Question

10. Omni Advisors, an international pension fund manager, uses the concepts of purchasingpower parity (PPP) and uncovered interest parity/international Fisher effect (IFE) toforecast spot exchange rates. Omni gathers the financial information as follows:(Note: The rand (ZAR) is the South African currency. USD refers to the U.S. dollar.The base year denotes the beginning of the period.)

Base price level (any country)100

Current U.S. price level105

Current South African price level111

Base rand spot exchange rate$0.175

Current rand spot exchange rate$0.158

Expected annual U.S. inflation7%

Expected annual South African inflation5%

Expected U.S. one-year interest rate10%

Expected South African one-year interest rate8%

(a) According to PPP, what should the current ZAR spot rate in USD (USD/ZAR)be?

(b) According to PPP, is the U.S. dollar expected to appreciate or depreciate relativeto the rand over the year? Why?

(c) According to the UIP/IFE is the U.S. dollar expected to appreciate or depreciaterelative to the rand over the year? Why?

(d) Compare your answer in b) and c). Are you surprised? Why?

Answer 1

(a) Current ZAR spot rate by PPP is given by S_t/S₀= P_h/P_f where S_t is the current spot exchange rate, S₀ is the base spot exchange rate. P_h is the price level in home country P_f is the price level in foreign country.

S_t= (0.175)(105/111)

=$0.165/rand

(b) According to PPP S_t/S₀=(1+i_h)/(1+i_f)

where S_t= Expected ZAR spot rate in USD in one year

S₀= Current ZAR spot rate

i_h= inflation rate in home country

i_f= inflation rate in foreign country

S_t=(0.158)(1.07/1.05)

= $0.1609/rand

Hence it is clear that Dollar is expected to depreciate relative to the Rand over the year since according to PPP the country's currency with higher inflation rate is expected to depreciate.

(c) According to IFE S_t/S₀=(1+r_h)/(1+r_f)

where S_t= Expected ZAR spot rate in USD in one year

S₀= Current ZAR spot rate

r_h= interest rate in home country

r_f= interest rate in foreign country

S_t=(0.158)(1.10/1.08)

S_t=0.1609$/rand

So dollar is expected to depreciate over the year as the country with higher interest rate will see it's currency depreciate according to IFE.

(d) Answers in (b) and (c) are identical as PPP implies that exchange rates move in the opposite direction of inflation rates and a rise in inflation will cause a rise in the interest rates. IFE combines the two phenomenon and gives the result that country with a higher interest rate will see it's currency depreciate relative to the country with a lower.Hence both PPP and IFE willl show identical answers.