## Currency Conversion (Triangulation Arbitrage)

Some systems use a single currency as a base, which is something that I noticed recently when working with IBM Congos Controller, e.g. USD to convert local currencies into. But what if you want / need to rebase into another currency but still retain the original base?

This doesn’t appear to be easy to achieve within Cognos Controller itself, but it is achievable within SQL and a wider SSIS framework.

The basis for rebasing exchange rates uses the technique of triangulation arbitrage. The technique is most often used within the banking system and more information can be found here: http://en.wikipedia.org/wiki/Triangular_arbitrage In principle you deal with two known exchange rates and one unknown.

For example, if you have an exchange rate base of USD and know that the GBP/USD exchange rate is 1.54631 and the EUR/USD exchange rate is 1.11470 and wish to rebase from USD to EUR. You would begin by finding the inverse rates of GBP/USD (1/1.54631 = 0.6467), multiply by the EUR/USD rate (0.6467*1.11470 = 0.72087649) which produces the EUR/GBP and then find the inverse (1/0.72087649 = 1.3872) to produce the GBP/EUR rate. In order to find the USD/EUR exchange rate one simply finds the reverse of the EUR/USD rate (1/1.11470 = 0.8971).

That might sound simple, but most exchange rates are held in a table across a range of dates. This complicates the calculation somewhat. I’ve used CTEs because I find that it makes the script neater and easier to debug. Below is an example of the triangulation using the Sales.CurrencyRate table in the AdventureWorks2012 database.

USE AdventureWorks2012

;

WITH

LocalExchange AS (

SELECT

ToCurrencyCode AS CurrencyCode

,CASE WHEN ToCurrencyCode <> 'EUR' THEN (1 / AverageRate) END AS LocalCurrencyConversion

,CurrencyRateDate

FROM [Sales].[CurrencyRate]

),

EuroExchange AS (

SELECT

ToCurrencyCode AS CurrencyCode

,CASE WHEN(ToCurrencyCode = 'EUR')THEN AverageRate END AS EuroConversion

,CurrencyRateDate

FROM [Sales].[CurrencyRate]

WHERE CASE

WHEN(ToCurrencyCode = 'EUR') THEN AverageRate END IS NOT NULL

)

SELECT DISTINCT

--Keys

C.CurrencyRateID

,C.CurrencyRateDate

,CASE

WHEN C.ToCurrencyCode = 'EUR' THEN 'USD'

WHEN C.AverageRate = 1 THEN 'EUR'

ELSE C.ToCurrencyCode

END AS CurrencyCode

,1/(CASE

WHEN C.AverageRate = 1 THEN 1 ELSE

(1 / (CASE

WHEN C.ToCurrencyCode <> 'EUR' THEN (L.LocalCurrencyConversion * E.EuroConversion)

ELSE C.AverageRate

END))

END) AS ImplicitEuroExchangeRate

--Measures

--,C.ExchangeRate AS ExchangeRate

FROM

[Sales].[CurrencyRate] AS C

INNER JOIN LocalExchange AS L

ON L.CurrencyRateDate = C.CurrencyRateDate

AND L.CurrencyCode = C.ToCurrencyCode

INNER JOIN EuroExchange AS E

ON E.CurrencyRateDate = C.CurrencyRateDate

WHERE

CASE

WHEN c.ToCurrencyCode <> 'EUR' THEN (E.EuroConversion * L.LocalCurrencyConversion)

ELSE 1

END IS NOT NULL

ORDER BY C.CurrencyRateID

As always, if you have any feedback and can suggest a simpler way of performing the triangulation I would love to hear it.