Exerci Six: Exchange Rate Theory – PPP and IRP
graduatefrom1. The real exchange rate is defined to be E(CPI*/CPI). If PPP holds, what is the rate of change of the CPI when the foreign inflation rate is 3 percent per year and
1) the nominal exchange rate is fixed?
2) the domestic currency is depreciating at 7 percent per year?
3) the domestic currency is appreciating at 3 percent per year?
Answer: R=E(CPI*/CPI)
Then dR/R=dE/E+dCPI*/CPI*-dCPI/CPI
PPP holds means that dR/R=0, so
1) the CPI will grow at 3 percent per year
zm 2) the CPI will grow at 10 percent per year
3) the CPI will not change
2. male是什么意思idefragSuppo a U.S. exporter expects to receive a payment of Singapore Dollars (SGD) 1 million
mell
affectin 12 months.
a) The one-year interest rate on SGD deposits is 3 percent per annum. The one-year interest rate on dollar deposits is 6 percent per annum. The prent spot exchange rate is $ 0.65469 for SGD. What is the one-year forward exchange rate?
Answer:
Covered interest rate parity indicates that
jya (1+iUS)=(1/e)(1+iSGD)e*, where e is the spot rate in $/SGD and e* is the forward rate.
Therefore e*= (1.06/1.03)*0.65469 = 0.674
Intuitively, when you invest in $ now you should get exactly the same amount when you change you $ for SGD now and invest in SGD and then change SGD for $ after a year.
b) Assuming the exporter views dollars as his or her ba currency (i.e., ultimately needs
dollars), there are two ways to cover himlf against the exchange rate risk that aris from
not knowing what will be the value of the Singapore Dollar in 12 months. Describe them
(using only information given here) and show their equivalence computationally.
Answer:
You are getting 1 million SGD in one year. You can either:
木醋酸
i) ll them forward and get 1*e*=1*0.673758 million US dollars a year from now on, or
ii) borrow 1/((1+iSGD)=1/1.03 = 0.970874 million SGD, convert into US$ to obtain 0.970874*0.65469 million dollar in the US, which yields 1.06 times US$ 0.673758 million, which is exactly equal to the amount in the first option. Finally, u 1 million SGD you receive to pay back your borrowing obligation.
c) Now suppo the claim on SGD 1 million is due in six months. The interest rate on six-
month SGD deposits is 2 percent per annum. The interest rate on six-month dollar deposits is
2.7 percent per annum. What is the six-month forward exchange rate?
Answer:
(1+iUS)=(1/e)(1+iSGD)e*英语在线词典
Then e*=e (1+iUS)/(1+iSGD)= 0.65469*(1+2.7%/2)/(1+2%/2)=0.65696
d) What do a) and c) imply about “the market’s expectations” regarding the future path of the
exchange rate?
Answer:
Parts a) and c) imply that, “the market expects” that the exchange rate will be higher in the future – increa from 0.65469 today to 0.65696 six months from now- and that it will ri further over the subquent six months, to 0.673758. The dollar will depreciate against SGD. The reason is that, since the dollar interest rate is higher than that of SGD, for investors to be indifferent between holding dollars and SGD the value of dollars has to decrea over time. But this might not be the true expectation of market participants. If they are uncertain about the future path, and are risk-aver, then they will not necessarily drive the forward rate into equality with their best guess. There may be a risk premium, in which ca uncovered interest parity will not hold.
e) Assume that the Polish Zloty is worth 0.52 SGP today and obeys one-year covered interest
parity relationship. Suppo, however, that today investors know with certainty that in one
year, 1 zloty will be worth $0.3285 in the spot market. Suppo that the U.S. interest rate
remains the same. (The United States is a big country.) What will investors do? To what
level will they drive the one-year forward exchange rate? What will that imply for the
interest rate on one-year deposits in zloty?
Answer:
Today’s spot exchange rate for the Polish Zloty is (0.65469$/SGP)(0.52SGP/PZL)=0.340439 $/Zloty. If investors know with certainty that in one year 1 Polish Zloty will be worth $0.3285, then they will drive today’s forward rate to that level. According to the covered interest rate parity, there should be:
