Econ - FX

Suppose the AUD trades for USD 0.735802 in New York and JPY 79.3048 in Tokyo. The USD trades for JPY 109.2343 in Tokyo. Is there an arbitrage opportunity available for a currency trader? A- Yes, the trader can make USD 0.0135 per USD invested. B- No, there is no arbitrage opportunity. C- Yes, the trader can make USD 0.0872 per USD invested.

What I did is to compare the AUD:USD quote in both cities as follows: JPY:AUD in Tokyo = 1 / 79.3048 = 0.0126 USD:AUD in Tokyo by multiplying USD:JPY X JPY:AUD = 109.2343 X 0.0126 = 1.3774 AUD:USD in Tokyo 1 / 1.3774 = 0.7266 And this is all I can reach,what did I do wrong ?

You want to check if there is an Arbitrage for USD/JPY (triangular, through AUD)

USD/AUD x AUD/JPY = 79.3048/0.735802 = 107.7801

Ans is (A)

Guys fell free to correct, haven’t done many Q’s might be some error.

First, the answers are all in USD so you should start in USD. You’re given three quotes:

AUD:USD 0.735802

AUD:JPY 79.3048

USD:JPY 109.2343

To determine if you have an arbitrage opportunity, create another USD:JPY quote from the first two quotes. Divide the AUD:JPY quote by the AUD:USD quote to get USD:JPY 107.78 (this does not equal the 109.2343 quote so there is an arbitrage opportunity).

I like to make three columns on my sheet, one for USD, one for JPY, one for AUD.


1 USD = 109.2343 JPY

(109.2343 JPY) 1.377398 AUD

(1.377398 AUD)

1.013492 USD

You subtract the $1 that you started with, and come up with $0.0135 as an arbitrage profit.

thank you guys for the help

stunnerrunner , I can prefectly understand what u did ,but could u plz tell me the exact calcualtion for reaching the 1.013492 USD , I cant really follow this

I got A also

(109.2343/107.7801)-USD1 = 0.0135

Damn i am not able to post the answer

i’ve written up the answer, but when i post the page is crashing, copied it to notepad, anyone knows how to fix this? tried restarting browser

I am experiencing the same issue, thats why i posted the question and the answer separately

1.377398 AUD / 0.735802 = 1.013492. You have AUD and you’re trying to end with USD.

… this is not too hard folks, when they throw in bid/ask rates in it, it gets more fun!

Tried posting in parts, not working

If you want, I’ll e-mail you the answer, mine is

Dreary bid/ask was killing me at first, makes head spin, damn

Was able to put in following by editing-

109.2343 - 107.7801= 1.4542 JPY difference

Hence your profit = 1.4542/107.7801 = 0.0135 USD

Look up triangular arbitrage in google, if you draw a triange then it becomes much clearer, i have used a short-cut method, thats why i wasn’t sure.

aditya8232 , I sent u an email

If you’re using bid-ask spreads, use the trick “up the bid, down the ask”. It helps. OR always choose the rate that gives you the least amount of the currency.

I doubt this short cut…check it out carefully before using it.

lolll highrisk, nice ID, have sent the detailed method with reasoning, hope it helps.

When doing this kind of calculations I follow the same patter.

  1. Calculate crossed price. In this example it would be AUD:JPY/AUD:USD, or for 1USD I get 1/.735802=1.35906AUD. Buy for JPY for AUD = 1.35906*79.3048 = 107.78.

  2. The USD costs less JPY when crossed => I long crossed and short direct.

  3. For 1USD shorted, I get 109.2343 JPY. For 109.2343 JPY I get 109.2343/79.3048 = 1.37740 AUD.

  4. For 1.3774 AUD I get 1.37740*.735802 = 1.01349USD.

JPY is overvalued though the USD/AUD - AUD/JPY rate,

we get 109.2343 for 1 USD directly and 107.7801 thorugh AUD, so i get the difference and convert back to USD using the better rate of 107.7801.

Can you point me in which step might be wrong/land me in trouble?