178 CHAPTER 5. USING FORWARDS FOR INTERNATIONAL FINANCIAL MANAGEMENT
Figure 5.4: Synthetic and actual forward rates: some conceivable combi-
nations
109.5 109.7
case 1110.3 110.5
case 2
109.7 109.9
case 3110.1 110.3
case 4
109.75 110.15
case 5109.80Synth110.20- The usual shopping-around logic means that, in situations like Case 3 and
Case 4, there would not be customers in the direct market at one side.- If there were only one market maker, competing against the synthetic
market, Case 3 or Case 4 could occur if—and as long as—that market
maker has excess inventory (Case 3) or a shortage (Case 4). These situ-
ations should alternate with Case 5. - But the more market makers there are, the less likely it is that not a
singleone of them would be interested in buying.^3 Likewise, with many
market makers, situations where none of them wants to sell become very
improbable. Thus, Cases 3 or 4 should be rare and short-lived, unless
there are very few market makers.
- If there were only one market maker, competing against the synthetic
- With many market makers, then, Case 5 should be the typical situation: the
direct markets dominates the synthetic one at both sides.
5.2.3 Back to the Second Law
How wide is the zone of admissible prices? The example has a spread of 0.4 percent
between the two Worst Combinations, but that cannot be realistic at all possible
maturitiesT−t. Let us first trace the ingredients behind the computations of the
synthetic rates in [5.2] and [5.4]. The spot bid-ask spread is, in the example, 0.02 Pe-
sos wide, which is about 0.02 percent. In the (1+r)∗part of the formula, multiplying
by 1.211 instead of 1.209 makes a difference of +0.17 percent (1.211/1.209=1.0017),
(^3) In Case 3, for instance, 109.7 is by definition the best bid; all other market makers must have
been quoting even lower if 109.7 is the best bid.