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I have a question about VaR mapping for FX forwards. Please bear with me while I outline the problem.

Philippe Jorion's book discusses VaR mapping; a means to break down complex instruments into simple risk factors and calculate the amount of risk against these risk factors across the portfolio.

The example given for FX forwards is a 1 year contract to buy 100 MM EUR for 138.09 MM USD. The forward rate is $1.3013. The FX contract is broken down into 3 components:

a long position in the EUR spot ($1.2877) a long position in a EUR risk free bill (2.281%) a short position in a USD risk free bill (3.330%)

A VaR is given for each of the above positions, along with a correlation matrix. The author then calculates the present value of the cash flows from each of the 3 positions above as such:

PV cash flow of long position in the EUR spot = $130.09 * 1/(1+USD risk free bill rate) = 125.89

PV of the cash flow of long position in the EUR risk free bill = 100 EUR * EUR spot * 1/(1+EUR risk free bill rate) = 125.90 MM USD

PV of the cash flow of short position in the USD risk free bill = -130.09 USD * 1/(1+USD risk free bill rate) = - $125.89 MM USD

The PV cash flows are then multiplied by the given VaRs for those risk factors and summed up to produce an aggregate undiversified var.

My question:

I don't understand why the cash flow for the EUR spot long position is being calculated the way it is. It makes no sense to me. Seeing as it is a spot rate why is it's cash flow not simply spot * 100 MM EUR notional ?

Here is a YouTube video on this problem in case my textual description isn't clear. https://www.youtube.com/watch?v=Um8e_teI_dw

(This contrived question is a topic on my Financial Risk Manager exam)


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