Triangular Arbitrage Question

CFA Level II
#1

Are you guys seeing a mistake in this problem? Or is it me - bugged out at 1AM doing Arb Triangle questions?.. Schweser Qbank: 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 Bid Price Ask Price USD:EUR €1.0000 €1.0015 USD:GBP ₤2.0000 ₤2.0100 GBP:EUR €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 USD:EUR and the USD:GBP, what will be the profits from triangular arbitrage, starting with $1,000? A) $243.78. B) $248.46. C) $245.65.

#2

I got A.

#3

USD:EUR €1.0000 sell 1,000 buy € 1,000 GBP:EUR €0.4000 sell € 1,000 buy GBP 2,500 USD:GBP 2.0100 sell GBP 2,500 buy 1,243.78

#4

Check out this post by CFASniper. Very helpful. http://www.analystforum.com/phorums/read.php?12,1138394,1151381#msg-1151381

#5

A is my answer.

#6

i would appreciate it if someone could walk through this problem using the method cited by cfasniper!

#7

As per CFA Snipers method Path 1) EUR/USD*GBP/EUR*USD/GBP = 1/1.0015 * 0.3985 * 2 = 0.795806 (<1 no arbitrage) Path2) GBP/USD*EUR/GBP*USD/EUR = 1/2.01* 1/0.4*1 = 1.243781 (>1 arbitrage exists) USD 1000 * (1.234781-1) = USD 234.78

#8

thanks! but uuuuuugh. i cannot stand the feeling that i spend half my study time trying to understand why things are wrong when i took the information down wrong to begin with. son of rtfq.

#9

Answer is 243.78. I finally figured out a system on doing this and takes less than a minute to do. Tried it out on every triangular arb questions I could find. Super easy now and hope it’s gonna show up on the exam for some easy points. Do this: BID ASK multiply divide Think of two things: 1. What currency do I have? 2. Which one do I want? This example… 1. I have the USD $1000. 2. I want GBP. So find USDGBP and divide $1000 by 2.010. 3. Now you have GBP, repeat the above, starting with “I have GBP” 4. Until you get your arb profit.

#10

Nomad,

When I follow the CFA snipers method, I get arbitrage opportunity starting with USD TO EURO 1.243 (ARBITRAGE)

Starting with USD TO GBP gives me the answer 0.795 (NO ARBITRAGE)

Was your answer a typo or am I doing something wrong?

#11

I wrote an article on triangular arbitrage that explains this very clearly: http://www.financialexamhelp123.com/triangular-arbitrage/.

(Full disclosure: as of 4/25/16 there is a subscription fee to access the articles on my website. You can view free sample articles here: http://www.financialexamhelp123.com/sample-articles/.)

In a nutshell:

If you go from USD to EUR to GBP to USD, you end up with:

USD1,000 × EUR1.0000/USD1.0 × GBP1.0/EUR0.4000 × USD1.0/GBP2.0100 = USD1,243.78.

If you go from USD to GBP to EUR to USD, you end up with:

USD1,000 × GBP2.0000/USD1.0 × EUR0.3985/GBP1.0 × USD1.0/EUR1.0015 = USD795.81

Start by converting your USD to EUR.

#12

I was taught the ladder approach, quick calculation.

http://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91310994

#13

Ok, I’ll give a shot at giving a quick explanation:

Three Steps:
Step 1:

where to start?

Here it tells you to start with dollars so its a good one to get an understanding on. there are three currencies and you start with $ so you only have two choices

buy euros or buy pounds

so one option: start with $ buy Euros - buy pounds - buy dollars

second option: start with $ buy pounds - buy euros - buy dollars

if you end up with more than a thousand dollars doing one of these transactions, you have made money obviously.

Step 2:

do you use USD/EUR or EUR/USD

Step 3:

do you buy on the bid or the offer/ask ?

STEP 2 and STEP 3 are intertwined.

STEP 2:

Obviously USD/EUR is the same thing as EUR/USD

remember the bottom currency is the “BASE” currency its always 1 so it is the easy one to work with so if you say in an example where you have a quote of EUR/USD = 1.5 say: “1 dollar buys 1.5 euros”.

So, always put the currency you have in the BASE that makes it easy

  • its tedious and a pain, just do the calc it saves making mistakes -

STEP 3:

use the bid or the ask -

in my opinion this is backwards - sort of - you buy on the bid and sell on the ask - this is the opposite of stock quotes

  • the thing to remember is in both situations either stocks or fx, obviously you get the worst price

so just keep it simple and take the worst deal

in the example lets start buying Euros

so we have dollars and we want to buy euros

so we start by making sure the quote is the right way around: dollars in the base so we know exactly what one dollar buys.
EUR/USD is quoted at 1.000 - 1.0015

do we buy euros at 1.000 or 1.0015? well, we’re buying so we get the worst deal which means the fewest euros (to mess with your head, you buy on the offer in the stock market, why, because when you pay the higher price you get fewer shares - its the worse deal; so you can think of it as stocks quote the price, and fx quotes the AMOUNT)

so lets put it together

we have dollars and want to buy euros and we get the worst deal; so we buy at 1; now we have 1000 euros

then we want to buy pounds with our euros

so we turn the quote around and write it as GBP/EUR or 1/.4 - 1/.3985 or 2.500 - 2.50941

so again were buying so we get the fewest pounds: 2500

Now we just need to buy dollars

so we need a quote: USD/GBP or 1/2.0100 - 1/2.000 or 0.4975 - .5

again we’re buying so we get the worst deal: 2500 x 0.4975

or 1243.78

so we started with 1000 and ended up with 1243.78

there are lots of different mathematically equivalent ways of doing this; to me I recommend just finding one way that is clear in your mind and plug and chug

there are shortcuts, but they just risk confusing or introducing errors.

so its not the only way to do it, but it is the way i keep it simple in my head

  1. put the currency you have in the base

  2. always buy at the price in the quote that gives you the worst deal

you may want to go through this problem buying pounds, then euros, then back to dollars

and hopefully this makes it clear so you can do other problem easily as well.