It is often said that interest rate parity is satisfied when the diffe

It is often said that interest rate parity is satisfied when the differential between the interest rates denominated in two currencies equals the forward premium or discount between the two currencies.

Explain why this is an imprecise statement when the interest rates are not continuously compounded.

ANSWER

Answer: Interest rate parity requires the equality of returns from investing directly in the domestic money market versus converting domestic currency into foreign currency, investing the foreign currency, and selling the foreign currency forward. Symbolically, we have
(1 + i(t,DC)) = (1 / S(t,DC/FC)) x (1 + i(t,FC)) x F(t,DC/FC)

If we divide by (1 + i(t,FC)) on both sides and subtract one from both sides, we get
[(i(t,DC) – i(t,FC)) / (1 + i(t,FC))] = [(F(t,DC/FC) – S(t,DC/FC)) / (S(t,DC/FC))]
The left-hand side is the interest differential between the domestic and foreign rates adjusted for the denominator term and the right-hand side is the forward premium or discount on the foreign currency in terms of the domestic currency.