I am a bit confused as to the computation of interepretation of variance on an FX portfolio.

Assume i have three pairs:
EURUSD
USDJPY
GBPUSD

I computer the covariance matrix in excel and mutliply with the weight matrix.

For weights, i use the GBP equivalent for each position divided by the total GBP for all positions. So, for example, if i am 1000 units of EURUSD long, i will multiply that by the GBPEUR rate to get the amount in GBP and divide by the total in GBP.

For the covariance matrix, i simply run the COVAR excel function between the pair time sequences.

This yields a standard deviation of 0.7040%
Does this sound resonable? If so, how do i interpret this result?

The result of COVAR isn’t a standard deviation. It’s more like the R-squared of a linear regression (but isn’t that). It indicates how much the data changes together. A high COVAR indicates data series which tend to move in similar fashion.

I’m no expert here, though. Stats class was a LONG time ago. You should do some research on the subject.

Thanks for the input Rhody. The standard deviation of the portfolio of any assets is computed by multiplying two x*y matrices, one covariance matrix and one weigth matrix. The calculation methodology is correct as i simply follow what is done for a portfolio of any securities.

It is the computation of the weight of each pair that i am not sure i am doing correctly.

Also, i am not sure how to interpret the standard deviation of a forex portfolio. I am not even sure if it is in GBPP…

Regardless of methodology, the issue that immediately jumps out at me is the fact that you are trying to create a “portfolio” out of relationships rather than assets (or liabilities), and more specifically out of a trio of relationships which all included the dollar as part of the pair. The dollar is the single most important global currency and those three pairs are going to be significantly impacted by what it’s doing most of the time.

That’s what makes everything not as clear… We can think of a pair as an asset that is denominated in the currency quoted first in the pair. So, the EURUSD asset will return euros in losses or gains.

The fact that each pair has the USD in it means that they will have high correlation but portfolio theory should still be applicable.

I could be wrong. Does anybody else have any input to this? Anybody trading more than one currency concurrently should be interested!

I consulted with a finance professor friend of mine. His response was this:

" – this is not an appropriate application of “old style” Markowitz portfolio theory. First, the theory assumes independent assests – the currency pairs listed are not independent because of USD influence. While technically it can be done, the benefits of diversification would be minimal because of extremely high correlation. The correlation coefficient is: COVAR(1,2) / (std dev1) * (std dev2).

The theory also needs the assumption that correlations (covar) is constant over time – try that on for size in the forex mkts…"

I understand the professor’s point; however i am not trying to diversify between currency pairs, but between startegies trading on currency pairs. This can get quite complicated to explain, that’s why i avoided mentioning it in the beginning.

The point is, if i could understand the intepretation of variance on the first simple example, it would be the same for the more complicated scenario.

Realize that as soon as you say “covariance” in a forum like this you are getting into an area most folks here don’t have much experience with. That means you’re already in “complicated” territory and much better off providing more information related to your question than less.

The professor says:

“That is an interesting thought. It appears that the goal is to define how much advantage can be realized by understanding the interrelatedness of trading strategies for each pair. While interesting I would ponder if any conceptual gains would be realized as the correlations must be quite high (less benefit in diversification of trading strategy). It might be more useful to focus on researching forecasting each of the pairs and timing investment stratgies accordingly. Just a thought…”

My reaction to that, though, is to say that systems can have decidedly different performance depending on the underlying market conditions. As such, you want to compare the performance of systems which perform best in trending markets vs. ranging ones, high vol markets vs. low vol ones, etc. The question, however, which has to be addressed is what to do when your combination of systems creates and overweight in a certain currency.