FX portfolio variance

[ioannist]

Hi there,

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?

Thanks!
Ioannis

 

[Dafe]

You can convert your positions (EUR, JPY, GBP) to their USD equivalent positions (For example in the EUR/USD pair, if you are long 1000 EUR after converting using 1.2161 as the EUR/USD exchange rate, you will have an equivalent short position of 1216.1 in USD). The summation of all the USD equivalents will give you the Net Open Position in USD; from this you can determine the weights using your Net Open Position in USD as the portfolio value.
Then estimate the variance of the individual pairs using the historical exchange rate for each of the currency pairs (EURUSD, USDJPY, and GBPUSD). The portfolio variance formula (Portfolio Variance = w12 σ12+ w22 σ22 + w32 σ32 + 2 w1 w2 ρ1,2 σ1 σ2 + 2 w1 w3 ρ1,3 σ1 σ3 + 2 w2 w3 ρ2,3 σ2 σ3 ) can then be used in deriving the portfolio variance.
OR
If your primary concern is loosing value with respect to your domestic currency (GBP), what you can do is to properly identify the positions in the currency pairs. (For example, in this pair, EUR/USD, if you are long 1000 EUR you are automatically short 1216.1 USD and vice versa using 1.2161 as the EUR/USD exchange rate). So also for the rest of the pairs you are concerned with. Using the 3 pairs you have mentioned, you will have positions in EUR, USD and JPY.
Using only the EUR/USD pair as an example, you will have an FX portfolio where you are long 1000 EUR and short 1216.1 USD. You can then convert this to GBP using the EUR/GBP (0.8317) and USD/GBP (0.6838) exchange rates to get the value of your individual positions in GBP ie 831.70 and -831.57. The summation will give you the portfolio value in GBP. Based on this you can then derive your weights.
For the variance, what I will do is to use historical rates for the EUR/GBP and USD/GBP in computing the variance of the USD and EURO positions. After which, I will use the portfolio variance formula (Portfolio Variance = w12 σ12+ w22 σ22 + 2 w1 w2 ρ1,2 σ1 σ2) in estimating my portfolio variance.