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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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