Question

A... We know that the yen and the swiss franc have a 100yen/sf 1 exchange rate, meaning one swiss franc buys 100 yen in the spot ER market. The 1 year forward rate is 108 yen/swiss franc, or 1 franc buys 108 yen in the forward market. If the swiss franc has an interest rate of .11, what should the yen rate be for IPT (interest parity theory) to be attained? If the yen rate were 16%, would there be equilibrium? If so, what would transpire? Show both amounts and differentials. Also, show everything in both yen and franc terms. B. The inflation rates in the British pound and the Australian dollar are 12% and 8% respectively. What should the Sex/Forward ER be, if the Spot ER is BP/A$ . 1 i.e., . 1 BP equals 10 Australian dollars.? Describe the concept of purchasing power.

Answer 1

A

To use interest rate parity, you can come up with a borrowing case problem. Assume you borrow 1 swiss franc. In 1 year from now you need to pay back 1*(1+rS) = 1*(11%) = 1* (1+.11) or 1.11 since you need to pay back the swiss franc plus an extra 11 cents. If you took that initial swiss franc and converted it into yen, I would have 1*S where S is the spot rate, so 1*100 yen/sf since I have 1 sf. I would thus have 100 yen. Then, I can take that yen and invest it at the yen interest rate to get 100*(1+rY) where rY is the annual yen interest rate. Thus, in one year from now I would have 100*(1+rY). But since I need to pay my liability of 1.11 or 1*(1+rS), my investment of 100*(1+rY) needs to be hedged at the forward rate, so I would have 100*(1+rY)/F if F is in terms of Yen per sf. Thus, my investment of 100*(1+rY)/F = (1+rY).

In simple terms, we have derived the equation:
S*(1+rY)/F = (1+rY)

100*(1+r)/108 = 1.11 so r = 0.1988 or 19.88%. If the yen rate is at 16% then no, there wouldn’t be an equilibrium since the parity equilibrium interest rate for the yen is actually 19.88% and not 16%.

If the yen is 16% we would borrow at the 16% rate since we know in reality it should be higher at 19.88%.

I'm not too sure what it means by "show both amounts and differentials in yen and franc terms", maybe you can elaborate on that? I think that's related to a specific in-class exercise you did so if you can send me slides/notes for it that would be great.
B

Higher inflation rate reduces that currency because now more of that currency is required to buy the same goods. To use the purchasing power parity equation, we simply take the difference in inflation rates. Since the pound has a 4% higher inflation rate than the Australian dollar (12%-8% = 4%), the pound should drop 4% relative to the AUD. Since 1BP = 10 AUD this means that now, 1BP = 0.96*10 = 9.6AUD now. Purchasing power just means how much one good costs in another country.