5.5. USING FORWARD CONTRACTS (4): MINIMIZING THE IMPACT OF MARKET
IMPERFECTIONS 195
rescaling the whole operation, in rule-of-three style:
- time-tinputjpy 1 produces time-T output ofusd 0 .0010189905;
- time-tinputjpy 0. 00101899051 produces time-T output ofusd1;
- time-tinputjpy 0. 0010189905785 ,^235 produces time-T output ofusd 785 , 235.
⇒(short version: ) jpyt=785 , 235
0. 010189905
= 77, 060 , 090. (5.8)
This seems easy enough. What can (and often does) go wrong is that you mix
up computational in- and outputs with financial in- and outputs. In computations
or math, the term input refers to the data, and the term output to the result of the
exercise. Financially, however, we defined input as what you feed into the financial
system and output as what you get out of it. Sometimes the mathematical and the
financial definitions coincide, but not always. In application 3, we exchange spot
Yen for future Dollars, so the financial input isjpytand the outputusdT. But for
the computations, the data isusdT= 785.235 and the result isjpyt= 776, 841 .15.
If you’re hasty, you risk thinking that the trip you need to make is from data (the
mathematical input, future dollar) to result (the mathematical output, spot yen),
while the actual money flow is in the other direction. Because of the mistake, you
go through the graph the wrong way, using borrowing not lending rates of return
and bid exchange rates instead of ask. In short, it is tempting to work back from the
end point (usdT) to the starting point: how muchHCtis needed for this? If you are
really good, you will remember that going from financial output to financial input
means going “against” the arrows, and chosing on the basis of a “Less Is Better”
rule (less input for a given output is better). But if you are new to this, it may be
safer to start by provisionally settingHCt= 1, then identify the route that delivers
most output (FCT), and finally rescale the winning trip such that the end output
reaches the desired level.
A second comment is that, in the second and fourth problem, the direct deposits
yield more than the synthetic ones. This is what one would expect, at least if the
rates are close to interbank rates. But if the problem is retail, a smallfcdeposit
may earn substantially less than the wholesale rate (which starts atusd 1m or
thereabouts), and under these circumstances the direct solution may be dominated
by the indirect alternative.
Example 5.19
Suppose that theHG&CCholds a lot ofjpyso that it gets interbank rates for these;
but itsusddeposits are small. If the rate she gets onusdwere less than 3.58 %
p.a., Ms Takeshita would be better off moving herusdinto thejpymarket for six
months.
On the basis of the above, one would expect that, in the wholesale market,
swapping of deposits or loans should be very rare: a three-transaction trip should
not be cheaper than the direct solution. But this conjecture looks at bid-ask costs
only. In practice we see that swaps are often used, despite their relatively high