”TheBramble” said:
You have a system (you wish) where your R:R is 1:4. You had a trading capital base of $375,000. You risk 1% of your capital on every trade. Your system so far has yielded an average winning trade value of $464 and an average losing trade value of $295. Your winning trades outnumber your losing trades 1:1.5. You have executed 134 trades and are currently flat. You have been trading this system for 23 weeks.
My first observation is that for your average losing trade value to be $295 you’d have to be closing trades at a loss that had not hit your stoploss if you really are risking 1% capital each trade. You’d have to be moving up your stops with the price, closing trades on a signal of some sort or not following your system to the letter for this to occur.
In any case a statistical analysis based on the average loss would be very unwise.
The same comments can be made towards the average winning trade value. Comparing the two figures also bring the idea of R:R being 1:4 in to doubt.
The number of trades is only relevant for comparing your actual results to a statistical models on which your system is based. The number of weeks the system has been traded isn’t relevant, on it’s own, to any of the other information given.
”TheBramble” said:
What is your expectancy?
What, statistically, will be/will have been your drawdown?
What would you calculate to be the current value of your trading capital?
What is your Aw:Al?
What is your Pw
l?
How many consecutive winners/losers can you expect based on this system’s profile?
To calculate any of the above we first need to establish a model to compare our actual results to. This becomes difficult when considering things like sliding stops, closing a trade because of anything other than a stop etc.
The best way of doing this is to establish R:R as a ratio of stoploss:target and what percentage of signals result in successful trades – a hit rate if you were. This hit rate should be calculated using the outcome of all signals with stoploss and target set as per your system even if the stoploss would cause you to risk a higher % of your capital than you’d like. We do this because we can’t know what our trading capital will be at any point in time. We may have enough capital to trade 1 lot at our systems constraints, we might have enough to trade 10 or we might not have enough capital to enter the trade at all, while risking only 1% of our trading capital.
We must assume that all signals are traded, that stoploss and targets are not moved, that trades are only exited when stoploss or target is hit and that R:R is always maintained.
So then, lets pretend we have a system where our stoploss:target ratio is set at 1:4 when we get a signal to trade. Our expected hit rate is 60% (as suggested in your example) and that we trade our system to the letter, don’t move stops, targets etc, basically all the provisos given above.
”TheBramble” said:
What is your expectancy?
What would you calculate to be the current value of your trading capital?
To have an expectation of our equity curve we could use a
random equity curve generator. If you put the win/loss to 4, win prob to 0.6 and the lines quantity to 100 you can generate 100 different equity curves based on approximately 450 trades. As you can see from the curves if you weren’t in massive profits after 134 trades something would be seriously wrong!
Another way to look at your equity curve would be to test against a binomial model. We could take our number of wins/losses after X number of trades and, using our hit rate of 60% calculate how likely it is for that outcome to occur. If we chance of that outcome occurring is very low we can say one of 3 things: Our hit rate has changed, we aren’t trading our system in the way we set out to or we’ve been very lucky/unlucky over those trades.
How many consecutive winners/losers can you expect based on this system’s profile?
But what about losing streaks? Grantx made a good point in my journal thread about the fact that simply looking at the net outcome of 100 trades is not good enough.
As he rightly said if you expected an 80% hit rate you could get 20 losses followed by 80 wins which would fit perfectly into a binomial distribution. This is where a geometric distribution becomes very useful. We can calculated the likelihood of any length of losing streak and based on this decide whether or not our model is still accurate.
Going back to our model using a 60% hit rate we can calculate generate the geometric sequence in the attached spreadsheet. If you change the “chance of successful trade” you can see how the chances of getting various losing streaks changes as your hitrate changes.
To explain the number in the “losing streak” column a little better. The figure 5 means a streak of LLLLLW, 10 would be LLLLLLLLLLW and 1 would be LW.
By testing our results against these two distributions we can determine whether our original model is still accurate or not. When we start moving stop losses etc. our tests might show that we are either causing our results to be better or worse than expected if we hadn’t moved them at all. These kinds of actions do make interpretation of statistical tests more difficult. The test can only tell you whether or not something has changed from your model. Ideally you want the only possibility of a change to your model to be market conditions changing - knowing that your model has changed (because you're moving stops etc.) before doing such a test will muddy the waters considerably.
As far as
What is your Aw:Al?
What is your Pw
l?
Is concerned we can expect varios outcomes. If the ratio of our target:stoploss is always the same (but their size may vary), and we don’t move our stoplosses we would expect Aw:Al to be the same as Pw
l.
In our model Pw
l would be 4:1 and, over time, we would expect Aw:Al to converge on a ratio of 4:1. Aw:Al could be something like 100:25, 20:5 or anything else. You wouldn’t expect them to remain constant but their ratio should.
What, statistically, will be/will have been your drawdown?
This one is a little bit more complicated to model and it’s not something I’ve looked at doing myself as I’m not sure whether it really tells us anything more than we can learn from the study of randomly generated equity curves and binomial models for our system.
:edit: Forgot to add the attachment. Hope that post doesn't take too long to digest!
