount (+/- previous winnings/losing)? How does this strategy make any sense? If anything, shouldn't the results of earlier rounds effect how much you'd bet in later rounds? What changed that you are suddenly comfortable risking the full amount on the daily wager after week 10 regardless of the results of prior weeks? Lump sum or being invested for years is just taking the +0.03% EV with 0.98% SD daily wager everyday. On your whole portfolio, Dca just takes daily wagers of +0.003% EV with 0.098% SD on week 1, +0.006% EV with 0.196% SD on week 2, etc, up until week 10 where your betting strategy now mirrors the allin everyday strategy (aka lump sum or being invested for years). That's also why dca is repeatable. After week 20, you can sell and go back to doing 100 units on week 20, 200 units on week 21, etc. This would lower the EV and lower the SD just like it did on week 1.
Because sometimes the deck favors you and not the house.

Sometimes the market favors DCA and not LS.

Investing in the market IS gambling. The difference is the player generally has the advantage in the US market although there have been a few decades where the house wins (1929, 1966, 2000, etc).
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by nigel_ht »

absolute zero wrote: Mon Jun 15, 2020 11:48 pm
Beehave wrote: Mon Jun 15, 2020 11:22 pm
absolute zero wrote: Fri Jun 12, 2020 11:57 pm Didn’t read the whole thread, but the OP’s argument sounds like a variant of the concept of the sunk cost fallacy. Costs already incurred in the past should have zero bearing on investment decisions made in the present.

In the same way, whether a person inherited $100k in cash or built up $100k worth of stocks over the years, should not influence their decision for how to invest the $100k. The past is irrelevant. What matters now is the present state, and in both scenarios a person has $100k of investable dollars. Rationally, the decision for what to do with that money should be the same for those two scenarios.
In the sunk cost case there is one party involved.

In the inherit a windfall case there are two different parties. One has a sudden, large, unexpected cash infusion. The other has a steadily built-up stock asset. One's assets are out of balance (if they even know what balance they now wish to have) while the other is (presumably proceeding normally, no need to rebalance.

OP would have it that the windfall recipient DCA'ing the cash (or bonds) in is irrational, because it is identical to the person with the stocks dumping a bunch and then DCA'ing the money back in. But it is anything but identical. The windfall recipient is rationally rebalancing. The stock-seller is irrationally unbalancing her/his asset allocation.

If the windfall person is behaving irrationally, then so do all bogleheads who rebalance once a year rather than more frequently. That's obvious because someone who DCAs in over a year does "a better job" according to the OP's reasoning, than the once-a-year rebalancer. And for the rebalancers who trigger immediately when limit bands are exceeded, the ones with narrower bands are obviously (per OP's reasoning) behaving much more rationally than the ones with wider bands.
There are two “parties” in my sunk cost example. The person who has incurred a (sunk) cost and now has an investment opportunity before them. And the person who has the exact same investment opportunity, but was fortunate to avoid having to incur the same cost to get there. They should both treat the investment opportunity the same.
Only if their circumstances are the same.

Same age, same income, savings rate, same retirement target date.

In none of the scenarios so far have these been true.

One person has saved $1M in her portfolio.
One person has saved $0 in his portfolio but got a $1M windfall.

Person A has a large savings rate and this will likely continue.
Person B has no savings rate and this will likely continue.

Future outcomes differ for these two individuals. Risk is different for these two individuals.

Therefore behavior can be quite different for these individuals. This isn’t a sunk cost scenario.
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bertilak
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by bertilak »

At the risk of, of I'm not sure what, here is what I think is THE KEY POINT of the famous Constantinides (1979, peer reviewed) DCA paper:
  • Where, then, does the intuitive rationale of DCA fail? Its rationale is that the investor replaces one major gamble on a temporary shift of prices by a number of smaller gambles and thus diversifies risk. The fault of this argument is misrepresentation of the state of the world, before a decision is made.
For those who give a lot of respect to math, the paper goes (relentlessly) into the math of why replacing one major gamble (aka risk) with a bunch of smaller risks over time does no such thing.

The idea that there is some mathematical advantage to DCA is wrong. Read and understand the paper before disagreeing with it.

Pro-DCA discussions tend to give hypothetical (or past history) examples (scenarios) and draw conclusions based on observations of the state of the world AFTER the scenario plays out. Decisions need to be made beforehand based on facts known at that time.

Although DCA in and of itself is not mathematically superior (less risky) than an initial lump sum act, the paper does make the assumption that the DCA course WILL BE carried out all the way to the end. But DCA gives the hesitant a chance to change their minds part way through and that could have some value. In other words, the one advantage of DCA is that you can stop doing it! There are ways to achieve the same thing without relying on faulty analysis.
May neither drought nor rain nor blizzard disturb the joy juice in your gizzard. -- Squire Omar Barker (aka S.O.B.), the Cowboy Poet
ValuationsMatter
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

I spend quite a bit of time on the road thinking about things to and from work, at the moment. I'm really interested in exploring some of the points that have been made here, but this reply is not yet for them. I just realized something on my long drive home and wanted to float it:

DCAing in has the effect of buying more shares low and less shares high. This is not a bad thing from an investment perspective. However, DCAing out is not a good idea, for the exact opposite reason: you end up selling more shares when low than when the market is high. So, on the back end you should share cost average (SCA), to sell over the number of periods that you move out of the market if possible. Here's a thought experiment I ran when considering some of the points in this thread:
You start off with $1000. You have a stock whose price fluctuates between 2 values $1 & $100 per share with 50% probability of each on any given day. As a result, stock has 0 long-term growth. The volatility here is represented by a stocks value being 1 or 100 in any given day. You must make your decision in advance of how much you will purchase or sell tomorrow. This is representative of the fact that we cannot predict a stock's future price (in a day or in a year, etc...).
Results of lumping vs. DCAing.
Now, the guy who lump-sums in and out of this has exactly 4 possible outcomes:
1. He lumps in at a stock price of $1 and lumps out at a stock price of $1. He ends with $1,000. Return = 0.
2. He lumps in at a stock price of $100 and lumps out at a stock price of $100. He ends with $1,000. Return = 0.
3. He lumps in at a stock price of $1 and lumps out at a stock price of $100. He ends with $100,000. Return = 99,000. (9
4. He lumps in at a stock price of $100 and lumps out at a stock price of $1. He ends with $10. Return = -990.
His expected value is: 1/4 * (1,000 + 1,000 + 100,000 + 10) = $25,502.5.
But the Standard Deviation of this portfolio's outcome is: sqrt[(24,502.5^2 + 24,502.5^2 + 74,497.5^2 + 25,492.5^2)/4] = $43,013.05

If he DCA's in and SCA's out over 10 periods:
For this, I ran a stochastic simulation of 100,000 experiments... yeah, you made me work... I better be getting paid for this, lol. The results of the simulation (see attached if you want to check/critique):
Average End Portfolio Balance: $25,502.3
Standard Deviation: $11,427.91

That's a simple model. The volatility is extreme. No model is perfect... I'm sure people are about to make me feel bad for posting it, but whatever... Just thought I'd put something together to validate my understanding of the stats. I've gotta get back to work. Maybe I'll factor in a periodic ROI on the next round, or even model the daily ROI as a gamma distribution that essentially skews a normal to a slightly positive return. Then, I could work towards determining the optimum DCA & SCA periods to meet the desired proximity to the mean price desired and level of certainty that the investor falls within that price, but unless I'm really misthinking this thing, DCA/SCA is still going to cost some EV and still greatly reduce volatility. It's intuitive from a stats POV.

As a sidenote, why can't I add attachments? Are they disabled for everyone, or have I pissed off the mods again? Also 768 pixels max? WTF? I'm not even hosting it here... Anyways, here's a link so you can see it: https://stangnet.com/mustang-forums/med ... jpg.14848/
Last edited by ValuationsMatter on Tue Jun 16, 2020 1:48 pm, edited 2 times in total.
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FiveK
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by FiveK »

ValuationsMatter wrote: Tue Jun 16, 2020 1:31 pm As a sidenote, why can't I add attachments?
Is Posting images in the Bogleheads forum helpful?
ValuationsMatter
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

Well it confirms the limitations and lack of ability to host here. Thanks for linking the answers to my concerns, FiveK
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by bertilak »

ValuationsMatter wrote: Tue Jun 16, 2020 1:31 pm DCAing in has the effect of buying more shares low and less shares high.
In a rising market the effect is just the opposite. As you put off buying shares to the future you end up buying at increasing prices, even if it is not a steady increase. And remember, if you don't believe in a generally rising market you shouldn't be investing at all -- unless you are satisfied with just the dividends and that, too, makes DCA illogical.

With DCA you don't have the lower priced shares you MIGHT have bought (via an early lump sum purchase) working for you. This effect gets to the heart of many small bets NOT improving your odds over one big bet. The point is not that any of this WILL happen, but that it MIGHT happen and it is those "mights" that make up the odds. You certainly can't claim the opposite, that the odds will improve by delaying, even in part.
Last edited by bertilak on Tue Jun 16, 2020 2:13 pm, edited 1 time in total.
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ValuationsMatter
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

bertilak wrote: Tue Jun 16, 2020 2:09 pm
ValuationsMatter wrote: Tue Jun 16, 2020 1:31 pm DCAing in has the effect of buying more shares low and less shares high.
In a rising market the effect is just the opposite. As you put off buying shares to the future you end up buying at increasing prices, even if it is not a steady increase. And remember, if you don't believe in a generally rising market you shouldn't be investing at all -- unless you are satisfied with just the dividends and that, too, makes DCA illogical.

In the mean time you don't have the lower priced shares you MIGHT have bought (via an early lump sum purchase) working for you. This effect gets to the heart of many small bets NOT improving your odds over one big bet. The point is not that this WILL happen, but that it MIGHT happen and it is those "mights" that make up the odds.
FWIW, I was speaking with respect to volatility. Your point is well taken and understood. It's right in line with my repeated assertion that in a generally rising market, DCA-ing reduces EV by extension. However, if you're SCAing on the back end too, and you start each when the other guy lumps, then it means that you're getting into the market slower on the front, but also that you're staying partially in the market a little longer on the back. Although, my recent thought experiment has me questioning whether a DCA/SCA approach can be used to take enough advantage of normal market volatility to be worthwhile. It feels like I'm missing something there.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by bertilak »

ValuationsMatter wrote: Tue Jun 16, 2020 2:13 pm Although, my recent thought experiment has me questioning whether a DCA/SCA approach can be used to take enough advantage of normal market volatility to be worthwhile.
It certainly sounds like a lot of work, work based on fuzzy assumptions!
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by Northern Flicker »

Lump sum has a higher expected value of return.
Lump sum has a higher variance of return.

It is extremely likely that return and return variance for lump sum and DCA converge on each other in the limit as holding period increases without bound (probably need to know the probability distribution of future return to say for sure, but it may be estsblished independent of distribution, not sure). Thus, for a sufficiently long holding period, it does not matter which you use.
Risk is not a guarantor of return.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

bertilak wrote: Tue Jun 16, 2020 2:21 pm
ValuationsMatter wrote: Tue Jun 16, 2020 2:13 pm Although, my recent thought experiment has me questioning whether a DCA/SCA approach can be used to take enough advantage of normal market volatility to be worthwhile.
It certainly sounds like a lot of work, work based on fuzzy assumptions!
I know, man. That's part of the problem with arguments on the internet. People demand facts, research, math to an extent impractical for most who don't have the time. Also, when it's presented, it only invites criticism, and often that criticism takes the form of irrational personal attacks, attacking the source instead of the data, etc... I'm not suggesting that in any way is happening in this thread. I actually appreciate the somewhat logical and rational discussion here, which is why I'm taking part, for now.
Lump sum has a higher expected value of return.
Lump sum has a higher variance of return.
You see it the way I do, I think.
It is extremely likely that return and return variance for lump sum and DCA converge on each other in the limit as holding period increases without bound (probably need to know the probability distribution of future return to say for sure, but it may be estsblished independent of distribution, not sure). Thus, for a sufficiently long holding period, it does not matter which you use.
I somewhat agree. Time will take short term variance out of the equation. However, the endpoints are just as subject to volatility.

The greatest difficulty in the model is going to be the dependent nature of stocks. If the gains and losses were independent of the previous time period, it would be easy. The dependence, multivariate, and insufficient length of history utterly destroys our ability to model with much confidence using random numbers alone. Generating a random number from any probability distribution or empirical distribution function for each time period implies that it is independent of the preceding time period, and I'd have to go back to my notes from grad school to see if there's any reasonable way to tie that back in... Long-term is easier to model than short term, because if I remember time-series analysis right, a lot of short, dependent periods make up long-term periods that sometimes can be considered independent of each other. The problem there is that if we look at long-term as 20 year periods, then in a 200 year market history that we might consider 'modern history' we actually only have 10 data points.

So, I do not have too much faith in the "inevitable rising long-term market hypothesis," though I believe it enough to take my chances. That still takes me back to my name: any prudent investor should have some idea of the value of something before they agree to its price. Valuations Matter!
Last edited by ValuationsMatter on Tue Jun 16, 2020 4:46 pm, edited 1 time in total.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by happyisland »

I feel like reading and absorbing the contents of the 1979 paper Bertilak posted about would really help the proponents of Dollar Cost Averaging. It's worth your time, really:

A Note on the Suboptimality of Dollar-Cost Averaging as an Investment Policy
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

adherenceEnergy wrote: Mon Jun 15, 2020 9:32 pm I still am pretty sure I understand your post but don't think you understand my point.
Ok. I think I do. I have invested a considerable amount of time and thought to the subject since I first responded. However, I'll have another look when I get the chance. I'm feeling a little overwhelmed with other things at the moment, and honestly shouldn't be spending as much time as I am on this.

I take a comment like this seriously, because I believe people with opposing points of view often don't even try to understand each other in discussion. When I'm accused of not understanding, I typically try to "steel-man" the other's point of view. We've discussed a lot and this convo is moving fast. Again, I'm going try to come back to you on this.
I can try to explain in gambling terms as I suspect you are a gambler.
I prefer "Positive Equity Wagererer," but yeah... lol :sharebeer
Let's say, each day you are offered a bet with a +0.03% EV with a 0.98% SD and you can bet once per day. If you have 1000 units to bet, why would your strategy be to start betting 100 units for the first week (+/- daily winnings or losings), then 200 units for the second week, etc, then on week 10, betting the full 1000 units and every day from there on out betting the full amount (+/- previous winnings/losing)?


It wouldn't be. Either Kelley Criterion dictates my bet sizing (when I'm serious), or I'm playing very low stakes socially and usually prioritize social fun over the insignificant amount of money (though I'm usually still winning, lol).
How does this strategy make any sense? If anything, shouldn't the results of earlier rounds effect how much you'd bet in later rounds? What changed that you are suddenly comfortable risking the full amount on the daily wager after week 10 regardless of the results of prior weeks?
Your concerns sounds right for the scenario presented. I'm not sure... Need to think this one through a little more. At first glance, I think back to the period of 10-12% swings in March when I couldn't stop looking at the market and ask myself with a 0.03%EV/day and a 5+% SD (pure guesswork) how do I feel about my exposure at that point? Should I feel differently? How could I possibly choose to lower my AA in that scenario (I actually increased it) when I don't know if I'm coming out on the low side of fair value or the high side. Anyways, I digress. This is probably not the direction you're trying to get me thinking in.
Lump sum or being invested for years is just taking the +0.03% EV with 0.98% SD daily wager everyday.
This is where I definitely think you're missing the independent vs. dependent nature of the bets in the stock market, and I admit it's very hard to build a realistic model for it. Would you say that the prices today do not depend whatsoever of yesterday's movement? I would say it almost absolutely does, though I have never formally tested it. In fact, I can almost guarantee it does because emotional humans, whose emotions come in waves and linger from one day to the next, ultimately make the decisions that aggregate to market price and daily movement. It would be a simple correlation test, perhaps worth running, given the discussion. I'd just need to find a clean daily S&P500 market price data set for a long enough period to test.
On your whole portfolio, Dca just takes daily wagers of +0.003% EV with 0.098% SD on week 1, +0.006% EV with 0.196% SD on week 2,
This is not how SD works.
etc, up until week 10 where your betting strategy now mirrors the allin everyday strategy (aka lump sum or being invested for years). That's also why dca is repeatable.
My assumption that the market is not independent in short time intervals leads me to believe that if you've missed out on the run up or the back side of a market incident then you are also way more likely to deviate greatly from the mean market price. Being continuously invested allows you to absorb the shocks of drops because you experienced the run up before and the recovery after, and they are directly related/correlated/dependent on those shocks. For example, the market would not have grown by 40% since March if it hadn't dropped by 30% in that time period. If you experience one without the other (with the same magnitude of investment in terms of shares), you permanently change the EV & SD, due to the dependency... I think...
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by Beehave »

adherenceEnergy wrote: Tue Jun 16, 2020 12:33 am
Beehave wrote: Mon Jun 15, 2020 11:37 pm
But there are other problems with the argument that DCA is mental accounting bias:
Consider three bogleheads; B1, B2, and B3. Each has a 60/40 allocation target they maintain faithfully according to strict rebalancing rules that they do not break. Each inherits a $1 million windfall in cash (or in bonds - - doesn't matter), and it comes in (totally unexpected) the day after they just rebalanced.
B1 rebalances whenever their ratio changes outside the 55/45 to 65/35 range. So B1 rebalances by LS immediately.
B2 rebalances every 6 months. Therefore, B2 LS's in after a 6 month wait (B2's next rebalance window).
B3 rebalances every year. So B3 LS's all-in after a 12 month wait.

Are B2 and B3 irrational? They've followed their strict rebalancing rules (which I've seen advocated here many times with no one's hair on fire about it).

Now comes irrational B4 who in a fit of mental accounting bias DCA's their million dollar windfall in over a 12 month period.

Now, if you think about it, from a results perspective, B4 has obviously done a better job than B3 and arguably about as well at B2. After all, OP's ground rule is that we only look at results, not intentions and motivation. B4 got more money in faster than B3. As for B3 vs. B2, who did a better job is a horse race - mixed bag. So I'm guessing on those grounds both B2 and B3 are at least as irrational as B4, or maybe worse.
This is a goofy example that falls under the meta rule argument. Yes technically B4 did a better job of rebalancing than B2 and B3, but only because they did it faster, but lump sum rebalancing when the windfall received would have been best like B1. The rebalancing meta rule of every X months is to minimize time spent doing it and for tax reasons. Almost any investor getting a large cash/bond windfall would probably revisit their rebalancing "rule" after receiving a large windfall. The reason people don't question the rebalancing rules of doing it every X months is that it assumes no random large cash windfall, and typical performance of it only falling out of your target allocation by a few %. But just because b2 and b3 didn't revisit their Metarule doesn't mean b4 acted rationally either.
You wrote:
"Almost any investor getting a large cash/bond windfall would probably revisit their rebalancing "rule" after receiving a large windfall."

Exactly! And let's be clear about the implication. When we set up our asset allocation we do a self-analysis including our needs and wants and fears and motivations. Included is a risk-reward analysis and a risk tolerance analysis. And if the result of this needs, risk-reward, risk-tolerance self-evaluation is a 40/60 allocation with a twice annual rebalance, that's fine. And then, if upon receipt of this windfall you re-evaluate and determine that with this windfall you can go 50/50 (increasing risk) but feel like tempering the money in by DCA over 12 months (adding the risk component steadily rather than all at once) what's wrong with that? This person (note: you've said this is directed at bogleheads) understands time in the market, the risk of missing a big up day, the risk of hitting a big down day, the long term benefit of 60/40 over 40/60 and 50/50. And they have chosen a strategy. They have done the right thing because it's up to them. If they understand these fundamentals and choose what they are comfortable with, of course there are trade offs relative to some hypothetical optimization scheme. But that is exactly what the self-evaluation is all about - picking your tradeoffs.

To claim someone made an error by the DCA choice rather than the LS choice because it is the same as doing a sale of stock and then DCAing is proposing a model much more "goofy" than anything I've proposed. I've proposed nothing involving a self-imposed action that moves the windfall recipient farther away from their target allocation than they already are. Your standard for evaluating DCA involves comparison with action that does exactly that.

A boglehead strting out with a 50/50 allocation and immediate lump sum rebalancing plan can perfectly well choose, with open eyes and no self-deception, choose to move to a 40/60 allocation with DCA upon receipt of a large, unexpected sum of money. That's because, exactly as you say above, and I've said from the beginning, the huge sum causes a reset in the most fundamental aspects of planning. They are using this windfall to de-risk. That's their perogative. This is why is no equivalence between a boglehead who upon receipt of a 900,000 windfall now has a million bucks, and a different boglehead sitting on a million dollar account who has been growing it steadily for years. The first one absolutely needs to do a reset. The second has no reason to. And that reset, as long as the person making the decision is aware of the trade offs, is acceptable and will absolutely, by its nature, include trade-offs in the way they set their allocation and rebalancing scheme.

There's nothing wrong with encouraging people who seem too conservative to you to re-evaluate. And including any factual analyses of the value of time in the market and more aggressive allocations is surely acceptable and welcome information. But to accuse someone who has listened, understood, and then chosen some path less aggressive of having performed "mental accounting bias" and having done something that should "never" be done is a bridge way too far. I'm sure the intentions are good here and the information is valuable, but the language expressing the idea is just way too strong and really not compatible with a foundational pillar of the boglehead process, namely, performing your own self-analysis of risk tolerance and respecting the self-analyses of others.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by adherenceEnergy »

ValuationsMatter wrote: Tue Jun 16, 2020 3:28 pmThis is where I definitely think you're missing the independent vs. dependent nature of the bets in the stock market, and I admit it's very hard to build a realistic model for it. Would you say that the prices today do not depend whatsoever of yesterday's movement?
Hard to say. I would assume if there's any predictability on today's prices based on yesterday's prices, hedge funds would arbitrage that inefficiency out of the market. If you find an exploitable pattern in the market, there's really no reason to index, you should just print money with options or day trading. I haven't thought this 100% through, but just generally adhere to the idea that it's all random from the perspective of the buy/hold indexer. In terms of volatility, there does seem to be a lot of correlation with yesterday's volatility and today's volatility so my assumption might wrong in that it's predictable but not immediately profitable information.

My argument is essentially that dca employed the way most do generally doesn't make sense for a buy/hold indexer, not that dca can never be smart with some sophisticated modeling strategy. My gut is that even a sophisticated modelling strategy still wouldn't make dca a good strategy, because the strategy is so bizarre from a theoretical standpoint. Blindly increasing wagers at predetermined intervals seems to make no intuitive sense as to how it could possibly be an effective strategy under any conditions, imo. If a strategy had some math involved where if the market price changes by X or volatility changes deploy extra or something, I could maybe think it has some hope of accomplishing something.
That's not how SD works.
I'll admit I'm a bit rusty on calculating SD, but I plugged in some sample numbers into an online calculator. If you multiplied every result in the population by 10, the SD also multiplied by 10. In the example, I'm comparing risking 1000 units with the 0.98% SD to 100 units with 0.98% SD. So wouldn't all the possible results just be magnified by 10? I'm curious how you'd calculate it.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

adherenceEnergy wrote: Tue Jun 16, 2020 3:58 pm
That's not how SD works.
I'll admit I'm a bit rusty on calculating SD, but I plugged in some sample numbers into an online calculator. If you multiplied every result in the population by 10, the SD also multiplied by 10. In the example, I'm comparing risking 1000 units with the 0.98% SD to 100 units with 0.98% SD. So wouldn't all the possible results just be magnified by 10? I'm curious how you'd calculate it.
Pretty sure you can add their variances (SD^2) and then take the square root. Sorry, I usually let stuff do this for me. Sometimes I have to re-look the basics. I just knew you couldn't add them. Also, FYSA, you add the variances together, even if you happen to be subtracting the EVs.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

happyisland wrote: Tue Jun 16, 2020 2:59 pm I feel like reading and absorbing the contents of the 1979 paper Bertilak posted about would really help the proponents of Dollar Cost Averaging. It's worth your time, really:

A Note on the Suboptimality of Dollar-Cost Averaging as an Investment Policy
I actually took non-linear optimization in grad school, and as closely as I can follow that paper, I see no solution to the formulated problem. They took it as far as defining every term, formulating the problem, and then began making assertions without any solution that I can find. Also, I would point out, yet again, that the thing they maximize is total wealth + consumption. This is equivalent, so far as I can tell, to earlier statements I've repeatedly made about most studies clearly attacking DCA on those grounds alone without any priority given to volatility reduction.

I'm just curious, as it was not an easy read for me, how many of those of you who have read it actually understand it? The difficulty in following for me is that their format was not the standard my school used. Thankfully, they did a pretty good job defining terms. Also, why prop it up if it actually offers no solution and sheds no new light on the matter. We have already accepted DCA's inferiority in terms of EV in a growing market.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by FiveK »

ValuationsMatter wrote: Tue Jun 16, 2020 6:03 pmI'm just curious, as it was not an easy read for me, how many of those of you who have read it actually understand it?
Not every word. But enough to note the comments about a "minimax regret" (aka "minimize the largest amount of regret") strategy.

DCA is often suggested to new investors precisely for this reason: so the new investor doesn't experience so much regret if there is an immediate drop after a lump sum that the investor avoids further investing. That differs from "maximize expected value."

As the Pye reference (https://pubsonline.informs.org/doi/10.1 ... c.17.7.379) states, "First, it is shown that the conventional wisdom of dollar averaging is related to hedging against, large regrets rather than unfavorable outcomes.
...
It is shown that dollar averaging is a nonsequential minimax strategy...."

The answer to optimization problems usually depends on the objective function chosen. ;)
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

Uncorrelated wrote: Mon Jun 15, 2020 6:45 pm There is a mathematical proof in An Introduction to Computational Finance Without Agonizing Pain, page, 119, Theorem 1 (Ineffectiveness of Glide Path Strategies). Basically the theory states that is always possible to construct a constant allocation (i.e. lump sum) investment strategy that has the same expected return as a glidepath (i.e. DCA). However, the constant strategy has lower risk. On the next page, they extend their result to non-normal distributions.


Alternatively, just check the solution for merton's portfolio problem. There are extensions that work with transaction costs, non-static return assumptions, etc, etc...

For those that prefer a programming solution, it is quite easy to see that DCA violates the principle of optimality, which proves that DCA is suboptimal (this theory doesn't necessarily prove that lump sum is optimal, but it's quite easy to apply this theory to see that DCA is definitely not optimal).


adherenceEnergy's argument appears to be similar to bellman's principe of optimality.
:confused
again, unless I'm missing something, all of these are based on expected value 4 expected wealth + consumption, or the utility of the same.
I really appreciate the first link the most as I learned from it. However, I don't think it's applicable to the way in which most investors DCA, and particularly in the way that I am representing here. To start with, it seems to be focused on glide path from max Equity portfolio allocation to minimum, and again long-term asset allocation, including the continuously rebalancing approach thereof, is not reflective of a short-term DCA approach. Further, that study contrasts a glidepath approach against a fixed asset allocation with equal average proportion of equities over the course of time. The fixed asset allocation, therefore, never reaches the magnitude of the variance in the portfolio that the Glide path approach does. Whereas, in the approach I'm espousing, and that most people are interested in, DCA in the short-term is only used to achieve the exact same asset allocation as the lump sum approach.

Nevertheless, explicitly want to thank you for that first link and exposure to the rest as well. They were all interesting and enlightening, and I have a feeling I'll be referring to all three of them again.

Lastly, I apologize if this post is less readable due to the fact that I'm driving and dictating with voice recognition on my phone.
Last edited by ValuationsMatter on Tue Jun 16, 2020 11:28 pm, edited 2 times in total.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

FiveK wrote: Tue Jun 16, 2020 6:55 pm
ValuationsMatter wrote: Tue Jun 16, 2020 6:03 pmI'm just curious, as it was not an easy read for me, how many of those of you who have read it actually understand it?
Not every word. But enough to note the comments about a "minimax regret" (aka "minimize the largest amount of regret") strategy.

DCA is often suggested to new investors precisely for this reason: so the new investor doesn't experience so much regret if there is an immediate drop after a lump sum that the investor avoids further investing. That differs from "maximize expected value."

As the Pye reference (https://pubsonline.informs.org/doi/10.1 ... c.17.7.379) states, "First, it is shown that the conventional wisdom of dollar averaging is related to hedging against, large regrets rather than unfavorable outcomes.
...
It is shown that dollar averaging is a nonsequential minimax strategy...."

The answer to optimization problems usually depends on the objective function chosen. ;)
Exactly man!

Didn't the pie reference state that DCA could be a solution to those Minimax regret problems?

edit: LOL at how the voice recognition spelled pie. That made me hungry. Now my objective function is to Minimax my regret by lump summing some pie.
Last edited by ValuationsMatter on Tue Jun 16, 2020 7:03 pm, edited 1 time in total.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by FiveK »

ValuationsMatter wrote: Tue Jun 16, 2020 7:00 pmDidn't the pie reference state that DCA could be a solution to those Minimax regret problems?
Yes.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

In case you missed it, check out my edit.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by FiveK »

ValuationsMatter wrote: Tue Jun 16, 2020 7:04 pm In case you missed it, check out my edit.
:sharebeer
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by Northern Flicker »

ValuationsMatter wrote: Tue Jun 16, 2020 2:44 pm.
It is extremely likely that return and return variance for lump sum and DCA converge on each other in the limit as holding period increases without bound (probably need to know the probability distribution of future return to say for sure, but it may be established independent of distribution, not sure). Thus, for a sufficiently long holding period, it does not matter which you use.
I somewhat agree. Time will take short term variance out of the equation. However, the endpoints are just as subject to volatility.
There is no endpoint when looking at the limit as holding period increases without bound.
Risk is not a guarantor of return.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by Uncorrelated »

ValuationsMatter wrote: Tue Jun 16, 2020 6:57 pm
Uncorrelated wrote: Mon Jun 15, 2020 6:45 pm There is a mathematical proof in An Introduction to Computational Finance Without Agonizing Pain, page, 119, Theorem 1 (Ineffectiveness of Glide Path Strategies). Basically the theory states that is always possible to construct a constant allocation (i.e. lump sum) investment strategy that has the same expected return as a glidepath (i.e. DCA). However, the constant strategy has lower risk. On the next page, they extend their result to non-normal distributions.


Alternatively, just check the solution for merton's portfolio problem. There are extensions that work with transaction costs, non-static return assumptions, etc, etc...

For those that prefer a programming solution, it is quite easy to see that DCA violates the principle of optimality, which proves that DCA is suboptimal (this theory doesn't necessarily prove that lump sum is optimal, but it's quite easy to apply this theory to see that DCA is definitely not optimal).


adherenceEnergy's argument appears to be similar to bellman's principe of optimality.
:confused
again, unless I'm missing something, all of these are based on expected value 4 expected wealth + consumption, or the utility of the same.
I really appreciate the first link the most as I learned from it. However, I don't think it's applicable to the way in which most investors DCA, and particularly in the way that I am representing here. To start with, it seems to be focused on glide path from max Equity portfolio allocation to minimum, and again long-term asset allocation, including the continuously rebalancing approach thereof, is not reflective of a short-term DCA approach. Further, that study contrasts a glidepath approach against a fixed asset allocation with equal average proportion of equities over the course of time. The fixed asset allocation, therefore, never reaches the magnitude of the variance in the portfolio that the Glide path approach does. Whereas, in the approach I'm espousing, and that most people are interested in, DCA in the short-term is only used to achieve the exact same asset allocation as the lump sum approach.

Nevertheless, explicitly want to thank you for that first link and exposure to the rest as well. They were all interesting and enlightening, and I have a feeling I'll be referring to all three of them again.

Lastly, I apologize if this post is less readable due to the fact that I'm driving and dictating with voice recognition on my phone.
The first one is based on expected value + variance, and shows that for any glidepath, it is possible to choose a constant allocation that has the same expected return but lower risk, and thus takes a mean-variance approach.

The second one is based on consumption. However, the result does not depend on any particular risk preferences. If you are a risk-loving individual, then it is still optimal to choose a constant asset allocation.

The third one does not make use of any volatility, expected return or consumption based argument. It can be used to prove that DCA approach has certain characteristics, and those characteristics are sufficient to prove that DCA is suboptimal, no matter what the underlying utility function or market model is.

A glidepath is the same thing as a short term DCA approach. If you have $1m and invest immediately, then you have a constant asset allocation. If you have $1m and decide to DCA into the market, then you have a glidepath (in the terminology of that paper). It doesn't matter what the exact glidepath is. If you allocate 100% to equities every odd week and 100% to bonds every even week -- still a glidepath.
The fixed asset allocation, therefore, never reaches the magnitude of the variance in the portfolio that the Glide path approach does.
I believe you have this the wrong way around. Not that it matters, "X has lower variance than Y" is not a valid argument. A valid argument can be "X has lower variance than Y for equivalent expected return". The paper proves this a strictly better constant allocation exists for all possible glidepaths.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

Thanks for the recap, though I did it read all of them. No, I said it correctly. Also, lower variance alone regardless of EV can be a rational goal and therefore a valid position to take. That said, I made that comment implicitly accepting the premise of the article that equal proportion of equities over time comparing a sloped vs. fixed allocation resulted in equal expected returns.

The Glide path examined is continuously rebalanced over the long-term. DCA espoused here is discretely
rebalanced over the short-term at the end points. That's the main difference. We were also discussing reaching the same asset allocation until your example.

Quick example: if I invest half my wealth in equities today, and invest the other half in one week, and then on the back end, after 20 years, I sell half of my investment a week before I sell the rest, that is functionally the same thing as having a fixed 100% Equity allocation lump sum in for 20 years, except that I have reduced the impact of short-term volatility both on the front end and the back end. Each half of my investment was invested for 20 years just as the lump sum approach is invested for 20 years. The only difference is not going to be in expected value, portfolio volatility, or any other metric except in the short-term volatility at both the front and the back end. By staggering the investment I've taken short term volatility out.

So no, target-date retirement funds are nothing like that.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by Uncorrelated »

ValuationsMatter wrote: Wed Jun 17, 2020 7:45 am Quick example: if I invest half my wealth in equities today, and invest the other half in one week, and then on the back end, after 20 years, I sell half of my investment a week before I sell the rest, that is functionally the same thing as having a fixed 100% Equity allocation lump sum in for 20 years, except that I have reduced the impact of short-term volatility both on the front end and the back end. Each half of my investment was invested for 20 years just as the lump sum approach is invested for 20 years. The only difference is not going to be in expected value, portfolio volatility, or any other metric except in the short-term volatility at both the front and the back end. By staggering the investment I've taken short term volatility out.

So no, target-date retirement funds are nothing like that.
In the context of that paper, that is a glide path.

By the way, the order of operations is irrelevant. That means that all of these glidepaths:

Image

Image

Image

Image

Image

Have exactly the same expected return and volatility.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

Address my specific example, please.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by Uncorrelated »

ValuationsMatter wrote: Wed Jun 17, 2020 8:29 am Address my specific example, please.
I thought that was obvious. If i understand it correctly, your specific example is this:

Image

Which has exactly the same expected return and volatility, as this:

Image

Of if you prefer a slightly more complicated example, just randomly shuffle the days to obtain this asset allocation resembling a bar code.

Image

Surely there is no basis to think that this asset allocation (which has exactly the same expected return and volatility as the first one) "reduces short term volatility" in a way that is actually useful.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by alluringreality »

In An Introduction to Computational Finance Without Agonizing Pain, if investor Bob from 12.5.2 wanted to pursue the targets given in 12.5.4, DCA could have potentially moved him in that direction. The investment scenario from 12.5.2 begins with Bob at age 50 and does not address what happened before that point, so there is considerable leeway available to younger investors within the given scenario. In the lifecycle or target-date style example from Method MGP (12.96), Bob actually has 75% stocks at age 50, so maybe Bob might be willing to move large portions of net worth into or even out of stocks on any given day. If on the other hand Bob was more risk-averse, maybe due to limited investing experience, and was reluctant to lump-sum large portions of his life's savings into stocks in one day then DCA might be a reasonable pursuit based on 12.5.4 Criteria for Success. For example if Bob had used DCA to increase stock holdings from say 0%-30% up to say 55%-75% before age 50, then he might have moved in the direction towards the two values that Peter Forsyth offers as considerations to avoid running out of savings in retirement.
Last edited by alluringreality on Wed Jun 17, 2020 11:13 am, edited 1 time in total.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

Ok, let me think about that. One point you still haven't confirmed or refuted, and thus still haven't appropriately addressed in my view, is that the DCA/SCA investor did indeed improve the volatility of his ending portfolio balance by mitigating the variance of the mean purchase/sale prices. I think that point is pretty irrefutable with the central limit theorem backing up the notion that sample means converge into a normal distribution centered on the mean of the population. Thus, the only point you're making -- the one that's in the paper -- is that there is some p* over the 20yr + 1week time period, as opposed to just the lump sum's 20 year period, that will result in equal EV at lower variance. So, maybe if you invested 99.7% (or something) over 20 years and 1 week, instead of 100% over 20 years, that would result in a better outcome (equal EV, lower variance) than either of the alternatives that I presented.

I can see off the bat that you're talking about overall aggregated average portfolio volatility over time and ignoring short term price volatility at the end points, or just stating effectively that they are more than offset by reduced volatility in the portfolio through the entire period. I need to think about how p* over the entire time period would result in a lower ending portfolio balance volatility. It stands to reason and is something I can buy. I'll read the paper to see if the mathematical closed-form proof/solution is actually there and actually applies to this 'glide-path', and/or if it lacks that proof/solution, then perhaps build another stochastic model to prove or disprove that idea. I guarantee another model is not happening for the rest of this week, though.

Also, I found a small section on page 122 of the document that specifically addresses DCA. I need to follow that through to the end, which involves a relook at the formulas & solutions earlier on, and I'll come back to you on this. I remain fully tied to the evidence/data and wherever it leads. I'm happy to be proven wrong if it improves my investment strategies in the future. I can see one problem for most people even if all of that turns out to be correct: Lump sum is easy. DCA/SCA is easy. Research, estimating parameters on the long term market, validating constant assumptions about long-term EV & variance in the desired assets, and then mathematically calculating the optimal p* to mitigate the effects of short term volatility over the life of the investment is hard. I would wager 9, or more, of 10 CFAs would look at you cross-eyed if you came at them with this. The poor saps who can't spell math, but have enough wisdom to realize that short-term market swings can make or break them, still can handle DCA/SCA and an extra few days/weeks/months in the market.

Also, at some point I'm going to read that article cover to cover. I love what I'm seeing in the table of contents.

I guess I'd ask you to take a look at why the stochastic model demonstrated how a 10-period DCA/SCA mitigated price volatility massively with roughly 1/4 the standard deviation in ending balances, when compared to the lump sum approach. Since there's no EV due to growth, time in the market has no bearing; only the method of purchase/sale of the asset does.
Last edited by ValuationsMatter on Wed Jun 17, 2020 9:53 am, edited 1 time in total.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by Cycle »

Tldr. If I hypothetically have 423k from the sale of a rental property, should I lump sum or dca? Investment would be total world (vtwax)

My ips says to lump sum... But I have hypothetically never been in this situation before
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

Cycle wrote: Wed Jun 17, 2020 9:44 am Tldr. If I hypothetically have 423k from the sale of a rental property, should I lump sum or dca? Investment would be total world (vtwax)

My ips says to lump sum... But I have hypothetically never been in this situation before
You should make your own decision. Informing yourself will help. That takes research which can, but doesn't have to, involve reading. Or, if you can't force yourself to read/research, then go to someone you trust and do what they say. There's probably none here that you actually do trust enough, and the length of the thread should make it a given that there are conflicting points of view on the matter. Finally, if you have no one you trust that you can ask, then you might consider going to a CFA and paying them to tell you what to do. Good luck!
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by Steve Reading »

Cycle wrote: Wed Jun 17, 2020 9:44 am Tldr. If I hypothetically have 423k from the sale of a rental property, should I lump sum or dca? Investment would be total world (vtwax)

My ips says to lump sum... But I have hypothetically never been in this situation before
You should pick an allocation that you feel comfortable lump-summing with (VTWAX + VTBLX), and lump-sum it.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by bertilak »

Cycle wrote: Wed Jun 17, 2020 9:44 am ... should I lump sum or dca?
This entire thread and many other older ones are intended to answer just that question. Do you expect to suddenly get a more definitive answer at this point?
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by Cycle »

ValuationsMatter wrote: Wed Jun 17, 2020 9:54 am
Cycle wrote: Wed Jun 17, 2020 9:44 am Tldr. If I hypothetically have 423k from the sale of a rental property, should I lump sum or dca? Investment would be total world (vtwax)

My ips says to lump sum... But I have hypothetically never been in this situation before
You should make your own decision. Informing yourself will help. That takes research which can, but doesn't have to, involve reading.
My research said to just lump sum, I've researched this ad nauseum. But the force of market timing is strong, so strong I don't even want to face the issue by selling the property. Topic here... viewtopic.php?f=2&t=316567&p=5318981#p5318981
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by Steve Reading »

ValuationsMatter wrote: Wed Jun 17, 2020 8:49 am Thus, the only point you're making -- the one that's in the paper -- is that there is some p* over the 20yr + 1week time period, as opposed to just the lump sum's 20 year period, that will result in equal EV at lower variance. So, maybe if you invested 99.7% (or something) over 20 years and 1 week, instead of 100% over 20 years, that would result in a better outcome (equal EV, lower variance) than either of the alternatives that I presented.
Yes, you got it. And it's pretty intuitive right? To the extent the market cannot be predicted, why would you bet 50% on the first week and last part and 100% in the 20 years in between? That only makes sense if you believe the 20 years are somehow much more attractive. Like a portfolio of assets with equal risk/return but no correlation, you want to "spread" you stock exposure across time as evenly as possible (ex: 99.7% over all of the 20 years and 1 week).
ValuationsMatter wrote: Wed Jun 17, 2020 8:49 am I can see off the bat that you're talking about overall aggregated average portfolio volatility over time and ignoring short term price volatility at the end points, or just stating effectively that they are more than offset by reduced volatility in the portfolio through the entire period. I need to think about how p* over the entire time period would result in a lower ending portfolio balance volatility.
I don't know what "short term price volatility" even is, or what risk that is. All Uncorrelated shows with that proof is:
1) Given that you start with $X.
2) Given that the $X will grow to an average $Y after having some exposure to the market through the 20 years and 1 week.
3) The allocation that minimizes the variability about that average $Y (meaning, it has the smallest range of outcomes about that $Y final mean accumulation) is the constant allocation. Anything else (like the graphs he shows) will have equal means but a wider spread of final outcomes.

And isn't that final outcome (both mean and the spread/range about that mean) all that matters? We're saying that if instead of selling/buying all at once, but do it in steps, you actually end up with a wider range of potential outcomes (both good and bad).
ValuationsMatter wrote: Wed Jun 17, 2020 8:49 am I guess I'd ask you to take a look at why the stochastic model demonstrated how a 10-period DCA/SCA mitigated price volatility massively with roughly 1/4 the standard deviation in ending balances, when compared to the lump sum approach. Since there's no EV due to growth, time in the market has no bearing; only the method of purchase/sale of the asset does.
Can you link what you're referring to? I must've missed it. To the extent DCA (or any other glide path that has different percentages in the market at different times) produces lower standard deviation in ending balances, I would think it must be attributable to the DCA simply spending less time in the market (and we should see that in the mean accumulation). You're saying that's not the case so I'd be interested to read what you're referring to.

Thanks.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by ValuationsMatter »

Can you link what you're referring to?
Thanks.
This thread, same page (page 8), my post with timestamp: Tue Jun 16, 2020 1:31 pm.
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by CodeMaster »

adherenceEnergy wrote: Mon Jun 01, 2020 1:43 pm I think DCA makes 0 sense in any circumstance and is an entirely a mental accounting bias. Let's say today you had 300k in an 80/20 portfolio. Would you ever think, now is the time to take less risk, pull 200k out, and slowly put it back in? That's equivalent to having a 100k 80/20 portfolio and getting a 200k windfall and DCA the windfall. If you wouldn't randomly take 200k out of equities and DCA back in, why would you do that in the windfall scenario? The only difference is feeling that "this particular amount of money has less risk" but money is fungible, so why would that be important?

I think it should be never used, as it's only benefit is to make you feel better because you don't understand the mental accounting bias at play.

Am I missing something? Any other thoughts?

Edit: Maybe this example may be more clear to highlight the mental accounting bias. If you had a 100k portfolio of vtsax and inherited 200k cash or 200k vtsax, your decision going forward should be the same. You can essentially pick which one you receive with a few mouseclicks. However, many more people would dca the 200k cash than would convert the 200k vtsax to cash so they could dca right back into vtsax. These are of course the same decisions from a risk and return perspective though.
if you lump'ed sum everything at the peak of 2008 nasdaq highs ... it took 17 years just to come back , giving you zeor profits.

if you DCA'ed in, i ttook 2 years to turn around and start earning profits on the DCA you bought at bottom and low prices
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by papito23 »

"mental accounting bias" ... It seem strange to watch all the angst that people have expecting humans to act like algorithms. Have you ever met a human?
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Re: Why Dollar Cost Averaging (DCA) is a mental accounting bias and should never be used [vs. lump sum]

Post by bertilak »

CodeMaster wrote: Wed Jun 17, 2020 10:17 am if you lump'ed sum everything at the peak of 2008 nasdaq highs ... it took 17 years just to come back , giving you zeor profits.

if you DCA'ed in, i ttook 2 years to turn around and start earning profits on the DCA you bought at bottom and low prices
Hindsight would be great if we could convert it to foresight. If we could do that we would know when to sell off everything!

See my earlier post in this very thread: viewtopic.php?p=5316975#p5316975

Here is a quote:
  • Pro-DCA discussions tend to give hypothetical (or past history) examples (scenarios) and draw conclusions based on observations of the state of the world AFTER the scenario plays out. Decisions need to be made beforehand based on facts known at that time.
Your post is just what I was talking about.

Here's another nearly identical scenario. Someone DCAs leading up to the 2008 NASDAQ. Now what happens?
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