Re: Bill Reid, Kelly Criterion


<GoldenGemNetwork@xxxxxxxxx> wrote in message
news:e27cf2aa-0eb2-4de7-811e-d08e9bb58b56@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Hi Bill Reid if you are there:

I'm always somewhere...right now, I just got chased back from my
vacation by bad weather, so I'm sitting around in my home office in
my bathrobe wasting time the best way I know how...

I finally learned about what you had said about long term growth of
portfolios.

What'd I say? Was I drunk at the time?

Your recommendation (the formula involving logs) can be generalized,
and here it is applied to any Levi alpha stable shares with a risk
free bond

http://www.goldengem.co.uk/portfolio.html

I'll take your word for it that it is there...

Just enter the statistics and it will find the Bernoulli rate of the
portfolio.

I like my portfolios to fly like a mighty jet plane...

This is NOT the same as avoiding risk, as the blurb explains. Long
term growth can be many centuries in the future, and can include
losing all but one penny and gaining it back again.

Yes, at the limit in theory your portfolio can become infinitesemally
small, shrinking to $0.00000000000000001 from $1,000,000.00, and
you'll have to claw your way back over the next billion years or so.

But the chances of this are also infinitesamally small, equivalent to
like a 30,000-sigma event in a normal curve, or maybe 1 chance out
of a number that is bigger than all the atoms in the universe.

So maximizing the
Bernoulli rate can be viewed as risky.

Everything can be viewed as "risky", since the human animal has very
well-known behavior patterns when confronted with "games" with uncertain
outcomes.

A classic example is the illogical behavior concerning lotteries.
People buy lottery tickets with the rationalization that "it's only a
dollar but I could win a $million". Problem is, as soon as you buy
a lottery ticket, it's no longer a dollar, it's $0.50, based solely on
the "expectation" of the game.

The psychology here is that people are willing to take a SURE loss
of a very small portion of their net worth, and do NOT view it as "risky".
Likewise, people pass by very profitable opportunities on a regular basis
because they are terrified by the small chance of a small loss of a more
significant portion of their net worth.

But if that is what you want to
do , here is the program to do it generalizing your formula in the
simple case of a coin toss with odds.

I myself already have a "program" to do that, for the much more
complicated case of actual portfolio management of the complete
array of possible global investments for time frames ranging from
a few days to up to a year or so. Every night I run the program
which analyzes the current state of the world economy and global
investment instrument statistics, and after a few hours it spits out
a list of the predicted top 100 most-profitable "investments", ordered
by the "logarithmic portfolio growth factor", which for some reason
you call the "Bernoulli rate" if indeed we're talking about the same
thing...

But I have to backtrack a bit here, and clarify what I am really trying
to accomplish with this software, and put it in the perspective of
game and utility theory from which all of this is derived. What you
(and many others) call the "Kelly Criterion" (after the Bell Labs
researcher who first described it) can more properly be seen as
a particular utility function for "games" (investments) of uncertain
outcome, but just one of a class of several possible utility functions.

This general class was described by a later mathematician as
the "Constant Relative Risk Aversion Factors", and was an attempt
to categorize the various types of "risk/reward" ratios that an
"investor" might consider to be a "useful" (utility) compromise
to make money. All the utility functions are based on "betting"
a certain fraction of your net worth on an "investment" (game)
with a known probability distribution of possible outcomes and
monetary gain/loss for each outcome.

Now remember what I said about the purely psychological
rationalizations people make for losing half their money instantly
on lottery tickets. Note that the dream of the near-impossible
big payoff becomes "useful" (utility) for a very small fraction
of a person's net worth. So however illogical and innumerate
and money-losing this "utility" is, it can be described as
a mathematical function, as well as literally an infinite number
of other possible permutations of game results and payoffs
and people's willingness to commit a certain fraction of their
net worth to them. And once described, we can calculate
the rate of net worth growth (or loss, in the case of lottery
tickets) for each function if used for an infinite amount of time.

Now it just so happens that as we look at the entire spectrum
of possible "Constant Relative Risk Aversion Factors", what is
many times called the "Kelly Criterion" (or the "logarithmic
portfolio growth factor") can be proven to have a higher rate of
porfolio growth than any other function (as you might suspect
from the name "logarithmic portfolio growth factor", since how
can you grow your money any faster than logarithmically?).
Everything else either grows money more slowly, or eventually
loses all the money. On PAPER, it appears to be pretty
much the perfect way to "invest".

But of course nothing is "perfect", not even a closed-form
mathematical equation, in the "real world" (especially in the
"real world"). There are many, many, many hurdles to
overcome to in any way implement logarithmic portfolio
growth, but most of them boil back down to psychology.
Note carefully that YOU described this function as "risky",
based on a 1 in a 100,000,000,000,000,000,000,000 (etc.)
chance of practical ruin. I myself have a couple of times
admitted to losing over 20% of my stock portfolio value
in a matter of weeks right here in this newsgroup while
using the function as my investment instrument selection
and portfolio allocation criterium, causing no end of
derision of my "strategy" by the numerous "Lowbrow"s
here.

But of course the whole point is to make the BEST
possible LOGICAL choices when playing any "game",
and if you are so terrified of ANY type of loss then
YOUR utility is to not play ANY game of uncertain
outcome AT ALL (you use the "money in the mattress"
function). More typically, most market participants
display the classic "loose-scared" behavior described
as the opponents you look for in a poker game: they
nervously dip their toes in the black water of uncertainty
based on almost zero information about the game
odds, and either become recklessly emboldened
should they actually "win" (by "luck"), and begin
over-committing funds to the game and engaging in
ceaseless (Usenet) braggadacio about their investment
"prowess", or run screaming from the scene of their financial
near-disaster back to the safety of the "mattress"...

So for the great majority of market participants (and
non-participants), irrational fear and greed rule their
decisions, and they spastically under- and over-commit
their dwindling/increasing net worth to the markets
with a certain degree of predictability, given a knowledge
of THEIR "utility" functions as influenced by previous
and perceived successes/failures and current net
worth direction and size. So a knowledge of utility
theory can come in handy from that standpoint as
one factor to predict the behavior of market participants
in the future and thus future investment instrument prices
(the general trading term for a VERY crude way of doing
this is called "technical analysis" and "charting").

But put together all proven RELEVANT predictive factors,
and you now have the means to construct a reasonably-derived
probability distribution for future investment instrument prices.
By plugging in the "payoff" for each possible outcome, the
goal then becomes to calculate a SINGLE number that
indicates the BEST (most profitable) investment instrument
to buy (sell), for a given time frame and portfolio allocation.

And that's what the "Kelly Criterion" gives me, that single
number that allows me to rank the profitability of the many
10s of thousands of possible "investments" world-wide,
based on the data used in the program. You could make
a case that for various reasons the actual number I use
is not truly the "Kelly Criterion" (not truly the "logarithmic
function"), but it is close and errs on the side of less-"risky"
sub-optimal growth to ensure that I have the best possible
ranking strategy possible (ranking based on an eventually-ruinous
function would be silly, but reasonably you might use any
"sub-optimal" function for ranking, particularly if your actual
investment "utility" is less "risky").

I hope you read this....as it is totally based on what you often
say....

I say a lot of dumb stuff...

---
William Ernest Reid
Post count: 884



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