Five wins in a row...system seems to be back on track.
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DislikedWell I have taken Fly's 57 trades and used them as a basis for some rudimentary Monte Carlo testing.
What is Monte Carlo Testing?
For those of you who are not familiar with Monte Carlo methods, let me give a brief description. Monte Carlo testing is a method of simulating the performance of a system. It is neither back-testing, nor forward-testing. It is a way of simulating a random market environment to see how your system holds up. One investor gave a good analogy; he said, "Before you step on a ladder, you shake it to make sure it's sturdy. That's what Monte Carlo testing does for a trading system."
Research Goal
Why am I conducting this research? I wanted to see how changing the amount of risk (and potential reward), i.e. how position sizing would affect the overall profitability of the system. Ideally to answer the question: What is the optimal amount of risk per trade?...or...How should I size my positions for optimal return?
Procedure
Here I will detail exactly what I did in my testing. First I got a list of all 57 wins and losses (in PIPs) from Flyjetz. Next I generated a list of 500 random numbers. Then I mapped those random numbers to one of the 57 P/L values. Each of the 57 values is equally likely to come up. In other words I generated a list of 500 random outcomes to simulate making 500 trades in this system. Basically I just extended the 57 trades to 500 trades in a random way. These outcomes should be similar to typical outcomes you might expect from this system since I used P/L values (in pips) from Fly's actual data. This list of 500 simulated trades will have winners (and losers) with roughly the same frequently as the real system has had so far in actual trading. Furthermore, the magnitudes of the wins and losses is similar.
Next I calculated the compounding of profits. To do this we need some rule for choosing position size. The rule I used was: Trade the number of units such that a 200-pip loss would equal a loss of X% in the hypothetical trade account. For example, let's say X = 1. Then if a trade comes up as a loser of -200 pips, the account will decrease by 1%. If a trade comes up as a winner of 400 pips, then the account will increase by 2%, etc. Now the value of X is variable and that's the next part of my testing as you will see.
So I let this model test the outcomes and compound the returns over 500 trades for different values of X. I tried, what if X = 1% risk per trade? What if X = 2% risk per trade, etc. I tested:
X = 1, 2, 3, 4, 5, 10, 15, 20, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50. I did not only run one set of 500 trades, but I ran 124 sets of 500 trades for each value of X.
Finally I took the 124 compounded returns from the 124 sets of 500 trades and I found the median. I used the median, not the average since the median is a better indicator when the data has a very wide range. I also calculated the probability of the account running to ruin, i.e. the probability of a string of losing trades taking your account down to $0, effectively.
Results
http://www.gis.net/~giokas/data.png
The results are interesting. First we'll talk about the probability of ruin.
http://www.gis.net/~giokas/ruin.png
As you can see, the probability of ruin is zero until you start to risk 45% per trade, or more. Then the probability sharly increases to about 50%. So this seems to imply that this is generally a profitable system as long as you don't risk too much at once. It also gives up an upper limit on what we can safely risk at one time, viz. Do not risk more than 45% at any given time.
Next we will look at the compounded returns to estimate the optimal risk.
http://www.gis.net/~giokas/return.png
As you can see there is a peak between 25% and 35%. In particular, the maximum return for this data was achieved at 29% risk, and the penultimate return was acheived at 32% risk.
You will also note that these returns are staggering! I mean even only a 5% risk is expected to quadruple your account after 500 trades and at the optimal risk (an agressing 29%), it is expected to multiply the account over one-trillion times in 500 trades! Are these results too good to be true? Well, we have to be careful how we interpret these returns. First of all, see the caveats below. Also, note that this is 500 trades and Fly has recorded about 50 trades since January...so 500 trades would mean trading this system for about 5 years. In addition, risking 29% of your account on a single trade is insane! Maybe you could multiply your account thousands upon thousands of times, but who is going to do that? On the other hand, most of you are probably trading this system with more than one currency pair. Perhaps you might have 10 trades open at times. Now if we are to risk 29% at one, spread across 10 trades, that's 2.9% per trade, and that doesn't sound so wild anymore.
I will follow up with another post giving more details about the compounding and interpreting the return figures, as well as estimating returns when multiple currency pairs are involved.
Caveats
Of course these results are very rough. The testing is rudimentary. It is based on only 57 sample trades, which, as you know is a very small sample size, too small to put too much faith in these results. Furthermore, I only ran 124 tests of 500 trade sequences. Ideally I would run thousands of tests. Another consideration is that most likely, you will not be risking so much per trade and compounding after every single trade. A more likely scenario, is trading several currency pairs at once and compounding every week, perhaps. As I said, I will give more details about this in a following post.
The bottom line: This system certainly seems like a "sturdy ladder to climb."Ignored
DislikedExcellent work Mathematician. I have a few questions off the bat, and one observation. How do your stats account for leverage? When you say 29%-32% might be optimal, is that 29-32% at 1:1 leverage or 50:1 leverage? Can you expand a little on trading multiple pairs? I may only be risking 1-2% on say USDJPY. But when I add all my USD trades, I may have 9-10% of my account short on one currency. So my main questions are, is the 29% per pair? Per currency? At what leverage?
Here's my observation. You ask if these returns are truly possible. What I can tell you is that I don't want to push so close to the ultimate just to achieve gargantuan returns. I can get comfortably wealthy with modest returns with much less risk. The problem I have always run into when trying to calculate my actual performance return is that I am constantly adding funds to my account, and occasionally withdrawing funds. I found an excellent website on MS Excel's "XIRR" function. You plug in dates that money was added and subtracted and it automatically calculates your annualized return. I first funded my Live Forex trading account on Jan 14, 2008. I've made 24 deposits and 5 withdrawals over the course of the last five months. Excel has calculated my annualized return at 213%. I'm not saying this to brag in the slightest. But if I can even manage a quarter of that performance, year-over-year, I'll be taking an early retirement.Ignored
DislikedLeverage. Hmm...let's see. Well, my assumption during these tests was that a 1% risk means that a 200-pip loss would be a 1% loss on your account. Let's consider an example.
Assume an account with $1000. If you want to use 1% risk (based on a 200-pip move) then you can risk 1% of $1000 = $10 on that trade (or set of trades if you are spreading the risk across multiple currency pairs.) Your trade size would be 500 units because a 200 pip move amounts to 200/10000 = 1/50...so by trading 500 units your P/L for this 200-pip move would be 500*(1/50) = $10.
If I'm not mistaken, leverage has nothing to do with this. It only affects the amount of margin you are required to have in order to hold such a position. So higher leverage would require less margin.
Is this 29% per pair? per currency? It's 29% per compound unit. In other words, if you are trading only one currency pair at a time and you compound after every trade, then it's 29% for that one pair. That means you would size the position such that a 200-pip move represents a 29% risk on the account. Of course that is too risky. It is better to diversify this risk across multiple currency pairs. Let's say you are trading 10 pairs at a time. In that case you want the total risk to be 29%, i.e. about 2.9% risk per pair. Again, that would mean that you size your positions such that a 200-pip move amounts to a 2.9% risk on your account.
About your observation. I agree with you, I don't need gargantuan returns. However, if you look at the return graph, before 30% it's not a straight line, it's increases exponentially. So while the risk is increasing, the return is increasing faster, i.e. you can get a higher return/risk ratio.Ignored
DislikedMy own curiosity got me thinking. According to the rules I laid out, I only trade in the direction of the trend. In other words, I only trade from 20% to 80% or 80% to 20%. The theory behind that is that I'm more likely to be on the right side of the trade more often that way. But in my mind, I always knew that the price corrects, otherwise, I would never get an entry. So maybe the 80/20 system is only living up to HALF its potential. I decided to start tracking what would happen if I traded back and forth between the 20% and 80% level. In other words, if I am long at 20%, I TP at 80%, and immediately go short until 20% is hit again. Imagine a ping pong ball bouncing back and forth between those two levels. Trades should happen about twice as often, and results should be just as successful.
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NOTE: MODS, I'm about to name a website so delete if you must, but since this is my Trade Diary, and I have contributed a Heck of a Lot, I'm hoping you'll let it stand. I'm not posting the site to plug it or myself, just to show followers of this system where they can find updated statistics on how this system has performed.
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I decided to track my system(s) at www.zulutrade.com
If you go there, you can search for my Signal Providers:
"BBFM Low Risk" (only trades USD based pairs according to original 80/20 system rules)
"BBFM High Risk" (trades all major crosses according to original 80/20 system rules)
"BBFM Helter Skelter" (trades most major crosses in the ping pong fashion I mentioned)
Keep in mind, I did not start submitting signals to Zulutrade until the beginning of April, and Zulutrade still has a lot of bugs to work out with their trade entry system. A lot of times, I am prohibited from putting the exit price in that I want to put in. Also, I don't get to choose the amount risked on each trade. I simply put in buy and sell orders. But none-the-less, the systems have exceeded my expectations.
Here are the stats according to Zulutrade as of this post:
BBFM Low Risk:
31 Wins and 8 Losses (79.5% win rate)
+4439 Pips
-2266 Max Drawdown
BBFM High Risk:
59 Wins and 20 Losses (74.7% win rate)
+4281 Pips
-5299 Max Drawdown
BBFM Helter Skelter:
68 Wins and 18 Losses (79.1% win rate)
+7554 Pips
-2755 Max Drawdown
On the front page of the website, Zulutrade lists their "Top Traders". Frankly, I'm not sure why my systems are not on that list yet. On a pip/trade basis, I am killing those guys. When I opened and examined the systems of everyone in the Top 10, they have all been trading for at least 14 weeks. My systems have been on Zulutrade for 11-12 weeks. So I'm thinking a couple weeks from now, you will see these systems in the Top Ten List.
So getting back to the original point of this message, I haven't decided to pull the trigger yet on opening the system up to trading in both directions, but the idea is on the table for you all to discuss...Ignored
Disliked
But what does 29% mean? 29% of what? That means that your trades should be sized such that a 200-pip move represents a 29% risk on the account.
Ignored
Disliked
Here's my observation. You ask if these returns are truly possible. What I can tell you is that I don't want to push so close to the ultimate just to achieve gargantuan returns. I can get comfortably wealthy with modest returns with much less risk. The problem I have always run into when trying to calculate my actual performance return is that I am constantly adding funds to my account, and occasionally withdrawing funds. I found an excellent website on MS Excel's "XIRR" function. You plug in dates that money was added and subtracted and it automatically calculates your annualized return. I first funded my Live Forex trading account on Jan 14, 2008. I've made 24 deposits and 5 withdrawals over the course of the last five months. Excel has calculated my annualized return at 213%. I'm not saying this to brag in the slightest. But if I can even manage a quarter of that performance, year-over-year, I'll be taking an early retirement.Ignored
DislikedI'm doing the best I can to stay with you on all the math. Was the choice to use a 200-pip loss an arbitrary choice, or was there some mathematical logic behind that choice?Ignored
DislikedBut what does 29% mean? 29% of what? That means that your trades should be sized such that a 200-pip move represents a 29% risk on the account.Ignored
DislikedI'm having a hard time comprehending exactly what you are saying here. If a 200-pip move has the potential to wipe out 29% of my capital, then all it would take is 689 pips to completely wipe out the account (100%/29% x 200 pips).
It would not take much to be on the wrong side of a currency like the GBPJPY and see this totally wiping out the account.Ignored