Triangular Arbitrage Question (how do we know which way to go around the triangle?)

The bid-ask quotes for the , Pound, and Swiss Franc are: SF per : 1.6500 - 10 $ per Pound: 1.200 - 10 SF per Pound: 2.00 - 10 The potential arbitrage profits from an initial position of $1 million are closest to: A. $0 B. $8649 C. $10,495 D. 20,098 Also, do we go to SF to Pounds to ? or to Pound to SF to $ ?

you go around one way and you’ll show a loss, the other way shows a profit (if there’s an arb). so at worse you do 2x around. pick one and go. take it from the top- 1mm x 1.65SF/ (you always get screwed on the bid/ask, remember to get you to the smaller # always and you’ll be fine) = 1.65mm SF. 1.65mm SF / 2.1 SF/pounds = 785,714.857 pounds… x 1.2 dollars/pound = $942,857.1429 whoops you went the wrong way 1mm / 1.2 /pound = 826,446.281 pounds… x 2 SF/pound = 1,652,892.562 SF… / 1.651 SF/$ = $1,001,146.313. subtract the mil and i get you made $1,146.313 why do those look like weird answers to me? i usually do these in 2 seconds and wish the whole test revolved around tri-arb- did i just do something stupid?

The answer is B Solution: go from to Pounds to SF to I see, we have to go around both ways. One way shows a loss and the other shows a profit. In the solution, to Pounds is: 1 m / 1.2010 = 832,639 Pounds Pounds to Francs: 832,639 x 2 = SF 1,665,279 Francs to $: 1,665,279 / 1.6510 = $1,008,649 subtract 1,000,000, and you get $8649

In the solution, to Pounds is: 1 m / 1.2010 = 832,639 Pounds whoops i did it fast and divided by the bid (dumb), but even so I’d think $ per Pound: 1.200 - 10 would mean 1.210 on the ask, no, not 1.201??? is this problemo in the CFAI book? they use 1.651 so i think that answer has a small mistake. anyhoo- the point is multiply by the smaller #, divide by the bigger # (always think of yourself as getting the short end of the stick when you do exchange the currency). i don’t think there’s an easy way to figure out which way to go around in terms of what you said above, dollar to SF to pound to dollar or other way around. but if you practice these for a few, they get really fast and easy. one way around you’ll get less than what you started with, the other way you get a profit. if you get the same $$, there’s no arb.