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I'm not a mathematician, but this may help. See comments below.
Paul Altman wrote:
> Would one of you mathematicians kindly take a moment and explain to me why
> we'd require that a system demonstrate positive expected return
> historically, before we'd put any money on it?
>
> I'm specifically looking at Tharp's definition of expectancy, where he
> states: (p.148) "Expectancy is a way of comparing trading systems while
> factoring out the effects of time, position sizing, and the fact that one
> is trading various instruments that have different prices."
>
> Using _his_ definition, I think I can imagine a negative expectancy game
> that would make money, since you could conceivably have a position sizing
> algorithm that would "know" when to enormously increase your bet size on
> winning trades, even if those winning %'s were very small.
This thinking is absolutely incorrect. A negative expectancy game is just
that; over time the returns are negative. No position sizing routine, no
betting algorithm, no stop-loss strategy can change this. You will lose
playing a negative expectancy game.
You can change the rate of loss, but the final outcome is completely
determined.
You can see this when doing system development work. For example, you may
think you have a great entry technique so you test it. The results show a
loss. So, you decide to maybe make the stop loss targets smaller. What
happens? Well you just increase the number of losses and maybe don't lose as
much, but, since the entry technique is the same, you haven't changed the
expectancy of each trade.
>
>
> Obviously, all things being equal, I guess you'd want a higher expectancy
> rather than a lower one. But why would you insist it be positive? If I'm
> reading him correctly, he's saying that you don't want to play a negative
> expectancy at all. With his definition removing position sizing as an
> input to the expectancy formula, I don't fully understand his reasoning.
>
> Paul
For a better explanation than I can give, follow this link to the online book,
"The Mathematics of Gambling" by Edward Tharp. One of the later chapters in
the book discusses this very topic.
http://www.bjmath.com/bjmath/thorp/tog.htm
Regards,
Bill Vedder
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