Hi all,
Does anyone know the answer to this question?
Info given:
Spot JPY/USD exchange rate = 120
Spot EUR/USD exchange rate = 0.7224
US risk free rate = 7%
Eurozone risk free rate = 9.08%
Japanese risk free rate = 3.88%
Yield curves in all three currencies are flat
Question: According to the uncovered interest rate parity, in 12 months, the JPY/USD exchange rate would most likely be:
A: 116.50
B: 123.74
C: 117.96
The answer is A using this formula 120*(1.0388)/(1.07) = 116.50
But isn’t this formula for COVERED interest rate parity? F = S0 x (1+R(A) / (1+R(B))
Thanks!
It’s the formula for interest rate parity.
Whether it’s covered or uncovered doesn’t matter.
Thank you as always. So if the future spot rates end up being 116.50, then there is evidence that the market operates under covered interest rate parity? If it is not 116.50 then it is uncovered?
Covered interest rate parity means that you have a contract (forward or futures) that guarantees the future exchange rate.
Covered interest rate parity always holds (assuming nobody breaches the contract). It has nothing to do with what the spot rate is when the contract expires.
If the future spot rate ends up being 116.50, it would be (incredibly weak) evidence that uncovered (i.e., not guaranteed by a contract) interest rate parity holds. It would also likely be a coincidence. It says nothing about covered interest rate parity.
If the future spot rate ends up being something other than 116.50, it’s evidence (proof, actually) that uncovered interest rate parity doesn’t hold. It, too, says nothing about covered interest rate parity.
As per my understanding given a quote structure of A/B the base currency (here it is B) should appreciate by the difference in RA-RB as per uncovered interest rate parity. So the answer should be 120*(1+(0.0388-0.07)=120*(0.9688)=116.256. Obviously this is not in the answers given here. But I think it should be like this. The uncovered interest rate parity gives expected future rates and covered interest parity gives Forward rates. Please do correct me if I am making any mistake here.
Yes, this is exactly what I did as well. S2000, can you tell us why this approach is not correct??
It’s an approximation.
F = S0 × (1 + rP) / (1 + rB) is the correct formula for interest rate parity.
Under which scenario would you use the other formula? (Not the formula you mentioned).
I wouldn’t.
OK, maybe if I were stranded on a desert island with only sand and a stick and I needed to compute the forward rate because it would give me the combination to the lock on the cage and there was a komodo dragon bearing down on me so I didn’t have time to do long division, I would.
Note: I’m still dead: the other formula’s only an approximation, so it gave me the wrong combination for the lock.