Ok thanks. Do you have any links, books, or perhaps recommended software for proper Monte Carlo sims for traders? I've knocked up a crude one on my spreadsheet but I have to iterate by hand, and no idea how to isolate the biggest drawdown per run, my computing skills are weak.
An older thread on this subject http://www.elitetrader.com/vb/showt...163574&highlight=rabbitone+consecutive+losses
I think the question asked is fundamentally flawed. I have seen the trading world littered with mathematical jargon for years and no real increase in performance (at the individual level). The web is filled with all kinds of information on statistical analysis as related to trading etc. One would think that we would have better traders now that information is plentiful. But the % of successful traders seems to be about the same assuming that ET is a valid sample set. The fact that the question is being asked shows that there is confusion between a system and a temporary pattern exploitation the two 'systems' are being used inter-changebly. In my opinion exploiting a certain pattern will at some point fail and fail for a prolonged period of time. Yet, the user might be okay since many patterns repeat themselves. So, the rinse and repeat will eventually work if the other facets are optimal (i.e. money management etc.) But a real system involves the understanding of the current trading environment, formulating a strategy to exploit the perceived behavior and then putting together a tactical plan to execute the vision of the trader. Now, with this approach an experienced trader will win at a far higher rate than any 'system' exploiting patterns. Why? Because the trader is flexible and has the experience and techniques required to put the odds in his favor over and over again. Also, when he does not see a favorable environment he can choose to sit out. Okay guys, back to work.
Any reason why you added one to the max losing streak S=12.16? If I run a very large simulation, it converges to an average of 12, as the expected max losing streak (with your parameters). Here is an R script to run a single sample for illustration. Keep in mind it will take a very large number of trials to approach these expectations. There are also assumptions made about trade distributions being normal; depending on your trading strategy, that is not always the case. The script also shows tables of probabilities of contiguous runs of different lengths for another request that was made in the thread. #generate simulations of win/loss streaks use rle function trades<-sample(c("W","L","B"),1000,prob=c('.6','.4','0'),replace=TRUE) traderuns<-rle(trades) tr.val<-traderuns$values tr.len<-traderuns$lengths maxrun<-tapply(tr.len,tr.val,max) maxrun #streaks of losing trades lt<-tr.len[which(tr.val=='L')] lt.1<-lt[1length(lt)-1)] lt.2<-lt[2length(lt))] #simple table of losing trade run streak(n) frequencies table(lt) #generate transition table streak(n) vs streak(n+1) tt<-table(lt.1,lt.2) #convert to proportions options(digits=2) 100*prop.table(tt) maxrun P.S. frown smileys are colons
Quote from dtrader98: Any reason why you added one to the max losing streak S=12.16? If I run a very large simulation, it converges to an average of 12, as the expected max losing streak (with your parameters). It's probably just my quirkiness. I did it because I was looking for a expected or "normal" maximum losing streak. If I ran the simulation of 500 trades 7 different times I'd expect one of them to include 13 losing trades. The 13 losing trades would have been considered normal in my mind beacause the expectation was for a number greater than 12. If I were looking for expected average maximum losing streak then I would have rounded down to 12. Alan
Expected max losing streak and drawdown are related but not 1:1. You can get very small but several streaks of losers, like 3 losers in a row followed by 1 win and still get completely ruined. Then you can get a very large streak of winners that will bring your win rate back up high but too late then. Sounds familiar? If not, get prepared because the expectation that this will happen to you at least once is very high.
For me personally, if I experience two losses in a row in the same market, I cut my size back to a pre-determined level.
One of the easier formulas I am using is from this post: Maximum Drawdown in Trading Computation This is the formula for maximum losing streak with the probability of happening at 1 per 10,000 trades: Max = -4 /Log(L) Where L is the loss probability of the trading system. Supposing you have a 60% loss probability, then the maximum losing streak is: Max = -4 /Log(0.6) The logarithm is to the base 10, computing it would reveal: 18 consecutive losses. The interesting to note is that the probability of occurrence for this 18 consecutive losses is only 1 out of 10000 trades. That's rare isn't it? Now for those who are looking "formula for the probability of further losing streaks". It would mean computing for a drawdown that would occur at a much common probabilities, something like 1/100 or even 1/10 The math will be (supposing you would be interested to know what is the drawdown at 1/10 probability): Let D be the drawdown and L be the loss probability of the trading system: Converting to exponential function: L^D = 1/10 Taking logarithms in both sides: Log(L^D) = Log(1/10) D*Log(L) = -1 Solving for drawdown at 1/10 probability (the logarithm is now in base 10): D = -1 /Log(L) Looking back at the above example, what is my "usual" or "high probability occurring" consecutive losses (estimated at 1/10 probability) if my system has 60% loss probability? D= -1/Log(0.6) The answer is around 5 consecutive losses. To minimize consecutive losses, its much better to reduce the %loss probability or having a high winning trading system. Hope this post clarifies everything. I would be interested if someone could run an actual simulation as the above is plainly theory.
Hi Alan, pleasure to read your posts. Ralph Vince has a fair bit of mathematics on this in the book Portfolio Management Formulas (yes, with the caveat of the original optimal f system being, shall we say, less that optimal) relating to streaks and max expected drawdowns.
yes and also in his book "Mathematics of Money Management" he goes over runs test and z-scores.. good info on winning/losing streaks.