International Finance: Putting Theory Into Practice

100 CHAPTER 3. SPOT MARKETS FOR FOREIGN CURRENCY

jpy/usd, the way to obtain the synthetic rate is to multiply the rates, as follows:

[jpy/gbp] = [jpy/usd]×[usd/gbp] (3.5)

Note that on the right-hand side of the equation, theusdin the denominator of the
first quote cancels out with theusdin the numerator of the second quote, leaving
us with the desiredjpy/gbpnumber.

Step 2: bids or asks?The first quote is the natural quote for a Japanese agent,
the second one takes theusdas the base. Consider the synthetic ask (relevant for
buyinggbpfrom ajpyposition). Starting fromjpywe buyusd, so we need the
ask; and with theusdwe buygbp, so we again need ask. Thus,

Synthetic St,askjpy/gbp = Sjpyt,ask/usd×St,askusd/gbp (3.6)

= 101. 20 × 1 .3850 = 140. 16

By a similar argument, we can obtain the rate at which we can synthetically sell
gbpintousdand these intojpy:

Synthetic St,bidjpy/gbp = Sjpyt,bid/usd×St,bidusd/gbp (3.7)

= 101. 07 × 1 .3840 = 139. 88

This example is the first instance of the Law of the Worst Possible Combination
or the Rip-Off Rule. You already know that for any single transaction, the bank
gives you the worst rate from your point of view (this is how the bank makes money).
It follows that if you make a sequence of transactions, you will inevitably get the
worst possible cumulative outcome. This Law of the Worst Possible Combination
is the first Fundamental Law of Real-world Capital Markets. In our example, this
law works as follows:

• Note that we are computing a product. The synthetic ask rate for thegbp
  (the higher rate, the one at which you buy) turns out to be the highest possible
  product of the two exchange rates: we multiply the two high rates, ask times
  ask. Note finally that, if the purpose is to buy forex, then a high rate is also
  an unfavorable rate. In short, we buy at the worst rate, the highest possible
  combined rate.


• We see that, likewise, the synthetic bid rate for thegbp(the lower rate, the
  one at which you sell) turns out to be the lowest possible product of the two
  exchange rates: we multiply the two low rates, bid times bid. Note also that,
  if the purpose is to sell forex, then a low rate is also an unfavorable rate. In
  short, we sell at the worst rate, the lowest possible combined rate.

Let us look at another example. The data are the same except that the British
quotes now are direct not indirect.