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Bill:
> returned 5%, 50 of them returned -10%. Obviously, a negative expectancy
> > based on V. Tharp's definition (we've backed out and normalized the
> > position sizing, by examining only the return).
>
>I need to get very picky here because both our arguments rely on very precise
>definitions.
Yes, that's the crux of it, of course.
> But what if you had had an algorithm that somehow "knew" to leverage your
> > winning bets by 4/1. Now we have a very profitable game, but Tharp's
> > "expectancy" is still negative.
>
>This logic escapes me. How can you know ahead of time which trades will be
>winners? If you know this, don't bother trading the system when it's
>projecting a
>losing trade.
Yes, as stated I've learned that that was a flaw in my thinking. However,
V. Tharp's explanation and definition, it seemed to me, allowed for a
profitable game with negative expectancy. I may not have read him
correctly, though I've tried. I posted originally, not to criticize Tharp,
but in an attempt to get some guidance in understanding what he might have
meant. You are correct that it would be foolish to engage in such a game
without removing the smaller trades, but this still begs the question of
what the precise definition of negative expectancy is, when applied to a
series of historical trades of different position sizes, and unknown
probabilities.
>If you're saying that, based on your system testing you have developed filters
>(or whatever) that work to identify winning trades then you have now
>completely
>changed the premises! You have two completely different systems (one
>without the
>algorithm - the negative expectancy game and one with the alogorithm - the
>positive exp game). Tharp's expectancy has now changed as well... it
>positive for
>the second game.
Yes, I'm beginning to understand this and agree. Thanks. Since Tharp
merely listed the trade results of two different player's systems, in order
to calculate expectancy, this point was (insofar as I could see,) perhaps
slightly alluded to, but not sufficiently covered. It is a matter of some
subtlety that a system could be, from the _point of view of an expectancy
calculation_, a composite of multiple systems each with their own
expectancy, even though one's first impression would be: one .ela file, one
basket of capital, one market, etc. This composite effect would obviously
be worth knowing about, since you could then eliminate the negative
expectancy "sub-"systems.
This would all be harder still to detect and calculate in discretionary
trading.
> The "knowing" which bets to leverage is not absurd. There are many folks
> > who load up on what they consider to be higher probability bets.
>
>Ok. I'll buy that. But... their expectation is that these trades are winners.
>They are (maybe subconsciencely) adding a filter to their system, much
>like your
>example above.
OK, so we'll call that _two_ systems combined, instead of one. Again, I
must conclude that it is not quite so easy to calculate system expectancy
from historical trades as Tharp may have inadvertently implied.
Now that we (OK, I!) are getting a little clearer about this, I'm trying to
understand more clearly why one would track expectancy of a system. If a
system is profitable over time, then by definition it must be a positive
expectancy game, and vice versa.
I've learned that if you have a "negative expectancy" game that is
profitable over time, you have not sufficiently broken the game into
sub-games before calculating expectancy. Practically speaking, your larger
trades are positive expectancy and your smaller trades are negative
expectancy and should be eliminated. At least those smaller trades that
display a negative expectancy.
Conversely, if you have a "positive expectancy" game that is a loser over
time, you again have not sufficiently broken the game into sub-games before
calculating expectancy. Practically speaking, your larger trades are
negative expectancy and should be eliminated and your smaller trades are
positive expectancy. At least those larger trades that display a negative
expectancy.
(I'm not sure what would be learned from discovering that you have a
profitable, positive-expectancy game, or a losing, negative-expectancy game.)
Since this information could easily be learned by monkeying with your
position sizing, what is to be learned from calculating expectancy? Do you
more experienced guys really track this? If so, what do you hope to learn
from it? Tharp makes it sound as if understanding and tracking it is
simple, and one of the major ingredients to successful trading. To me,
it's beginning to sound like a hard-to-quantify, major pain-in-the-butt,
particularly if your position-sizing filter varies on a curve (you'd have a
theoretically infinite amount of probability bins to put trades in).
Despite you guys generously trying to pull me out of my confusion on the
subject, I still feel like I'm missing the punch-line to the joke. Thorp
and Tharp seem to me to be measuring apples and oranges, with expectancy.
In Edward Thorp's work, he is interested in calculating expectancy because
he is dealing with bets of _known_ probability, but with _no_ historical
outcome date. It's immediately obvious why he recommends calculating
expectancy before putting any money on the table. In this case, he's using
expectancy as a "decision-making in uncertainty" tool. With a sufficiently
lengthy track record of roulette wheel spins, expectancy calculations would
be primarily of academic interest, since you'd already know that the game
was a loser, and how much of a loser. E. Thorp knows that history will
repeat itself, in the sense that the various physical properties of the
game, those that cause the probabilities, are known and are reasonably
assumed to be constant into the future. So a quick expectancy calculation
should, at least theoretically, be as useful as measuring an infinite
amount of historical spins of the roulette wheel, none of which can be
known at all. Pretty neat.
But, when Van Tharp calculates expectancy with historical trades, there is
no uncertainty at all about the past, so expectancy seems to be a less
useful measure. And the relationship between the past and the future
probabilities is pretty darned elastic, and can only be very crudely
guessed at, so again expectancy seems like a less relevant
measurement. Additionally, I would not always choose a higher-expectancy
trading game over a lower one, because sometimes the lower ones have higher
trading opportunities. V. Tharp acknowledges this, and I think he
multiplies expectancy * opportunity to normalize it.
So isn't this (teasing out the sub-systems to assign probabilities to
historical trades, etc.) all a big circular calculation that gives you the
same information, but less precisely (when applied to _trading_), that you
would have had simply by tracking annual return, % of time exposed to the
market, and your favorite risk measurements? Tharp said that one of his
students, a money mgr, told him "Please don't write about expectancy, it's
our edge."
Why? What am I missing?
Paul
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