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You're going to need more than the average number of trades--how wide is the
distribution? Assuming a normal distribution (bell curve), that's the same
as asking for the standard deviation. In the example below, an average of 4
losing trades with a standard deviation of 1 trade (either way) would mean
about 16% of the of the losing streaks will last for 5 or more trades.
A warning about martingale betting systems: if you don't win strictly
greater than 50% then eventually you're going to be ruined. Gamblers get
around this by quitting before eventually happens. Here's one way to do it:
Assume a stock can increase or decrease by 1 dollar each day. The
probability for an increase is 50%, the probability for a decrease is 50%.
Buy the stock on the first day at S dollars. Wait until the price increases
to S+1 and then sell it. Wait till the price falls back to S and buy.
Repeat this for twenty days then stop.
Stock is held only in intervals where it is bought at S and sold at S+1. If
you buy at S and it goes down, you just wait till it goes back up and pocket
a dollar profit. The only way to lose is if you're holding the stock at the
end of the period. Oddly enough the expected profit and loss from this
system is zero, but 61% of the 20 day trade runs will be profitable.
Would you trade this system? Suppose you're down two dollars at the end of
the 20 day period after being down 10. Are you going to stop?
The key point is that these betting systems don't change the odds, but it
can seem like it for a little while. In the example above, you'll find that
the distribution of possible profit or loss has a long thin tail in towards
the losses and a short fat tail towards the wins That is, most of the time
you'll win a little, but when you lose, you'll lose big. Keep playing and
eventually the losses will ruin you.
In real systems, there are further complications. First there's
commissions,slippage, and drawdowns. Second, real distributions of trader
performance are more complicated than the ones used in typical martingale
examples, including the ones in this post. In KM's example below, the
losses from 4 bad trades may exceed the gains from 6 good ones. Finally,
you can never know the real performance distribution, you have to estimate
it. To be statistically valid, you need at least 30 runs for each market
traded. You can record results in a spreadsheet and take advantage of the
built in statistical functions. Histograms can be used to approximate
probability distributions for both the run lengths and of profit/loss per
length. These distributions can then be used to infer the probabilities of
events such as the probability of a profitable run greater than 4 or a run
whose losses are greater than the trader's account. The "betting" can then
be matched to the estimated probabilites as KM envisions below.
Final note: diversification is a betting strategy not available to gamblers
(except for maybe horseracing). Rather than just varying the amounts of the
bet, you're also varying the allocation of bets.
-- Jeff.
Above martingale stock trading example is from chapter 6 of
http://www.dartmouth.edu/~chance/teaching_aids/probability_book/pdf.html.
-----Original Message-----
From: POMPATIS@xxxxxxx <POMPATIS@xxxxxxx>
To: REALTRADERS@xxxxxxxxxxxxxx <REALTRADERS@xxxxxxxxxxxxxx>
Date: Tuesday, May 25, 1999 6:08 PM
Subject: FUTR: BET SIZE
>Traders,
>
>I know of a bond trader who uses some form of martingale position sizing
>nearly every day.
>
>The idea, as I see it, is to first, know your systems stats very well and
>second, use those stats to your advantage.
>
>Example: Your system currently has an average losing streak of 4 losing
>trades.
>Depending on your personal preferences, you could for example, begin to
>increase your bet size after 4 losing trades.
>
> You could use your stats another way - for example, lets say your system
>shows an historic tendency to have a longer than average winning streak
after
>a greater than average losing streak. If after 4 losing trades (your
systems
>average losers in a row) you begin to increase bet size and the losing
streak
>continues - you then reduce your bet size until you get 2 or 3 winners in a
>row - then you increase your bet size into the statisticaly anticipated
>winning streak.
>
>This is just to get some juices flowing. I am no statistician. The main
>point here is to know your trading results. I recomend creating an
extensive
>spread sheet which calculates all kinds of goodies about your cumulative
>trades. You can come up with many ideas which you might find useful to
>know, depending on your trading style, personal phsycology and your system
or
>method.
>
>Please share some ideas here guys and gals, this is a very important topic.
>
>Best wishes,
>
>KM
>
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