3. You are an arbitrager who starts with $1000 U.S. and wants to end up with U.S

Question

3. You are an arbitrager who starts with $1000 U.S. and wants to end up with U.S. dollars. Following are three spot exchange rates: $0.20/krone $0.01/yen How would you engage in arbitrage to profit from these three rates? What profit would you make from the arbitrage in part a? As a result of this arbitrage, will the krone appreciate or depreciate relative to the yen? Explain. What value of the yen-krone exchange rate would eliminate the opportunity for triangular arbitrage? 25 yen/krone a. b. c. d.

Explanation / Answer

a.) If I have $1000, the best approach is to convert my money first into krone then into yen and then finally back to dollars i.e., dollars = krone = yen = dollars. If I go other way round i.e., dollars = yen = krone = dollars, I will end up with a loss of $200.

b.) so lets see what profit we end up with :

$0.20 = 1 krone

$1 = 1/0.20 krone

$1000 = (1/0.20*1000) krone = 5000 krone

now converting 5000 krone into yen:

1 krone = 25 yen

5000 krone = (5000* 25) yen = 125000 yen

now, finally going back to dollars:

1 yen= 0.01 dollar

125000 yen = (0.01*125000) dollars = 1250 dollars

Hence, there is a profit of $250.

c.) Everyone will want to exchange their krone for yen as it yeilds profit, the demand for yen will increase. Resultantly, the value of krone will depreciate relative to yen.

d.) To eleminate the oppurtunity for triangular arbitrage, we need to find a new value of yen-krone exchange rate. As the yen-dollar exchange rate and krone-dollar exchange rate is unaltered :

$1000 = 100000 yen and $1000 = 5000 krone. Hence, to eleminate the possibility of any profit, we just need to equate 100000 yen with 5000 krone

100000 yen = 5000 krone

20 yen = 1 krone.

Therefore, the new exchange rate is 20yen/krone.

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