from the Fund Library

There are two (at least) Dollar Cost Averaging problems:

1. You've got $100/month to invest. Is it best to invest it each month (that's DCA) or should you collect the $100 each month under your pillow, waiting till the market goes UP or DOWN (or some such criterion) ... then invest all of what's under the pillow?
2. You've got LOTS of money (you sold your house, your uncle died, etc.). Is it best to put it into the market All-At-Once or should you DCA: say 6 equal investments over 6 months, starting immediately ? (we'll call this DCA/6) or 12 lump sums over 12 months (DCA/12), etc.

I'd like to talk about Problem 2, because somebody on some thread mentioned some website where somebody advised DCAing over 12 months or something (... sorry, can't remember who or where). That's DCA/12.
Now the road gets bumpy so you may want to turn back ... else, if you're a masochist ...
Suppose you have LOTS of money, say $A, and divide it into N equal parts (namely A/N) and you invest each part over the next N months (with the first part invested immediately).
Important note:
If you buy $K worth of units at $P per unit, you get K/U units.

Okay, suppose the unit price starts at $P and the Gains over one month, two months, three months, etc. are called G₁, G₂, G₃, etc. then the unit price at the end of month one is PG₁, and at the end of two months is PG₂, etc.
NOTE about what I mean by these "Gains":
If the total gain over two months is 5.3%, then G₂ = 1.053
If the total gain over seven months is 12.3%, then G₇ = 1.123

So how many units do you own after N months of DCAing?
You buy (A/N)/P units immediately ('cause you buy $A/N worth of units at $P per unit).
At the start of the next month you buy (A/N)/(PG₁) units.
At the start of the next month you buy (A/N)/(PG₂) units.
...
At the start of the next-to-last month you buy (A/N)/(PG_N-1) units.
Total number of units purchased (with N purchases of $A/N each) is:
(A/N)/P + (A/N)/(PG₁) + (A/N)/(PG₂) + ... + (A/N)/(PG_N-1)
Count 'em ... there are N purchases here.
The number of units (above) can be rewritten:
(A/P)(1/N)(1+1/G₁+1/G₂+...+1/G_N-1)
and, behold, the last piece, namely
(1/N)(1+1/G₁+1/G₂+...+1/G_N-1)
is the average of the reciprocals of the gains over zero, one, two, etc. months.

We'll call this average Q (why not?) so the number of units you hold after N DCA investments is (A/P)Q.
How about if you purchased all your units at the start?
You'd have $A to spend All-At-Once and each unit costs $P so you'd have A/P units.
Question:
Are you better off with (A/P)Q units (that's DCA/N),
or A/P units (that's DCA/1) ?
Answer:
DCA/N wins only if Q > 1.

Gummy,

I think I'm with you, and I'm not sure what kind of responses you're looking for. I would just make the observation that for the period 1975-1997 we would expect DCA to (on average!) be less effective that lump-sum investing, because the market has gone roughly straight up during that period. Thus the earlier you invested the better.

I doubt DCA would look so bad if you looked at 1968-1982. Also, the market in a 12 month period may go down, down then back up, etc., so using DCA to invest a large sum still makes sense.

JG

I understand why this thread was entitled DCA for masochists! If I have to work out these calculations, I'd rather go broke.

Gummy, It is possible that the comment you are referring to was posted by me (break the buys into 18 equal amounts ect., but I cannot for the life of me remember which thread it was). If I am correct them I would like to point out that I was suggesting this strategy given the uncertain markets that we are faced with at this time. As noted in the posting above, the time frame under consideration is going to be critical. In a bull market investing all at the beginning is clearly going to be better than investing in stages at ever higher prices. The reverse is also true, that is, during a bear market, where you would be buying at ever lower prices, a DCA program would be better than if you had invested all at the beginning. It certainly would be nice to wait for the bottom and then buy, but what if the market goes up rather than down. We have been fooled a number of times over the past few years. On a number of occasions it looked like the BIG ONE had finally come, but low and behold the market rose to new heights. So what about the guy who was waiting for the low to buy. CONCLUSION: the best time to start a dollar cost averaging program is at market tops, the worst time is at market bottoms. If it looks like we may be at a market top and you wish to invest, start a dollar cost averaging program. If it looks as if we are at a bottom get your money into the market at as fast a pace as possible. BWG

John ... gotta find me some more data, like 1968-1982.
BWG ... agreed. Indeed, I've been takin' money OUT of the market for the past three months.

gummy,

Is that the title of your forthcoming book on the subject?

rge - Thank you for one of the best laughs I've had in a long while. It was a great start to the day and mirrored my feelings exactly.

gummy - great analysis, the first reading was just a bit overwhelming. I do agree with BWG on this issue, uncertain markets allow this strategy to work to its fullest potential.

gummy,

I want to thank-you for sharing your analysis with us. I'm in the exact situation you desscribe i.e. a large sum to invest.

Although I agree with your conclusion, we all know that past performance is no indicator for future performance. I expect this 8 year bull market will regress to the mean some time soon.

That said, I have chosen to continue DCAing into the market very cautiously while taking advantage of any market dips on the way.

Averaging into the market is a great idea right now. I would schedule it for 12 to 18 months depending on the sum of money to be invested. Then if there is a significant short-term drop, add a little extra to your investment to take advantage of a sharper short term decline. So it's sort of a mix of systmatic investing with a sprinkle of market timing.

gummy -

Do you have a particular investment decision to make or are you just having fun?

Here's another question you may be able to answer with your data. It's not the right question, but I would guess it's one that the average investor off the street would like answered:

If I move my nestegg to equities now (DCA/1,3,6,12 or 24 from MMF), what is the chance that I will ever see a monthly statement showing my nestegg has declined to less than 95% of its original value?

BWG - as I recall, gummy's using ATP (all time periods) analysis.

Randy.

Anyone with a brain in his\her head realizes in 10 seconds that the only way DCAing pays off is in a declining market.Gummy gives a perfect example of what not to do when making an investment decision.

Randy ... just having fun (and I wanted to see if I could reproduce results similar to that given in the Do Not Dollar-Cost-Average for More than Twelve Months hotlink which Bylo has provided, above).
I'll work on the problem you suggest: "If I move my nestegg to equities now ... what is the chance that I will ever see a monthly statement showing my nestegg has declined to less than 95% of its original value?"
. I'll assume that "now" refers Jan/75 ... or did you want the answer for t > Nov/97? Remember, Rob has my (cracked) crystal ball.

jimmy,

It is incorrect to say that the only time dollar cost averaging works is in a declining market. It only works (to its maximum dollar advantage) in a declining market that has a subsequent advance which brings the price of the security to a level which is higher than the securities average purchase price.

Dollar cost averaging's main purpose (in my opinion) is to reduce/eliminate the risk that an investor will put all of his/her (or a major amount of) money into the market shortly before a major decline. If the purpose for which DCA is being used is to reduce risk (to a greater or lesser degree) rather than to somehow increase returns it will work at any time.

DCA does not and can not guarantee profit. As noted above (and this bears repeating) it will generate profit only if the price received at time of liquidation is greater than the average price paid. There is no guarantee that this will be the case.

BWG

With today's high cost of living I treat DCA as another payment which comes out of my account monthly . This way I am assured that the money will be invested before it is spent which would be easy to do now days .

Investing, as with many other things in life, is governed by the universal truth:
ya win some
ya lose some,
the important component being the first part.
I dislike the idea of DCA (or any strategy which involves "close your eyes, follow these rules, don't peek, don't think, just do as I say".
Here's a picture of the recent TSE (ending yesterday):

It's clear that one could never have predicted these gyrations or when to jump in with a large sum of money ... you might just as well have closed your eyes, invested weakly and relied upon
ya win some
ya lose some.

Gummy, I always DCA if one of my investments goes down due to fickleness of the market ie. no good reason. So far it works but of course, if u always were able to buy at the bottom(hah) DCA makes no sense. I never DCA on the way up and cant see any virtue in this strtegy at all.

Good thread. I think that Doug's approach is the one which is being generally accepted by most individuals. It does force them to invest on a regular basis and many (most) people have trouble disciplining themselves to put away money for retirement or non-registered savings. The fact that it serves them well in a declining or volatile market is just an added bonus.

Randy ... I've been playing with the problem you posed (which I interpret as: "How often would you lose more than 5% of your portfolio, after N months, if you DCAed over N months")

I must admit that I didn't believe the results and kept reworking the spreadsheet. Here's the result for the Canadian Large market:

What surprised me was not that the percentage was small, but that the percentage was practically independent of N!

ya win some
ya lose some
... ya pays yer money
ya takes yer chances

Gummy..... just invest, and keep doing it (DCA) hills, valleys, hills, valleys, hills, valleys, but there's always more hills.

6 mths, 12 mths, 18 mths, 24...etc it's not THAT important, just do it.

You'll get rich over time.

Cheers, The Wealthy Bartender

In Benjamin Graham's classic book The Intelligent Investor the author cites a study by Lucile Tomlinson. In her study of formula investment plans, Miss Tomlinson presented a calculation of the results of dollar-cost averaging in the group of stocks making up the Dow Jones Industrial Average. Tests were made covering 23 ten-year purchase periods, the first ending in 1929 and the last ending in 1952. Miss Tomlinson concludes her discussing of the DCA method with the statement "No one has yet discovered any other formula for investing which can be used with so much confidence of ultimate success, regardless of what may happen to security prices, as Dollar-Cost Averaging."

gummy,

From my readings most researchers now agree that a study period of 20-25 years is required to determine the validity or lack thereof of any investment formula. James O'Shaugnessy states in his book What Works on Wall Street that by using reliability mathematics (I suspect you are familiar with this) pension consultants have found that a minimum of fourteen time periods is necessary to begin to make predictions about future performance. With this in mind, I would therefore agree with the comments of others that a longer time period than the one you used to start this thread would be required before any valuable conclusions can be made.

What are my thoughts on dollar-cost averaging? I don't use it for the same reason most other people don't - it is hardly practical. When I identify what I consider (read hope) to be a good investment I act accordingly. I do point out that my crystal ball is like gummy's - cracked!

Lado

OK, I have the question for you. Here's someone with 60K invested in RRSP Mutual funds, don't need this money for 10 years. Also play money invested in stocks (they are doing well!). My question is how do I choose the best route, I've read everything under the sun, asked thousands of questions on mutual funds. But with the recent market upveals where the hell do I do. Stay and wait out the rollercoaster or do I sell some and place even though I will loose some. Now I've interviewed several fund advisors, I have not come accross one that I felt comfy with, what I felt was gees if you apply the general mumbogumbo if your an aggreesive you should invest like and well you should get this much by then. Is there a light at the end of tunnel for do yourselfvers.

Axiefox,

There are good advisors out there, keep looking, ask people that you respect who they use and why.

As to do-it-yourselfers: read, Personal Investment Portfolios, by Dr. J. S. Cochran, International Publishing Corp., Chicago, Asset Allocation: Balancing Financial Risk, by R. C. Gibson, Business One Irwin, Homewood Illinois, and The Art of the Long View, by Peter Schwartz, Doubleday. These will give you a good foundation. Knowledge is power and if you want to do-it-yourself you had better know what you are doing. Use the above texts as a beginning, read as much as you can, always take what you read or hear with a grain of salt, engage in the sharing of ideas (as we do in these threads).

For those interested in an in-depth analysis of Asset Allocation Strategies I refer you to, "Dynamic Strategies for Asset Allocation", by Andre F. Perold and William F. Sharpe, Financial Analysts Journal, Jan-Feb 1995. While this does not deal specifically with DCA it should provide much food for thought and provide for a framework within which to use DCA effectively as an asset allocation tool.

gummy, you in particular should enjoy the Perold/Sharp article.

gummy -

Too bad about your crystal ball.

Regarding your graphs: Like you, I'm amazed how flat they are! If my original question accurately reflects the average person's perception of risk, then DCA as a risk reduction strategy doesn't appear to be worth much.

Not asking for more graphs, but here's an interesting thought. I wonder if the results would be as independant of N if you looked at the end value of DCA/N always after 18 months. If you're in a generally appreciating market, this line may actually slope upwards, indicating that lump sum carries less "risk" (in many people's eyes)!?

Thanks for the interesting analysis. I haven't seen your voice on the "If you pay taxes - buy the index" thread... this has been my hobby for the last week while you were accounting for the missus. Any thoughts?

Randy.

Hi Gummy, I realize this is a bit much to suggest but it would be a great help if one could print all your excellent the math/graph info that you have provided from one consolidated thread source - untill your book comes out, that is! It could be "Gummy's math/graphs", for example.

A grateful Fan

Lado sez: researchers now agree that a study period of 20-25 years is required
and
a longer time period than the one you used to start this thread would be required before any valuable conclusions can be made
Well now young fella, ah figur AVERAGE(20,25) = 22 1/2 years am sho enuff fer testin' DCA/12.

Randy: good idea ... I'll try that. (Actually, I started to consider DCA/N, for N = 1, 2, etc., where you look at your portfolio every month until the end of the 22 1/2 year period, but that's over a half-million cases and this ribbon of blue smoke would rise from my computer ...)

Fan: good idea ... I'll do that!