matlab code
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a trading problem for mathematicians
- Thread starter trend2009
- Start date
Relax!
Before you try to solve a problem you should first state a model and the possibilities that arise.
The problem is that there are two systems both with win rate w and we will trade when both generate a signal. Since it is assumed that the systems are independent, given enough time there will be a long sequence of paired signals where each has probability w of win W and (1-w) of loss L. The possibilities are
W(1)W(2)
W(1)L(2)
L(1)W(2)
L(1)L(2)
Now, no assumption was made about the average win and average loss of those systems. These are the possibilities
assuming commissions are paid
W(1)L(2) > 0
W(1)L(2) < 0
L(1)W(2) > 0
L(1)W(2) < 0
As a results, there are the following 4 possibilities (I substitute + for a win of the paired system and - for a loss)
+,+,+,- +,+,-,- +,-,-,- +,-,+,-
that result in the following win rates:
100 - .16, 100 - .24, 100 - .24 - .24 - .16, 100 - .24 - .16
or
.84, .76, .36, .60
Before you try to solve a problem you should first state a model and the possibilities that arise.
The problem is that there are two systems both with win rate w and we will trade when both generate a signal. Since it is assumed that the systems are independent, given enough time there will be a long sequence of paired signals where each has probability w of win W and (1-w) of loss L. The possibilities are
W(1)W(2)
W(1)L(2)
L(1)W(2)
L(1)L(2)
Now, no assumption was made about the average win and average loss of those systems. These are the possibilities
assuming commissions are paid
W(1)L(2) > 0
W(1)L(2) < 0
L(1)W(2) > 0
L(1)W(2) < 0
As a results, there are the following 4 possibilities (I substitute + for a win of the paired system and - for a loss)
+,+,+,- +,+,-,- +,-,-,- +,-,+,-
that result in the following win rates:
100 - .16, 100 - .24, 100 - .24 - .24 - .16, 100 - .24 - .16
or
.84, .76, .36, .60
Quote from total_keops:
When we take a trade we have a win based on a uniform distribution [0,1]. If both systems have a uniform random number smaller than 0.6 we have a win, otherwise it is a loss.
Attached is a 10000 periods 50 times MC simul. Average is in thick black.
Win rate gives: 0.3594. (the expected 0.36).
You already assumed that you take a trade when both systems are winners. But of course this will have a win rate of 0.36. No MC simulation is required for that. This is equal to the probability of two heads in two independent coin tosses with a biased coin whose p[heads] = 0.6.
The problem solution depends on the distributions of winners and losers of the paired system. It is rather complicated in practice. I submited above a simple solution to show a possible range of results for the win rate.
Quote from alexandermerwe:
Relax!
Before you try to solve a problem you should first state a model and the possibilities that arise.
The problem is that there are two systems both with win rate w and we will trade when both generate a signal. Since it is assumed that the systems are independent, given enough time there will be a long sequence of paired signals where each has probability w of win W and (1-w) of loss L. The possibilities are
W(1)W(2)
W(1)L(2)
L(1)W(2)
L(1)L(2)
Now, no assumption was made about the average win and average loss of those systems. These are the possibilities
assuming commissions are paid
W(1)L(2) > 0
W(1)L(2) < 0
L(1)W(2) > 0
L(1)W(2) < 0
As a results, there are the following 4 possibilities (I substitute + for a win of the paired system and - for a loss)
+,+,+,- +,+,-,- +,-,-,- +,-,+,-
that result in the following win rates:
100 - .16, 100 - .24, 100 - .24 - .24 - .16, 100 - .24 - .16
or
.84, .76, .36, .60
Relax!
W(1)W(2) - 100%
W(1)L(2) - 100%
L(1)W(2) - 100%
L(1)L(2) - 100%
Quote from euclid:
Let's say both systems (A & B) give long and short signals such that e.g a long signal means the market will hit +X before it hits -X.
It follows that on occasions where both systems gave a signal, we have the following probabilities:
Market moved X:
A won, B won = 0.6*0.6=0.36
A won, B lost = 0.6*0.4=0.24
A lost, B won = 0.4*0.6=0.24
A lost, B lost = 0.6*0.6=0.16
So, 36% win, 16% lose, 48% no trade because the systems disagreed.
This leaves us with a win rate for the combined signal of 0.36/(0.36+0.16) = 0.69. A small improvement in hit rate, but a big reduction in the number of trades.
This looks right. However, I don't think the original poster formulated the problem precisely enough. Specifically, it's important to realize that any trade is a double-event, described by an entry and an exit. Now let's say you have systems A and B, and each one enters and exits independently. Each one has a win rate of 60%. System C enters the trade when both A and B agree on the entry, and it exits when both A and B agree on the exit. It's not that difficult to see that the win rate of system C may actually be less than 60%.
I'd love to see that modeled in Excel or Matlab.
The law of addition applies as the "events" are not mutually exclusive: P(X+Y) = P(X)+P(Y)-P(XY)
X is the event of system one winning, Y the event of system two winning. P(X+Y) is either one winning.
Note: winning probability is just a number, you can win 90% and feel happy about it but your capital still diminishes. Good luck!
X is the event of system one winning, Y the event of system two winning. P(X+Y) is either one winning.
Note: winning probability is just a number, you can win 90% and feel happy about it but your capital still diminishes. Good luck!