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Quantifying
risk
Currencies




As a first layer of currency types, there are countries with their own unique
national currency. Examples include the United States as well as other Group


TLFeBOOK
186 FINANCIAL ENGINEERING, RISK MANAGEMENT, AND MARKET ENVIRONMENT



of 10 (G-10) members. The next layer of currency types would include those
countries that have adopted a G-10 currency as their own. An example of
this would be Panama, which has adopted the U.S. dollar as its national cur-
rency. As perhaps one small step from this type of arrangement, there are
other countries whose currency is linked to another at a fixed rate of
exchange. A number of countries in western Africa, for example, have cur-
rencies that trade at a fixed ratio to the euro. Indeed, where arrangements
such as these exist in the world, it is not at all uncommon for both the local
currency and “sponsor” currency to be readily accepted in local markets
since the fixed relationship is generally well known and embraced by respec-
tive economic agents.
Perhaps the next step from this type of relationship is where a currency
is informally linked not to one sponsor currency, but to a basket of sponsor
currencies. In most instances where this is practiced, the percentage weight-
ing assigned to particular currencies within the basket has a direct relation-
ship with the particular country™s trading patterns. For the country that
accounts for, say, 60 percent of the base country™s exports, the weighting of
the other country™s currency within the basket would be 60 percent. Quite
simply, the rationale for linking the weightings to trade flows is to help
ensure a stable relationship between the overall purchasing power of a base
currency relative to the primary sources of goods purchased with the base
currency. A real-world example of this type of arrangement would be
Sweden. The next step away from this type of setup is where a country has
an official and publicly announced policy of tracking a basket of currencies
but does not formally state which currencies are being tracked and/or with
what percentages. Singapore is an example of a currency-type in this par-
ticular category.
Figure 5.6 provides a conceptual ranking (from low to high) of price risk
that might be associated with various currency classifications.
One other way to think of price risk is in the context of planets and
satellites. On this basis, four candidates for planets might include the U.S.
dollar, the Japanese yen, the euro, and the United Kingdom™s pound sterling.
Orbiting around the U.S. dollar we might expect to see the Panamanian dol-
lar, the Canadian dollar, and the Mexican peso. Orbiting around the yen
we might expect to see the Hong Kong dollar, the Australian dollar, and
the New Zealand dollar. Perhaps a useful guide with respect to determin-
ing respective orbits precisely would be respective correlation coefficients.
That is, if the degree of comovement of a planet currency to a given satellite
were quite strong and positively related, then we would expect a rather close
orbit. As the correlation coefficient weakens, we would expect the distance
from the relevant planet to increase. Figure 5.7 provides a sample of this
particular concept.
Statistical consistency suggests that there is a relationship between the
strength of a correlation coefficient and the volatility of a particular currency


TLFeBOOK
187
Risk Management




A non-G-7 country with its own currency that trades with no
Brazil
formal link of any kind to a G-7 currency or any other currency


A non-G-7 country with its own currency that is exchanged
Singapore
according to non-publicly-known criteria relative to a mix of
G-7 and/or other currencies

A non-G-7 country with its own currency that is
exchanged according to publicly-known criteria relative Sweden
to a mix of G-7 and/or other currencies

Ivory Coast and
other members
A non-G-7 country with its own currency that is
of the West African
exchanged at a fixed ratio to a G-7 currency
Monetary Union

A non-G-7 country that has adopted a G-7
Panama
currency as its national currency


U.S. dollar
G-7 currency


FIGURE 5.6 Price risk by currency classification.




Panama

U.S.
dollar
Canada



Mexico



FIGURE 5.7 Price risk in the context of planets and satellites.



pairing. That is, correlation coefficients are expected to weaken as the volatil-
ity between two currencies (as measured by standard deviation) increases.
Accordingly, and in contrast with what an investor might expect to see,
Panama is shown as having a closer orbit to the U.S. dollar than Canada.
The reason for this is that there is no volatility whatsoever between Panama™s


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188 FINANCIAL ENGINEERING, RISK MANAGEMENT, AND MARKET ENVIRONMENT



currency and the U.S. dollar; in fact, the volatility is zero. Why? Because
Panama has adopted the U.S. dollar as its own national currency. However,
this is not to say that commerce with Panama is not without potential cur-
rency risk. Namely, just as Panama decided to use the U.S. dollar as its
national currency, it might decide tomorrow that it no longer wants the U.S.
dollar as its national currency. With respect to Canada, the correlation
between the U.S. dollar and Canadian dollar has historically been quite
strong.
Something that a correlation coefficient cannot convey adequately is the
degree to which a planet country (or grouping of planet countries) may or
may not be willing to help bail out a satellite country in the event of a par-
ticularly stressful episode. An example of single-planet assistance would be
the United States and Mexico in 1994“1995. An example of a collection of
planets (and satellites, for that matter) supporting another entity would be
International Monetary Fund loans to Russia and Eastern Europe in 1998.
These more obvious examples (and certainly many others could be cited)
reinforce the notion of credit risk within the global marketplace”credit risk
that is, in this particular context, at a sovereign level.
And as one other consideration here, it may not necessarily be a posi-
tive phenomenon in every instance for a satellite currency to have a close
orbit with a planet currency. Planet currencies do indeed experience their
own volatility, and a reasonable expectation would be to see volatility among
satellite currencies at least as great as that experienced by respective planet
currencies, perhaps even greater as correlation coefficients weaken. The
rationale for this expectation is simply that when times get tough and uncer-
tain, currencies with a less obvious link to tried-and-true experiences are
more likely to be hurt than helped in fast-moving uncertain markets.
As alluded to previously, currencies do not trade on a particular
exchange, but are traded as nonlisted or over-the-counter products.
Accordingly, no certificate is received, as with an equity purchase. In this
sense, there is really nothing that we can touch or feel when we own cur-
rencies, except, of course, for the currency itself. Some kind of formal receipt
or bank statement might be the closest currency investors get to their trades
in the currency market.
How do we judge what a given currency™s value should be? Again, just
as an equity™s value is expressed as being worth so many dollars (or euro or
yen etc.), a dollar™s value is expressed as being worth so many yen or euro
or whatever other currency is of interest to us. A stronger dollar simply
means that it takes fewer dollars to buy the same amount of another cur-
rency, a weaker dollar requires that more dollars must be spent to acquire
the same amount of the other currency.




TLFeBOOK
189
Risk Management




Quantifying
risk
Forwards
& futures




Recall from Chapter 2 that forwards and futures are essentially differenti-
ated from spot by cost of carry (SRT). It is not difficult to show how spot-
based risk measures such as duration and convexity can be extended from
a spot to a forward context. Here we also discuss unique considerations per-
taining to financing risk (via the R in SRT) for all products (though espe-
cially for bonds), and conclude by showing how forwards and futures can
be used to hedge spot transactions.
Calculating a forward duration or convexity is simple enough. We
already know from the duration and convexity formulas that required
inputs include price, yield, and time; these are the same for forward calcu-
lations. However, an important difference between a spot and forward dura-
tion or convexity calculation is that we are now dealing with a security that
has a forward settlement date instead of an immediate one. Accordingly,
when a forward duration or convexity is calculated, an existing spot secu-
rity™s duration and convexity are truncated by the time between the trade
date and the expiration date of the forward agreement. Figure 5.8 helps to
illustrate this point. Although the figure is for duration, the same concept
applies for convexity. Further, although the figure also describes a forward
contract, the same concept applies for futures contracts.
Notice how the potential duration profiles of the forward agreement in
Figure 5.8 are not always a horizontal line as for the duration profile at *;
they may reflect a slight slope. This slope represents the price sensitivity con-
tribution that a forward embodies relative to the underlying spot. The pre-
cise price sensitivity is linked directly to the carry component of the forward.
Recalling that the basic formula for a bond forward is F S (1 T(R Yc))
(where S for a bond is the bond™s price, and duration is a measure of a bond™s
price sensitivity), it is the carry component (the ST(R Yc) component) that
affects the price sensitivity (or duration) of a forward transaction. Note that
because R and Yc tend to be small values, carry also will tend to be a small
value. Observe also that because carry is a function of time (T), the incre-
mental duration contribution made by carry will shrink as the expiration
date of the forward approaches, and eventually disappears altogether at the




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190 FINANCIAL ENGINEERING, RISK MANAGEMENT, AND MARKET ENVIRONMENT



For reference purposes, the duration profile of the
underlying spot bond prior to expiration of the forward
agreement. The duration of the forward will be less than
this (will be below this line) and with a zero cost-of-carry
will be equal to *.
Duration
Potential duration profiles of the bond forward agreement;
Cost-of-carry™s effect on
forward duration becomes equal to the spot bond™s
duration depending on
duration at the time of the forward agreement.
a positive or negative
carry scenario.
* O
If cost-of-carry is zero,
then the duration of the
Point of convergence between spot
forward agreement is *.
and forward durations




O O O Time
Maturity date
Trade date Expiration date of
forward agreement
Duration profile of the underlying spot
bond; its duration declines as its maturity
date approaches and is zero at maturity.

Although the duration profiles are shown as
linear, in practice they may deviate from a
strictly linear profile.

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