General Topics
Markets
Technical Topics
Brokerage Firms
Community Lounge
Site Support

# How to tell if 2 strategies are independent?

Discussion in 'Strategy Development' started by zedDoubleNaught, Jul 16, 2010.

1. ### 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.

2. ### Arthur Deco

Do you have both fully coded up and backtested?

3. ### zedDoubleNaught

Yes, but I meant in general, so to compare any 2 of the 30-40 strategies I have.
For example, suppose one is based on a MA crossover, the other on a RSI oversold/oversold basis.
I suppose in theory these should be independent as oneis a trend follower and one is an oscillator. But I'm hoping to develop an actual score, or at least to generate some measure that they are independent instead of going off assumptions.

In this case, I suppose looking at a 2x2 table of win-win, win-loss, loss-win, loss-loss would be most helpful. But then I got tripped up on the case where strategy one had a large limit-low stop-low winloss ratio, and strategy 2 has a low limit-large stop-high winloss ratio. Then, if they both win, 2 possibilities are they could be winning independently for different reasons, or they could both be catching the same move and not independent.

If they are independent, the outcome could move in 4 steps (win-win, win-loss, loss-win, loss-loss). If they are not independent, they would tend to move in 2 steps (win-win and loss-loss, or win-loss and loss-win).

4. ### Arthur Deco

Simple (stupid) approach. If you have Excel, create two columns, one for strat 1 and the other for strat2. For every day that the two strategies trade the same day, make profit or loss entries in the columns. Then run a correlation analysis. You then have a hard number for reference in the correlation coefficient. Plot the scattergram and you have a visualization that is intuitively helpful. You can also run a Student's T test to get some (unrelaible) notion of the probability that the result is correct.

5. ### zedDoubleNaught

I've done that in the past with the 2 issue prices (actual prices and percent changes from bar to bar). That's a good starting point for strategies. I think it would work best with strategies that have close signals so the profit or loss could be variable.

I always use fixed stops and limits, so the results fit best into a 2x2 table (only matters who won and who lost, since the amounts are always the same they can be left out). I recall there is a 4-square correlation test, that may be a good place for me to start.

As you note -- match the trades from the 2 strategies that occur on the same day -- that's one of the factors I thought to measure in generating a score. For example, if they (on average) enter within 10 minutes they show less independence than if they entered on average within half of the trading day (I guess that's what an independent entry would average).

So far I've gotten measures from the correlation, a score from the difference in the entry time, direction and outcome. I wonder, is there a theory or a model that expands one these kinds of measurements? So far, I think I have a few measurements, but no real conceptual context in which to understand them.

Also -- any other factors useful to measure?

6. ### Arthur Deco

What's the typical number of total trades, wins and losses, in a backtest?

7. ### zedDoubleNaught

I've been using 2 strategies for developing a score and model. I chose them because I think they are fairly close, wanted to start with easy ones first.
strategy 1 - 57
strategy 2 - 65
matches = 55 within a 12 bar window.
same direction = 80%
win-win or loss-loss - 73%
win-loss or loss-win - 27%

Strategy 2 has a stop and a limit that are about 50% larger than the stop and limit of Strategy 1.

I'm fairly sure that number of trades and matches is not a large enough sample size. I have a hard time making up my mind about going over a longer time span -- would give a better sample size, but would not necessarily match current conditions that could affect independence (just trying to project forward for next week, then run the test again next weekend to project for the following week). It's always possible like so many things that their independence goes up and down from time period to time period.

I suppose the outcome is what I'm most interested in, so should be the largest factor in the score.

8. ### Arthur Deco

Hahahahahahaha! I cheerfully BT and trade strategies with only 24 samples! You have waaaaay more than you need for sadistical significance. If you can believe in any such thing.

So, here's what I do in a similar circumstance but for different reasons. Write code that conditions one on the other. That is if strat1 trades, then let strat2 trade if it will. And vice versa. Then compare the two. I think what you are going for is a way to combine strategies without worrying about the equivalent of "portfolio allocation."

What I don't understand is why you have 30-40 strategies. I mean, I watch that many things as possible scale in triggers, but I only have five strategies. That few is a handful to keep optimized.

BTW, I also optimize only once a week, but with more samples, like 120.

What I strive to do is avoid the necessity for statistical analysis. If I have a question, I devise a backtest to answer it, not go through any multivariate statistics bullshit.