Hi all,I am trying to measure the exposition of a given portfolio in FX marekts. Let's say i made some deals in some currency pairs (eg EURUSD, EURGBP, USDGBP to keep it simple) so i have some positions in my portfolio :EUR +3USD +1GBP -4 (all measured in millions of EUR) so my PnL at this time is zero.I would like to know what my exposure in EURGBP is ? First of all i think this question doesnt have an answer since we need to specify how we make things move in EURGBP. Because EURGBP can not move while EURUSD and USDGBP remain constant. And my PnL after a move is going to be very different whether EURUSD moves, USDGBP moves or both move...Is there a good model to measure the risk of a pure FX portfolio ?Thanks a lot !

Hi,You are looking for exposure of the portfolio value in EUR and you have 2 foreign currencies : USD and GBP.You have N=3 currencies, so only (N-1)=2 Forex can be used as an independent variable (the only one you can bumpindependently without allowing trivial forex arbitrage). All other forex must be computed from your basis set.So if you choose EUR/GBP as one of them you can choose the other one between: - first choice: EUR/USD and make decompositon USD/GBP = EUR/GBP / EUR/USD, - second choice: USD/GBP and make decompositon EUR/USD = EUR/GBP / USD/GBP.Usually when computing portfolio value in EUR it is easy to choose Foreign/EUR forex as basis: in this caseyour sensitivity will be the amount of foreign currency you need to Delta hedge your forex exposure.Hope this help,Mars.

Hi,Thanks for your reply, however i should disagree with this amswer, maybe i misunderstood it ?Let's assume i have the following positions in my portfolio: (in millions)EUR +10USD -25CHF +15and EURUSD=1.32 USDCHF=1.22 => EURCHF=1.6104I pick EURCHF now and bump it, here are the results depending if i take as other fixed currency EURUSD or USDCHF as in your example:i bump EURCHF -1% =>EURCHF=1.5943if i let EURUSD constant =1.32 my PnL is 92K and if i pick USDCHF it becomes -100K so very different although i just bumped EURCHF rate ! The reason is that i also have risk in EURUSD and USDCHF that i cant ignore and depending whether i move one or the other or both everything changes.Does anyone have a good model or reference paper for market risk in FX ?Thanks

Hi,"The reason is that i also have risk in EURUSD and USDCHF "No, you have risk in EURUSD or in USDCHF. You must choose which one."that i cant ignore and depending whether i move one or the other or both everything changes."Sure, you must use triangular arbitrage relation between forex.If you look the value in EUR of your portfolio it is:10 EUR - 25/ (EURUSD) +15 / (EURCHF). In this case if you choose EURUSD and EURCHF as the basis forex your exposure is clear with basis EURUSD and EURCHF.But using EURCHF = EURUSD * USDCHF you can also express your portfolio value in EUR as10 EUR - 25/ (EURUSD) +15 / (EURUSD * USDCHF). and your exposure is (a little less) clear with basis EURUSD and USDCHFAnd using EURUSD = EURCHF / USDCHF you can write10 EUR - 25 * USDCHF / (EURCHF ) +15 / (EURCHF). and your exposure is (also a little less) clear with basis EURCHF and USDCHFNow the problem is when you say: "I bump EURCHF -1%". When you say such a thing it as no meaning, you hide somethingwhich is what remain constant when you bump. The mathematical reason is that most of time when we have 3 variables theyare independant and when you say I change one of them the assumption is that all other remain constant. But here you have only 2 independant variable an it is impossible that all other remain constant. You have exactly the same problem (and the mathematic is also the same) with basic thermodynamic problem with perfect gaz3 variable are temperature T, volume V and presure P but due to perfect gaz equation P V = n R T with a fixed gaz quantity n (R is a constant).If you ask whats going on if I raise temperature by one percent its not the same if you do it by keeping a constant volume or a constant pressure.I do not know good reference for computing delta (as you done) in forex market. There is a paper of Wystup concerning the consequence of triangulararbitrage relation for vega and crossed vega (correlation exposure). But from a mathematical point of vue it is just coputing derivatives of a function of n variable with constraint (not so easy, very useful for thermodynamic and forex, by experience it seems that less that the third of studentin mathematic at university understand a little of this).Hope it is most clear.Mars.

Ok, thanks mars, now i think we have the same vision of the problem. But i think there is more to do for real trading. In my example with EUR,USD and CHF when EURCHF moves, which other currency pair is the most likely to move ? EURUSD or USDCHF ? I would say most likely they move in the same direction, because USD moves are not very correlated to EUR or CHF moves, as these two currencies are in the same geographic and economic region so are more likely to be affected in the same way... Does anyone know how to model this phenomenon ? thanks

Friends see if this is what is happening .My P&L currency is USD .The difference in P&L is due to the P&L currency.original position initial position USD Rate USD value EUR 10.00 1.32 13.20 USD -25.00 1.00 -25.00 CHF 15.00 1.22 12.30 mtm 0.50 scenario1 EURUSD constant initial position USD Rate USD value EUR 10.00 1.32 13.20 USD -25.00 1.00 -25.00 P&L in USD 124,161.59 CHF 15.00 1.21 12.42 mtm 0.62 scenario2 USDCHF constant initial position USD Rate USD value EUR 10.00 1.31 13.07 USD -25.00 1.00 -25.00 P&L in USD -131,967.21 CHF 15.00 1.22 12.30 mtm 0.36

No this doesnt really make sense that the currency in which you compute your PnL makes the difference. This is a misconception i made at the beginning, but actually this is because you made very big moves in your rates, try with 0.01% difference to see... Usually you have positions in millions and a PnL in the order of 10K and whether you measure it in EUR or USD it can move by 10k*difference in rate change=10k*0.01=100dollars (=nothing) for example if EURUSD goes intraday from 1.31 to 1.32 which is already huge...

Is that a big secret or nobody knows ? Please help ...

I think the only reason you are seeing any differences is because changing X by 1% if not the same as changing (1/X) by 1%. For a consistent set of FX moves (and I agree with the previous posters on the degrees of freedom you have) the P&L is not economically impacted by the change in numeraire.

Sorry i was more asking help about real risk measure of a FX spot portfolio, maybe using PCAs ... Thanks for your help

How about using historical spot fx rate moves to compute 'hypothetical historical P&L" and use the dsitribution to come up with the risk measure of your choice?? VaR, Condiitonal tail loss etc etc??

How about using historical spot fx rate moves to compute 'hypothetical historical P&L" and use the dsitribution to come up with the risk measure of your choice?? VaR, Condiitonal tail loss etc etc??