Suppose the spot exchange rate quote is ZAR/EUR = 8.385. The 1-year nominal rate in the eurozone is 10% and the 1-year nominal rate in South Africa is 8%. Calculate the expected percentage change in the exchange rate over the comling year using uncovered rate parity.
The answer to this problem is:
The rand interest rate is less than the euro interest rate, so uncovered interest rate parity predicts that the value of the rand will rise (it will take fewer rand to buy one euro because of higher interest rates in the eurozone. The eyri (the base currency) is expected to “appreciate” by approximately Rzar - Reur = 8% - 10% = -2%. Thus the euro is expected to depreciate by 2% relative to the rand, leading to a change in exchange rate from 8.385 ZAR/EUR to 8.217 ZAR/EUR over the coming year.
My challenge:
I don’t get my hear around the fact that the currency with the higher rate (here EUR) depreciates. I thought that if EUR pays 10% and ZAR 8%, people would want to sell ZAR and by EUR which would have meant the EUR appreciates. Obviously I am getting this wrong so any insight would be appreciated.
Cheers
In reality, traders would do that (borrow in ZAR and invest in EUR). But the question here is asking you to calculate the expected percentage change using uncovered interest rate parity (UIRP).
UIRP works under a no-arbitrage assumption. So, if EUR interest rate is 10% and ZAR interest rate is 8%, and UIRP holds, then EUR is expected to depreciate by 2%, in order for the arbitrage-free assumption to hold (i.e. traders doing carry trades would earn nothing on this strategy).
FTFY
In reality, I see no reason for UIRP to hold; i.e., I see no economic force that would cause exchange rates to move in the direction of interest rate parity.
Learnt a new abbreviation today
fino_abama and S2K, I remember from the curriculum that the higher int rate currency is expected to depreciate by the interest rate differential.
However, the IRP formula using the 10% (EUR) and 8% (ZAR) interest rates (assume annual) leads to the EUR depreciating by 1.81%. Using a ZAR/EUR spot rate of 1… IRP would say the expected spot rate in 1 year is = 1 * (1.08/1.1) = .981818 repeating.
.9818 - 1 = -1.8182%
When the curriculum speaks on UIRP it simply states what I said earlier on the higher int curr depreciating by the difference, but that does not seem to even be accurate when utilizing the IRP formula, which would be covered if actually using a forward contract to lock it in.
Any insight between you or S2K?
That’s an approximation. The way you’re doing it is accurate.
Amazing, thanks for the reply, figured that was the case but nice to have a little stamp of approval.
My pleasure.
Note that at Level III they tend to use the approximation. There, the emphasis is on whether you know what to do when you have a premium or discount, rather than calculating the premium/discount accurately.
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What to do when you have a prem/disc… i.e. more motivated to sell a foreign currency forward at a premium if you are long a foreign asset, especially if 1) the managers forecast is for the foreign currency to depreciate, or 2) especially if interest rate parity derives a forward premium that is less than the market traded forward premium for the foreign currency. and 3) probably other scenarios as well
Interest rate parity isn’t trying to predict exchange rates in the future (any more than the forward price on, say, GOOG is trying to predict the future market price of GOOG); interest rate parity’s only job is to prevent arbitrage.
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