from the Fund Library

I'm not a fan of Dollar Cost Averaging (DCA). Putting money into investments at the end of each month (without thought, synchronized with the phases of the moon) seems an admission of cerebral frailty. So I decided to prove that waiting for a correction would have been a better strategy (in the past, of course, since Rob has my cracked crystal ball so I can't predict what'll happen tomorrow).

PROLOGUE

Having found (with Bylo's help) a website which has monthly returns from Jan, 1975 to June, 1997, for various world markets, I set out to prove my thesis:
SAVE YOUR $100/month in Money Market (MM) UNTIL A CORRECTION,
then INVEST IT ALL AT ONCE.
(Of course, there are those who will argue that DCA is to reduce your risk, not to improve your return ... so I address this to those who want to maximize returns.)

I chose a very volatile market (annualized return = 14% over this period), namely Pacific Large Cap, with a Standard Deviation (SD) of 6.3% over this time period (compared to U.S. Large Caps with SD=4.1%).

I considered nine strategies:
Keep putting your $100 each month into MM (at 5%/annum) until there are FOUR successive drops in the (Pacific) market, then invest it all at once. If the market drops again the following month, invest your $100 again. Continue until the market goes up, then switch to putting your $100 into MM again ... waiting for the next drop for FOUR consecutive months. (Below, I call this strategy DOWN-4.)

I repeated this strategy, waiting for corrections over THREE, TWO, and ONE consecutive month(s), as well as waiting until the market has gone UP for ONE, TWO, THREE or FOUR months.
(These last strategies are for those who mumble, "Aah, now we're on a roll ... time to jump in.")

In the following table, the value of your investment (in some FUND which mimics the Pacific Index) and the amount in MM and your TOTAL portfolio is given as of June, 1997 (assuming you began these strategies in Jan, 1975):

PACIFIC LARGE CAP

STRATEGY	FUND	MM	TOTAL
DOWN-4	$93,337	$7,037	$100,374
DOWN-3	$113,458	$7,037	$120,495
DOWN-2	$117,277	$504	$117,781
DOWN-1	$122,609	$301	$122,910
DCA	$126,229	$0	$126,229
UP+1	$124,847	$0	$124,847
UP+2	$123,241	$0	$123,241
UP+3	$122,338	$0	$122,338
UP+4	$115,198	$5,411	$120,609

EPILOGUE

"SweetiePie," I groan, "Look at this! Must be something wrong here! Lemme check the calculations ... no ... okay ... so lemme try U.S Large Cap ... same thing!! ... Cdn Small Cap? ... Aaargh! ... DCA wins again!!!"
"That's okay HoneyBun, you're right sometimes," she sez. "You married me, didn't you?"

I read your results with EXTREME interest. The truth seems to hurt more often than not (boy do I hate facts!). Thank you for the effort. I can now let another (read fund manager) play with my money and I can get on with life.

P.S. Which fund manager employs DCA?

I read your results with EXTREME interest. The truth seems to hurt more often than not (boy do I hate facts!). Thank you for the effort. I can now let another (read fund manager) play with my money and I can get on with life.

P.S. Which fund manager employs DCA?

Shoe,

I can't think of any that DON'T DCA. So probably any you are interested will be fine.

Gummy:please refrain from using french in your titles.As a patriotic English Canadian I consider the use of french in this forum an extreme obsenity.I am also against DCAing.

Mamma mia!

Bonjour larry. Moi, je pense que votre remarque n'est pas gentile du tout. Moi, je souhaite que les gens qui parle la langue de Moliere ou decide de utilizer cette langue ne pas tenir compte de votre avis.

Thanks for the work gummy. Very interesting! Beats the hell out of my idea of saving for drops. Now....I wonder what a graph would show about a portfolio of set percentages (say 10% us small cap, 10% us large cap, 10 cdn small cap, 10% cdn large cap, 10% far east, 10% europe, 10% south american and 30% world value) with a strategy of saving every month then buying the funds back to percentages every quarter (or half) would fair vs a strict monthly DCA.

:-)

gb

This Article on DCA was in the October Efficient Frontier Website. http://mail.coos.or.us/~wbern/ef/997/dca.htm

Thanks for the research and calculations gummy! I have to admit to being surprised.

I have never seriously considered a strategy that consistently keeps available money out of the market. As you know from my bantering with jd a few weeks ago, I have compared DCA with a leverage strategy funded by would-be DCA dollars (grossed up for account for tax savings). I know you're not interested in a leveraged strategy, but I raise it to extend your point that for all but the worst timing, the earlier you get your money into the market the better.

Nellie, thanks for putting larry in his place. I couldn't have done it as well.

Randy.

I'm a fairly bilingual Francophone surfing this web site on a regular basis and my goal is twofold:

a)To broaden my knowledge by listening to what other mutual fund unitholders have to say.

b)Try to bring my own POSITIVE contribution--whenever I can-- to my peers whether Francophones, Anglophones or any other nationality--it does not matter.

I'm glad to see that there are still some people who have respect for their peers--no matter their language or nationality.

Larry's racist remark above only serves to reinforce what I've always believed: it is personality that differentiates people. Not their nationality.

Thanks to all people who have shown some respect for their French speaking peers on this forum.

Thank God, remarks like the one above are very seldom encountered here.

Un merci special pour toi Nellie pour etre venu a la defense des Francophones et merci de l'avoir fait en Francais.

Sorry Larry for the extreme "obscenity" (not obsenity) of the previous paragraph. And BTW, "As a patriotic English Canadian" I think you should devote a little more time learning how to spell the words of this language that you so highly praise.

Best regards to all--including you Larry.

Andre

Andre

Gummy,

what would be the "Total" for putting all funds in on day 1 without waiting for the first month up?

Larry, if you care so much about your language you should at least learn how to write its words properly ;-)

Andre,I couldn't agree more with your sentiments.As a French Canadian born and raised in southwestern Ontario,I am proud to say that I understood all of your words,as well as Nellie's welcome reproach to Larry.Can you imagine the likes of Larry in Europe where most people speak at least two languages.A wordly type he is not.

Un grand bravo pour ceux qui réalisent que le Canada billingue est quelque chose de quoi etre fier.

It's nice to see that most people don't support racism and welcome the existence of several other nationalities.

I don't think Larry realizes just about how many francophones, and other people from diverse background, visit this site.

Cheers, Rice

Gummy: How about doing the MM deal, but only waiting until each 5% market drop (from whatever was its previous high), then investing all available cash.

I suspect though, that DCA going to be hard to beat, no matter what the strategy.

Cheers!

larry: larry? are you still there?

Greg B: too much work ... can't seem to get off this couch.

Jurgen:
what would be the "Total" for putting all funds in on day 1 without waiting for the first month up?
I assumed each contestant has $100 to invest each month. Miss DCA invests immediately (1^st $100 on Jan 1/75. 270^th on June 1/97). The other contestants wait till their respective criteria are met. The annualized return (Jan 1/75 to June 30/97) was 14%/year (actually 13.83%) and the total gain over this period was 1743%. (Uh ... I guess I don't understand the question.)

Jay: I'll try that (and report back) ... if I can extricate myself from this couch.

In order that no one be confused about this $100/month-DCA-strategy, let me suggest

A COMPLETELY DIFFERENT QUESTION:

At time T₀, Sam & Sally each have $1000 in MM.
Sam takes out $100/month for 10 months to DCA-invest in the PacificIndexFund (PIF).
Sally puts $1000 all-at-once into PIF, at time T₀.
There are 260 possible T₀s (between Jan 1/75 and Sep 1/96).
What percentage of these will see Sam the winner, on June 30, 1997?
Nice question, no?
The closest answer will receive one bushel of bananas.

... or a bushel of gold, whichever is cheeper.

87.2%

Randy.

Oops, that was for lump-sum-Sally. Leaving a 12.8% chance that DCA-Sam will win.

Gummy, It would be interesting to run your competition for a less volatile market for comparison - I'm assuming this would be fairly easy now that you have the spreadsheet built.

Randy.

Gummy...Ya, I thought it would be allot of work and just threw it out as a suggestion; Would be interesting to see those results though. No problemo.

gb

Gummy,

please let me try again. 270 month x $ 100 = $27000 total input?

Your basis was that the investor has $100 per month available for investing.

What if he has the total $27000 available on day one but chooses to DCA $100 a month, keeping the rest in a MM. What would be the difference in return a) for the case with the lumpsum payment of $27K on day one and b) with $ 100 DCA on the basis of your data?

Gummy, I was lying in bed last night tossing and turning with visions of DCA'ing dancing thru my head.

When what should appear, but a thought that current DCA'ing is a time-based timing strategy (how queer!).

The reason DCA is so powerful is that it takes the emotion (and second-guessing) out of investing by requiring discipline on the part of the investor.

But let's take DCA somewhere else: a DCA strategy based on market place changes. How about something like this:

Common sense suggests that one excellent day (month, year) in the market is likely to be followed by an average or subpar day (month year). Therefore some strategy that levers that rationale or variant thereof, could possibly produce a return exceeding DCA

Suggestion 1) Money is invested into the market at the usual rate ($100/month), where the prior month showed a return rate between 0.5%-3%.

Money is built up into the money market fund under the following conditions: if the return on any particular month exceeds 3%, then the following month, only ½ (or maybe none if greater than ??4%, 5%?) of the usual is invested into the market, with the rest going into the MM fund.

Money is expended from the MM fund under the following conditions: if the return rate in any one month is less than ½%, then one-half of the money market funds are invested the following month. On any market dip of 5% or greater, ALL MM funds are invested into the market.

Suggestion 2) Your variation of above idea?

I'll bet that some form of this thinking will beat regular DCA.

Is this too much work to test gummy?

Cheers! Jay

Jurgen: AHA! I understand ... and that's the basis for the Question I posed above:
At time T₀, Sam & Sally each have $1000 in MM.
Sam takes out $100/month for 10 months to DCA-invest in the PacificIndexFund (PIF).
Sally puts $1000 all-at-once into PIF, at time T₀.
There are 261 possible T₀s (between Jan 1/75 and Sep 1/96).
What percentage of these will see Sam the winner, on June 30, 1997?
The closest answer will receive one bushel of bananas (or gold, whichever is cheeper).

I now have the answers (for a Pacific Index, Cdn or US Large Cap Index, etc.). Indeed, the spreadsheet I devised allows one to choose N, the number of months over which Sam DCAs into the market. (In the Question above, N = 10.)
I note that, as N increases beyond N = 20 or so, DCA is usually a VERY BAD move (cuz, by holding $$$ back in MM, you lose out on all the gains most markets achieve during N months ... when N is large). Of course, it depends upon when you begin this DCAing. In general, at the beginning of a run-up in the market, DCA spread over too many months is BAD. If the market is bearish, that's a horse of a different hue.

Jay: Nice problem ... I'll work on it.

I gotta figure a way to put these neat graphs into my posts ... showing the MarketIndex and, superimposed, the periods (from Jan/75 to Jun/97) when all-at-once investing beats DCAing.

P.S. Jay, I'll make my spreadsheet more understandable and e-mail it to you ... and you can play, too!

P.P.S. I just read the article pointed out earlier in this thread (Bruce: 09-Nov-97-07:07 PM) and find a similar analysis!

gummy, re "I gotta figure a way to put these neat graphs into my posts". Can you put them on your website and add links to them here?

P.S. Thanks for the Remember thread. It's especially meaningful to me since I'm playing an alien today. It'll be interesting to see what happens at 11:00 this morning.

Good idea, Bylo!

S'funny, I done did that B4, but forgot ... old age, ya know,

Gummy, someone is going to have to dream up a special economic-mathskill award for you!!!

You are a really MOST interesting contributer, indeed.

Thanks for all your work- this adds real perspective to what most of us are trying to do. I checked out your graph on the other thread- Great stuff...

Thanks again- Keep up the new and interesting ways to illustrate your ideas:)

gummy, where is your website?

shhh ... secret ... can't divulge where I live ... besides, nothing much to see ...

Just bringing this thread up again.

The benefits of DCA would appear to be obvious for small investors (like myself). However, once a person has a significant lump invested in the market, won't their returns be driven by the amount of capital invested, rather than the method it was invested? In Gummy's example the investor who DCAed for 270 months has $126 K in the market. I would suggest that at that point the method of investing will have little effect on future returns (i.e. whether they invest an additional $100 each month, or make $1200 annual investments). But unlike Gummy, I have no empiracal data to support this position!!!!!!

Don

Aah, but the next 270 months would be like the last 270 ... for the NEW money invested. Two strategies which gave 120 and 126 Kilo-bucks the first time 'round would presumably give 120 and 126 the NEXT time so the two contestants (in this DCA competition) would now have 120G+120 and 126G+126 where G is the Gain over the NEXT 270 months.

The ratio is:
(120G+120)/(126G+126) = 120/126 as it was at the end of the first 270 months.

P.S. It's interesting: the difference is about 5% in this example and would also have been about 5% if the investment had been in Cdn Large Cap (instead of Pacific Large Cap).

I forgot to mention this P.S.:
If you have $1200 at the beginning of the year,
invest it at once,
do not pass GO,
do not collect $200.

Gummy!

Now you have me really confused! Having lucked out on Fidelity Far East (and I mean- lucked out because I sold a week before the big slide for other reasons), I now have a pile of cash in a crappy (Fidelity) MM. Should I DCA into this other fund (Cdn Asset All.) which I started to do, or wait until January and throw the whole works in?

Having read the Efficient Frontier article "Do Not Dollar-Cost-Average for More than Twelve Months, I presume that this means that if you have a cash amount on hand you should get it into the market in 12 months or less, preferably in 6 months.

However, I would naturally assume that if one has a surplus over 7 above monthly living expense needs then it should be invested each month as long as the surplus is still available.

My very sophisticated, very scientific analysis (cough) seems to indicate that:

1. If you have $100/month (or some such fixed amount) then you should DCA (putting that amount into the market each month).
2. If you have a large, lump sum, you should put it in all-at-once.

If you're investing in Canadian Large Cap, I have a graph which shows the periods over which investing $10,000 all-at-once beats DCAing $100/month for 10 months... during the period Jan/75 to June/97.

Thank you for YOUR math supported view, gummy.

Jay, I've played with your suggestion which I interpret as:

One has $100/month to put either into Money Market (MM) @ 5%/year or into a "market Portfolio" ... according to the following criteria:

1. If the gain for the previous month is less than A= -5%, then put the $100 into your Portfolio as well as ALL the money currently in MM.
2. If the gain is greater than -5% but less than B= 0.5%, put the $100 into your Portfolio as well as HALF of the money currently in MM.
3. If the gain is greater than B, just put your $100 into MM (and nothing into your Portfolio).

I found the following interesting result (assuming you started this strategy in Jan, 1975 and continued to June, 1997 and "the market" was Cdn Large Caps):

STRATEGY	PORTFOLIO	MM	TOTAL
JAY's	$104,758	$302	$105,060
DCA	$107,505	$0	$107,505

During long runups in the market (with monthly gains > 1/2%), you never put any money into your Portfolio. Indeed (for this market and this period of time) the monthly gains exceeded B=0.5% about 55% of the time. If the criteria are changed so that B= -4% (Cdn Large Caps did this about 86% of the time), the result is that your Portfolio+MM ends up with $108,485.

I think the notion that you hold back your $100/month until there is some significant downturn in the market (but don't wait too long!) warrants further investigation.

... I'm workin' on it ...

I am wondering if performing these calculations using Canadian large caps is somewhat misleading.

Cdn large caps tend to plod slowly inexorably forward, which would tend to make straight DCA more profitable than trying to buy more on the dips (i.e. get your money in as soon as you have it).

I would be interested to see the results of your calculations using the NASDAQ index as the source of data. This index seems to be much more volatile and subject to momentum buying, yet still trending up in the long term. This may result in a "buy more after corrections" approach being more successfull.

So Gummy, if you're up to it....

... I'm workin' on it ...

Chuck M., I can't find appropriate data for Nasdaq, but for "U.S. Aggressive Growth" I found that:

Here's a strategy dedicated to the proposition that one should Bylo & Selhi:
Put your $100/month into Money Market but keep track of the the market highs (meaning "record" or "all-time" highs). When the market drops by 15% below the last all-time high, dump every cent of your MM funds into the market.

This strategy would have beat DCA at $100/month during the period Jan/75 to June/97.

Take a peek at the graphs, where the market is shown as well as the "record high" as well as the periods when you put everything into the market (them's the wee rectangles along the horizontal axis).

Thanks for posting all your work gummy.

Interesting that you found a scenario that supports a momentum investing approach... hmmm.

Randy.

Very interesting Gummy. Thanks.

Your latest strategy also seems interesting, do you have the total return numbers for this strategy vs DCA and lump sum?

I know I have been sitting on a reasonable percentage of cash since 2Q '96 waiting for a significant correction (15% or even more). I have been missing out on a lot of gains and it would be nice to think my patience will pay off in the long run :)

Chuck, the answer to your question is a little complicated:
The Cdn Large Cap market had an annualized return of 11.1% over the period Jan/75 to June/97. If you had a bunch of money on Jan/75, that's the return you'd get if you put it all into this market.

Aah, but consider that you have only $100/month.
Now there are several possibilities, among them being:

1. Put your $100/month into this market (for 270 months).
2. Put the $100 into MM until the market drops by 15% from its most recent record high, then put it all into the market.
3. Put the $100 into MM until the monthly return drops by 6%, then put it all into the market ... or, if it only drops by 4% put 3/4 of your MM fund into the market ... or if it does neither, just keep putting your $100 into MM.

Thanks gummy. I think both you and I believe that DCA "can and will, be beaten". Of course, I am not knocking the actual contribution of DCA.

Simply, as you had earlier stated, the "cerebral frailty" associated with always putting it directly into the stock market.

Thanks and Cheers!

Jay

gummy,

"My very sophisticated, very scientific analysis (cough) seems to indicate that:
1.If you have $100/month (or some such fixed amount) then you should DCA (putting that amount into the market each month).
2.If you have a large, lump sum, you should put it in all-at-once."

Is it fair to conclude that
"the best time to invest is when you have the money" (Templeton), and
"it's time in the market, not timing the market" (?)
were spot-on after all?

I'll drink to that!

Bylo, gummy:

Those are nice sounding sentiments for conservative investors (I recall Templeton also said never leverage). But I would hestiate to simplify gummy's findings to that extent.

For example, if you want to increase the return (and risk) of a well diversified equity portfolio by using leverage, the question of how to get into the market is of major importance. This strategy makes you a timer whether you want to be or not and the greatest (perceived) risk is within the first 6-12 months of taking the plunge. The same would hold true for someone investing an inheritance.

Based on what I've learned so far, I would use up the room on a (sample) 100,000 line of credit by investing a declining dollar amount on a monthly basis. Eg: 30K, 25K, 20K, 15K, 10K. Or if you're feeling less confident: 25K, 20K, 15K, and 4 x 10K. Of course, this assumes that you can keep your transaction fees low (preferably zero) and still maintain your diversification as you go.

Randy.

This may be slightly off topic, but is there a formula that combines the future value of a present lump sum of money with a series of identical periodic payments (i.e. monthly) at an estimated annual rate of return?

I would like to estimate the future value of the lump sum I have invested now, plus future monthly DCA comparing different rates of return.

Thanks in advance

Stephen, after N years, at I% per year (or N months at I% per month)
a lump sum now worth $A will be worth:

A(1+I)^N

and a series of N payments, each of amount $P and starting immediately, will be worth:

P(1+I){(1+I)^N-1}/I

or, if the N payments start in one year (or one month, as the case may be), they're worth:

P{(1+I)^N - 1}/I

Note: If we equate:
P{(1+I)^N - 1}/I = A(1+I)^N
(so the N payments add up to the future value of the lump sum) we get the formula for your annual payments (or monthly, as in a mortgage) when paying off a loan of $A, namely:

P = A I/{1-(1+I)^-N}

You may want to consider visiting http://www.dynamic.ca/ for info on Dynamic's unique no management fee Dollar-Cost Averaging Fund, which just became available on January 2, 1998.

Thanks. Jeff.