Economics - Covered vs Uncovered Interest Rate Parity

CFA Level II
#1

From the textbooks,

where Ra = interest rate of foreign country, and Rb = interest rate of domestic country

Covered Interest Rate Parity
Forward Rate = Spot Rate X (1+Ra)/(1+Rb)

Uncovered Interest Rate Parity
Expected Change in Future Spot Rate = Ra-Rb

Assuming forward rate parity, we can say that the Forward rate = expected future spot rate

My question is how can we equate the forward rate and expected future spot rate using both equations for covered and uncovered interest rate parity when one formula uses a geometric difference in interest rates (covered) and the other using a simple difference in interest rates (uncovered)?

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#2

The second one is an approximation.

\frac{1 + R_a}{1 + R_b} = 1 + R_a - R_b - R_aR_b + R_b^2 + \cdots

So,

F - S = S\left(\frac{1 + R_a}{1 + R_b}\right) - S
= S\left(1 + R_a - R_b - R_aR_b + R_b^2 + \cdots\right) - S
= S\left(R_a - R_b - R_aR_b + R_b^2 + \cdots\right) ≈ S\left(R_a - R_b\right)
\frac{F - S}{S} ≈ R_a - R_b
#3

Thanks for the reply.

May I ask how we derive the approximation below? Do we just assume that the other products are relatively small and tend towards zero?

#4

Exactly.

Suppose that R_a = 7\% and R_b = 3\%.

Then, R_aR_b = 0.21\%, R_b^2 = 0.09\%, and so on.

\frac{1.07}{1.03} - 1 = 3.8835\% ≈ 4\% = 7\% - 3\%
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