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In the "Zero score and 7 years ago" thread I mentioned in passing
a simple technique that I use for position sizing, which started a big digression.
Sorry about that, cerruti!

Since the digression raised some questions, I thought I'd post the
responses as a fresh thread since others might be interested.
It started with my brief comment
"I'm using a simple technique to get a great price: I just
check every day or two and ensure that the dollar value of my holding
is constant, buying more on dips and selling a little on rises.
This ratchets down the average cost basis, and gets me an entry close
to the bottom price---a great technique, provided the thing
you're buying is well supported by value."

Zee asked
Is this a simplified version of Robert Lichello's AIM technique?
Any comments on AIM? (I have the book here, ready to read...)

I was doing this before I heard about AIM, and was of course struck
by the similarity and bought the book, which I've just about finished.
(for "get rich quick" books I have a habit of reading the chapters
in random order, so I'm never sure when I've finished the book).
Tpoto kindly sent me his spreadsheet.

My first reactions are
(a) what an execrably written book. But of course this has no
bearing on the ideas being proposed.
(b) it really does seem to be a very effective way of ensuring that
you have an absolutely safe experience being in the stock market over
any combination of years, good bad or indifferent. The end returns
come out OK. But, the system is extraordinarily conservative, and
you can wind up well over 80% cash for years at a time. I think
most MI folks would find that maddening.
(c) so, you end up trying to tweak it. Of necessity, this cuts back
on its biggest charm, which is its extreme resilience and safety.

There is a nice web site all about AIM at and a very
concise summary of AIM at this page
This site has a pretty sensible tweak which simply puts a soft cap
on the cash allocation. When the cash allocation gets above a
certain percentage, you add a bit to the "portfolio control" figure.
As an example I've tried (in a monthly-checking series), if the
cash allocation gets above 60% then add 5% of the current portfolio
value to the "portfolio control" value.

I haven't really played around with the AIM formula enough to say
much more about it, or how it might be improved, but another things
which seems at first blush to improve returns a bit is a value for
"safe" which is smaller than the recommended 10%. But the original
formula as presented has rather more subtlety in it than is apparent
at first blush, so this kind of tweak is like a random stab in the dark
without testing it on a wide range of possible price paths.

Certainly the one tweak which seems to make sense to me (which in the
book is discussed briefly but not recommended) is running multiple
AIM portfolios, each with its own cash allocation. This makes sense
to the extent that your investment choices are uncorrelated. Each
portfolio could be a single investment, or a collection of them.
As it gets down to one per investment, that's where is becomes more
similar to what I have been doing.

Which leads to Steve's questions...

1. What percent of all stocks would end up being in the following baskets?
A. Cost basis is actually ratcheted down as buys / sells are entered where you get in at a lower price each time than what you sell at.
B. Cost basis is increased as one ends up re-entering at higher and higher prices. This would seem to be the norm in any bullish market.
C. Cost basis remains static -- the rules are such that you act on them but little to no improvement, or loss, results.

Worst case for this system is a long, smooth price rise, since that's
the only time the system underperforms the underlying stock. Of course,
this is just fine for your pocketbook. Worst case for your pocketbook
is a long period of smoothly sliding prices, but of course you work
as hard as you can to pick something that will eventually rise again,
at which point the system has added a lot of value for you.
Situation B can't really happen, since you never buy on a price rise.
Rather, you would be doing a continuing series of small sales (all
of them profitable, incidentally) but underperforming the security
itself because you are gradually liquidating a lot of stock below
the (unknown) end of the stock's rally.

In short, as long as there is a bit of jaggedness, the system gives
short run price improvement whether the price trend is up, down, or sideways.
What happens is that, if your position is underwater, each down-ratchet
increases your average cost basis a bit on each sale, and each up-ratchet
reduces it a bit on each purchase, with a ratcheting down effect. If you graph
current average cost basis to date as a function of how many shares you
own, you get a jagged descending squiggle with each jag sloping down
to the right. This is my graph for my (losing) holding in EWJ, with the
most recent situation represented as the green dot:
Conversely, when your position is in a profit situation, your average
cost basis goes down on sales and up on purchases, so the zigzags
slant the other way. This is a graph of my (winning) holding in BNI:
If the price is crisscrossing back and forth from being a winning
position to a losing one, you get a scalloped look. This is my
graph for my position in USB:

What you can glean from these graphs is that the zigzags gradually
descend in all cases, meaning that you get price improvement on
each pair of trades whether you're in a winning or a losing situation.
Sounds perfect, right?
Well, what it doesn't show you is the longer cycle: over time you are buying
a lot more stock as the price goes down, and selling as it rises. So,
it's important for it to be an investment that you definitely WANT
to own more and more as the price goes down. For example, I'm fairly
content to own more and more Japanese equities right now, even if they
don't move in price for a long time, since I think the cyclically
adjusted fair value of EWJ is something like $18.00, not today's $12.71.
The graphs also don't show you that during a long steady rise your
position is shrunk much too soon, so you underperform the stock
during those periods. The way I think of it is that you've moved
some of those profits in time to the help fill in the bad periods.

2. What are the exact (clearly defined and repeatable) rules that you are using to pull this off?
For most of the stocks I'm doing it with, it's exactly as described, no more.
On a regular basis, check to see how much your stock holding differs
from your target amount, and buy or sell the difference to set it right.
About the only extra things to decide are:
(a) what minimum trade you consider worthwhile. I like lots of
activity in order to keep myself from doing other, more harmful things,
so I often use around $1500 as a minimum trade size. Each zigzag
might make me about $40, and cost $1 in commission.
(b) what maximum purchase you might make on a stock. Say you're
doing it with a stock that really does have a problem. Maybe something
you bought at under half book value, and you *think* is going to
stay in business. MTH is my example here. You need to realize that
the price can keep going down forever, and you don't want to buy
an infinite amount of stock, so you have to set a cap. One sensible
cap might be twice the number of shares you started with, because
the price has halved in value. If it goes lower, just ignore any
buy signals. If it comes up higher again, act on the first sell
signal and you're back off to the races. This has happened to me.
(c) how big your original purchase will be. If you're going to
increase the size of the position later on, you need money to do it with.
So, you either have to leave cash on hand, or be willing to use margin.
(d) somewhat less obvious, you have to commit a lot of money to a stock.
If your position size is small, only very rarely will you trade,
and your you won't get advantage from short run noise.

That's the simplest version, and what I'm using for most positions.
But, there are always endless ways to tweak things.

If you want to be more aggressive, you can pick other formulae that
exaggerate the amount to buy and sell. You'll get out of the position
entirely at a price not too much above the current one, and load
up a really huge amount on a moderate drop. This might be appropriate
for an undervalued sector ETF which isn't going to go to zero.
A sample formula: first, pick a price "P" at which you want to own a
certain amount of stock "SIZE". I picked "P" above today's price and
below what I thought the fair value was.
Then, your position size could be set as SIZE * ((P / pricenow)^2)
This is the formula I used for XLF recently, and it has worked very well.

Of course, the very best formula is one which takes into account your
estimate of the true intrinsic value (IV) of the stock. (For anyone not
familiar with the term, here are some notes of min on the subject: )
If you have a good estimate of today's intrinsic value, you have a
much better handle on how much stock is sensible to own. I like this
formula: Leverage = 2 * (intrinsic value / current price ) - 1
This is a good formula for values anywhere near or below the intrinsic
value, since it will aggressively pump money out of the noise. It needs
to be capped at both ends, though, especially on the upside. From
a sensible theoretical point of view, the correct amount of stock
to own if the price is above intrinsic value is zero (or short it!).

For one stock in particular, Berkshire Hathaway, I calculated the
"optimal" ratio using a time series of intrinsic value estimates.
I simply used the (very good) figures from here:
Pick the "conservative" setting in the pull-down box. Historically it
has not paid to own any Berkshire stock when the price is more than 4%
above the value that this gives you, which would be $4898*1.04 = $5094 per B share today.
This is my original write-up on the "optimal" formula I developed.
This is a revised, much simplified version of about the same thing.
This post provides some data on Berkshire's performance based on the ratio at purchase time:

So, what formula should you use? The very best is this: estimate the
underlying intrinsic value of the security. Figure out how much of
it you would buy today at a series of different hypothetical market
prices staggered downwards from there, and pick any simple formula that
roughly matches that curve. The "constant dollar portfolio" rule is
simply one such curve, based on the idea that at half fair value you
want twice as much stock.

3. Are you including trading costs in your evaluation of this strategy?
Yup. I use IB where commissions are pretty much always $1, so it
isn't really a big issue as long as the minimum trade size is
respectable enough. Obviously it's a strategy that likes stocks which
are liquid. I have been doing it with some stocks which are not very
liquid, so I have a check for that. For example, if it says it's time
to buy, I put in the *ask* price and see if it still says to buy
(considering minimum trade size), and if so I place the order at
market. That way, the decision is made also taking into account the bid/ask gap.

4. What would be the optimal screen for selecting stocks suitable for this approach?

Ah, now that's a tough one. I'm not sure I would go about it with a screen.
I have been hand-picking the things I put into it, since the criteria
I mentioned are not well suited to automation. The ideal candidate
would include all of the following:
- First and foremost, a firm support on value. An intrinsic value
which is not going to go down, ever. You're potentially going to be
buying very large quantities of the stock on big drops, and holding onto
it for several years of being underwater, so (as far as is possible) you
want to know in advance that the drop is irrational and temporary.
To quote the immortal Mr Graham,
  Real investment risk is measured not by the percent that a stock
may decline in price in relation to the general market in a given
period, but by the danger of a loss of quality and earning power
through economic changes or deterioration in management.
Thus, the main criterion you need is the profitable sustainability of the
underlying business activity, less so the current situation.
- Something which zigs and zags in price a lot. A very high average
ratio of monthly high to monthly low would be a good criterion.
JNJ might be a nice company, but its price line is awfully smooth.
However, if you can avoid it, long-lasting downswings are not good.
- Liquidity.
- Low correlation to the other picks (medium to long cycle correlation)
- Did I mention that it should be firmly supported by value?
- Good general safety criteria can't hurt. I like the one "long term
debt is less than five years' profits", since it means the firm can
probably weather a very bad period and survive.
- Good long term prospects, the usual Buffett criteria. The technique
does NOT particularly improve the long run results, it just makes
them safer and steadier, so you want a firm that has high and
sustainable margins.

An ideal candidate which I like right now is Wells Fargo (WFC). It is
very undervalued right now, extremely capably and safely run, it
has been fairly volatile, and its long run returns are similar to
those of Berkshire itself, with years of steady growth ahead of it.
It's the only AAA rated bank in the US, one of only a few in the world.
I believe the value of the firm has been rising at a fairly constant
rate in the last decade (using long run estimates), so I think it is
a significant buying opportunity that the current price is 2.1
standard deviations below its log trend since mid 1997.
A couple of months ago I was buying heavily when it exceeded -4.3SD.
I have been holding the dollar value of my position steady using
the simplest rule since Dec 5th, and have improved my average cost basis
per share by a pinch over 7% since then. The stock has gone down, so I
am in a loss position, but hugely smaller than it would otherwise have been.
I own 2.89% more shares than I did then, and my total skin in the game
(net of all purchases and sales to date) is 3.86% lower than if I had
simply been buying and holding since that date.

Quite aside from any "price improvement", I believe the more fundamental
reason that this is a valid approach is that it makes economic sense.
The size of every position should be proportional to how undervalued the
stock is at the moment. Risk is proportional to the ratio of price
to intrinsic value, so risk rises as the price rises.

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Jim writes: << "In the "Zero score and 7 years ago" thread I mentioned in passing a simple technique . . . which started a big digression. . . Sorry about that, cerruti!" >>

Whoa, Jim!
Don't be sorry about that.
One of the best things about this board is the way ideas bounce around.
Glad you took the opportunity to teach us a few things.
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Quillnpenn (a TMF-US user) used to be an avid advocate of Lichello's methods. I think so methods like these are valid because stock markets are never predictable.

If a share doubles in a period and then halves later an investor who partially books profit at doubling and who increases his position size at halving makes money even though share has come back to where it started. The investor who doesnot adjust his position size will make no money.

For example if 50 percent are invested in such a share you will have after doubling a "portfolio" which has two thirds money in stock. So we sell 25 percent of holding (to bring back the level in shares to 50 percent) and book profit. When it halves stock holding becomes 37.5 cents but you already have 75 cents in cash per dollar of starting money. So effectively you get 12.5 cents per dollar. Share price is at same spot and an investor who did not adjust made zero percent but you made 12.5 percent.

Ralph Vince and Dr Van Tharp also advocate position size adjustment to maximize returns. Ralph Vince had written in one of his books about Kelly criterion in this connection. Bernt Oksendal in his book on "Stochastic Differential Equations" shows that in a commission-free world an investor with holding in cash and a stock whose price is explained by a Geometrical Brownian Motion model with parameters r=average return and variance of returns=v, the returns will be maximized if proportion in stock is held at:


where rho is risk-free return rate. Oksendal also uses Kelly's criterion.

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A HUGE thank you for raising this topic. As I have mentioned in several posts...this type of discussion is the last missing link to the "Complete MI Investor." Glad to see the post got the recs it did. There are many ways to do this of course and I have been amazed that people have not caught on to the fact that Bakulesh can make money on a stock that goes absolutely no where as long as it does so in a zig zag fashion.

I've been messing around with some backtesting using this and a more simple formula using the new Ultra ETFs. The daily compounding structure of these ETFs actually works in your favor if you employ the above methods as you are buying even more shares on the downside and selling fewer on the upside...ah the wonderful magic of compounding.

Cheers Kev
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I wonder if you are aware of Peter Ponzo`s AIM spreadsheet:


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I wonder if you are aware of Peter Ponzo`s AIM spreadsheet:

Not that version, but another implementation of AIM.

I have been playing with it quite a bit, but I am becoming more and more
of the opinion that there is no magic bullet which will get you in when
things are down and out when things are up, without some sort of
anchor of an estimate of intrinsic value. If the system is based
purely on current market price, any strategy that is safe enough will
end up mostly in cash much too much of the time, and underperform
the underlying asset by a country mile. As an example, try feeding
in the Nasdaq. Any system that keeps gains from the bubble tends not
to get you reinvested again to take much advantage of the 2003-2007 rally.
This "too safe" effect is not a total failure, as the safety is real
and the returns are still better than all-cash.
But, it's not what the typical mechanical investor would wish for.

The solution seems to be more like what I wrote about Berkshire. Base
the position size in relation to the instrinsic value, and do the
trades in relation to changes in the price-to-intrinsic-value ratio
over time. Interestingly, it doesn't have to be a very fantastic
estimate of intrinsic value---a suitable constant multiple of book value
often works just fine. On this basis, you can end up with a system
which beats buy and hold on both risk and returns.

The reason that the "dumb" approach in my post works so well is that I
have been careful to use it only on things for which I have strong
belief that the entry price was way below intrinsic value, and that the
fundamental value wasn't going to change downwards in any meaningful way.
Given that, you're not overpaying on entry, and movements in price
are good proxies for movements in the price-to-IV ratio.
However, it's good to remember that this is just an approximation,
and it's best to use an explicit IV estimate if you can.

So, how is a mechanical investor going to estimate intrinsic value?
It's not exactly our core circle of competence around here. One idea:
each Value Line chart page includes the original "value line"---the
line based on a fundamental metric which is the best single predictor
of the share price. Usually it's a multiple of earnings or cash flow,
but it can be other things too. This is a great starting point for a
very simple IV estimator, and picking one that the trend line never
kinked downwards is a quick test of "non declining IV" companies.
And, of course, never buy a stock which is above that line.

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AIM is a system that does well in a wobbly market and shows its weakness in a prolonged uptrend (takes you more or less out of the market) or downtrend (gets you in deep too soon).

So if you combine it with a method for recognizing such situations, maybe...
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Are there any new ideas on the ideas in this old thread?
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Are there any new ideas on the ideas in this old thread?

Well, I have a nice scheme that matches the return of the Nasdaq 100 Equal Weight index but with an average cash allocation of about 45%.
It can be tuned, but it trades a bit about once a month.
The median trade size is about 3.6% of portfolio increase or decrease in stock allocation, never under 3%.

But that cash pile is not as comforting as you might expect.
Rationally speaking, you want maximum stock exposure when stocks are maximally cheap.
But that's when the prices are low, most volatile, and subject to violent short term plunges.
So, you get a portfolio that's wildly choppy and frequent low values when markets are low, and smooth portfolio values with an annoying large cash allocation when markets are doing really well.

Contrarianism works, but it's emotionally taxing!

The scheme is based on a smoothing of the earnings yield of that index.
Since it's equally weighted, it's the simple average of the earnings yield of the Nasdaq 100 components.
That [real] earnings figure has historically trended pretty well.
The scheme uses a simple formula based on that trend earnings yield to estimate the stock allocation percentage to hold.
It checks each day to see if the rebalancing would require a trade big enough to be worth bothering with, the 3% figure mentioned above.
Sometimes it goes a long time without a trade, but it recommended 15 in two months in October/November 2008, biggest was 14.1% of the portfolio.

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What I am looking for is an idea of selling and buying at intervals based on movement of a stock or my portfolio.
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What I am looking for is an idea of selling and buying at intervals based on movement of a stock or my portfolio.

That's what the scheme I mentioned does.
It trims on every rise in the market, and buys on every dip.
But rather than determining the size of the trim based on nothing but the size/direction of the
market move as AIM might, it bases it on the change in the estimated trend earnings yield at the new price.
The earnings yield gives you an absolute, rather than relative, target for stock allocation.
You could just as easily use an estimate of annualized stock return in the next five years, which would work better for high growth firms that might not yet be profitable.

Because this approach has a tie to some metric of value, it works better over the long run.
AIM has no tie to value. It just wanders around, reacting to short term movements, not knowing
whether an "up" move is from cheap to less cheap, or from overvalued to more overvalued.
If you started an AIM process when the market was high, you'd tend towards a 100% stock allocation quite quickly.
If you start when the market is low, your portfolio will trend towards 100% cash quite quickly.

A valuation based system (like trend earnings yield) on the other hand, will give you the same
allocation for August 2020 whether you start the trading program in in July 2020 or July 2000.
If things look expensive, the recommended allocation will be low, no matter how much stock you had the month before.

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In reading through this thread, I remembered that someone had hijacked Peter Ponzo's "gummy stuff" website some time ago and so the links in the older posts here no longer work. Here's a link to the original "Gummy Stuff" page (thanks to the Financial Wisdom Forum):

Here are all of his tutorials listed in one place:

and here is Gummy's introduction to AIM:

Looking through these pages brought back some fond memories and I'm grateful for all that he shared... I do hope that he's doing well!

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