Should real interest rates be equal across countries? Can a financial arbitrage take place in case of significant and persistent real interest rate differences? To answer this question:
a. First assume that exchange rates are fully predictable and follow purchasing power parity (PPP).
b. Then assume that they are uncertain but that PPP holds.
c. Finally, assume that exchange rates are uncertain and that PPP does not hold.

Question

Quizplus · Accepted Answer

The Answer is Not necessarily. This can be shown by observing that no risk-free arbitrage can exploit differences in real interest rates. Let's start with a simple world and progressively add more complex realities. Assume that the real rates on euros and U.S. dollars are respectively 2% and 4%. Let's use the linear approximation:
a. Exchange rate is fully predictable and PPP holds.
Differences in real interest rates can be arbitraged away. One can simply borrow in €, transfer the € in $ at the spot exchange rate and lend the $. It can easily be seen that this strategy yields exactly the real interest rate differential (2%) without any capital investment.
Since the exchange rate is fully predictable and follows PPP, we know for sure that its future depreciation is exactly equal to the (certain) expected inflation differential. The net result on the investment strategy is the real interest rate differential.
b. Exchange rate is uncertain but PPP holds.
We know that the future exchange rate will exactly reflect the observed future inflation differential (PPP) but we are not sure about future inflation rates. The interest rate differential is equal to the real interest rate differential plus the expected inflation differential, while the exchange rate depreciation will be equal to the ex-post realized inflation differential. The deviation between expected and realized inflation makes the above arbitrage uncertain. However, the deviation is likely to be small for short horizons, so arbitrage will insure that the short-term real interest rate differential is small.
c. PPP does not hold.
Real exchange rates can be very volatile in the short run. No riskless arbitrage can take place to take advantage of real interest rate differentials.

Should Real Interest Rates Be Equal Across Countries? Can a Financial