Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
Indirect Hedging With Currency Futures
Eric Terry*
We examine the problem of hedging a foreign exchange exposure using a futures contract
on the value of the local currency in terms of the foreign currency. A general formula for
the minimum-variance indirect currency futures hedge ratio is derived and special cases
of this formula are obtained for commonly-made assumptions about the joint spot and
futures price process. The performance of the indirect hedge is found not to depend
heavily on the assumed joint spot and futures price process. Furthermore, it is found that
the indirect currency futures hedge is as effective at reducing foreign exchange risk as a
corresponding direct hedge.
JEL Codes: F31, G19
1. Introduction
Global trade has meant increased foreign exchange risk for many firms. Although currency futures
are a useful financial instrument for managing foreign exchange exposures, they are not as
commonly used as many other financial products. In a survey of financial officers at large U.S.
corporations by Jesswein, Kwok, and Folks (1995), OTC forwards, options, swaps, and cylinder
options were used more frequently to manage currency risk than were futures.
One limitation of exchange-traded currency futures is that the contract required to hedge a particular
currency exposure directly is often not available. Consider the case of a European firm facing a $1.5
million exposure to the U.S. dollar. A direct hedge of this foreign exchange exposure would require a
futures contract on the value of the U.S. dollar relative to the Euro. Such a contact does not currently
exist. However, futures contracts do trade on the indirect exchange rate: the U.S. dollar value of the
Euro. These Euro futures contracts could be used by the European firm to manage its U.S. dollar
exposure. Computing the minimum-variance futures hedge is straightforward in the absence of basis
risk. If the futures price was $1.50, the firm would simply go long contracts on one million Euros. The
minimum-variance futures hedge in the presence of basis risk, however, is not immediately obvious.
This is because the statistical properties of this basis risk will be altered when it is translated from
U.S. dollars into Euros. As a consequence, the appropriate hedge for the European firm cannot be
determined by making a simple adjustment to extant direct hedging formulas.
The above example is far from unique. Futures contracts on both the direct and indirect exchange
rate exist for only three major currency pairs: the U.S. dollar against the Canadian dollar, the
Japanese yen and the Swiss franc.1 As a consequence, the situation will frequently arise in which a
firm that wants to hedge a given foreign exchange exposure using currency futures must indirectly
hedge using a futures on the value of its own currency relative to the other currency. Although the
translation of basis risk causes indirect hedging formulas to differ significantly from corresponding
direct hedging formulas, the efficiency of indirect hedging and direct hedging is expected to be
similar. The rationale is that the same underlying basis risk is present regardless of currency
translation.
In this paper, we investigate the indirect currency futures hedging problem. A general formula for the
____________________________________________________________________________
* Ted Rogers School of Management, Ryerson University, Canada. Email: eterry@ryerson.ca
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Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
indirect currency futures hedge ratio is derived and compared to the corresponding formula for direct
currency hedging. Special cases of this formula are obtained for commonly-made assumptions about
the joint spot and futures price process. Then, the efficiency of the indirect currency futures hedge is
examined for six hedging scenarios.
2. Literature Review
A number of papers have examined the issue of a firm being unable to directly hedge a foreign
exchange exposure. Usually, it is presumed that the firm will seek to cross-hedge the exposure using
forward or futures contracts on a related currency. Examples of this literature include Adam-Muller
and Nolte (2011), Broll (1997), Chang and Wong (2003), Eaker and Grant (1987), and Wong (2013).
Surprisingly little attention has been paid to the possibility of indirect currency futures hedging. Other
than a few papers on the more general issue of hedging using a futures contract that is denominated
in a foreign currency, the literature appears silent on this topic. The issue of hedging with foreigndenominated futures contracts was first raised by Thompson and Bond (1985). Thompson and Bond
(1987) derive the optimal commodity futures hedge under the implicit assumption that the foreigndenominated commodity futures contract requires a 100% cash margin to be maintained at all times
and that the hedger does not take any position in currency futures. Nayak and Turvey (2000) examine
the case of a foreign hedger simultaneously seeking to manage crop price risk, crop yield risk and
currency risk. To operationalize their model, they make the stringent assumption that changes in the
levels of the exchange rate (both spot and futures) and of the commodity price (both the local spot
price and the translated futures price) have fixed first and second moments. Haigh and Holt (2002)
and Wang and Low (2003) also examine the issue of hedging using foreign-denominated futures, but
simplify their analyses by assuming that the hedger seeks to maximize utility in the foreign currency
rather than in their own one. As a consequence, the hedging strategies in these two papers involve
direct currency hedging rather than indirect currency hedging.
3. The Model and Empirical Methodology
A. The Model
Consider a foreign company that will receive a fixed payment in the domestic currency at time t+1.
There is no traded futures contract on the domestic currency that is denominated in the currency of
the foreign firm. However, a futures contract denominated in the domestic currency does exist on the
foreign currency and the firm would like to hedge its currency exposure at time t using this futures
contract. Let xt and ft represent the spot and futures value of the foreign currency. The return on the
firm's hedged portfolio in their foreign currency is given by
f
 1
1  ht  ft 1  ft 
 

xt 1 xt 
xt 1
x

f
Rt 1 
 t 1  ht f  ft 1  ft    1,
1
xt 1
xt
where ht f represents the futures position long per unit of currency risk.
We assume that the firm seeks to minimize the conditional variance at time t of this return, which is
the most commonly assumed objective within the futures hedging literature. The conditional variance
at time t of the firm's hedged return is
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Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5

 1 
 ft 1  ft 
 1 ft 1  ft
f 2
f
Vart  Rt f1  = xt2  Vart 
,
   ht  Vart 
  2ht Covt 
xt 1
 xt 1 
 xt 1 
 xt 1

The first-order condition for a minimum is

f f 
 1 ft 1  ft  
0 = 2 xt2  ht f Vart  t 1 t  +Covt 
,
 ,
xt 1  
 xt 1 
 xt 1


 .

which implies that the minimum-variance indirect currency hedge ratio is:
 1 ft 1  ft 
Covt 
,

xt 1
xt 1 

f
ht = 
.
(1)
 ft 1  ft 
Vart 

 xt 1 
Comparing this formula with the minimum-variance hedge ratio for a domestic firm hedging the
foreign currency,2
Covt ( xt 1 , ft 1  ft )
htd = 
,
Vart ( ft 1  ft )
we see that indirect currency hedge ratio is a simple transformation of the standard hedge ratio: (i)
xt+1 is inverted to get the value of the foreign currency per unit of local currency, 1/xt+1, and (ii) the
futures price change, ft+1 - ft, is translated into the local currency, (ft+1 – ft)/ xt+1. Because (ft+1 – ft)/ xt+1
≠ ft+1/ xt+1 – ft/ xt in general, the indirect hedge ratio cannot be calculated using futures prices that
have first been converted into the local currency and then differenced.
To implement this formula, an assumption must be made about the joint spot and futures price
process.
i. The Indirect Unitary Hedge
Suppose that spot and futures prices will converge at the end of the period, i.e., futures traders face
no end-of-period basis risk. Under this condition, a domestic hedger would go short one futures
contract for each unit of exposure to the foreign currency. This strategy is known as the unitary
hedge. We will refer to the corresponding position for the foreign hedger as the indirect unitary hedge
ratio.
Substituting ft 1 = xt 1 into equation (2), the indirect hedge ratio becomes
 1
 1 
f 
Covt 
,1  t 
ft Vart 

xt 1 
 xt 1
 xt 1  ,
ht f = 
=

 1 
f 
Vart 1  t 
ft 2 Vart 

 xt 1 
 xt 1 
which reduces to
ht f =
1
.
ft
(2)
Whereas the unitary hedge ratio is fixed at -1, the indirect unitary hedge ratio involves going long by
the reciprocal of the futures price per unit of risk exposure and will vary through time as the futures
price changes.
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Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
ii. The Indirect Conventional Hedge
Suppose instead that changes in the indirect spot price, x’t = 1/xt, and in the foreign-translated futures
price, f’t = ft/xt, have fixed first and second moments. Substituting x = 1/ x and f  = f / x into equation
(1), the indirect hedge ratio can be rewritten as
Covt  xt1 , ft1  ft  xt1 
ht f = 
.
Vart  ft1  ft xt1 
Expanding the covariance and variance terms,
ft Vart  xt1   Covt  xt1 , ft1 
ht f =
.
Vart  ft1   2 ft Covt  xt1 , ft1   ft 2 Vart  xt1 
(3)
Because the cost-of-carry model implies that the foreign-translated currency futures price must
always be close to one, the covariance term in this formula will tend to be close to zero in value. This
implies that the indirect currency hedge ratio itself will be positive; i.e., the firm indirectly hedges using
a long currency futures position.
Hedge ratio (3) will be referred to as the indirect conventional currency futures hedge ratio. It should
be noted that this case is not strictly comparable to the conventional hedge for a domestic hedger.
First, the moments assumed to be fixed under the conventional hedge, the covariance between spot
and futures price changes and the variance of futures price changes, are not the same as are
assumed to be fixed here. This is unavoidable, as the first and second moments for a specified
exchange rate (or futures price) bear no necessary relationship to the moments for the corresponding
indirect exchange rate (or foreign-translated futures price). Second, the indirect conventional hedge
ratio is a non-linear function of the futures price and so cannot be estimated from a simple linear
regression.
iii. The Indirect Lognormal, Cointegrated and Cointegrated-GARCH Hedges
Finally, suppose that conditional spot and futures changes follow a bivariate lognormal distribution.
Mathematically, this can be written as
ln  xt 1 / xt  = s ,t 1   s ,t 1
ln  ft 1 / ft  =  f ,t 1   f ,t 1
where the unexpected log returns are given by
  x ,t 1 
 t 1 = 
  N  0, H t 1 
 f ,t 1 
and the conditional variance-covariance matrix has elements
 hxx ,t 1 hxf ,t 1 
H t 1 = 
.
 hxf ,t 1 h ff ,t 1 
Although it is commonly asserted that the minimum-variance hedge ratio for a domestic hedger under
this condition is htd = hxf ,t 1 / h ff ,t 1 , Terry (2005) has shown that correct direct hedge ratio is
htd =
xt exp   x ,t 1  hxx ,t 1 / 2  exp  hxf ,t 1   1


.
ft exp   f ,t 1  h ff ,t 1 / 2  exp  h ff ,t 1   1
The corresponding hedge position for the foreign hedger is found as follows. Under the assumption
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Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
that xt 1 and ft 1 have a bivariate lognormal conditional distribution at time t ,
 1 ft 1  ft 
Covt 
,

xt 1 
 xt 1
 exp   
ft exp    x ,t 1   x ,t 1  exp   f ,t 1   f ,t 1   1 
x ,t 1   x ,t 1 

= Covt 
,


xt
xt


f
= 2t Et exp   f ,t 1  2 x ,t 1   x ,t 1  2 x ,t 1   exp  2 x ,t 1  2 x ,t 1  
xt


 Et exp   f ,t 1   x ,t 1   f ,t 1   x ,t 1   exp    x ,t 1   x ,t 1   Et exp    x ,t 1   x ,t 1   .
Taking expectations and then simplifying, we find that
 1 ft 1  ft 
Covt 
,

x
xt 1 
 t 1
=
ft
xt2

h ff ,t 1


 2hxx ,t 1  2hxf ,t 1   exp  2  x ,t 1  2hxx ,t 1 
exp   f ,t 1  2  x ,t 1 
2




h
h
h
h





 
 exp   f ,t 1   x ,t 1  ff ,t 1  xx ,t 1  hxf ,t 1   exp    x ,t 1  xx ,t 1   exp    x ,t 1  xx ,t 1  
2
2
2 
2 





=
ft exp  2  x ,t 1  hxx ,t 1 
where
xt2
 ab  c  ,
a = exp  hxx ,t 1  hxf ,t 1   1,
b = exp   f ,t 1  h ff ,t 1 / 2  hxf ,t 1  , and
c = exp  hxx ,t 1   1.
Following the same steps, it can be shown that
ft 2 exp  2 x ,t 1  hxx ,t 1 
db 2  2ab  c  ,
Vart  ft 1  ft xt 1  =
2
xt
where a , b , and c are as given above and
d = exp  hxx,t 1  h ff ,t 1  2hxf ,t 1   1.
Substituting these results into indirect hedge ratio (1), we find that
1
ab  c

ht f =  2
,
ft  db  2ab  c 
where
a = exp  hxx ,t 1  hxf ,t 1   1,
(4)
b = exp   f ,t 1  h ff ,t 1 / 2  hxf ,t 1  ,
c = exp  hxx ,t 1   1, and
d = exp  hxx ,t 1  h ff ,t 1  2hxf ,t 1   1.
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Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
Three alternative assumptions are commonly made regarding the above return moments. First,
assume that the first and second moments of the log returns are time invariant. This implies that
coefficients a-d are fixed and thus that the minimum-variance indirect hedge ratio is a linear function
of the reciprocal of the futures price. This will be referred to as the indirect lognormal currency futures
hedge.
Second, if domestic and foreign interest rates are stationary, the cost-of-carry model implies that the
spot and futures exchange rates will be cointegrated (Kroner and Sultan 1993). The precise form of
the cointegrating vector is
zt = ln( ft )  ln( xt )  c(T  t ),
where T is the futures maturity date and c is the net cost-of-carry per period, which equals the
foreign and domestic interest rate differential (Low, Muthuswamy, Sakar, and Terry, 2002). By
Granger's Representation Theorem (Engle and Granger, 1987), conditional mean spot and futures
returns can be written in error-correction form as
 x,t 1 =  x   x zt   x  xt  xt 1    x  ft  ft 1 
(5)
 f ,t 1 =  f   f zt   f  xt  xt 1    f  ft  ft 1  .
This specification includes only one set of lagged terms; most studies have found that one lag is
optimal. Indirect hedging formula (4) with fixed second moments and conditional means specified by
error-correction model (5) will be referred to as the indirect cointegrated currency futures hedge.
Finally, as with many financial time series, spot and futures currency rates display periods of
persistently high or low volatility that can be succinctly modeled using a bivariate GARCH(1,1) model.
The most common representation is the BEKK model (Engle and Kroner 1995), in which the
conditional volatility evolves according to
(6)
Ht 1 = CC  A t 1 t 1'A  BHt B,
where A and B are 2×2 parameter matrices and C is a 2×2 lower triangular parameter matrix. Indirect
hedging formula (4) with conditional means given by error-correction model (5) and conditional
second moments described by GARCH process (6) will be referred to as the indirect CI-GARCH
currency futures hedge.
B. Empirical Methodology
The effectiveness of the indirect currency futures hedge was examined using futures and spot prices
obtained from the Commodity Research Bureau. Six scenarios were considered: hedging a U.S.
dollar exposure by a foreign firm whose home currency is either the Canadian dollar (CAD),
Japanese yen (JPY), or Swiss franc (CHF) and hedging either a Canadian dollar, Japanese yen, or
Swiss franc exposure, The other by an American firm.
Futures prices for the U.S. dollar against the CAD, CHF, and JPY are settlement prices from the U.S.
futures section of the Intercontinental Exchange and futures prices for the CAD, CHF, and JPY are
settlement prices from the IMM section of the Chicago Mercantile Exchange. The nearest available
futures contract was used in all hedges.3 The sample period begins on the first date on which both
the IMM and the ICE futures contracts traded - December 9, 1994 for the CHF and JPY and
December 3, 1997 for the CAD - and ends on August 31, 2006. This allows the relative effectiveness
of direct and indirect currency futures hedging to be directly compared for these three currencies.
The first two years of data were used to estimate the parameters in the hedging models; these
parameters were then used to compute hedge ratios and hedging returns over the subsequent four
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Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
weeks. Although the parameters in the hedging formulas were not changed over this four week
period, the hedge ratios themselves were updated daily (or weekly). The two-year estimation window
was then advanced by four weeks, the parameters in the hedging models were re-estimated, and
hedge ratios and hedging returns were computed for the next four weeks. This procedure was
repeated until the end of the sample period was reached. Other estimation windows and updating
frequencies were also examined. The results were not qualitatively different from those presented
here. Hedging effectiveness was measured by the percentage reduction in return variance that was
achieved under each hedge vs. an unhedged currency position. This methodology provides a realistic
snapshot of the hedging performance that could be expected in practice by a currency hedger.
Hedging performance was examined using both daily and weekly returns.
The superior predictive ability (SPA) test of Hansen (2005) was used to compare the effectiveness of
alternative hedging strategies. The SPA test requires the a priori specification of a benchmark, with
the null hypothesis being that none of the other hedging strategies provides variance reduction that is
superior to this benchmark strategy. Let di   b2   i2 represent the difference in residual variance
between the benchmark hedging strategy and alternative hedging strategy i, i = 1,…,n. Then, the SPA
test statistic is given by
d
tSPA  max i .
i
wˆ ii
The estimated standard deviations ŵi,i and distribution of the test statistic under the null hypothesis
were determined using the stationary bootstrap of Politis and Romano (1994). The indirect unitary
hedge (and the unitary hedge for the case of direct hedging) was used as the benchmark hedging
strategy.
4. Empirical Findings
The relative performance of the alternative indirect currency futures hedging strategies is presented in
Table 1. For daily returns, none of the indirect hedging strategies consistently outperformed the
others. The best indirect futures hedge for an American firm facing a CAD exposure was the indirect
lognormal hedge, with an average hedging effectiveness of 92.70%. When facing a JPY exposure,
the indirect cointegrated hedge, which reduced the daily return variance by 95.48%, provided the best
hedge for the American firm. Finally, for an American firm facing a CHF exposure, the indirect CIGARCH hedge provided the best hedge (89.00% effectiveness). For a U.S. dollar exposure, the
indirect unitary hedge was best for a Swiss firm (95.07%). For a Canadian firm facing a U.S. dollar
exposure, the conventional and lognormal hedges provided the best indirect hedge, with a hedging
effectiveness of 93.81%. Finally, the lognormal and cointegrated hedges performed best in the case
of a Japanese firm with a U.S. dollar exposure, providing an average hedging effectiveness of
96.49%.
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Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
Indirect hedging
strategy
A) Using daily returns
Unitary
Conventional
Lognormal
Cointegrated
CI-GARCH
tSPA(unitary hedge)
B) Weekly returns
Unitary
Conventional
Lognormal
Cointegrated
CI-GARCH
tSPA(unitary hedge)
Table 1
Effectiveness of Indirect Currency Hedging
CAD/
CHF/
JPY/
USD/
USD/
USD
USD
USD
CAD
CHF
USD/
JPY
92.48
92.68
92.70
92.59
92.33
3.73***
87.78
88.07
88.01
87.89
89.00
2.11*
95.39
95.45
95.45
95.48
94.86
2.95***
93.64
93.81
93.81
93.74
93.09
3.77***
95.07
94.80
94.88
94.97
94.68
-1.68
96.43
96.47
96.49
96.49
96.28
2.57**
98.32
98.30
98.31
98.31
98.22
-0.40
97.46
97.44
97.44
97.45
97.43
-0.86
98.92
98.87
98.86
98.91
98.58
-1.28
98.37
98.37
98.37
98.37
98.30
0.11
99.07
98.99
99.02
98.99
98.97
-2.14
99.20
99.11
99.13
99.14
98.94
-1.14
*=10%, **=5%, and ***=1% significance levels.
In five of the six scenarios, the SPA test rejected the null hypothesis that the indirect unitary hedge
performed as well as any of the other indirect hedging strategies at the 10% significance level.
Interestingly, the indirect CI-GARCH hedge provided the worst average hedging performance in five
of the six hedging scenarios. This is surprising considering the popularity within the futures hedging
literature of the assumption that spot and futures returns are cointegrated with GARCH residuals.
However, differences in effectiveness across the five alternative indirect hedges were generally small
in magnitude.
To reduce the chance of spurious results due to ``noise'' in market prices from market microstructure
effects such as non-synchronous trading, the analysis was also done using weekly data instead of
daily data. Friday closing prices (or Thursday prices in cases where either no spot or futures price
was available on Friday) were used. The reported effectiveness of the indirect hedge is significantly
higher for weekly returns than for daily returns, which is consistent with the assumption that weekly
returns are less noisy than daily returns. The indirect unitary hedge performed as well or better than
the other indirect hedging strategies in all six scenarios. The indirect CI-GARCH hedge performed
worst in all six scenarios. Otherwise, observed differences in effectiveness across the indirect hedges
were generally small in size.
In summary, the performance of the indirect hedge does not appear to depend heavily on the choice
of indirect hedging model, though the indirect unitary hedge appears to be the best choice for
currency hedges that are adjusted weekly (or less frequently).
To evaluate the effectiveness of direct vs. indirect futures hedging, the performance of the
corresponding direct currency futures hedging strategies were computed for each of the six scenarios
was computed. The results are given in Table 2.
8
Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
Direct hedging
strategy
A) Using daily returns
Unitary
Conventional
Lognormal
Cointegrated
CI-GARCH e
tSPA(unitary hedge)
tSPA(indirect hedge)
B) Weekly returns
Unitary
Conventional
Lognormal
Cointegrated
CI-GARCH
tSPA(unitary hedge)
tSPA(indirect hedge)
Table 2
Effectiveness of Direct Currency Hedging
CAD/
CHF/
JPY/
USD/
USD/
USD
USD
USD
CAD
CHF
USD/
JPY
93.50
93.66
93.65
93.59
93.17
3.63***
3.05***
92.12
92.36
92.42
92.36
92.07
1.33
1.62*
95.95
95.99
96.00
96.00
95.76
1.42
2.96***
92.64
92.87
92.87
92.76
92.43
4.00***
-2.11
90.68
90.70
90.67
90.65
90.41
0.24
-1.57
95.79
95.88
95.86
95.86
95.03
3.30***
-2.52
98.37
98.36
98.37
98.37
98.26
-0.14
0.83
97.53
97.47
97.45
97.44
97.43
-1.73
0.34
99.03
98.95
98.94
98.97
98.19
-1.06
0.87
98.32
98.31
98.32
98.31
98.21
0.45
-0.81
98.85
98.83
98.81
98.85
98.79
-0.19
-1.22
99.03
99.01
98.99
99.02
98.75
-1.68
-1.12
*=10%, **=5%, and ***=1% significance levels.
For daily returns, the conventional hedge was the best direct hedge. It was most effective in four of
the six scenarios and was second-best in the other two. In three of the six direct hedging scenarios,
the SPA test rejected the null hypothesis that the unitary hedge performed as well as any of the other
direct hedges (including the conventional hedge). A significantly different picture emerged for weekly
returns. The unitary hedge performed as well or better than the other direct hedges in all six
scenarios. As was true for indirect hedging, the reported effectiveness of the direct hedges was
significantly higher for weekly returns than for daily returns.
Comparing direct and indirect hedges for an American firm, the most effective direct currency hedge
(using the CME contract) performed better than the corresponding indirect currency futures hedge
(using the ICE contract) facing an exposure to any of the three currencies when using daily returns.
This difference in hedging effectiveness was relatively modest in the case of CAD and JPY exposures
but significant for a CHF exposure. In all three cases, the SPA test rejected the null hypothesis that
the indirect unitary hedge performed as well as any of the direct hedges. For a foreign firm facing a
U.S. dollar exposure, however, the best performing direct currency hedge (using the ICE contract)
was consistently less effective than the corresponding indirect currency futures hedge (using the
CME contract). The improvement in average effectiveness of the indirect currency futures hedge over
the direct hedge was relatively minor for Canadian and Japanese hedgers but was significant for
Swiss hedgers. Consistent with these results, the SPA test could not reject the null hypothesis that
the indirect unitary hedge performed as well as any of the direct hedges in any of the three cases.
The results were similar for weekly returns. As before, the direct hedge performs better than the
indirect currency futures hedge for the three cases of an American firm hedging a foreign currency
exposure, while the indirect hedge outperforms the direct hedge for the three cases of a foreign firm
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Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
hedging a U.S. dollar exposure. In all six cases, the difference in hedging effectiveness between the
direct and indirect currency futures hedges is minor and the SPA test could not reject the null
hypothesis that the indirect unitary hedge performed as well as any of the direct hedges. This
confirms our hypothesis that indirect currency hedging can achieve hedging performance that is
comparable to direct hedging.
It is instructive to note that the model that provided the best direct hedge for a particular currency
futures contract did not always provide the best indirect currency futures hedge. For daily returns, the
CI-GARCH hedge was the worst performing direct hedge (for the US/SF exchange rate) using the
US/SF futures contract but the same model and futures contract provided the best indirect currency
futures hedge (for the CHF/USD exchange rate).
5. Conclusions
In this paper, we examined the problem of hedging a foreign currency exposure using a futures
contract on the value of the local currency in terms of the foreign currency. A general formula for the
indirect currency futures hedge ratio was derived and compared to corresponding formula for direct
currency hedging. Special cases of this formula were obtained for commonly-made assumptions
about the joint spot and futures price process.
The efficiency of the indirect currency futures hedging was examined for six scenarios. It was found
that a direct currency hedge performed slightly better than an indirect currency futures hedge for
cases of an American firm hedging a foreign currency exposure, while the indirect currency futures
hedge outperformed the direct hedge for cases of a foreign firm hedging a U.S. dollar exposure. The
performance of the indirect hedge did not appear to depend heavily on the choice of indirect hedging
model, though an indirect unitary hedge appear to perform best for currency hedges that are adjusted
weekly or less frequently.
This paper opens a new line of research on currency futures hedging. Further work could be done to
determine whether other models of the joint spot and futures price process can produce more
effective indirect currency futures hedges. The effectiveness of the indirect currency futures hedge
could also be examined for other currencies. Additionally, the optimal multi-period indirect currency
futures hedge could be derived and empirically tested. Finally, the model could be extended to the
case of hedging using foreign-denominated futures, such as a Canadian oil producer hedging the
value of its crude oil using light sweet crude oil futures, which are denominated in U.S. dollars,
combined with Canadian dollar futures.
End Notes
1. Futures contracts are also available on both the direct and indirect exchange rate for the U.S.
dollar vs. the Swedish krona.
2. The conventional hedge for a domestic hedger was derived by Johnson (1960) and Ederington
(1979).
3. Alternative choices for the futures maturity used to hedge (e.g., rolling over to the next contract
one week before maturity) produced similar results.
10
Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
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