How to tell if 2 strategies are independent?

[asiaprop]

of course, which of your investors care when you entered positions, nor does your brokerage account care. What you want is to run strategies at prudent risk levels, with manageable downside. You want to gain diversification benefits, otherwise you should just run one strategy and employ more capital into that.

Well, after varying parameters of your strategy and you end up with completely different correlations between that strategy and other strategy then you have other things to worry about. It first points to the possibility that your strategy is not robust to input parameters, something you should avoid because it strongly hints you fit to past data. The performance should not vary too much if you slightly adjust parameters.

If you want to keep it simple, just correlate the daily returns very simple.

Quote from zedDoubleNaught:

thanks for the suggestion. I'll have to research for more background info for my own understanding and come back to this, but I think I get the idea you're pointing towards. Further, it sounds like your vote is to weight the returns more heavily than the entry time, direction, or other factors.

So from Arthur Deco's suggestion, get the correlation value from OpenOffice (not too difficult), then from asiaprop's suggestion, draw a scatter plot as well (also could be done in the same spreadsheet in less than a long time). Then vary parameters, see how the outcomes and correlation are affected. I'll start with this -- doable within one sitting, and will give me a number, and a visual to give an intuitive feel for the number.

Initially I thought fixed stops and limits would have an effect on the OpenOffice correlation value, but now I suppose it would not -- it would reflect the holding time, a factor I have not yet considered.

I'm not too worried about correlated or not; instead not knowing the degree to which they are correlated or not is the problem I'm trying to solve. I hope graphical observations are sufficient, I'd prefer a solution in fewer steps than a solution in more steps. But also feel free to drop the statistical test names -- that gives me something I can search for and learn about, the best part of reading through threads. Often, even if I cannot master it, it will introduce me to a new perspective on a problem.

 

[Trader666]

Have you heard of Parrondo's paradox? Some systems, when traded alternately, DO combine in unexpected ways.

Given two games, each with a higher probability of losing than winning, it is possible to construct a winning strategy by playing the games alternately.
http://en.wikipedia.org/wiki/Parrondo's_paradox

Quote from zedDoubleNaught:

Suppose you have 2 strategies on 2 different but closely related issues. How do you tell if the strategies are independent or not? This is for the purpose of generating an outcome estimate; if the strategies are dependent, the outcome estimate based on the strategies' win/loss ratios will be different.

The things I'm putting into a score are:
- entry time (closer entry time, less independence)
- direction (further away from matching 50% of the time means less dependence)
- win/loss outcome (if there are no or very few instances of strategy 1 wins + strategy 2 loses, means less independence)

I don't know how to judge this, looking for ideas or suggestions.

 

[zedDoubleNaught]

Trader666 -- thanks !! From that wiki article, I think you've led me to exactly what I was looking for. When starting this, I had a vague gut feeling something was not quite right, and this line from the article clearly states the problem in words:

"In summary, Parrondo's paradox is an example of how dependence can wreak havoc with probabilistic computations made under a naive assumption of independence."

So, now I'll take a look at this paradox. Too humble to say I'll be a mathematician and understand it fully, but I'll try to force my head through some of the math and understand the concepts, see if there's some way I can benefit and use them. I hope it can help me find ways to avoid naive assumptions of independence.

Keeping it simple in the meantime, I'll settle on a measure that factors in:
- entry time and exit time (.25)
- spreadsheet correlation of positions from opening to exit (.15)
- chi-square of 2x2 outcome table (.35)
- chi-square of 2x2 trade direction table (.25)
(I will probably change all of this radically based on how actual results turn out)

 

[propseeker]

Quote from zedDoubleNaught:

Keeping it simple in the meantime, I'll settle on a measure that factors in:
- entry time and exit time (.25)
- spreadsheet correlation of positions from opening to exit (.15)
- chi-square of 2x2 outcome table (.35)
- chi-square of 2x2 trade direction table (.25)
(I will probably change all of this radically based on how actual results turn out)

what you're measuring above is portfolio level market-risk/exposure and imo better dealt with at the portolfio level. not normally what comes to mind when people think of strategy independence.

as other posters have mentioned, strategy independence is best measured by correlation of returns.

 

[abattia]

Quote from Arthur Deco:

... I cheerfully BT and trade strategies with only 24 samples...

...That is why if I find that when an incertain denomenon recurs within a sample size of twenty I feel no rambunction whatsoever testing down to a subsample size of four to six to make trading derisions...

AD, I am neither mathematician nor quantum physicist, but would welcome your comments on the following.

Firstly, my current approach:

I will only trade an intraday strategy that a) I can backtest over at least the last 5 years, b) trades at least 200 times each year, c) has been consistently profitable over the “whole” backtest period (i.e. generates a nice, positive, smooth, upwardly sloping equity curve, with just a few little “kinks” here and there), and d) has a win/loss % > X%, av. trade > Y%, and PF > Z.

The reason I like a backtest over lots of trades is not because I strive for “statistical significance” per se. It is because I reason an edge that existed consistently over this period of time (from several years ago right up to the present) is less likely to stop working as soon as I start trading it myself! Therefore, when the inevitable drawdowns come, I am more comfortable that I am just going through a (hopefully short) losing streak within a successful strategy, and that each loser brings me closer to the winners, etc … I find it easier (and less risky) to keep trading if I can be comfortable my edge is likely still intact. I am more comfortable about sticking with the strategy and just comparing real performance stats with backtest stats to check the strategy is behaving. And I guess I am comfortable with the backtest stats because I have lots of backtested trades to compare against …

Having said the above, I am also aware that perfectly good opportunities to make money from the markets arise from edges that exist more fleetingly, that cannot be backtested over years of data as the market structure they derive from was more transient. However, my problem with trading these opportunities has been that, in drawdown, one must worry more that the edge has had its day. Therefore, it is harder to keep trading if you cannot be comfortable your edge is likely still intact. And you have fewer historical trades to compare your results with.

How do you deal with this dilemma?

Or am I merely providing further examples of the Dunning-Kruger effect at work?

 

[Arthur Deco]

Quote from abattia:

AD, I am neither mathematician nor quantum physicist, but would welcome your comments on the following.

Firstly, my current approach:

I will only trade an intraday strategy that a) I can backtest over at least the last 5 years, b) trades at least 200 times each year, c) has been consistently profitable over the “whole” backtest period (i.e. generates a nice, positive, smooth, upwardly sloping equity curve, with just a few little “kinks” here and there), and d) has a win/loss % > X%, av. trade > Y%, and PF > Z.

The reason I like a backtest over lots of trades is not because I strive for “statistical significance” per se. It is because I reason an edge that existed consistently over this period of time (from several years ago right up to the present) is less likely to stop working as soon as I start trading it myself! Therefore, when the inevitable drawdowns come, I am more comfortable that I am just going through a (hopefully short) losing streak within a successful strategy, and that each loser brings me closer to the winners, etc … I find it easier (and less risky) to keep trading if I can be comfortable my edge is likely still intact. I am more comfortable about sticking with the strategy and just comparing real performance stats with backtest stats to check the strategy is behaving. And I guess I am comfortable with the backtest stats because I have lots of backtested trades to compare against …

Having said the above, I am also aware that perfectly good opportunities to make money from the markets arise from edges that exist more fleetingly, that cannot be backtested over years of data as the market structure they derive from was more transient. However, my problem with trading these opportunities has been that, in drawdown, one must worry more that the edge has had its day. Therefore, it is harder to keep trading if you cannot be comfortable your edge is likely still intact. And you have fewer historical trades to compare your results with.

How do you deal with this dilemma?

Or am I merely providing further examples of the Dunning-Kruger effect at work?

You are a brave man to ask my advice. You would be even braver if you took it.

Testing over five years means that the optimized stop loss and profit target probably are averaged across a range of volatilities, that you may not have the right values for current conditions, and that you may be leaving money on the table. I have never tried it, because I use one-minute futures data, I get only six months of history from EasySignal, and it would be a horrendous pain in the ass for me to go get such a data history and write or get code to handle it. I am a lazy fuck.

By requiring at least 200 trades a year I assume you want to trade every day. If that is right I don't understand why. There are days you just shouldn't trade. If somehow you are explicitly requiring that in your code or decsion making then I suspect that removing it would make the expectoration better.

Can't argue with a smooth upward curve. I tweak to get shorter drawdowns at the expense of total expectation so that I don't find at the end of a loooooong drawdown that the system has cratered.

Win/loss %? You can tune that too to get fewer losses at the expense of lower expectation. This is the same thing as reducing the drawdown duration. I personally can't stand worse than one win for four losses. I find it leads to drink.

Average trade? Obviously has to be large enough that if slippage starts to exceed your model you still make a profit. Again, you can make more per trade at the expense of total expectation.

I don't know what you mean by PF, please unlighten me.

I would not trade a system that I thought might be evanescent. I avoid that by requiring that systems have some market logic behind them.

In the interest of full disclosure, I live in a broken down drafty old single wide in a ratty trailer park, let the dogs sleep with me, drink a quart of cheap vodka a day, get my internet via bootlegged DirectTV, and only try to make enough to keep me in booze and dogs in flea powder. So do what I do in trading at your own peril.

 

[abattia]

AD, Thank you for the prompt and full response; there is much for me to chew over here …

Quote from Arthur Deco:

... I don't know what you mean by PF, please unlighten me...

“PF” is “Profit Factor”; from investopedia PF is “defined as the gross profit divided by the gross loss (including commissions) for the entire trading period. This performance metric relates the amount of profit per unit of risk, with values greater than one indicating a profitable system”. I calculate it as (average winner * % winners)/(average loser * % losers) … which I hope is the same thing …

I continue to aspire with to your glorious, successful trailer existence (hoping one day also to lift myself, from life as a sewer rat beneath one of southern Europe’s oldest, and grubbiest, cities).

 

[Arthur Deco]

Periodically I quit dialogueing with intelligent people here like you because I get horribly embarrassed. Thank goodness for anonmunity (that's immunity by way of anonymity). So thanks to you I have to go silent again for a while until the cheap vodka does its work on a frail old man's memory.

My embarassment? I don't even look at PF as you defined it. I note the total profit and the total loss on my backtest records, but never ratio them. So I must be doing something wrong, yes? But wait, limiting the run length of drawdowns while maintaining a semi-proportional profit indirectly influences PF. I didn't know it before, but thanks to you I am proud to discover that I like a PF of 2 to 3.

I guess I am just not cut out for the life of a glamorous daytrader. I have to pack a gun all day and night to ward of the various critters that want in my single-wide. Lazy damn dogs just look at 'em. What self-respecting snake wants to be in a trailer? Or 'possum or 'coon for that matter. You would think that the fact that I bathe only once a week, if in fact I need it, would keep them at bay. The upside is that what I plug is fresher than roadkill. Keep a pot 'a chili bubblin' on the barbecue grill 24/7. Cain't say 24/7/365 because these damned cans I find along the roadside to cook in rust out from the Messican chili powder afore a week is up. How's them southern Europeein rats?

As to me giving you "much to chew over", I can only quote you the punch line from my favorite Little Johnny joke (doubt that they translate well into whatever yore native language is): "Spit it out, Johnny! It's a piece of ass!"

 

[zedDoubleNaught]

Hi everyone -- thanks for your input, this helped me think things through. I've come to agree with asiaprop the outcome should have the highest weight, after all, I was originally looking for something to help with the combined outcome probabilities. But I also added in the other factors because 2 strategies could show very high win-win matches (especially after over-optimizing) yet still be independent. I'll explain here in case you've been waiting to see how it turned out.

My algorithm combines these factors, along with their weighting, for a total possible score of 15:
- same outcome, weighted at 5
- same signal, weighted at 4
- chi square (a type of correlation for a 2x2 categorization table of the performance), weighted at 3
- matching trades score, weighted at 2
- entry time score, weighted at 1

Then multiply that score by the percent of matched trades (eg, so if 5 trades match out of 100, the high score will be reduced by multiplying by 5%).

And, write out all the component scores and raw data, so if the summary score is too simple, I can stare at the raw data for a long time and make a totally different interpretation.

The similar signal component may be better served with a chi-square, like the performance. But in the interest of getting going, I'll leave it off for now and possibly consider adding it in the future.

I don't know if this will be of any use whatsoever or not, probably not until a few months of trying it out.