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crackfox


Total Posts: 3
Joined: Apr 2018
 
Posted: 2018-12-17 11:36
I'm trying to create an 'index' of different products, just like a currency index, e.g.,

USDX = 50.14348112 × EURUSD^ -0.576 × USDJPY^0.136 × GBPUSD^-0.119 × USDCAD^0.091 × USDSEK^0.042 × USDCHF^0.036


What I noticed about this though is that if one product is very differently priced from another the same percentage move will not impact the index in the same way. So if I gave a 10% weight to Product A (priced in the thousands) and a 10% to Product B (price in the hundreds) then a 1% move in each will affect the index differently.

How do I create an index that will give the same weight to percentage moves?

TakeItAndRun


Total Posts: 97
Joined: Apr 2010
 
Posted: 2018-12-17 23:31
By rebalancing once a day the arithmetic average of the form FX / FXc or its inverse where FXc is the previous day FX close. For instance:
Day 0 : Avg = 100
Day 1 : Avg = 100x (EURUSD0 / EURUSD1 +USDJPY1/USDJPY0 +...) / n which gives 100.12 at the close of Day 1.
Day 2 : Avg = 100.12x ((EURUSD1 / EURUSD2 +USDJPY2/USDJPY1 +...) / n

Edit: divided by n pairs to get the arithmetic average

crackfox


Total Posts: 3
Joined: Apr 2018
 
Posted: 2019-01-08 06:18
thanks for the reply.

If I'm multiplying the index by some number aren't I just scaling up the whole index, so that it still won't matter how much one product moves in percentage terms but anything priced in low absolute dollar value will have a much lower impact?

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