International Finance: Putting Theory Into Practice

3.3. THE LAW OF ONE PRICE FOR SPOT EXCHANGE QUOTES 97

Figure 3.11:Triangular arbitrage and triangular shopping around

P. Sercu and R. Uppal The International Finance Workbook page 1. 14

3. 3 Triangular Arbitrage and the LOP

3. Law of One Price

• Relationships between spot rates quoted in various currencies—e.g. GBP/USD,
  EUR/USD, EUR/USD.
  Triangular arbitrage: Triangular shopping-around:
  Do I make money doing this:? which of the two gives me the best price?

USD

JPY

GBP

USD

JPY

GBP

USD

JPY

GBP

is out > in? go direct or indirect?

The forces that support these linkages are again arbitrage and shopping around. For

our purposes, we can ignore the many market makers: when we talk about bid and

ask, we now mean themarket quote, that is, the best bid across all market makers,

and the best ask. The new issue is how these market quotes in various currencies

are linked.

• Someone engaging in triangulararbitragetries to make money by sequentially
  buying and selling various currencies, ending with the original currency. For
  instance, you could convertaudintousd, and then immediately convert the
  usdintogbpand thegbpback intoaud, with the hope of ending up with
  moreaudthan you started out with. The no-arbitrage condition says that
  you should not make a profit from such activities. Actually, when there are
  transactions costs or commissions, you are likely to end up with a loss. The
  potential loss is due to commissions, notably the bid-ask spread. Thus, in
  this context, arbitrage implies that the set of exchange rates quoted against
  various base currencies should be such that you cannot make any risk-free
  instantaneous profits after paying transactions costs.


• Shopping aroundis the search for the best way to achieve a desired conversion.
  For instance, an Australian investor who wants to buygbpmay buy directly, or
  may first convertaudintousdand then convert theseusdintogbp. Shopping
  around implies that the directaud/gbpmarket can survive only if its quotes
  are no worse than the implied rates from the indirect transaction.

In the case of perfect markets, the regular arbitrage and shopping-around arguments

lead to the same conclusion. We illustrate this in the following example.

Example 3.12

Suppose onegbpbuysusd1.5, while oneusdbuysaud1.6; therefore, if we directly