|
PureBytes Links
Trading Reference Links
|
OK, repeat after me: "Van K. Tharp is a hypnotherapist, not a
mathematician." :-)
First of all, let's get our terminology straight. The term "positive
expectancy" is not a mathematical one. The correct mathematical term is
"expectation". This is precisely defined and explained in courses on
probability and statistics. The expectation of a simple gambling game is
a sum of products, one product for each possible outcome. Each product
is the probability of the outcome times the payoff from it.
Let's use Ralph Vince's classical example of a coin toss that pays $2 if
the coin comes up heads and costs $1 if the coin comes up tails. The
expectation is
0.5*2 +0.5*-1 = $0.50
In other words, this game has a positive expectation of 50 cents per
play. OK, now we want to state a well-known result from probability
theory:
There is no betting system (position sizing scheme, to use Tharp's
terminology) that can make money playing a game with an expectation less
than *or equal to* zero.
Now, suppose we have a game with a positive (*greater* than zero)
expectation. Then, certain calculations can be made to determine optimum
bet sizing. I won't derive them here or even state them. The concept
originated with Kelly in 1956, was adapted by the legendary blackjack
card counters of the late 1950s and early 1960s, applied to horse racing
by Ziemba and to trading by Edward O. Thorp. Somehow Ralph Vince latched
on to all of this and is today the person most recognized among traders
as having "invented" it.
With that background, how do we determine whether a trading system has a
positive expectation? And can it be done in Easy Language or Excel? Now
we've moved from probability to statistics. Fortunately the most
elementary tools of statistics apply, but they do have to be understood
to be of much use in thinking about trading systems. I'm currently
working on some simple tutorials on the subject, but it's a spare-time
project and I can't say when it will be done.
Briefly, what you want to do is create a list of all the trades made by
your system. Test it over as many years of data and as many different
tradeables as you can. The more trades you have the better the answer
you will get. For each trade, remember to subtract out a reasonable
value for commissions and slippage. Most futures traders use $100 per
round turn for this. I think that's low for the S&P 500 and coffee, but
reasonable for most other futures.
Now you want to compute some simple statistics on these trades. The best
*estimate* in the statistical sense of the expectation is simply the
average of the P/L values of the trades. But since this is an
*estimate*, you will want to do a little more. You will want to compute
a 95% confidence interval for the average. I'm sure you *could* code
this in Easy Language, but I'm pretty sure it's built into Excel. It's
in one of the data analysis addin; you may have to load it. If this 95%
confidence interval is positive on both ends, you have a system with a
positive expectation with 95% confidence. If not, you don't have
squat -- back to the drawing board.
For example, suppose you do the calculations and you get an average P/L
of $10 per trade, with a lower confidence limit of $2 and an upper limit
$18. This is a good system. However, if your average is $100, the lower
limit is -$100 and the upper limit is $300, you have a bad system.
--
M. Edward Borasky znmeb@xxxxxxxxxxxx http://www.teleport.com/~znmeb
If God had meant carrots to be eaten cooked, He would have given rabbits
fire.
----- Original Message -----
From: <TWA7663@xxxxxxx>
To: RealTraders Discussion Group <realtraders@xxxxxxxxxxxxxx>
Sent: Sunday, March 28, 1999 07:05
Subject: Positive Expectancy
> Has anyone developed ela or Excel code for Tharp's expectancy to
compare
> systems. I believe he contradicted himself in his chapter devoted to
> expectancy. If so, that contradiction has me confused. Would someone
share
> their expectancy code?
>
> Russ
>
|