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MartinGale7
Topic Author
Posts: 152
Joined: April 1st, 2011, 7:42 am

### Cleanest expression of a single currency?

Currencies are expressed as pairs, eg AUD/USD. However if I wanted to express the value of the (somewhat nonsensical) AUD alone (or changes in its value), how might we attempt/approximate this? I realise that this is an intractable problem and also is very much based on what objective function you seek. So, there is no one answer, and it's very much a crude subjective goal.

For example, I've seen the USD index calculated using this form:

https://www.thebalance.com/u-s-dollar-i ... ta-3306249

My thinking is this - imagine that hypothetically currencies did have absolute values. And that they were stochastic processes with correlation between them. Given a deep enough time series, we should be able to reverse this back from a covariance matrix.

Any thoughts would be appreciated. I do recognise the nonsensical problem with this question, so please take it as being fuzzy. I'm fishing for useful ideas, so that we could visually express say a chart of AUD without undue influence from the effect of other currencies.

MartinGale7
Topic Author
Posts: 152
Joined: April 1st, 2011, 7:42 am

### Re: Cleanest expression of a single currency?

Perhaps a PCA of pairs (AUD/USD, AUD/JPY, AUD/EUR, AUD/GBP etc). We could weight them by the importance before performing the PCA. Thoughts?

MartinGale7
Topic Author
Posts: 152
Joined: April 1st, 2011, 7:42 am

### Re: Cleanest expression of a single currency?

I've also seen people try to do this using multiplication, eg AUD/USD * AUD/JPY * ..., and also a linear 1.5 * AUD/USD + 1.0 * AUD/JPY + ... etc.

SeftonBoyd
Posts: 6
Joined: January 22nd, 2015, 3:18 pm
Location: London
Contact:

### Re: Cleanest expression of a single currency?

Aren't you looking really to recreate a basket like the RBA's Trade Weighted Index (https://rba.gov.au/statistics/frequency ... 91129.html) ?

Mars
Posts: 115
Joined: November 13th, 2002, 5:10 pm

### Re: Cleanest expression of a single currency?

Currencies are expressed as pairs, eg AUD/USD. However if I wanted to express the value of the (somewhat nonsensical) AUD alone (or changes in its value), how might we attempt/approximate this? I realise that this is an intractable problem and also is very much based on what objective function you seek. So, there is no one answer, and it's very much a crude subjective goal.

For example, I've seen the USD index calculated using this form:

https://www.thebalance.com/u-s-dollar-i ... ta-3306249

My thinking is this - imagine that hypothetically currencies did have absolute values. And that they were stochastic processes with correlation between them. Given a deep enough time series, we should be able to reverse this back from a covariance matrix.

Any thoughts would be appreciated. I do recognise the nonsensical problem with this question, so please take it as being fuzzy. I'm fishing for useful ideas, so that we could visually express say a chart of AUD without undue influence from the effect of other currencies.
Quantity of Big Mac you can buy with 1 unit of currency?

katastrofa
Posts: 10084
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: Cleanest expression of a single currency?

or a cup of Starbucks coffee. Big Mac is getting obsolete because of Beyond Meat