3.3. THE LAW OF ONE PRICE FOR SPOT EXCHANGE QUOTES 95
Figure 3.10:Arbitrage and Shopping-around opportunities across market
makers
...50 ...58-
X...70 ...75-
Z...55 ...63-
X’...64 ...72-
Z’...60 ...68-
YWhat we now want to figure out is how arbitrage works when there are bid-ask
spreads. The point is that, because of arbitrage, the rates cannot be systematically
different; and if the quotes do differ temporarily, they cannot differ by too much.
3.3.1 Arbitrage across Competing Market Makers
Suppose bank X quotes youinr/nzd20.150–20.158 while bank Y quotesinr/nzd
20.160–20.168. If you see such quotes, you can make money easily: just buynzd
from bank X atinr20.158, immediately resell it to bank Y atinr20.160, and
pocket a profit worthinr0.002 for eachnzd. Note two crucial ingredients: (1) you
are not taking any risk, and (2) you are not investing any capital since the purchase
is immediately reversed and both transactions are settled on the same day. The fact
that you immediately reverse the transaction explains why this is called arbitrage.
If such quotes are found in the exchange market (or elsewhere, for that matter),
large trades by a few alert dealers would immediately force prices back into line.
The original quotes would not be equilibrium quotes. In equilibrium, the arbitrage
argument says that you cannot make money without investing capital and without
taking risk. Graphically, any empty space between the two quotes would correspond
to an arbitrage profit. Thus, the no-arbitrage condition says that any two banks’
quotes should not be separated by empty space; that is, they should overlap by at
least one point, like the quotes X’ and Y in Figure 3.10.
3.3.2 Shopping Around across Competing Market Makers
Shopping-around activity implies that small differences like those between the pair
(X’, Y) in Figure 3.10 will not persist for very long. Rather, the two quotes will
sometimes be the same, and if at other times one bank is more expensive then