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Simplified method of measuring currency risk


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When banks analyze currency risk, we prefer to use advanced simulation tools to get accurate results. Our selected method is to have the analysis software generate 2000 different scenarios for future currency development and monitor the distributions worst case scenarios. We normally look at the 5% scenarios where a company has its largest loss, when assessing the risk.


There are simpler ways of doing this kind of analysis, and get a fairly accurate result. The interesting question is: How far can a currency rate move within 90% likelihood (a 90% confidence level)?


Described in a more operational context, a case like this could be:
A company with EUR as it functional currency is expecting to receive a 10 million USD payment in one year. How much can the value of this USD amount change within 90% likelihood?


If we use the currency market to find the forward rate for EURUSD in one year, we can calculate the expected value of the USD payment.  If the forward rate is at 1,2200, the expected value of the USD payment is EUR 8.196.721. This amount is possible to lock in using currency forward contracts.


The company is evaluating what could happen with the value of this USD payment if the currency rate is not locked in with currency forwards. What is the expected risk?


Another element of information needed to assess the risk, is the market volatility for EURUSD. This is the currency markets expected standard deviation for the year to come. The volatility is a measure on how much the market rate can move during a specified time period. This volatility is observable in the currency options market. It might be found through different sources of financial information (Thomson Reuters, Bloomberg, or your bank). If you can’t find the accurate market volatility, and you are look at currency rates between developed countries, you might use 10%. The actual EURUSD 1 year volatility is at 7,5% (November 2017).


You are now ready to calculate the simplified risk on your expected USD payment. The formula to use is this:


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The number 1,65 in formula is a scaling factor.

If we input the information we have gathered, the formula might look like this:



Formel 2b.JPG 

We then end up with the risk amount of EUR 1.014.344.
The market has provided us with the information that there is a 90% likelihood that the value of this USD payment will not change with more than +/- EUR 1.014.344 through one year. There is a 5% likelihood of an increase in value with more than +EUR 1.014.344.  This 5% is not a concern, since the company receives much higher values than expected.

There is a 5% likelihood of a decrease in with value with more than -EUR 1.014.344. This is the company’s worst case risk.


Hence there is a 95% likelihood that the company will not lose more than EUR 1.014.344 on this USD payment in one year. You now have facts about the risk and can now asses if you want or need to hedge all or parts of the expected payment.



Hi Ståle,


Thanks for sharing!


I am wondering whether this simplified method can be applied when measuring VaR as well? I.e. balance sheet exposures which are basis for translation risk? In that case would it just be to replace "expected payment" with "expected exposure", applying the same parameters and then ending up with a proxy on expected decrease in balance sheet exposure?


Also, if the timeperiod is less than one year, e.g. 1-3 months, would it still be reasonable to apply 10 % as expected volatility for developed currencies?


Appreciate any sort of feedback.


Best regards, Tom-André W. Hansen (PRA Group Europe AS)


Hi Tom-André


Good to hear from you.


The methodologies in Cash Flow at Risk and Value at Risk are basically the same.

The cash Flow at Risk modell is used to measure risk connected with cash flows in the future, while Value at Risk is used for balance risk.

Time horison in these two analysis might be different. A cash flow at Risk analysis often covers cash flows through one year or more, while a Value at Risk modell on easily sellable assets might look at value changes through a shorter time (maybe a week).

The replacement you propose in the formula will work fine. The time horizon you select will be based on how easy it is to sell the assets.


We have been going through some of the market volatilities today (current market conditions).

Most of the currency volatilites in developed economies are lower than 10%.

If you look at current USDNOK volatilites, the one year voltility is at 9,2%, while the one month volatility is 8,2%.

EURNOK volatilites are even lower.

You overshoot your risk estimates with a 10% volatility.

If you need accurate markets volatilites, feel free to send me an email.


Best regards, Ståle


Ståle Johansen, Risk Advisory, DNB Markets




Thank you for article.  

Excuse ignorance but how do you get the scaling factor of 1.65

Thanking You



Hi Raelliss


The scaling factor comes from the normal distribution. The assumption that the currency rate changes are normally distributed will define a 90% confidence level. You might find the scaling from finding a Standard Normal Distribution Table, and look for the one sided 45% likelyhood, which is 1.65 standard deviation from the expected value (the forward rate).