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Interest rate parity conditions

So covered interest rate parity says

  • Ff/d = Sf/d [(1 + if (Actual/360)) / (1 + id (Actual/360))]

And uncovered interest rate parity says

    • %∆Sf/d = if – id

Forward rate parity says if covered and uncovered interest rate parity hold

    • Ff/d = expected future Sf/d

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The problem gives you the spot rate today, and the interest rates for both countries.

If the problem says ”if uncovered interest rate parity holds, today’s expected value for the exchange rate one year from now is?” How would you calculate?

I thought you take the interest rate differentials to get the change in spot rate, then multiply it by spot rate. But that is not correct answer. They used covered interest rate parity equation to get forward rate, and then used forward rate parity to say the forward rate is the expected spot rate. 

The way I did it should be correct right?

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No, it shouldn’t.

The formula you have for uncovered interest rate parity is an approximation.

Interest rate parity is interest rate parity – whether it’s covered or not – and the formula you have for covered interest rate parity describes it.  (Well, it describes it when interest rates are quoted as nominal rates; the formula’s slightly different when the rates are quoted as effective rates.)

The only difference between covered interest rate parity and uncovered interest rate parity is that the former has a piece of paper that guarantees the future exchange rate, while the latter has no such piece of paper.

Simplify the complicated side; don't complify the simplicated side.

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