Please Explain

Donna Ackerman, CFA, is an analyst in the currency trading department at State Bank. Ackerman is training a new hire, Fred Bos, a recent college graduate with a BA in economics. Ackerman and Bos have the following information available to them: Spot Rates Euro/US$ = €1.0000 - €1.0015 British Pound/US$ = 2.0000 - 2.0100 Euro/British Pound = €0.3985 - €0.4000 Ackerman and Bos are interested in pursuing profitable arbitrage opportunities for State Bank. Using the appropriate bid or ask rates for the Euro/US$ and the British pound/US$, what will be the profits from triangular arbitrage, starting with $1,000? A) $248.46. B) $245.65. C) 243.78. The correct answer is option C. I got option B by doing the following: I actually used two different calculations: ----------------------------------- 1st Calculation: Euro/US = €1.0000 - €1.0015 ------------- Test if profitable arbitrage is available. EUR/USD = British Pound/US$ = 2.0000 - 2.0100 X Euro/British Pound = €0.3985 - €0.4000 = 0.7970 - 0.8040 >>> not equal to Euro/US$ = €1.0000 - €1.0015 so profitable arbitrage is available. buy British Pound = $1,000 / 2.01 = 497.5124 GBP buy Euro = 497.5124 GBP / 0.40 = 1,243.7810 EUR buy USD = 1,243.7810 EUR * 1.0015 = $1,245.6467 Arbitrage profit = $1,245.6467 - $1,000 = $245.65. >>> Wrong Answer Option B. ------------------------- 2nd Calculation: $1,000 to buy euros (1,000 × €1.0015/) = €1,001.50. €1,001.50 to buy sterling (€1,001.50 / €0.4000)= 2,503.75. 2,503.75 to buy dollars (2,503.75 / 2.0100/$) = $1,245.6468 Arbitrage profit = $1,245.65 - $1,000 = $245.65. >> Wrong Answer Option B. -------------------------------- Correct answer is option C (Schweser’s Calculation) - The euro/dollar and sterling/dollar rates imply that the arbitrage free cross rates for the euro/sterling are: bid = €1.000/2.0100 = €0.4975 ask = €1.0015/2.0000 = €0.5008 Since the cross rates given (€0.3985/€0.4000) are outside of the arbitrage-free cross rates, profitable arbitrage is available. It takes too few euros to buy 1 pound, so we want our arbitrage trades to go in the direction that will cause us to sell overvalued euros for pounds at the ask rate of €0.4000. Start with $1,000. Use the $1,000 to buy euros (1,000 × €1.000/) = €1,000. Use the €1,000 to buy sterling (€1,000 / €0.4000) = 2,500. This step is the key here. Use the 2,500 to buy dollars (2,500 / 2.0100/$) = $1,243.78. Arbitrage profit = $1,243.78 - $1,000 = 243.78. \>\>\>\> Correct Answer Option C. Why did the correct answer used €1.000/ to convert USD to EUR as opposed to the ask price of €1.0015/$?

Your selling dollars for euros and dealers will buy your dollars at the bid price, not ask.

I read this here earlier and it’s helped me a ton - follow two rules W/R/T Trianglular Arbitrage: 1) Watch the Units. In the first step, you have USD and you want to get EUR. The bid-ask is given in EUR/USD. So you can do straight multiplication to get the USD value. USD*(EUR/USD) = EUR. 2) You always get screwed. In the bid/ask, you always get the less appealing number. So, in the first step, you would recieve the lesser amount of EUR for your USD, which would be 1000 - vs. 1001.5 for the $1000. I try not to think of the quote as a straight bid-ask. I look at it and think which number screws me the most, and go from there. I hope that doesn’t confuse you that much more. Good luck!

Ah, thanks!

I think figuring out which number to use is one of the most difficult things to get right. people always try to figure it out by saying… “I have dollars and want another currency so I must need to sell my dollars.” and since the word sell is in there they automatically think “ask price”, however, that is wrong REMEMBER: the exchange rate is ALWAYS from the perspective of the broker. If you are selling, then the broker is buying. ie. use the bid (the rate the broker buys at) when figuring out which rate to use I always put the exchange rate into the form: A:B. *If I have A and want B I use the Bid This is easy to remember b/c A is on the lft side of the : and the bid quote is on the left side of the - *If I have B and want A I use 1/Ask