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Purchasing power parity, Interest rate parity

1. Smith knows that if the forward rate is lower than what interest rate parity indicates, the appropriate strategy would be to borrow:

A) pounds, convert to dollars at the spot rate, and lend the dollars.
B) pounds, convert to dollars at the forward rate, and lend the dollars.
C) dollars, convert to pounds at the forward rate, and lend the pounds.
D) dollars, convert to pounds at the spot rate, and lend the pounds.

2. Smith also knows that if the forward rate is higher than what interest rate parity indicates, the appropriate strategy would be borrow:

A) pounds, convert to dollars at the spot rate, and lend the dollars.
B) dollars, convert to pounds at the spot rate, and lend the pounds.
C) pounds, convert to dollars at the forward rate, and lend the dollars.
D) dollars, convert to pounds at the forward rate, and lend the pounds.

3. Now, suppose Smith has the following information available to him: the current spot exchange rate for Indian Rupees is $0.02046. Inflation over the next 5 years is expected to be 3 percent in the U.S. and 5 percent in India. Smith must calculate the U.S. Dollar / Indian Rupee expected future spot exchange rate in 5 years implied by purchasing power parity (PPP). The answer is:

A) $0.02010.
B) $0.02250.
C) $0.01858.
D) $0.01946.

4. Smith routinely calculates the expected spot rate for the Japanese Yen per U.S. dollar. He knows that the current spot exchange rate is $189.76 Yen/USD. He is also aware that the interest rates in Japan, Great Britain, and the U.S. are 8 percent, 4 percent, and 5 percent respectively. Calculate the expected spot rate for Yen/USD in a one year period.

A) 187.95 Yen / USD.
B) 189.76 Yen / USD.
C) 195.18 Yen / USD.
D) 184.49 Yen / USD.

5. Smith observes that the $/ spot exchange rate was 0.9857 two years ago. What does a comparison of the spot rate predicted by PPP with the current spot rate, i.e., 0.9808, tell us about changes in the relative cost advantage of U.S. exporters vs. German exporters? Since the spot rate predicted by the PPP relationship is:

A) $1.0615 per euro, U.S. exporters have a competitive advantage relative to German exporters.
B) $0.9153 per euro, U.S. exporters have a competitive disadvantage relative to German exporters.
C) $1.0615 per euro, U.S. exporters have a competitive disadvantage relative to German exporters.
D) $0.9153 per euro, U.S. exporters have a competitive advantage relative to German exporters.

Solution Preview

1. Smith knows that if the forward rate is lower than what interest rate parity indicates, the appropriate strategy would be to borrow:

A) pounds, convert to dollars at the spot rate, and lend the dollars.   
B) pounds, convert to dollars at the forward rate, and lend the dollars.   
C) dollars, convert to pounds at the forward rate, and lend the pounds.   
D) dollars, convert to pounds at the spot rate, and lend the pounds.

Answer: A) pounds, convert to dollars at the spot rate, and lend the dollars.   

Assume the UDS/GBP forward rate is lower than what interest rate parity indicates.
This means that the USD is overpriced in the forward market
Dollar is overpriced in the forward market and underpriced in the spot market
Arbitrage means buy cheap and sell dear
Therefore buy dollar in the spot market and sell dollar in the forward market.
ie invest dollars now and convert to pounds in the forward market

An example
Suppose
USD/GBP spot is $1.6115 / £

1 year interest rate on dollars is 10%
1 year interest rate on pounds is 5%

According to interest rate parity condition
Forward / Spot = (1+ dollar interest rate) / (1+ pound interest rate)

or Forward = Spot x (1+ dollar interest rate) / (1+ pound interest rate) = $1.6882 / £ =1.6115x *(1+10.%) / (1+5.%)
Let us assume that in the forward market, 1 year forward rate is
USD/GBP 1 year forward rate is $1.6525 / £ instead (thus forward rate is lower than what interest rate parity indicates)

Therefore, arbitrage opportunity is
Borrow £1
Convert it to dollars at the spot rate of $1.6115 / £
You get $1.6115
At the same time buy forward contract to convert your dollars back to pound at the end of 1 year at the forward rate of $1.6525 / £

Principal and interest on the pound loan to be returned at the end of 1 year
Principal = £1
Pound interest rate = 5%
Thus principal + interest on the loan= £1.0500 =1.x (1+5.%)

Invest $1.6115 at the interest rate of 10%
Principal and interest received at the end of 1 year= $1.7727 =$1.6115x *(1+10.%)
Convert it to pounds at the forward ...

Solution Summary

Answers to 5 multiple choice questions on Purchasing power parity(PPP), , Interest rate parity, exchange rates (forward/spot)

$2.19