B481/S98/NOTES/Grabbe-5 FORWARDS, SWAPS, AND INTEREST ...

B481/S98/NOTES/Grabbe-5
FORWARDS, SWAPS, AND INTEREST PARITY
This is a busy chapter. It covers the following:
Introduction to forward markets (terminology);
Interest rate parity;
Arbitrage;
Interest rate parity with bid/asked spreads;
Arbitrage and costly information;
History of forward markets
Dual interest bonds.
FORWARD RATE QUOTATIONS
If the value of a foreign currency, in terms of the domestic currency is
greater forward than spot, then the foreign currency is at a premium and
the domestic currency is at a discount, and vice versa. Note that value and
exchange rates run in opposite directions.
E.g., suppose the spot rate is DM2.4370/US$ and the 30-day forward is
DM2.4320/US$. The 30-day forward of the DM, vis-a-vis the US$, is lower.
That is, in 30 days it will take fewer DM to buy a US$. Thus, the DM will
have gone up in value, so that the DM is at a (forward) premium against the
$ and the $is at a (forward) discount against the DM.
The premium is usually quoted as a ratio a/b where a is to be added to or
subtracted from the bid rate and b is to be added to or subtracted from the
asked rate. E.g., suppose the premium for 30-day forward DM is given as
30/20, and suppose the spot rate is quoted as DM2.4273/90.
[Aside. You have now seen three ways to express bid/asked rates. Using
the foregoing numbers, the first was DM2.4273/2.4290 per US$1, the
second was DM2.4273-2.4290/US$, the third is DM2.4273/90. In the last,
the "per 1US$" is understood, and the "90" is shorthand for 2.4290. To get
2.4290, go to the right end of the quoted bid price, 2.4273, and replace the
requisite number of digits with the trailing number, 90. Thus, 2.4273
becomes 2.4290.]
1

The quoted DM2.4273/90 is equivalent to DM2.4273-2.4290/US$, and the
30/20 is simply the amounts to be subtracted from 2.4273 and 2.4290,
respectively.
Question -- How did we know to subtract See page 105 for the rule:
(form 1) spreads always get bigger
(form 2) for a/b, if a > b, then subtract; if a < b, then add.
Clearly, form 2 is the easier to remember. But it is ad hoc; so you should
understand the logic behind firm 1.
Example 5.1
Suppose the spot rate is DM2.5005/10 per US$ and the one-month forward
margins are 100/95. Find the one-month outright forward rates.
Since 100 > 95, i.e., we have the a > b case. Therefore, we subtract.
The spot bid-asked is DM2.5005 - 2.5010 and the forward margin is
100/95. Thus, the one-month forward bid/asked is DM2.4905 - 2.4915,
which would be quoted as DM2.4905/10. Note that since the forward rate
ius lower than the spot rate, the DM is at a premium against the US$.
Suppose, however, the one-month forward margins are quoted as 95/100
and the spot rates are as given above. Find the one-month outright
forward rates.
Now we have 95 < 100, i.e., we have the a < b case. Therefore, we
add. The spot bid-asked is DM2.5005 - 2.5010 and the forward margin is
95/100. Adding, we have the one-month forward bid/asked as DM2.5100 -
2.5110, which would be quoted as DM2.5100/10.
INTEREST PARITY
This section starts out in exactly the right direction. The issue is Where
do premiums and discounts come from The answer is interest rates, and
the relationship between forward rates, spot rates, and interest rates is
called interest parity. Actually, there are two such conditions, one riskfree,
called ‘covered’, and the other risky, called ‘uncovered’. The
equations are easy to derive, since they result from an arbitrage
condition.
2

First, we must consider the conventions surrounding the quoting of
interest rates. The key point is this -- eurocurrency interest rates are
stated as annual rates. For example, if the interest rate is 8% and the
deposit is for 30 days, then the 30-day hence value of a $1 deposit is
$ ( 1 + .08( 30
360 ) ) = $ 1 . 0066 6 .
1
12
Note that it is not ( 1 + .08) . The second key point is that for most
currencies there are 360 days in the year. However, for the British and
Australian dollars there are 365 days in the year. Thus, a £1 30-day
deposit at 8% has a maturity value of
£ ( 1 + .08( 30
365 )) = £ 1 . 006575.
For ease of exposition, we will assume that there is only one value for
each of the spot, forward, and interest rates.
NOTATION
S(t) = the domestic currency price of spot foreign exchange at time t
F(t, T) = the domestic currency price of forward foreign exchange at time
t for a contract that matures at time t+T.
(E.g., if the domestic currency is the US$, then the spot rate for the DM
might be S(t) = US$0.40/DM.)
i = the yearly interest rate paid on eurocurrency deposits denominated in
the domestic currency
i* = the yearly interest rate paid on eurocurrency deposits denominated in
the foreign currency
For ease of exposition, suppose the two currencies are 360 days/year
currencies.
3

COVERED INTEREST ARBITRAGE
The derivation here is slightly “reversed” from that given in the text.
Note that here we begin holding a foreign currency; in the text we begin by
borrowing US$.
Suppose we start with X units of the currency of a country C. We can
convert the C-currency into US$ at today’s spot rate S(t). This yields
S(t)X US$. These US$ can be deposited for a period of T days in a
eurocurrency account paying i. When mature, this deposit is worth
(1+i(T/360))S(t)X US$. Finally, we can convert this amount, without risk,
in currency-C at the forward rate for time t+T. Thus, leaving S(t) and
F(t+T) stated in the same terms, we have as the time t+T value, in
currency-C, as (1+i(T/360))S(t)X(1/F(t+T)). Alternatively, we could have
simply deposited the X units of C-currency at the interest rate i*. This
would yield at time t+T a value, in C-currency, of (1+i*(T/360))X. There
are no arbitrage profits if and only if these two values are equal, i.e., if
and only if
(1+i(T/360))S(t)X(1/F(t+T)) = (1+i*(T/360))X.
Eliminating X and rearranging terms, we have the famous (covered)
interest parity condition:
F ( t + T ) = S( t ) [ 1 + i ( T
)]
360
[ 1 + i ∗ ( T
)] .
360
Now note that if i > ( ( S(t), then it costs more US$
in the future to buy one unit of C-currency. Thus, if i > i*, so that F(t+T) >
S(t), then the US$ is at a discount and the C-currency is at a premium.
Similarly, if i < i*, so that F(t+T) < S(t), then the US$ is at a premium and
the C-currency is at a discount. Finally, if i* = i, so that F(t+T) = S(t),
then the US$ and the C-currency are at parity.
4

Graphically, we have the following:
C-currency
X C-currency
US$
S(t)X US$
S(t) $/C
i* i
F(t+T) $/C
indirect:
1
[1+i*(T/360)]S(t)
F ( t + T ) X
[1+i*(T/360)]S(t)X
direct:
[1+i(T/360)]X
5

Example 5.2
Suppose S(t) = US$.40000/DM and the one-year forward rate F(t,T) =
US$.40026/DM. Assume the contract will mature in T = 365 days from the
spot value date. Suppose the rates on eurodollar and euro-DM deposits are
i = 11.3% and i* = 6.0%. The example, like the text derivation of the
interest parity condition, compares domestic borrowing with covered
foreign lending. Suppose we begin by borrowing one US$. Then we must
pay back, in 365 days, $(1+i(T/360)) = $(1+0.113(365/360)) = $1.114569.
If we take the borrowed US$ and buy DM, deposit the DM and sell the total
forward, then we would receive $(1/S(t))(1+i*(T/360))F(t,T) =
$(1/.40)(1+.06(365/360))(.42026) = $1.114565. As noted, these two
values are sufficiently close that arbitrage is not likely to be possible.
Thus, the currencies are at interest parity.
INTEREST PARITY AND SWAPS
The key question here is What is the relationship between interbank swaps
and the interest parity theorem There are many answers.
First, the swap rate should be the difference F(t,T) - S(t). Rearranging the
interest parity theorem yields
F(t,T) - S(t) = S ( t ) 1 + i ( T
) 360
1 + i ∗ ( T
) − 1 = S ( t ) ( i - i * )( T
) 360
1 + i ∗ ( T
) .
360 360
Marketmaking banks use the interest parity theorem to quote forward
rates. This removes the risk of quoting swap rates that are
disadvantageous to a bank.
Note that eurocurrency interest rates are used, in lieu of other interest
rates, because the former are set in accordance with the presumptions
behind the derivation of the interest parity theorem.
Example 5.3
This example, while simple, shows the role of banks, which have access to
the interbank market, in the FX market.
6

DIVERGENCES FROM INTEREST PARITY
Like the perfect gas laws, the interest parity theorem often fails to hold.
Also like the perfect gas laws, it fails to hold because markets, etc. are
not perfect. However, the interest parity theorem is used to detect
arbitrage opportunities and to compare hedging costs.
Example 5.4 (Arbitrage Profits)
Suppose we have the following conditions:
S(t) = US$0.40/DM
F(t,T) = US$0.42/DM for T = 360 days
i = 10% (US$)
i* = 6% (DM)
Does an arbitrage opportunity exist To answer this question, we check
to see if the interest parity equation holds.
The equation is F ( t + T ) = S( t ) [ 1 + i ( T
)]
360
. The left-hand-side is , by
[ 1 + i ∗ ( T
)] 360
observation, F(t,360) = US$0.42/DM. The right-hand-side is
S ( t ) [ 1 + i ( T
)]
360
[ 1 + i ∗ ( T
360
360
[ 1 + . 10(
= ( US$ . 40/ DM) )]
360
)] = US$ . 41509 / DM.
[ 1 + . 06( 360
)] 360
The actual forward rate, US$0.42/DM, is larger than the synthetic forward
rate, US$.41509/DM, so arbitrage is possible. Note that the interbank
trader can borrow US$1 at 10%, convert the US$ to DM at DM/.40US$,
deposit the DM at 6%, and convert the resulting DM to US$ at US$.42/DM,
yielding US$1.113. The difference, US$1.113 - US$1.10 = US$0.013 is the
trader's profit (per dollar) On a deal involving $1,000,000, the profit is
$13,000.
Note that the interest parity equation tells you whether there is an
arbitrage profit to be had. The box diagram and its related calculations
tells you the size of the profit.
7

Hedging Costs
The interest parity equation can be used to determine an optimal hedging
plan. The key point is that a corporation, if it faces interest rates, does
not face the interbank eurocurrency rates. Corporations rarely engage in
currency arbitrage, but they regularly engage in hedging.
Example 5.5 (Hedging Costs)
Suppose a US corp. must pay DM2million in 6 months (180 days). The corp.
can borrow US$ at 10% or DM at 5.5%. The relevant exchange rates are S(t)
= US$.3752/DM and F(t,180) = US$.3900/DM. The corp. wishes to lock in
the US$ cost of the DM2million now. How should it do so
The possibilities are to hedge via the forward market and to use a money
market equivalent. We need simply to compare the two. Of course, they
are the two sides to the interest parity equation.
The hedge requires the corp. to buy forward DM$2million, which costs
(DM2million)(US$.3900/DM) = $780,000 to be paid in 180 days.
The money market equivalent is to acquire and deposit sufficiently many
DM to generate DM2million, at 5.5%, in 180 days. Thus, we need to find X
where [1+.055(180/360)]X = 2million. Clearly, X = DM1,946,472. To
acquire DM1,946,472 today, the corp. must borrow US$ in the amount
(DM1,946,472)(US$.3752/DM) = $730,316.30. If the corp. borrows this
amount today, it will have to pay back ($730,316.30)[1+.10(180/360)] =
$766,832.12 in 180 days.
Thus, we have two comparable numbers:
the hedge costs $780,000 to be paid in 180 days;
the money market plan costs $766,832.12 to be paid in 180 days.
Clearly, the money market plan costs less and should be adopted.
The key point is this -- the corp. faces interest rates other than the
eurocurrency rates. Therefore, the interest parity equation does not hold
for the rates faced by the corp. Hence, the equation provides a means for
determining the superior plan. Note that we have ignored, for simplicity,
both the bid/asked form of exchange rates and transactions costs.
8

INTEREST PARITY WITH BID/ASKED SPREADS
Notation:
Sb(t) = the bid spot rate at time t
Sa(t) = the asked spot rate at time t
Fb(t,T) = the bid forward rate at time t for T days hence
Fa(t,T) = the asked forward rate at time t for T days hence
ib = the bid eurocurrency interest rate on the domestic currency
ia = the asked eurocurrency interest rate on the domestic currency
ib* = the bid eurocurrency interest rate on the foreign currency
ia* = the asked eurocurrency interest rate on the foreign currency
Assume a 360 day year. If a trader engages in arbitrage, then the trader
must buy (or borrow) at the other party's asked rate, and he will sell or
lend at the bid rate. there are two approaches to arbitrage -- borrow
domestic currency and borrow foreign currency.
9

Borrow Domestic Currency
The trader can borrow 1/[1+ia(T/360)] units of domestic currency at time
t and repay 1 unit of domestic currency at time t+T. Using the domestic
currency at time t, the trader can sell the currency forward while placing
the foreign currency on deposit at ib*. The spot rate Sa(t), the forward
rate Fb(t,T) and the interest rate ib* determine the value of the hedge via
1 1
the equation
[ 1 + ib( T / 360) ] Fb( t , T ). To see this, simply
[ 1 + ia( T / 360] Sa( t )
fill-in the box diagram, as follows:
DOMESTIC CURRENCY
time t:
1
borrow
[ 1 + ia( T / 360]
FOREIGN CURRENCY
1
receive
[ 1 + ia( T / 360]
1
Sa( t )
Sa(t) $/for.
ia
ib*
Fb(t+T) $/for.
time t+T
direct:
owe 1 unit
indirect: receive [ 1 + ib∗ ( T / 360) ]
[ 1 + ia( T / 360]
Fb( t , T )
Sa( t )
receive [ 1 + ib* ( T / 360) ]
[ 1 + ia( T / 360]
1
Sa( t )
10

Clearly, arbitrage profits exist if and only if the trader receives more, at
time t+T, from the indirect route than he owes via the direct route.
Therefore, arbitrage is not profitable if and only if
[ 1 + ib ∗ ( T / 360) ] Fb( t , T )
< 1.
[ 1 + ia( T / 360] Sa( t )
Rearranging terms yields the following: no arbitrage profits exist if and
only if
[ 1 + ia( T / 360) ]
Fb( t , T ) # Sa( t )
[ 1 + ib ∗ ( T / 360) ] .
Note that this is only half of the system. The trader could have gone in
“the other direction” by borrowing foreign currency, converting to US$,
depositing the US$, and converting them back to foreign currency. This
procedure is parallel to the foregoing, and provides the other half of the
system.
11

Borrow Foreign Currency
The trader can
The trader can borrow 1/[1+ia*(T/360)] units of foreign currency at time
t and repay 1 unit of foreign currency at time t+T. Using the foreign
currency at time t, the trader can sell the currency forward while placing
the domestic currency on deposit at ib. The spot rate Sb(t), the forward
rate Fa(t,T) and the interest rate ib determine the value of the hedge via
1
the equation
Sb( t )[ 1 + ib( T / 360) ]( 1 / Fa( t , T )). To see this,
[ 1 + ia ∗ ( T / 360]
simply fill-in the box diagram, as follows:
DOMESTIC CURRENCY
FOREIGN CURRENCY
time t:
1
receive
[ 1 + ia ∗ ( T / 360] Sb(t) borrow 1
[ 1 + ia ∗ ( T / 360]
Sb(t) $/for.
ib
ia*
Fa(t+T) $/for.
time t+T
direct:
indirect: receive
[ 1 + ib( T / 360) ]
[ 1 + ia * ( T / 360]
owe 1 unit
Sb( t ) receive
[ 1 + ib( T / 360) ]
[ 1 + ia ∗ ( T / 360]
Sb( t )
Fa( t , T )
12

Clearly, arbitrage profits exist if and only if the trader receives more, at
time t+T, from the indirect than he owes via the direct route. Therefore,
arbitrage is not profitable if and only if
[ 1 + ib( T / 360) ] Sb( t )
[ 1 + ia ∗ ( T / 360] Fa( t , T ) < 1.
Rearranging terms yields the following: no arbitrage profits exist if and
only if
[ 1 + ib( T / 360) ]
Fa( t , T ) $ Sb( t )
[ 1 + ia ∗ ( T / 360) ] .
Note that a trader always has both paths available for arbitraging the
market. Therefore, there are no arbitrage profits if and only if both of the
foregoing inequalities hold simultaneously. Thus, we have the following:
no arbitrage profits exist if and only if
and
[ 1 + ia( T / 360) ]
Fb( t , T ) # Sa( t )
[ 1 + ib ∗ ( T / 360) ]
Fa( t , T ) $ Sb( t )
[ 1 + ib( T / 360) ]
[ 1 + ia ∗ ( T / 360) ] .
Example 5.6
This example puts the two halves of the system together. Suppose we
have S(t) = US$.4428-.4438/DM and F(t,30 days) = US$.4450-.4460/DM.
The rate on one-month euro-DM is 5 7
( = 5 . 875) to 6 percent, while the
rate on one-month eurodollars is 10 11
percent. Is there an arbitrage possibility
8
16
( = 10. 6875) to 10
13
16
= ( 10. 8125)
13

First, consider borrowing dollars. We have the following:
Sa = US$ .4438/DM
Fb = US$.4450/DM
ia = 10 13
= ( 10. 8125) percent
ib* = 5 7
16
8
( = 5 . 875) percent
1
If we borrow
= 1
dollars, convert them
[ 1 + ia( T / 360] [ 1 + . 108125( 30 / 360) ]
at the spot rate Sa = US$.4438/DM, place them at the interest rate ib* =
5 7
8
percent, and convert the DM back to US$ at Fb = US$.4450/DM, then we
will receive [ 1 + ib∗ ( T / 360) ]
[ 1 + ia( T / 360]
Fb( t , T )
Sa( t )
=
[ 1 + . 05875( 30 / 360) ]
[ 1 + . 108125( 30 / 360) ]
. 4450
. 4438 = $.9986.
Since this is less than the US$1 that we owe, there are no profits in
arbitrage via borrowing US$.
Now, consider borrowing foreign currency. We have the following:
Sb = US$ .4428/DM
Fa = US$.4460/DM
ib = 10 11
( = 10. 6875) percent
16
ia* = 6 percent
If we borrow
1
[ 1 + ia * ( T / 360] = 1
[ 1 + . 06( 30 / 360) ]
DM, convert them at the
spot rate Sb = US$.4428/DM, place them at the interest rate ib = 10 11
percent, and convert the US$ back to DM at Fa = US$.4460/DM, then we will
[ 1 + ib( T / 360) ] Sb( t ) [ 1 + . 106875( 30 / 360) ] . 4428
receive =
[ 1 + ia ∗ ( T / 360] Fa( t , T ) [ 1 + . 06( 30 / 360) ] . 4460 = DM.9966.
Since this is less than the DM1 that we owe, there are no arbitrage profits
in arbitrage via borrowing DM.
Therefore, there are no arbitrage profits in the setting described by the
data given here.
16
14

The no-arbitrage conditions are
[ 1 + ia( T / 360) ]
Fb( t , T ) # Sa( t )
[ 1 + ib ∗ ( T / 360) ] = Sa( t )[ 1 + ia( T / 360) ]
= Y
[ 1 + ib ∗ ( T / 360) ]
and
[ 1 + ib( T / 360) ]
Fa( t , T ) $ Sb( t )
[ 1 + ia ∗ ( T / 360) ] = Sb( t )[ 1 + ib( T / 360) ]
= X.
[ 1 + ia ∗ ( T / 360) ]
Note that Sa > Sb and ia > ib, so that [1+ia(T/360)] > [1+ib(T/360)]. Thus,
the numerator of Y is greater than the numerator of X. Furthermore, note
that ia* > ib*, so that [1+ia*(T/360)] > 1+ib*(T/360)]. Thus, the
denominator of X is greater than the denominator of Y. Therefore, Y > X.
Diagrammatically, we have the following:
Fb(t,T) < Y
Fa(t,T) > X
range of F(t,T)
0
X Y
If X < Fb(t,T) < Fa(t,T) < Y, then there are no arbitrage profits. If Fa(t,T) < X
or Fb(t,T) > Y, then arbitrage profits exits, but of only one kind. That is, if
Fa(t,T) < X, then we can make arbitrage profits by borrowing foreign
currency, and if F(t,T) > Y, then we can make arbitrage profits by
borrowing US$. But, we can not have both, since then we would have
Fa < X < Y < Fb which is inconsistent with Fb < Fa.
15

Example 5.6 displayed a case wherein no arbitrage profits were available
to an interbank trader. However, that does not mean that a corporation
would be indifferent to hedging at the rates given in Example 5.6. This
case is displayed in Example 5.7
Example 5.7.
Consider the data given in Example 5.6 and a corporation that does not
engage in arbitrage but is sufficiently large to have access to the
interbank market. Suppose the corporation is buying DM for payment 30
days hence. The corp. can go in either of two directions:
#1 -- The corp. can set aside US$, collect interest (at the US$ rate),
and sell the US$ forward for DM.
#2 -- The corp. can buy spot DM and deposit the DM at the DM
interest rate.
The data is as follows:
Sa = US$ .4438/DM
Sb = US$ .4428/DM
Fb = US$.4450/DM
Fa = US$.4460/DM
ia = 10 13
= ( 10. 8125) percent ib = 10 11
( = 10. 6875) percent
ib* = 5 7
16
8
( = 5 . 875) percent ia* = 6 percent
16
If the corp. takes path #1, then for each US$ set aside, it will receive, 30
1
days hence, DM in the amount 1 [ 1 + ib( T / 360) ]
Fa( t , T ) =
1 [ 1 + . 108675( 30 / 360) ]
1
. 4460 = DM2.2621.
16

To see this, consider the box diagram, as follows:
DOMESTIC CURRENCY
time t:
set aside US$1
FOREIGN CURRENCY
ib
Fa(t+T)
time t+T:
receive 1[ 1 + ib( T / 360) ]
= 1 [ 1 + . 106875( 30/ 360) ]
1
receive 1[ 1 + ib( T / 360) ]
Fa( t , T )
1
= 1 [ 1 + . 106875( 30/ 360) ]
. 4460
= DM2 . 2621
17

Alternatively, the corp. could take path #2, i.e., buy spot DM and deposit the DM
at the DM interest rate. Then, for each US$, it will receive, 30 days hence, DM in
1
the amount 1
Sa( t ) [ 1 + ib 1
∗ ( T / 360) ] =1 [ 1 + . 05875( 30 / 360) ] = DM2.2643.
. 4438
To see this, again consider the box diagram, as follows:
DOMESTIC CURRENCY (US$)
time t:
US$1 receive 1
Sa(t)
FOREIGN CURRENCY (DM)
1
Sa( t ) = 1 1
. 4438
ib*
time t+T:
receive 1 1
Sa( t ) [ 1 + ib∗ ( T / 360) ]
1
= 1 [ 1 + . 05875( 30/ 360) ]
. 4438
= DM2 . 2643
Thus, the second path, using the spot rate and the money market, yields more DM
then the first path, using the forward market, and therefore would be the
preferred hedge.
18

INTEREST PARITY AND THE COST OF INFORMATION
The foregoing examples make a serious point -- the forward market is not
necessarily the superior route for a hedge. Note that if the interest parity
equation holds exactly, then both the forward market hedge and the money
market hedge will yield the same result. However, if the interest parity
equation does not hold exactly, then one of these two is superior to the other.
Note Grabbe's discussion of the difference between the information effects
from a corp. that is continuously in the interbank market and one that is in the
market only occasionally. Herein lies the grounds for concluding that the money
market is not inefficient.
We will return to the issues surrounding information costs later.
FORWARD MARKETS AND INTEREST RATES: HISTORICAL BACKGROUND
This section hits four interesting points:
(1) The FX forward market starts in Vienna;
(2) The FX forward market was considered to be mysterious even after
Keynes explained its inner workings in 1922;
(3) The hedging calculations shown in the foregoing example are done
rather matter-of-factly by modern financial mangers;
(4) Most of the empirical tests of the interest parity equation are
seriously flawed.
19

FORWARD CONTRACTS AND DUAL CURRENCY BONDS
Dual currency bonds are quite simple, though they may sound complex. A dual
currency bond is a bond that is purchased in terms of one currency -- with
coupon interest paid in that currency -- but is redeemed in terms of another
currency. The text example is the dual currency bond issued in 1985 where each
bond could be purchased for its full face value of SF5,000. Interest on the bonds
is paid in SF. At maturity (in 10 years), the bond principle is repaid in the
amount of US$2,800.
The key point is this -- a dual currency bond is equivalent to a standard bond
together with a forward contract. (See, e.g., Thomas J. O'Brien, Global Financial
Management, pp. 141-143.) Thus, since forward contracts lock-in exchange
SF5 , 000
rates, the locked-in exchange rate for this bond is
US$ 2 , 800 = SF1.7857/US$.
As with all forward contracts, a dual currency bond allows the individual to
speculate against future exchange rates.
Grabbe notes that one may wish to use a dual currency bond when the market is
not quoting forward rates for a particular time. The example Grabbe uses is a
10 year forward on SF. Typically, one can not obtain forward rates for a 10 year
horizon.
20