just catching up here... first comment, on the "expectancy" formula. i know acrary knows this, but it should probably be explicitly stated the formula as presented applies to one trade only, not to a series of trades where there is a finite probability of losing everything - so there is an implicit assumption of relatively low risk-taking. second comment, lots of talk about correlations, but i didn't see any talk about the charactersistics of the data being correlated: is any check being done on the data to ensure it meets the criteria for even being correlation-testable? ie, stationarity, etc? if it doesn't meet those criteria, data sets will show much more extreme levels of correlation than actually exist which will lead to inappropriate combinations and poor control of exposure. fascinating thread, hope it keeps up!
No I haven't. If you check the posts since my last post you'll see either comments or completely off topic posts. As I said in the beginning, I'm ignoring most comments. It's impossible for me to provide the full depth of info. and still keep it fairly easy to follow, so it's been necessarily simplified. I'm also giving people a chance to catch up. Maybe someone that owns aberration will use the ideas presented and check to see if Keith has the correct markets selected. I don't own it, but I'd be interested in the results. Maybe someone else has an idea that should be incorporated that I haven't thought of (such as the revelation by bdixon619 that this is old news...I'm waiting to see what direction I should have investigated as bdixon619 has said he'll post). Maybe someone will develop a formula for estimating the chance of winning in a period based on the frequency of trades and profit factor (I've been playing with a quadratic equation to see if even with my limited math skills I can find something). I don't want to continue until I've given everyone a chance to post relevant insights on the material. I'd love to learn something just as much as everyone else. Since the info. presented is cumulative it won't do much good to move on unless we're all on the same page. The last thing I want to do is fill this journal with q & a to posts from 50 posts ago. Be patient, more will follow.
Shouldn't be each such a formula designed specifically for a specific method and specific market ? It would be very labor intensive as you would need to make adjustment based on changes in the trading method ( system ) parameters as market conditions change .
Maybe someone else has an idea that should be incorporated that I haven't thought of (such as the revelation by bdixon619 that this is old news...I'm waiting to see what direction I should have investigated as bdixon619 has said he'll post). Hey Acrary, I was talking about this the other day with someone...I wanted to wait until you had got things going again since it is your Journal and then thought I would just post a method I used for equities. I am not the center of attention here...I think it would be rude of me not to post but, wanted to be sure you were firmly in charge again before making any more contributions. Ah, I'll reiterate...the methods you are using for selecting systems and evaluating results are strikingly similar to those used by Tushar Chande. I've since had a look at the table of contents of the book I mentioned and another poster has independently made the observation that, I'm afraid the Fig 6.5 on page 237 of Chande's book may be a very ideal example to follow, as a Perfectly and Negatively correlated system could not be easily created/designed in daily life. Any shifting in timing with one (or both) of the systems caused by (uncontrollable) market movements in the future could potentially cause unexpected big DD. All I was saying by my comment (that I had learned and forgot this) was that I had seen it before...I went back and re-read the article interviewing Chande in the October '97 issue of TASC and recommend it to you as well as the book. It is fairly easy to confuse intent on an internet message board, no? I'm sorry if my comments were more confusing than revealing. I'll try to be more direct.
i suggest to look more at what i call stress correlation than normal correlation. take equity curve x on daily basis and equity curve y. look at all days where x was negative and take the y values from that day as well. now you have two time series, one with the negative x values, one with corresponding y values. now correlate them. a matrix of such values is necessarily asymetric. the reason why this is more importnat than normal correlation is that what we fear most is +1 corr in times of crisis. stress corr should point that out. nevertheless for practical purposes we combine trading systems by mixing them up and see what the mixture adds in terms of sharpe to the average and the max of the two. it becomes increasingly difficult and requires more and more effort to add to sharpe. we as well look at monte carlo analysis of daily returns in order to get a feeling for maximum draw downs. but i think max draw dwon is a misleading figure. let me explain why: 1. when we look at maxdd we do that only after we have an equity curve that ended somewhere near its high. bias no1. 2. we then reduce the chart to half a dozen of draw downs, among them the max dd. compared to taking all days we now have a very limited number of observations with an increasing standard error. the mdd itself is a single number with huge standard error and literally no statistical significance. nevertheless it is so tempting to answer this question "how much loss can you stand?" accurately, that we use limited draw down figures as if they were key figures in our analysis. flawed by fear and desire for siple answers. bias no2. 3. almost by definition the max dd is the best point to start into an upward sloped equity curve. conceptual weakness. bias no3. the three together make me believe draw down is an awful concept to deal with. i still prefer sharpe ratio. and testing it back in real portfolios where loss of one portfolio is shared among all systems as well as gain. spelling r e a l portfolio tests. i tried acrarys concept of correlation and could not make it work so far. it did not add to the picture, but i might need to give it more time. i also tried out the edge test. i used shapre ratio of my system and compared it with randomly takekn daily returns from the makret itself. systems i liked where on top of the list and made the effort useless. i did something to define trendiness of markets by taking there actual histogramm of returns and plot that against a montecarlowise drawn (=randomly normalised) histogramm of these returns. then i calculated the difference for each point on the histogramm and added up these differences. this sum is my deviation of randomness and indicates trendiness. i have not used the concept in excess so far, since we still have so many things we are testing, that we spend only little time for this baseresearch in the moment. but we will catch up with system testing and will soon be able to do more in this field. this summer we will study the emini on minute data in detail. we will use our way to define patterns and try to find inefficiencies. question: in which circumstances do probabilities shift away from randomness? peace
unless you can actually prove an inverse relationship between two series, you have to assume the "+1 correlation" worst case anyway because it will happen. there has been a great deal of work on the non-randomness of the market at short time frames. a place to start looking is 1995 paper by Guillaume et al. "From the Bird's Eye to the microscopic". historically it has also been true that 2 consecutive green days are more likely than 1 green day only (and same the other way round, 2 red days more likely than 1 red day) but probability != expectation.
i slightly disagree with the worst case assumption. always assuming worst case means that you do not trade at all. key is whether overall sharpe is increasing or not. do you have that paper? peace
As an aside, I am in the middle of some extensive backtesting and have began using profit factors. Something I noticed about the impact of filters on profit factors. I started with a system with the following characteristics # trades 230 profit factor 1.12 net income 95 when I overlayed a filter it transformed into # trades 127 profit factor 1.25 net income 104.3 What became clear to me is that while the filter succeeded in removing 103 more or less useless days to trade, the profit factor failed to reflect the vast improvement in the system's efficiency. Going to the algebra ... Profit factor : PF = - Prob(W) x Avg (W) / Prob (L) x Avg (L) Assume that we have a system where Prob (W) = 50% and Avg (W) = 10, Prob (L) = 50% and Avg (L) = 4. PF = 50% x 10 / 50% x 4 = 10 / 4 = 2.5 Now, let's assume that these results were achieved with 100 trades. If we now add 100 more trades with the following characteristics(Prob(w) Prob (l) = 50%, Avg(w)=Avg(l)=0) what is the new profit factor PF*? PF* = Prob (W*) x Avg (W*) / Prob (L*) x Avg (L*) Since, Prob(W) = Prob (w) and Prob(L) = Prob (l), the new Prob (W*) = 50% and Prob (L*) = 50%. But Avg (W) is effectively diluted by the addition of the Avg (w) such that Avg (W*) = [Avg(W) + Avg(w)]/ 2 = 5 Avg(L*) clearly then becomes = 2 As such, PF* = 50% x 5 / 50% x 2 = 5 / 2 = 2.5 hence, it does seem that one weakness of profit factors is that it is a poor tool for detecting efficiency and profitability per trade. While useless trades with zero expectancy arguably never hurt anybody, they do consume time, commissions and slippage! That said, I have found profit factors very useful within the context of Acracy's discussion.
Hi Student, long time between reading your posts. Did you think about using any other measure of efficiency, such as number of trades, trade cost, price of the trading vehicle, etc.? I was wondering because this is the direction my experiments with different markets led me.