I had to explain this type of problem in my study group yesterday. The book provides a great way to simplify all the cross rate problems in 2 steps:
1) Determine your common currency then form the problem so that it eliminates it
Example:
USD:Sfr = 2-3
USD:¥ = 100-150
Solve for SFr:¥
Solution:
USD is the common currency
We want Sfr in the numerator and ¥ in the denominator
So,
(USD:¥)/(USD:SFr) = (SFr/USD) * (USD/¥) = SFr/¥
2) Remember your Bid is the smallest possible number (and your ask is the largest possible
number.
Lets solve for the bid:
To get the smallest value, we need to have the smaller number in the numerator and the
larger in the denominator. Remember: ¥ is ultimately our denominator. Don't get confused!
Formula: (USD:¥)/(USD:SFr) - NOTE: We discovered this in step 1
SFr:¥ (bid) = (USD:¥)/(USD:Sfr) = 100/3 = 33.33
Try working through the problem for the ask. Remember, the ask is the largest possible
value.
Pgiger, i like your method. Its lot easier than CFAI text. But i have confusion over your notations.
"Solve for SFr:¥
"We want Sfr in the numerator and ¥ in the denominator"
I read as per CFAI, the quoting convention is SFr:Yen means price of one SFr in Yen( number of Yen per Sfr). = Yen per Sfr,
= Yen/Sfr i.e Yen is in numerator and SFr in denominator. Correct me if i am wrong.