# can an fx forward price simply be divided into 1 to quote the inverse?

Qu 1. Say I ask for EURUSD 1 week and get prices: 1.120986 / 1.120216

Does that mean to price USDEUR 1 week I can divide 1 / 1.120216 and 1 / 1.120986 and get rates: 0.8921 / 0.8927

Or is that result wrongly pitched according to the facts there's a bid/offer spread in the EUR interest rate to USD interest rate differential, and that the inverse of the EURUSD interest rate differential is not the same as the USDEUR interest rate differential? i.e. to get the inverse of the forward price the deposit and loan rates need to be swapped. The deposit and loan rates being the rates the FX forward rates correlate with to prevent arbitrage between FX markets and money markets.

Qu 2. If EUR 1 week LIBOR is -0.16286% and USD 1 week LIBOR is 0.15375% then what's the interest rate differential between them? (source http://www.global-rates.com/interest-rates/libor/european-euro/euro.aspx)

Yes, you can just invert (i.e. 1/x) the EURUSD quotes to get the USDEUR bid and offer, as you did in your example.

Deposit and loan rates are really just bids and offers for deposits. The difference between them is what creates the bid-offer difference in the fx prices. All 4 rates (USD loan, USD deposit, EUR loan, EUR deposit) are used in the calculation of the bid and offer for EURUSD. All the information is already there. And inverting the fx rates reverses the direction of the trade, using all that same information.

Your second question is lacking the detail you need to create a bid and offer side. You quote a single rate for each currency, rather than their bids and offers (i.e. deposit and loan). So you can calculate a single forward fx rate, using the 0.3166% differential, but not a two-way market.

• Thanks: "inverting the rates reverses the direction of the trade" duh! So they have to reflect each other exactly – rupweb Oct 1 '15 at 9:06
• although what if the provider sets different spread bands depending on which ccy is base ccy and which is terms ccy? I think that's what my intuition that there's a problem with simply inversing FX spot or forward rates is about. For example with USDJPY the spread given to make a price in 1mio USD could well be different compared with the spread given to make a price in 100mio JPY right? Even though the amounts are roughly equivalent. – rupweb Feb 9 '17 at 11:53
• @rupweb I suppose there will always be small differences. Just rounding to whatever precision they are quoting will introduce imperfections, as 1/x doesn't preserve the precision. Which means that, yes, there must always be a cheaper way to execute that same trade, at the sub-tick level. You shouldn't, however, find arbitrage opportunities in the 1/x relationship. Or, if you do, let me know first. – RaveTheTadpole Feb 9 '17 at 15:46