How to do correlation

[Rapunzel]

Hi folks, curious to know your approach to using correlations to limit overall risk on trades that are open simultaneously. Say 2 simultaneous trades to begin with.


First Thoughts

My first thought is to use the Portfolio Risk Formula. If I know the worst case correlation for the 2 pairs (I trade fx), and the standard deviation of the PnL of the 2 pairs over 1,000 trades. Then I could rearrange the formula to find the total amount of new risk to take on pair 2 considering the risk already exposed to, on an open trade in pair 1. With a view to keep the 'portfolio' standard deviation within a prescribed level.

Problems

I wasn't sure about the formula so I decided to try simulations in excel. This presented a problem with how to implement the correlation between pair 1 and 2.

Do I generate 2 random distributions between 0 and 1 for pair 1 and 2, with a specified correlation between them. And then consider a trade to have won if the random number is below my win rate. e.g. Random Number (RN) = 0.345, Win Rate (WR) = 0.667 would be a win since RN <= WR. My R:R is 2:1.

The problem with doing it that way is that the distributions of the random numbers in 1 and 2 may have a specified correlation, but the ultimate sequence of wins and losses that result from conditioning them on the win rate are not correlated in the same way.

I found a way to generate a sequence of wins and losses in pair 1 and 2 that do correlate as required. In this case the overall win rate on the sequence of wins-losses on pair 2 is very skewed, either very high or very low i.e. not realistic. This is probably because it is derived as a distribution on the value of pair 1.

Point is in either case; the standard deviation of the PnL on the combined profit outcome of the 2 pairs is usually much higher than that predicted by the formula.

New Direction: Maybe I am overcomplicating the issue, and the formula takes into account how the Win Rate, PnL and StDeviation of the PnLs on 1 and 2 would interact given their correlation, to produce a final result.

Is there a way I can test which version is more accurate using backtesting?

 

[guest_trader_1]

You could use Monte-Carlo simulations and run them on both versions to find out which one would be more accurate.

These simulations would have a much closer look to the data you are after.

 

[Rapunzel]

You could use Monte-Carlo simulations and run them on both versions to find out which one would be more accurate.

These simulations would have a much closer look to the data you are after.

Thanks for the post, i'll give it a try.

 

[Rapunzel]

The correlation model can be quite complex. It seems that you should only enter a new trade in general; if the direction correlates with the open trade in the range 0 < x < -0.4 (No new risk at all with any positive correlation).

I have been previously using the untested correlation standard of: -0.3 < x < 0.3.

There is a maximum amount of risk to add in the new trade, so that the total risk is equal to or less than the risk on only pair 1 with 95 confidence. And which maximizes the risk adjusted return (RAT), defined here as: Combined Average Return / Combined Maximum Risk @ 95% Confidence.

Or which maximizes the improvement in RAT, from having 1 trade to having 2.

Other important factors so far not accounted for:

• Model depends on probability of win on trade 1 which is uncertain. (using normal distribution around average WR)
• Model assumes both trades are open at the same time, which does not reflect reality.
• Correlation is based on historic PnL differences in Price Action, not future or current correlation after the trades have be opened.

Interesting subject. Monte-Carlo must be the answer.

 

[ph1l]

Hi folks, curious to know your approach to using correlations to limit overall risk on trades that are open simultaneously.

One way is pick assets from a set where each asset is correlated to each other asset less than a threshold as described in this post.