Re: Bill Reid, Kelly Criterion


<GoldenGemNetwork@xxxxxxxxx> wrote in message
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On Jan 20, 3:51 am, "Bill Reid" <hormelf...@xxxxxxxxxxxxxxxx> wrote:
<GoldenGemNetw...@xxxxxxxxx> wrote in message

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Below, you
discuss two very relevant examples,
one theoretical and one from actual examples. I'll re-present these
and then try to comment briefly and clearly.

Uh, sure, but I'm not sure what the point is...if it's because of
this:

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.

Well, there's better ways to calculate this than what I alluded
to...but
I'm really NOT sure what your point is...

For example, say the standard deviation of logs of price changes
year to year is .1

Here's some actual numbers that I just noticed laying around:

DJIA 1990 - 2000 Daily Change Distribution

-7.18% --> -5.97% = 2 0.07%
-5.97% --> -4.75% = 1 0.04%
-4.75% --> -3.53% = 4 0.14%
-3.53% --> -2.32% = 34 1.22%
-2.32% --> -1.10% = 198 7.12%
-1.10% --> +0.11% = 1230 44.26%
+0.11% --> +1.33% = 1121 40.34%
+1.33% --> +2.55% = 167 6.01%
+2.55% --> +3.76% = 16 0.58%
+3.76% --> +4.98% = 6 0.22%

The average daily change was +0.0528% (+0.1050% compounded),
with a standard deviation of 0.6491%. So you're saying that there
is
some calculational inconsistency if we take the "logs" of something
there and project it out another 10 years in the future?

I will take some time to read your comments.

Print 'em out for the bathroom...

My emails should NOT have been so long. I think in the end you
answered my questions, but also
answered my mistakes, which makes it confusing to read.

Welcome to...

I'd like to just restate everything and I will soon, trying to keep it
to like six or seven lines. I think you answered my question already,
but the thread is much more confusing than it should have been.

....Usenet.

One thing I want to say, is that I didn't mean to make a big deal
about logs; if a person is talking about a percentage change in the
ordinary way, they are doing that anyway with a small error.

For example a ratio of 1.00123 is a 0.12300 percent increase.
The natural log of 1.00123 is 0.0012292

I didn't mean to say I care about the decimal point being 2 places to
the right or not, I was saying the sequence of digits is (slightly!)
different, it starts out the same with the good old 0123 but then
gets a tiny bit off. So if we ignore this tiny difference

Kelly = thinking about percentage
changes.

------------------------------------------------------

But, if one cares about that tiny difference, the log is the right
thing to use, not the percentage change.

Well, I guess I don't, at least not in whatever context you're
trying to look at...

I hope MY context is clear: I just use the best "tool" for the
job. I don't fix a watch using a sledgehammer, and I don't drive
piles with a jeweler's screwdriver...and I don't try to make them
"equivalent" just because I happened to use a sledgehammer this
morning and now I want to fix a watch...

-----------------------------------------------------

Um, your post was full of lots of clever reparte etc which I'm feeling
a bit dumb about as I haven't even understood it all,

Aren't I a little stinker?

but skipping to
the end, I think what your answer is, is that yes, the model where the
log changes are normally distributed and have a mean larger than 0
does say the probability of going broke goes to zero as time goes to
infinity. But that, real life is not like that.

No, I was kind of saying the opposite: real life IS like that.

"What we have here is failure to communicate"
- Strother Martin, "Cool Hand Luke"

I used an example of the DJIA, which was something like 40 a hundred
years ago, look at it now, even with its current losses...can you figure out
what's going on there?

I wanted to think: why is real life not like that?

OK, forget that right now, let me back up, and try to justify my blather
about a log-optimal strategy practically never going bankrupt. Now this
is an example of what I was talking about when I was yammering about
"equivalent to a 30,000 sigma event on a normal curve".

You see, it is standard operating procedure in THIS home office to use
a set of probablistic techniques to answer, if only for grins, the burning
question of "what are the chances I'm gonna lose a whole lotta money
doing something" (of course, if you know this, you won't be quite so
suprised when you do lose a fair amount of money).

As it happens, there is well-known technique that uses the normal
curve and plots the area under the curve given the number of trades,
the mean result of each trade, and the standard deviation from the
mean result. In other words, something like what you seemed to
be talking about, but not a "logs" in sight; just a standard method
to APPROXIMATE the "odds" that we will have a certain result over
a certain period of time given a certain projected distribution of
possible results. In practice, this has been shown to work well
with stochastic processes, and basically shows the CORRECT
approach to APPROXIMATING the long-term odds of a given
"strategy".

To do this, we "normalize" our "risk-adjusted" mean result to
"0" so that it may be plotted out on a normal curve of possible
results over time, from -.5 to 0 to +.5, as follows:

( 0 - ( mean_result * number_trades ) ) / ( sqrt( variance*number_trades ) )

See what we're doing here? We're dividing the mean loss over a certain
number of trades by the square root of the TOTAL VARIANCE of a certain
number of trades. In addition to the "logs", you kept insisting on taking
the square root of the STANDARD DEVIATION, which is of course itself
actually the square root of the variance. Remember, in "real life" variance
goes up linearly right along with the mean as the number of "trials"
increase;
they never get "out of sync" as you keep suggesting, but rather follow
the "law of large numbers", that is, "as the number of trials grows large,
the smaller the expected deviation from the mean".

Or to put it another way, "the more you play, the more likely you are
to win (if you are playing a winning strategy, or to lose if playing a
losing
strategy)".

We can then find the "area under the curve", perhaps most quickly
by table lookup indexed to (result*trials)/(sqrt(variance*trials)), to find
the
corresponding percentage of time that we can expect to be at a certain
loss or gain. It is by using this approach that I have several times made
the claim that I can predict fairly precisely how long it will take a
"day-trader" to lose all their money, given a known strategy and
a "bankroll" size. What you will find is that even for strategies with
a positive "expectation", if they are making bets that are "large" in
relation to their net wealth, "day-traders" have an increasingly high
probability of going broke the more they trade.

The beauty of the "logarithmic portfolio growth strategy" is that it
summarizes this effect as a NEGATIVE growth factor for large "bet"
sizes, saving us any further debate or extensive calculations like
the above to make a quick determination: betting a large amount
of your net wealth on ANY known "day-trading" strategy is a
SURE money-loser over time, SO DON'T DO IT, FOOL!!!

We shouldn't let the fact that this is also "common sense" and
"common wisdom" dissuade us fom the oracular infallibility of this
assertion...

Even Mandelbrot's
adjustment (which is the one which allows any distribution which is
constant over scale, so the day-to-day distribution is going to look
the same as when it is iterated to get year to year etc) is not like
real life where things go crashing out of existence.

What's going out of existence? The planet Earth, due to asteroid
collision? Who the hell cares, we'll all be dead anyway! Global
thermo-nuclear warfare, complete collapse of all civilization, etc.,
all fall into the category of definite possibilities, but you shouldn't
worry about them because everybody else will be dead too, and
isn't your real goal to "beat the other guy"? IF HE'S DEAD TOO,
YOU WIN, YAAAYYYY YOUR CORPSE!!!

I was thinking, perhaps there should be an error distribution about
the means, like "I think the probability is 40% that my estimate of
the mean log change is correct, and here is the distribution"

Precision of your "projection" is an issue, but you're also forgetting
a fundamental point: the distribution itself INCORPORATES UNCERTAINTY.

This simple fact is one of the hardest for people to grasp who can
NEVER intellectually "grok" probability; in fact, it's impossible. They'll
just keep falling back on, "but ANYTHING can happen, right?"

Well yeah, ANYTHING can happen, and as a practical matter I always
have a non-zero probability for 100% loss for any individual stock results
projected distribution, but seriously: take the case of a one-day trade
period, HOW MANY FRIGGIN' STOCKS HAVE LOST 100% OF THEIR
VALUE IN A SINGLE DAY IN THE LAST TWO HUNDRED YEARS
COMPARED TO ALL THE US STOCKS THAT HAVE TRADED EVERY
DAY FOR THE LAST TWO HUNDRED YEARS?

Get it? If you can't, YOU CAN'T WORK WITH THESE CONCEPTS,
AT BOTH AN INTELLECTUAL AND EMOTIONAL LEVEL (despite what
you may "think", your "emotions" are more firmly in control of your
"intellect" than vice versa, particularly if you are unable to face THAT
simple fact of the human "mind").

Or, basically, just do like most market participants do, what people
at Las Vegas craps tables do: just "guess" like hell, scream that your
a genius if you "guess" right, run home to mommy if you "guess"
wrong.

OR perhaps the distributions should have, at the left, a tail that
includes a finite chance of the thing crashing to - infinity.

As I said, I waste a little of my "risk envelope" by doing just that,
but that's more MY "psychology", and my advantage is that I KNOW
I am over-estimating my "risk" just because I'm a big 'fraidy cat,
NOT THAT I "THOUGHT" IT THROUGH...you, on the other hand,
have revealed here and several times that you let your emotions
control your actions more than your logic...

Again, I provided an example of ten years of the daily DJIA.
How many times did the DJIA lose ALL of it's value in ONE DAY?!!??!
How many times did it lose ALL of it's value in a one-year period,
a five-year period, a ten-year period, whatever, over the last
150 years or so?!??!!

If it NEVER DID (and it NEVER DID), WHY THE HELL ARE YOU
SO WORRIED ABOUT THAT???!!?? You certainly don't have a
"reason" to be...

Will write more later

OK. Also, you need to take very seriously the concept of "diversification"
that I brought up previously that demolishes your only possible CORRECT
assertion about "risk of ruin". As I said in this post, I personally obey
the
"law of large numbers" and recommend every else do the same, because
it's not only the law, it's the God's-honest truth about the way God created
the universe. "Diversification" is just a synonym for "the long run" (large
numbers getting larger over time), and is statistically essential to surely
acheive our "mean" result, and the great thing is that you can "diversify"
several different ways (time, instruments, trade time periods, etc.) to
more quickly get into "the long run" (which itself is a synonym for
"at the limit (INF)" for our "logarithmic portfolio growth strategy".

---
William Ernest Reid
Post count: 904



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