Question

You are a retail investor. Opening Bloomberg, you observe the following quotes:

AUD/USD = 0.6785 – 89

AUD/EUR = 0.6128 – 31

Assuming no arbitrage opportunities exist, how many Euros would you get by selling $10,000?

A) It cannot be inferred from the available information

B) 9,036.11

C) 11,078.65

D) 9,026.37

Answer 1

First we need to find the cross bid and ask rates between the EUR and USD:

1. AUD/USD refer to the amount of USD are required to get 1 unit of AUD
2. AUD/EUR refer to the amount of EUR are required to get 1 unit of AUD
3. Bid refers to the rate at which the dealer buys the currency in the denominator or the USD and EUR in the above rates
4. Ask refers to the rate at which the dealer sells the currency in the denominator or the USD and EUR in the above rates
5. If you want to buy EUR or USD in the above rates, you will have to look at the ask because that is the rate the dealer is selling these currencies at
6. If you want to sell EUR or USD in the above rates, you will have to look at the bid because that is the rate the dealer is buying these currencies at
7. To find the cross rate, we need to do the following:
   • 
     EUR EUR AUD USD AUD * USD
     
   • Also, the bid will become the as and the ask will become the bid if we rotate the currency pair AUD/EUR to EUR/AUD as the Ask should always be greater than the bid

   • Currency pair	Bid	Ask
     AUD/EUR	0.6128	0.6131
     EUR/AUD	1/0.6131 = 1.6311	1/0.6128 = 1.6319
     AUD/USD	0.6785	0.7589

   • Finding the bid rate using this formula:
     • 
       EUR EUR AUD USD AUD * USD
       
     • 
       EUR = 1.6311 x 0.6785 USD
       
     • 
       EUR USD = 1.1067
       
   • Finding the ask rate using this formula:
     • 
       EUR EUR AUD USD AUD * USD
       
     • 
       EUR USD = 1.6319 x 0.6789
       
     • 
       EUR USD = 1.1079
       
8. Next we are selling the USD and buying EUR so we need to look at the bid rate of the cross rates calculated above as that is the rate at which the dealer is willing to buy the USD and sell us the EUR
   • Dealer buys USD 1.1067 in exchange of selling EUR 1
   • So Dealer buys USD 10000 in exchange of selling EUR 10000/1.1067 = EUR 9036.11
   • So the correct answer is B