Question

Suppose the japanese yen exchange rate is ¥73.47 = $1, and the british pound exchange rate is £1 = $1.53.
a. what is the cross-rate in terms of yen per pound? (do not round intermediate calculations and round your answer to 2 decimal places,
e.g., 32.16. do not include the yen sign (¥).) cross-rate ¥
b. suppose the cross-rate is ¥115 = £1. what is the arbitrage profit per dollar? (do not round intermediate calculations and round your answer to 4 decimal places,
e.g., 32.1616.) arbitrage profit per dollar $

Answer 1

Answer: Cross-rate can be found by using the given formula ,

$¥73.47 = 1 £1 = 1.53$

So,

$£1 = 1.53 1 = \frac{£1}{1.53} 1= £0.6536$

Substituting this into the exchange rate for Yen and dollars, we get

$¥73.47 = 1 ¥73.47 = £0.6536$

$¥73.47/0.6536 = £1 ¥112.4082=£1$

Cross-rate in terms of Yen per Pound is 112.41

b. If cross-rate is $¥115=£1$, this means that Yen is quoted high relative to pound. So, the arbitrage profit per dollar will be,

Suppose we take a a loan for $1 and buy £0.6536. Then we use the pounds to purchase yen at the cross-rate, so we have

£0.6536 (¥115/£1) = ¥75.164

Now, we replay the loan in dollars by exchanging Yen back to dollars. The cost to repay will be:

¥75.164($1/¥73.47) = $1.02305

Your arbitrage profit is $0.02305 per $1 used.