Cross Rate with Reciprocal

CFA Level III
#1

Hi,

When we do the cross rate calculation where we have to do the reciprocal, why does the bid become ask and the ask become bid?

#2

If you go to a bank and get a quote of USD/GBP 1.2900 - 1.2910, that means (as the end user):

  1. you will buy GBP 1 from the bank using the ask rate for USD 1.2910 (sell USD).
  2. you will sell GBP 1 from the bank using the bid rate for USD 1.2900 (buy USD).

Note that GBP is the base currency in this case (following how it is defined in CFA syllabus).

So, if I do a reciprocal, we will get GBP/USD, so:

  1. if you want to buy USD 1 (which means you will sell GBP 1), you will use the bid rate from the original quote (1.2900).

=> To buy USD 1, then you will sell GBP 1/1.2900 = GBP 0.7752 (ask rate for GBP/USD)

  1. if you want to sell USD 1 (which means you will buy GBP 1), you will use the ask rate from the original quote (1.2910).

=> To sell USD 1, then you will buy GBP 1/1.2910 = GBP 0.7746 (bid rate for GBP/USD)

To conclude, once you do the reciprocal, you now have GBP/USD 0.7746 - 0.7752.

#3

Thank you for taking the time to reply to my post.
I think I’m still confused on this concept. I did understand the procedures and that bid becomes ask and ask becomes bid and also it makes sense because bid has to be lower than the ask. But I still don’t get why the bid became the ask

#4

Take your time to digest. The bid became the ask because you are switching the base currency (from sell GBP to buy USD).

#5

Think of it this way:

  • Given (USD/MXN)_offer = 0.0935/1 means you want to sell 1 MXN for 0.0935 USD.

In other words, this means you want to buy USD and sell MXN for [1/(USD/MXN)_offer] = [1/(0.0935/1)] = 10.70/1 (MXN/USD)_bid

Can you see now that when you want to sell MXN (Offer) means you want to buy USD (Bid)?

#6

If you hand me some GBP and I (as the cheapskate dealer) hand you some CHF, then either:

  • I bought GBP from you, using my CHF/GBP bid, or
  • I sold CHF to you, using my GBP/CHF ask