For example.
- A widget costs $150 USD in the US
- The same widget costs £100 in the UK
What is the implicit FX rate between US dollars and pounds?
Well, you should be able to buy the same widget with either $150 USD or £100, so the implicit exchange rate (assuming PPP holds) is:
= $150 / £100
= $1.5 / £
Obviously, there are some HUGE assumptions required for this theory to hold. Minimal or zero transaction costs (including transportation, cross border tarrifs etc). In practice, it is probably more realistic to say that there is a threshold for which arbitrage probably won't happen in PPP because of the real costs incurred to handle transactions.
Also to be more accurate, rather than just use a "widget" it would be more appropriate to use a basket of goods to reflect a more broad use of the currency.
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