# cross currency arb

how would you do the math on this?

bid ASK EURO:\$ 0.8 .8012

\$:YEN 12.80 12.818

EURO:YEN 10.10 10.102

IF SKYWALKER EMPLOYS THE CAPITAL HE HAS AVAILABLE FOR ARB, HIS PROFITS WILL BE:

A. ,13,661 YEN

B 16,810 YEN

C. NONE

Isn’t there something missing in this question?

thanks. he has access to 1,000,000 yen

can somebody provide the working out plz

Convert to euro by dividing by ask: 1,000,000 / 10.102 = 98,990

Convert to USD by multiplying by bid: 98,990 x 0.8 = 79,192

Convert back into yen by multiplying by bid: 79,192 x 12.8 = 1,013,661

i think? anyone else care to comment?

Sorry for the terse email. I had to write so much, so couldn’t really care about the format etc. Please point out if my approach is not correct or I have made any errors in the calculation. Here is what I do:

lol not email, post*…ughh

*not security, currency

The shortcut to this approach is, try both paths and see which one yields profit for you. But if one path leads to the loss, doesn’t mean the seond one will be profit automatically. You have to make sure you are calculating both.

@sgupta , amazing explanantion . I had trouble with this concept , now its sorted . for the purpose of exam I will not check the overvalued or undervalued rates to determine which path to choose , rather i would pick any path and see whether any arb is present .

thanks a ton

Awesome write up sgupta. I haven’t spent much time on this stuff, I have a few questions. So the only reason to calculate the cross rate is to decide which path to take, not to actually use the rates in your calculation for Arb? When calculating the bid ask for Euro:\$ should you multiply the bids together to get the new bid and the asks to get the new ask?

Example:

\$:Yen = .07802 - .07813

Yen:Euro = 10.10 - 10.102

Thus: \$:Euro = (.07802*10.10) . 788002 - (.07813*10.102) . 7892692

Your conclusion is still the same.

Thanks

@Factor Hedge I had trouble with this concept too. I think this is one of the hardest one. I am yet to figure out swap calculations.

@CFAWorldwide: You can multiply or divide depending upon what rates are given to you. Division is in fact easier as you don’t have to flip the bid and ask so many times, in fact not even once. But for people who have problems with exchange rate conventions, I wanted to make it easier. Yes, the cross rate is only for the path selection. I think randomly also you should be fine but you are increasing the probability of getting the questions wrong as the concept is bit harder and it takes time to realize where goes what.