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Calculate USD return from local return between two dates

​For this example we assume we have an index for which we have calculated a time-series of total returns (TR) in its local (non USD) currency terms. We want the equivalent total return in USD terms.

For this we need 5 pieces of information

​1.The Total Return of the index (in local currency terms) on date D1
2.The Total Return of the index (in local currency terms) on date D2 

3.The local currency/USD cross rate on date D1

4.The local currency/USD cross rate on date D2

If you just want the Total Return performance between the two dates that's all you need. If you want to put an absolute value on the Total Return you also need

5.The USD return of the index on date D1

Let's look at an a example

Show USD return of a Hong Kong Dollar index between 31-dec-2010 and 03-Jan-2011
HK local TR value on 03-Jan-2011 = 281.201193

HK local TR value on 31-dec-2010 = 280.685321
HK/USD cross rate on 03-Jan-2011 =  7.7737

HK/USD cross rate on 31-Dec-2010 =  7.7711

Finally USD TR value on 31-Dec-2010 = 167.6067  

So now we can calculate what the USD TR value is on 03-jan-2011  

​USD TR performance = VAL1/VAL2


VAL1 = Local TR (03-Jan-2011)*cross rate (31-Dec-2010)

VAL2 = Local TR (31-Dec-2010)*cross rate (03-Jan-2011)

So plugging in the figures we get

VAL1  -   281.201193*7.7711 = 2185.243

​VAL2  -   280.685321*7.7737 = 2181.963

USD ​TR perf = 2185.243/2181.963 = 1.015 i.e 1.5%  

​USD TR (3-Jan-2011) = 167.6067 * (2185.243/2181.963) = 167.858652

​If you wanted to do the same for other currencies you would obviously just get the appropriate cross rates on the dates required and use them instead.