Practice Quiz 7 Solutions — Interest Rate Parity & Forwards
Setup: S = $/€ = 1.10. US rate 5%, Eurozone rate 3%.
(a) 1-year forward rate using covered interest rate parity (CIP)?
\[F = S \times \frac{1 + r_{US}}{1 + r_{EU}} = 1.10 \times \frac{1.05}{1.03} = 1.10 \times 1.0194 = 1.1214 \text{ \$/€}\]The forward rate is $1.1214/€.
The euro is at a forward premium relative to the dollar — it costs more dollars per euro in the forward market than in the spot market. The country with the lower interest rate (Eurozone at 3%) sees its currency at a forward premium because the forward rate compensates for the interest rate differential: investors earning less interest in euros are compensated by the euro appreciating in the forward market.
(b) Forward premium or discount? Why does the lower-rate currency trade at a premium?
The euro is at a forward premium. If the euro did not appreciate in the forward market, investors could earn a risk-free arbitrage by borrowing euros at 3%, converting to dollars, investing at 5%, and locking in the forward rate. CIP ensures there is no free lunch — the forward premium on the euro exactly offsets the interest rate advantage of dollars.
(c) UIRP: expected future spot rate and excess return?
Under uncovered interest rate parity, the expected future spot rate equals the forward rate:
\[E[S_1] = F = 1.1214 \text{ \$/€}\]If UIRP holds, the expected excess return from investing in Eurozone bonds instead of US Treasuries is zero. The higher US interest rate is exactly offset by the expected depreciation of the dollar (appreciation of the euro). This makes sense because UIRP says you cannot earn excess returns simply by chasing higher yields in another currency — the exchange rate is expected to move against you by exactly the interest rate differential.