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# How to calculate VAR for a portfolio of FX of 3 currencies

#### vietnam

##### New Member
HI David

In the forum, calculating VAR for two asset, I find your calculations: VAR=critical-z * sqrt(Positions matrix row vector * Var-covar matrix * Positions matrix column vector)

I would like to ask whether I can use this formula to calculate VAR for a portfolio of FX volatility of 3 currencies based on the FX rates.

I have one formula as follwed:
VAR=sqrt(undiversified VAR matrix * correlation matrix * transposed undiversified VAR matrix)
undiversified VAR matrix = volatility matrix * ABS weighting matrix

Please help me to explain which formula can be used to calculate VAR for a portfolio of FX volatility of 3 currencies

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi vietnam

Yes, you can give an FX portfolio the traditional variance-covariance treatment. The general form given by:
portfolio variance = exposure row vector * covariance matrix * exposure column vector

... where the exposures can be weights (%) or dollar exposures (\$)
... and the covariance matrix (V) = diagonal volatilies * correlation matrix * diagonal volatilities

i.e., the forex VaR is like any other except the risk factor is FX.

And you have the same issues that you have in applying any normal linear VaR; e.g., is the assumption of normal distribution for the risk factor wrong (for FX: yes, heavy tails); is the linear dependence okay? ... so it is not to suggest the mean-variance is an appropriate fit for FX

David

#### andreluse

##### New Member
Hi @David Harper CFA FRM ,
I would like to ask you how to calculate VaR and ES for bonds and forex positions.
Thank you.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @andreluse We are quite happy to help but that is a very general topic, and especially in the month before the exam, it's difficult to start "new essays." Can you be more specific (if you have a specific exam-type question, maybe that will suffice). Otherwise, among my recommendations on this topic is Carol Alexander's book III which focuses on products and instruments (https://www.bionicturtle.com/forum/...-trading-financial-instruments-volume-iii.92/) and book IV which is focused on VaR models (https://www.bionicturtle.com/forum/resources/market-risk-analysis-value-at-risk-models-volume-iv.93/).

But even more efficient is probably Jorion's VaR (3rd Edition) which has long been assigned in the FRM, see our Market Risk list at https://www.bionicturtle.com/forum/resources/categories/frm-p2-t5-market-risk.3/ Thanks!