3.1. EXCHANGE RATES 81
cross rates all the time, banks just showed primary quotes and then computed
cross rates if and when needed.By the 1980s desktop computers were around everywhere and, for many pairs of
“big” currencies the volume of cross transactions had become large enough to make
direct cross exchanges competitive compared to exchanges via theusd. Official
exchange rates were gone in many cases, or in theermcase had become multilateral.
So we now see explicit quotes for some of the cross rates. Look at Figure 3.2 to see
what rates have active multilateral electronic markets—a good indication of there
being a reasonable volume. Note also that for some neweumembers the market
against theeurworks well while the market against theusdlacks liquidity; that
is, for these countries the rate against the euro is economically the key one even
though Americans would regard it as just a cross rate.
3.1.6 Inverting Exchange Rates in the Presence of Spreads
The next issue is how a pair of quotes for one currency can be translated into a pair
of quotes for a different currency. The rule is that the inverse of a bid quote is an
ask quote, and vice versa. To conceptualize this, consider the following illustration.
Example 3.6
An Indian investor wants to convert hercadintousdand contacts her house bank,
Standard Chartered. Being neither American nor Canadian, the bank has no nat-
ural preference for either currency and might quote the exchange rate as either
usd/cadorcad/usd. The Indian bank would make sure that its potential quotes
are perfectly compatible. If it quotes from a Canadian viewpoint, the bank gives a
cad/usdquote (which says how manycadthe investor must pay for oneusd—for
instance,cad/usd1.5). If it uses theusperspective, the bank gives ausd/cad
quote, which says how manyusdtheusinvestor gets for onecad, 0.66667.
The bank’s alternative ways of quoting will be fully compatible ifSCAD/bid,t usd =1
Sask,tusd/CAD(3.3)
SCAD/ask,t usd =1
Sbid,tusd/CAD(3.4)
To fully understand this, recall that what looks like buying (at the ask) to aus
resident looks like selling to a Canadian—at the Canadian’s bid. Alternatively,
recall that the ask is the higher of the two quotes. But if you invert two numbers,
the inverse of the larger number will, of course, be smaller than the inverse of the
smaller number. Because the inverse of a larger number is a smaller number, the
inverse ask must become the bid, and vice versa.