I have a theory about dollar cost averaging that is probably not new but I haven’t seen much on it – although maybe it’s so well known or so dumb that few talk about it.

Dollar cost averaging is an investment strategy whereby a constant amount is invested periodically in a given fund or stock over a long period of time. It is a strategy that is used by a large number of people who have retirement plans through their workplace, such as 401K and 403B type plans. Companies will usually offer a set of funds or other financial instruments that employees can choose for investing part of their salary each pay period. Such an investment strategy has the feature that when the fund or stock price is high, fewer shares are bought and when the price is low, more shares are bought. This fact leads us to the following conclusion:

If there are two or more investment alternatives for which the expected gains are assumed to be equal at any point in time, you will get the highest return by investing in the most volatile alternative.

This conclusion is a result of a simple arithmetic property of reciprocals, which is the mathematical operator in dollar cost averaging. You can see this with simple examples, and I proved it mathematically for a fairly general case.

For example, assume you are deciding between two funds, both of which are now priced at $10 per share. You expect both funds to do equally well, say increase share price about 10% per year. Over the course of three pay periods, Fund A goes to $11, then $9, then $10.50 and Fund B goes to $12, then $8, then $10.50. If $100 were invested in each of the two middle periods, you would have 20.20 additional shares for Fund A and 20.83 shares additional shares for the more volatile Fund B. Not a big advantage at this time, but making 26 investments per year for a number of years can lead to a significant difference in fund total value – again, under the assumption that for each pay period, the expected gain for each fund is the same..

While there is obviously greater risk with a more volatile fund, that risk is minimized because of the long term aspect of such investments, where withdrawals at retirement usually can be done on a planned basis rather than on an emergency basis.

Any thoughts?

You've considered what it means to buy on dips.

Now consider what it means to sell on dips.

I did to a small extent in my last paragraph. Generally you will be buying every pay period by the 401 K company rules, but once you retire you have more control over how you cash in. And, over the course of many years, if the theory is correct, hopefully you will have made enough gain over a more stable fund that you can take a hit if you have to sell on a dip.

I've never been a fan of dollar cost averaging. I just don't think its worth the trouble of even thinking about it, and statistically it becomes less significant the longer the time period of investment is.

In general, if I like something, I buy it and hold it. If you are buying something and going to sell it within a few years and want to minimize your risk exposure and going though these dollar cost averaging scenarios, I think you should just buy something that is less risky.

Just dump the money in and hold it. Making incremental investments over time can help if the fund is going downwards. Upwards, you are costing yourself money. If its an individual stock, you are costing yourself money in transaction fees.

Any thoughts about my logic here? Feel free to call me an idiot, but I did look at this scenario about 8 years ago and came up with the above conclusion, and nothing has changed my mind about it since.

I started the thread with the idea that many employees invest every pay period to take advantage of a company benefit. My company contributes up to 11% of my salary into a 403B. I must designate where that money goes each pay period, say into a money market fund, a fairly stable stock or a volatile stock. If the three investments grow at the same rate, I will have the most value with the volatile fund. If it was my own money I was investing, then, yes, I could save it up and buy something once every x months or so.

Those three won't even come close to growing at the same rate. The difference in growth rates between cash (money market) and stocks is *staggering*, in a historical sense.

What is the investment difference between the stable stock (which, in my mind, is an oxymoron) and the volatile thing? What do they both invest in?

I probably should have said funds. Fund (or stock) volatility can be measured by the Beta statistic, how much a fund varies compared to the overall market. Different funds can grow at the same rate but one can vary just a small amount around its expected growth rate and the other can vary much more. The whole point of this is to show that the arithmetic works out that you will buy more fund shares with the more volatile fund. If the two funds end up at the same price -- and that is the assumption made at the very start, then having more shares of the volatile fund means more value.

I'm pretty sure DCA has been shown to be ineffective. I think that is due to the fact that you are holding money out of the market though which doesn't apply here. I'm certainly no expert though so I could be screwing something up.

Your math is bad. The expected value/gain/increase of DCA ALWAYS trails lump sum investing.

No, the math isn't bad. You ignored the constraint. You can't do lump sum investing. Suppose I get paid 500$ a week. Each week the company contributes $50 to a fund I select from a set of funds. I can't retrieve that money until I retire or reach a certain age. In other words, I'm forced to do dollar cost averaging or else just refuse the company contribution, I suppose.

I don't think what you are talking about is DCA, though. DCA is when you do interval buy orders in a set amount of time to minimize the negative effects of investing a lump sum when the price is depressed.

What you are talking about is just investing at regular intervals in a mutual fund, through a retirement program. The difference is you don't have a choice in the matter.

This should be obviously true to everyone (but sadly it isn't), is easily demonstrated theoretically and has been demonstrated empirically as well. However, I don't think anything in OP's post is contradicting this.

One thing DCA can do is reduce your variance. For some people, a variance reduction may be worth a decrease in EV. But your EV still goes down if you dollar cost average (instead of lump sum).

Fund A Move 1: 10% gain
Fund A Move 2: 18% loss
Fund A Move 3: 16% gain

Fund B Move 1: 20% gain
Fund B Move 2: 33% loss
Fund B Move 3: 31% gain

If you're timing your buys after each of these moves, thats really poor investing and you're better off doing "true" dollar cost averaging once a month or whatever.

Once you move beyond quarterly dollar cost averaging, it simply becomes lump sum investing, IMO.

Plus you're making numbers up to fit your theory. Theres some logic term for that, Thremp could probably help in that regard.

FYP

Yeah, I was reading the above and projecting the lump sum/DCA argument. I have not really considered what he wrote, perhaps I should. It seems to be somewhat... bad though at first glance. I dunno. Maybe checking out a model for this would be worthwhile in my time allocated for mental masturbation.

One more time

1. If you want to take advantage of the company's retirement benefit,you select a fund from a choice of funds provided.

2. Every payday, a fixed amount is contributed by the company to invest in the fund or funds of your choice.

3.That is equivalent to dollar cost averaging - a fixed amount invested periodically, at least as I understand it. By the way, I don't think that this is so unusual.

4. I have proven mathematically the following:

If you assume two funds have the same expected growth rate with a uniform distribution of the price for each investment action, then you will buy more shares of the fund with the greater variance (greater Beta, greater volatility). The example I used was just a way of illustrating this.

So, I believe the talk about lump sum vs. DCA is not the issue -- the issue is -- given you must dollar cost average, what is the best choice of investment. My point is that volatility has a benefit, while I think the general consensus among investment professionals is to leave the more volatile choices to the risk takers.

Its not really DCAing. You're entering 100% of your monies as soon as you get them.

The general consensus of investment professionals is to see where volatility fits into a mean variance portfolio. It is not to avoid volatility, for security specific volatility can decrease portfolio volatility.

The main reason for Dollar Cost Averaging is a lack of information/trading ability coupled with a desire to gain exposure to an asset. There is no economically superior reason to dollar cost average, unless doing otherwise would lead you to incur excessive trading costs (implicit and explicit). Hence, you are right, the more volatile stock is the one you are going to want to DCA in a world where you are DCA'ing. The reason for this is because if it's more volatile, you are at an even higher risk of getting a poor price that may take years to return from due to your poor execution of trading. But let it be clear, it is not some optimal thing to do, and yes it's good in the sense that it will protect you from being fully weighted in the absolute high if you have no idea when or how to trade.

I understand now, my apologies. You have 2 investments that have the same expected return but the volatility in the 2nd fund is much higher, therefore increasing your chances of buying shares when the price is lower. If the expected final return is equal, then those times when you bought into the fund when the prices were lower will benefit you in the end with a higher total account value.

Makes sense, my gut reaction was it would simply even out over the long run, or that something strange is going on here, since this concept is something that should have been proven out already, and generally accepted. In other words, if I don't know about this then I don't know how "true" it is. In my mind, taking on more risk/volatility should almost never have the same return as another fund. Whatever, maybe I'm wrong. But, I found this for you, take a read and let me know what you think

"Volatility is not automatically better
Sure, it's possible that dollar cost averaging into a volatile fund may beat making the same investment in a more stable fund. But there's nothing inherent about volatility guarantees you'll end up with more money by investing regularly in a volatile fund. And you could just as easily do better in the less flighty fund.

To prove this, let's engage in what Albert Einstein called a "thought experiment."

Assume you plan to invest $5,000 a year for five years and have a choice between two funds: the Steady Eddie fund and the Roller Coaster fund. And let's assume both funds will return an annualized 8 percent over the course of the five years you invest.

As its name implies, Steady Eddie earns that return, gaining exactly 8 percent each and every year.


The Roller Coaster, not surprisingly, gives more of a white-knuckle ride. It loses 20.5 percent the first year, loses another 10.5 percent the second year, recovers for a 10.5 percent gain the third year, surges to a 20 percent gain the fourth year and then finishes with a bang, a 55.7 percent gain the fifth year.

Those returns, however, still translate to an 8 percent compound annual gain over the five years, the same as Steady Eddie's annualized gain.

Which fund would increase the value of your $5,000-a-year investment more? Well, if you do the arithmetic, you'll find that at the end of five years you would have ended up a lot more in the Roller Coaster fund than the Steady Eddie fund: $44,034 vs. $31,680. So case closed, right. The more volatile fund wins.

Not so fast.

What if the Roller Coaster fund had the exact same annualized return and even the exact same annual returns, but the order of the returns was reversed?


In other words, let's say market conditions were such that, instead of getting the lousy returns first and the stellar returns at the end of the period, the fund started off with a bang and ended with a whimper, gaining 55.7 percent, then 20 percent, then 10.5 percent, then losing 10.5 percent and then losing 20.5 percent? Could happen, right? Nothing says returns have to play out any particular way.

Guess what. Do the arithmetic based on the new sequence of returns and the Roller Coaster fund ends up with $23,526, much less than Steady Eddie's $31,680. The fund is just as volatile as before, but it didn't come out a winner.

Random chance and investing
So what does our little "thought experiment" tell us? Well, it tells us that volatility can work in your favor, but whether it does or not is largely dependent on the time period you choose and how the returns play out over that period.


If you get lousy returns at the beginning of the period and great returns at the end, volatility works in your favor because the higher returns are applied to more of your capital. If the reverse is true -- you get the best returns at the beginning and horrible ones at the end -- then volatility works against you. "


Makes sense to me too. Also, keep in mind something very important : you have to time how you take the money OUT. If you are ready to start taking distributions or coming close to that time, you have to make a decision of whether you will just take the money out regularly, or move it all out in a lump sum. Lets hope you take it all out at a high, instead of a low.

This comes completely in line with the thought that "if you beat the market, you got lucky". There's nothing wrong with luck. In fact, I got extremely lucky last year. But don't think you are beating the expected returns by getting lucky or not seeing certain scenarios.

Let me know what you think, I'm interested.

So how is this new? This is just market timing and/or analyzing your investments. We all know most people will fail at this.

Are you sure you proved this? Seems like you haven't considered all the cases. The one that's more volatile could also lead to less shares in some cases, right?

yea i gotta chime in here. unless im missing something this is uber basic.

volatility has a benefit only if it comes with higher expected returns. otherwise the sharpe ratio will be lower than the alternative. that said, utility of higher returns may warrant selecting a slightly lower sharpe ratio instrument absent the ability to lever the higher sr (lower returning/lower vol) instrument.

otherwise, what your'e saying seems ludicrously obvious and has been proven a billion times over:

assumptions:
1. long investment horizon
2. youngish investor
3. employer pays into defined contribution benefit scheme.

given a choice between a 5%/15% ret/vol fund and an 8%/24% ret/vol fund, obv you select the 8%/24% one as the predominant allocation (and maybe even 8%/26% etc. as noted above) given the long investment horizon and inability to lever the 5%/15% one.

however, over time, as the investment horizon shortens, utility is reduced by significantly higher vol andt he marginal benefit from increased return is lowered as well. these two factors mean that over time, you should switch from mostly 8%/24% to a more even mix, then to mostly 5%/15%, then to a mix of 5%/15% and cash etc.

i guess i dont get the point of your initial post? this is like <investments 101 right?

Barron

PS - also, wtf does DCA have anything to do w/ this? the same logic applies to lump sum and i guess you're calling it DCA simply b/c you get paid every period? the point of your post is portfolio allocation though and the results will be identical in terms of your choices if you got your entire discounted lifetime salary at time t0 or it is spread across time. the only difference there is that you have to manually rebalance the discounted lifetime earnings scenario vs. being able to rebalance w/ future allocations.

"Investments" go to zero all the time...
Or to penny stock = effectively zero.

That's the real world reason DCA doesn't work... because DCA "advantages" are wiped out be occasional HUGE losses. More volatile investments will incur HUGE losses more often. So your 3 data point "analysis" is silly.

You may say that doesn't apply to conservative, diversified mutual funds... not really, lots of Blue Chip financial and REIT funds went to "effective zero" in 2007-8.

DCA is a subset of the Free Lunch Fallacy.

The Securities Industry is built almost entirely on the Free Lunch Fallacy. The Business Model as applied for 100 years by smooth talking stockbrokers is: "Let's convince this moron (er, client) that HE CAN TAKE MONEY AWAY FROM ELITE PROS in a Zero Sum Game using this simple, high school level method: DCA, TA, Charts, hot tips from a salesman, etc, etc"

If you believe any version of the Free Lunch Fallacy...
You will never be successful is any endeavor.

You don't know what zero sum means.

what 'advantages' does dca have? of course volatile investments will incur huge losses more often. so even though i dont even knowwhat you're responding too so i'm just addressing that statement by itself.

so how does it not apply to conservative, diversified portfolios (forget mutual funds) given that some blue chips went to 'effectively zero'?

diversified ports will outperform other ports.

the issue NOW is that there is a way higher propensity for corrs to really go super close to one across the asset spectrum so all ports can suck for periods of time.

Barron