Foreign Currency Risk Premium (FCRP)

[Question]

The foreign exchange expectation theory and interest rate parity hold between DC (domestic currency/country) and FC (foreign currency/country).

Interest rate: r_DC=2%, r_FC=5%

What is the foreign currency risk premium?

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Answer:

FCRP = Expected exchange rate movement - Interest rate differential between DC and FC
= (E(S₁) - S₀)/S₀ - (r_DC - r_FC)

S₁, S₀: DC/FC

If interest parity holds, the foreign rate, F, reflects the differences between country interest rates.
F = S₀ * (1 + r_DC - r_FC)

FCRP
= (E(S₁) - S₀)/S₀ - S₀*(r_DC - r_FC)/S₀
= (E(S₁) - S₀*(1 + r_DC - r_FC))/S_{0
= (E(S1) - F)/S0}

The foreign exchange expectation relation states that the forward rate is an unbiased predictor of the expected future spot rate:
F = E(S₁)

So, if the foreign exchange expectation relation holds, then the foreign currency risk premium is equal to zero.

FCRP

= (E(S₁) - F)/S₀= 0/S₀= 0

In other words, there is no risk premium for exposure to currency risk.