CFA Reading 18 problem 16 cross-rate

Given USD:CHF, USD:AUD and CHF:AUD fx rates, your supposed to find out argitrage opportunity , i.e. calculate cross rate. How do you decide which cross to calculate? I started calculating USD:CFH, found out CHF overvalued. The correct cross to calculate was CHF:AUD, results in CHF being overvalued anyway. So how do you know which cross to start calculating? Might well calculate all, but on exam day that might take too much of the precious time. Thanks!

Rocci- To check if triangle arbitrage is possible, first you need to determine what cross rate you get for CHF:AUD. USD:CHF= 1.5971 USD:AUD=1.8215 CHF:AUD=1.145 1) CHF/USD x USD/AUD= CHF/AUD 1.5971 1/1.8215= .8768 AUD/CHF so inverse is 1.1405 CHF/AUD Since 1.405 is lower that 1.145 CHF is overvalued and there is arbitrage. So you want to sell CHF and buy AUD. 2) You have \$1,000,000 USD, you sell USD and buy CHF at 1.5971 and you get 1,597,100CHF. 3) Sell CHF to get AUD using 1.145 as CHF:AUD. 1,597,100CHF x 1.145 AUD/CHF = 1,828,679.50 AUD 4) Then sell AUD and buy back USD at 1.8215. 1,828,6179.50 AUD/ 1.8215 AUD/USD= 1,003,941.53 USD. You net this with the \$1,000,000 and you have 3,941.53 as profit. Hope this helps.

Thanks adee 1031, I get the math, so that’s no problem. What I was wondering is how you decide, in the first place, you need to start calculating the cross for CHF:AUD (eg. why not USD:CHF like I started)?