I I P a b a A R R A A K C F H I I C 1 i d c a n s F e t i t b M e a e 2 F h 1 The Quarterly Review of Economics and Finance 54 (2014) 459–472 Contents lists available at ScienceDirect The Quarterly Review of Economics and Finance j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / q r e f nflation and interest rate derivatives for FX risk management: mplications for exporting firms under real wealth hilipp Koziol a,b,∗ Chair of Finance, University of Goettingen, Platz der Goettinger Sieben, 37073 Goettingen, Germany Deutsche Bundesbank, Wilhelm-Epstein-Strasse 14, 60431 Frankfurt am Main, Germany r t i c l e i n f o rticle history: eceived 15 October 2013 eceived in revised form 27 March 2014 ccepted 11 April 2014 vailable online 2 May 2014 a b s t r a c t Firms that export goods face risks such as product price, cost, and exchange rate risks. Price and cost risks can substantially reduce the FX hedging performance in real wealth. We thus investigate hedging strategies that are intended to improve the performance of the FX hedge in real terms using inflation and interest rate derivatives. The impact of these additional instruments is not clear and has only been briefly analyzed in the hedging literature so far. For this purpose, we derive variance-minimizing hedge positions of an exporting firm. A cointegrated VAR and bootstrap methods are used to evaluate the effi- eywords: orporate risk management X risk edging nflation derivatives nterest rate derivatives ciencies of several hedging strategies. While inflation derivatives work better in the short run, interest rate derivatives perform better over longer hedge horizons. © 2014 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved. c t d s a i A p i d ( e t T p b ointegrated VAR . Introduction Consider, as a starting point, an international firm whose profit s exposed only to nominal exchange rate risk. If there is a forward erivative market for this nominal exchange rate risk, a full hedge an eliminate the FX risk completely, so that the firm no longer faces ny risk (e.g., Broll & Wong, 2002). Unfortunately, this scenario is ot realistic. In addition to exchange rate risk, firms usually bear pecific revenue risks such as uncertain demand and price risks. urther risk factors have to be considered when analyzing a firm’s xchange rate risk. On the one hand, a typical exporting firm is exposed to addi- ional product price risk in foreign currency and uncertain costs in ts home currency (e.g., Korn & Koziol, 2011). On the other hand, as he domestic price level is, in reality, not stable, firms are affected y inflation risk when concentrating on real profits (e.g., Adam- ueller, 2000, 2002; Briys & Solnik, 1992). Combining these two ffects, the nom ...

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The Quarterly Review of Economics and Finance 54 (2014)
459–472
Contents lists available at ScienceDirect
The Quarterly Review of Economics and Finance
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c
a t e / q r e f
nflation and interest rate derivatives for FX risk
management:
mplications for exporting firms under real wealth
hilipp Koziol a,b,∗
Chair of Finance, University of Goettingen, Platz der Goettinger
Sieben, 37073 Goettingen, Germany
Deutsche Bundesbank, Wilhelm-Epstein-Strasse 14, 60431

3. Frankfurt am Main, Germany
r t i c l e i n f o
rticle history:
eceived 15 October 2013
eceived in revised form 27 March 2014
ccepted 11 April 2014
vailable online 2 May 2014
a b s t r a c t
Firms that export goods face risks such as product price,
cost, and exchange rate risks. Price and cost
risks can substantially reduce the FX hedging performance
in real wealth. We thus investigate hedging
strategies that are intended to improve the performance of
the FX hedge in real terms using inflation
and interest rate derivatives. The impact of these additional
instruments is not clear and has only been
briefly analyzed in the hedging literature so far. For this
purpose, we derive variance-minimizing hedge
positions of an exporting firm. A cointegrated VAR and
bootstrap methods are used to evaluate the effi-
eywords:
orporate risk management
X risk
edging
nflation derivatives
nterest rate derivatives
ciencies of several hedging strategies. While inflation
derivatives work better in the short run, interest
rate derivatives perform better over longer hedge horizons.

4. © 2014 The Board of Trustees of the University of
Illinois. Published by Elsevier B.V. All rights reserved.
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ointegrated VAR
. Introduction
Consider, as a starting point, an international firm whose profit
s exposed only to nominal exchange rate risk. If there is a
forward
erivative market for this nominal exchange rate risk, a full
hedge
an eliminate the FX risk completely, so that the firm no longer
faces
ny risk (e.g., Broll & Wong, 2002). Unfortunately, this scenario
is
ot realistic. In addition to exchange rate risk, firms usually bear
pecific revenue risks such as uncertain demand and price risks.
urther risk factors have to be considered when analyzing a
firm’s

5. xchange rate risk.
On the one hand, a typical exporting firm is exposed to addi-
ional product price risk in foreign currency and uncertain costs
in
ts home currency (e.g., Korn & Koziol, 2011). On the other
hand, as
he domestic price level is, in reality, not stable, firms are
affected
y inflation risk when concentrating on real profits (e.g., Adam-
ueller, 2000, 2002; Briys & Solnik, 1992). Combining these two
ffects, the nominal FX forward intended to lower FX risk
exhibits
dditive and multiplicative basis risks, which lower the hedge
fficiency of the FX hedge (e.g., Adam-Mueller, 2000; Korn &
Koziol,
011).
∗ correspondence to: Deutsche Bundesbank, Wilhelm-Epstein-
Strasse 14, 60431
rankfurt am Main, Germany. Tel.: +49 69 9566 3343.
E-mail address: [email protected]
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ttp://dx.doi.org/10.1016/j.qref.2014.04.004

6. 062-9769/© 2014 The Board of Trustees of the University of
Illinois. Published by Elsevi
In this study, we investigate how additional hedge instruments
an improve the performance of an FX hedge in real terms. In
his way, the basis risks are reduced significantly, but the impact
epends crucially on whether the appropriate instruments are
cho-
en. Since the basis risks arise from the price risk in the
revenues
nd costs as well as from considerations of real wealth, they
orig-
nate from price changes in the domestic and foreign country.
lthough, from the theoretical perspective of purchasing power
arity (PPP), an FX hedge is not necessary as there would be no
risks
n real terms, it is known from many empirical investigations
that
eviations from the PPP are substantial even over short horizons
e.g., Abuaf & Jorion, 1990; Mishkin, 1984). An FX hedge
alone, how-
ver, does not eliminate all real FX risks either, because it is
known
hat there are also deviations from relative PPP (e.g., Officer,
1982;
aylor, 2002). Thus, additional hedge instruments are necessary
to
otentially improve a firm’s hedging performance. However,
their
ehavior is not clear at first sight.
Derivatives based on price indices seem to be appropriate for
educing the evolving basis risks. The underlying of these
contracts
orrelates strongly with the corresponding risk factors. As firms
re exposed to several risks, the corresponding risk factors inter-

7. ct to some extent and, therefore, the impact of possible inflation
erivatives in certain hedging strategies remains unclear, which
mphasizes the need for the investigation in our study. The
impor-
ance of the inflation derivative market becomes apparent when
ooking at the growing market size. Inflation derivatives
increased
er B.V. All rights reserved.
dx.doi.org/10.1016/j.qref.2014.04.004
http://www.sciencedirect.com/science/journal/10629769
http://www.elsevier.com/locate/qref
http://crossmark.crossref.org/dialog/?doi=10.1016/j.qref.2014.0
4.004&domain=pdf
mailto:[email protected]
dx.doi.org/10.1016/j.qref.2014.04.004
4 conom
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60 P. Koziol / The Quarterly Review of E
iquidity as they raised market breadth, integration with nominal

11. arkets and flexibility (Canty & Heider, 2012, p. 107). The inter-
ealer trading volume of inflation derivatives was estimated at
round $60 billion in 2012 (Deutsche Bank, 2012; JP Morgan,
2013).
urthermore, the inflation derivative market in the euro area and
n the United States (US) has been growing significantly during
he last few years (Canty & Heider, 2012, p. 276ff). The usage
of
nflation derivatives to transfer inflation risk has been
established
onsiderably in the last few years, which supports the application
f inflation derivatives as a reasonable hedge instrument in our
tudy.
Interest rate derivatives are also appropriate hedge instruments.
f course, the relationship with the basis risks is not that strong,
but
here are several reasons for using interest rate derivatives to
hedge
he inflation-induced basis risks. First, the Fisher effect
describes
he relationship between nominal interest rates and inflation
rates
Fisher, 1930), which exists for short-term as well as long-term
nterest rates (e.g., Ang, Bekaert, & Wei, 2008; Berument,
Ceylan,
Olgun, 2007; Lee, Clark, & Ahn, 1998). In general, the
empirical
tudies of Fama (1977) and Soederlind (1998) indicate that inter-
st rates are good predictors of inflation rates. Second, real
interest
ate parity (RIP) describes a relationship between interest rates
nd inflation, extending the Fisher effect to a multi-country case

12. nd stating that the real interest rates (i.e. the difference between
he nominal interest rate and inflation) should be equal across
ountries.1 Third, Soederlind (1997), Soederlind and Svensson
1997), and Svensson (1993) suggest that forward interest rates
ould serve as an indicator of the future path of inflation.
Soederlind
nd Svensson (1997) show that the forward rate theoretically
con-
ists of expected future inflation, expected real interest rates, the
nflation risk premium and forward-term risk premia. Since the
orward rate rule assumes that real interest rates are constant and
hat both inflation-risk and forward-term risk premia are negli-
ible, the relationship between the forward interest rate and the
xpected inflation rate is dominant in this case. Not only is there
theoretical relationship between interest rates and inflation, the
nterest rate derivative market is also a very large and liquid
one.
his market grew rapidly in the last decade. The total OTC trad-
ng volume in interest rate derivatives averaged at $2.3 trillion
per
ay in April 2013, which is 39% more than in 2007 and
emphasizes
he importance of this market segment. The market for interest
ate derivatives in Germany and in the US thus reached a consid-
rable market size. More precisely, Germany and the US are the
ourth and second largest markets in this field with market
shares
f 3.7% ($101 billion) and 22.8% ($623 billion), respectively
(Bank
or International Settlements, 2013; Gyntelberg & Upper, 2013).
This paper aims to investigate how a firm facing product
rice, cost, and exchange rate risks can substantially enhance its
xchange rate risk management. The analysis is based on a model
of

13. n exporting firm, which is used to derive the variance-
minimizing
edge position in currency forward contracts and additional
hedge
nstruments. The purpose of this study is to empirically analyze
he influence of different sorts of underlyings on hedging perfor-
ance with respect to the time horizon. We obtain an insight on
ow and to what extent those new hedge instruments which are
ased on either inflation or interest rates are useful. To this end,
e conduct an empirical study to quantify the hedge ratios and
edge efficiencies of the different hedging strategies for a
German
rm that exports to the US. This study estimates a cointegrated
1 While the majority of earlier studies on RIP find that it is
rejected for most
ountry pairings (e.g., Hallwood & MacDonald, 1999), more
recent papers using
ore appropriate econometric methods, such as those of
Berument et al. (2007)
nd Wu and Fountas (2000), support RIP.
(
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14. ics and Finance 54 (2014) 459–472
ector autoregressive (VAR) model. On the basis of simulated
sam-
le paths from this model, which are generated by a bootstrap
lgorithm, hedge efficiencies are quantified for several hedging
trategies.
This analysis shows that the impact of the additional instru-
ents on the FX hedge depends crucially on the hedge horizon.
For
horter hedge horizons, inflation derivatives are very useful, but
for
onger hedge horizons interest rate derivatives perform best.
This
s because, due to the integration properties of the prices, the
infla-
ion derivatives contain additional unhedgable risks which
increase
xponentially with the hedge horizon, which means that the FX
edging strategy cannot benefit from their use in the case of
longer
edge horizons.
The study is organized as follows: the related literature is
eviewed in Section 2. Section 3 starts with the setup of the basis
odel of an exporting firm that hedges with different forward
ontracts. Section 4 provides a brief description of the dataset
nd the study design, followed by an introduction of the empiri-
al model. Then, in Section 5 the performance of various hedging
trategies containing inflation and interest rate derivatives is pre-
ented. Based on this, Section 6 compares the results with the
xisting literature and discusses their implications for risk man-
gement practice. Finally, Section 7 draws conclusions on the

15. main
esults.
. Related literature
More than 40 years after the breakdown of the Bretton Woods
ystem of fixed exchange rates, the literature on FX risk man-
gement is abundant and closely related to the evolution and
evelopment of research on financial derivatives. However, only
few papers provide concrete, theory-based guidance for corpo-
ate risk management. In this area, the literature differs in terms
of
i) the hedging decision criterion, (ii) the considered types of
risk,
iii) the hedge instruments, (iv) the hedge horizon, and (v) static
or
ynamic strategies.
The decision criterion for hedging (i) is often determined by
he variance minimization approach and certain utility functions
r alternative approaches such as value-at-risk, cash flow-at-risk,
nd earnings-at-risk. A number of authors analyze the firm’s
hed-
ing strategies as a maximization problem of the expected utility
f profits according to a concave utility function (e.g.,
Battermann,
raulke, Broll, & Schimmelpfennig, 2000; Benninga, Eldor, &
Zilcha,
984; Feder, Just, & Schmitz, 1980; Holthausen, 1979). The vari-
nce minimization approach is applied, for instance, by Castelino
2000), Eaker and Grant (1987), Giaccotto, Hedge, and
McDermott
2001), and Veld-Merkoulova and de Roon (2003). Chen, Lee,
and
hrestha (2003) provide a general overview of hedging crite-

16. ia.
One form of considered risks (ii) are basis risks. Briys, Crouhy,
nd Schlesinger (1993) provide qualitative results for different
pecifications for additive basis risk, whereas Adam-Mueller and
olte (2011) obtain results for independent multiplicative basis
isk. The analysis of additional inflation risk for one country is
xtensively conducted in Adam-Mueller (2000), Adam-Mueller
2002), Battermann and Broll (2001), and Briys and Solnik
(1992).
urther imperfections in hedge instruments such as default risk
e.g., Cummins & Mahul, 2008) and liquidity risk (e.g., Adam-
ueller & Panaretou, 2009) as well as the impact of asymmetric
nformation (e.g., Zhao, 2004) are also discussed in this
literature.
The application of different hedge instruments (iii) such as for-
ard contracts, futures, swaps (linear derivatives), and options
nonlinear derivatives) is investigated by Adam-Mueller (2000),
attermann et al. (2000), Brown (2001), Brown and Toft (2002),
and
conom
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20. t
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a
which the variable rh,T denotes the current T-period interest
rates
with a low risk premium in the home country and rf,T the
interest
rates for the foreign country.2 This means that the forward
contract
P. Koziol / The Quarterly Review of E
astelino (2000). Gay, Nam, and Turac (2002) and Gay, Nam,
and
urac (2003) answer the question of how firms should choose the
ptimal mix of linear and nonlinear derivative instruments in the
resence of both quantity and price risk. In addition, Huang,
Ryan,
nd Wiggins (2007) investigate why firms use nonlinear deriva-
ives. In contrast, Dionne and Ouederni (2011) examine the
effect
f corporate risk management using linear derivatives and
Frestad
2009) carves out the reasons why firms favor linear hedging
strate-
ies. Moreover, Battermann et al. (2000) show theoretically that
risk averse exporting firm which maximizes its expected util-
ty prefers futures to options. They thus show that even in the
resence of a biased futures market the hedge effectiveness of
dversely biased futures is greater than that of fair priced options
ince income remains stochastic when using options as a hedge
nstrument.

21. Korn and Koziol (2011) investigate the behavior of FX hedge
atios for different hedge horizons (iv) and Adam, Fernando, and
alas (2008) show the impact of the hedge horizon for a sample
f gold mining firms. Juhl, Kawaller, and Koch (2012) conduct
an
mpirical investigation by applying a case study that analyzes
opti-
al hedge size and hedge effectiveness for a firm using gasoline
utures to hedge delivery of gasoline at six locations. In an error
orrection model the authors find that the hedge ratios vary with
espect to the hedge horizon and that the cointegration proper-
ies of the underlying time series play a crucial role for the
optimal
edging strategy. Castelino (1989) and Castelino (1990) provide
an
xplanation for the relationship of the hedge horizon and basis
risk
ithin variance-minimum hedges.
The majority of papers concentrate on static hedging strate-
ies (v), as is the case in most of the studies above. However,
ynamic hedging strategies are also applied in the literature (e.g.,
riys & Solnik, 1992; Fehle & Tsyplakov, 2005; Kroner &
Sultan,
993; Veld-Merkoulova & de Roon, 2003). Fehle and Tsyplakov
2005), Ho (1984), Leland (1998), and Stulz (1984) use dynamic
odels for corporate risk management in a continuous-time
frame-
ork. Fehle and Tsyplakov (2005), for instance, show that firms
can
ynamically adjust their usage of hedge instruments. Moreover,
eld-Merkoulova and de Roon (2003) present a dynamic model
ith a two-contract hedging strategy. Different model-based

22. trategies for hedging long-term price exposures with short-term
utures contracts are analyzed, for instance, by Brennan and
Crew
1997), Buehler, Korn, and Schoebel (2004), and Neuberger
(1999).
However, the literature primarily focusses on theoretical ana-
yzes of hedging approaches rather than the empirical
investigation
f specific hedging strategies. While hedging criteria (i), hedge
nstruments (iii) and the type of hedging strategy (v) have been
xtensively discussed in the literature, the fields of the
considered
ypes of risk (ii) and the hedge horizon (iv) have not been inves-
igated in detail. Our paper extends the literature by providing
broad empirical analysis of the hedging performance of vari-
us strategies and provides an insight on why and how additional
edge instruments can enhance FX risk management for different
edge horizons if the firm is exposed to risks beyond FX risk.
The
ontribution does not consist in providing a theoretical
framework
o determine the hedge positions using multiple instruments, as
as first shown in Anderson and Danthine (1981).
. Model
.1. Setup
The analysis follows the framework developed by Korn and
oziol (2011). We construct a model for a firm exporting a sin-
le good which is sold on the foreign market at the end of the T
ics and Finance 54 (2014) 459–472 461
eriod at time T. The initial point is in period zero. It is assumed

23. hat the quantity of the output per period Q is already defined
y the firm and is thus non-stochastic. Since the firm produces at
ome and sells on the foreign market, the product prices P̃T are
enominated in foreign currency and the corresponding exchange
ates X̃ T are denominated in units of the home currency per unit
f foreign currency, while the production costs C̃T are measured
n the firm’s home currency. All three variables are exogenous
and
tochastic. The uncertainty in foreign revenues and domestic
costs
s partly determined by industry- and firm-specific components
nd modeled by the uncertain rate of price changes in the foreign
f) and the home (h) country until T, �̃f,T and �̃h,T . More
explicitly,
he future product price P̃T is dependent on the current product
rice P0 and the random percentage price change in the foreign
ountry until T, �̃f,T , and can be expressed by P̃T = P0Ẽf,T at
which
˜f,T = (1 + �̃f,T ), i.e. Ẽf,T can be interpreted as the growth
rate of the
roduct price. Since the production quantity Q is assumed to be
onstant, the percentage change in revenues in foreign currency
s equal to the percentage price change. Moreover, the produc-
ion costs until T, C̃T , are a function of the current production
osts C0 and the uncertain percentage price change in the home
ountry until T, �̃h,T , which is determined by C̃T = C0Ẽh,T
where
˜h,T = (1 + �̃h,T ). Furthermore, the changes in sales prices and
rev-
nues, respectively, can be interpreted as the changes in the
foreign
ountry’s price level whereas the changes in production costs are
etermined by the changes in the home country’s price level.
This

24. mplies that revenues and costs move according to the (produc-
ion) price level by the factor Ẽf,T and Ẽh,T . The general price
level
s used as a benchmark for the analysis of hedging strategies in
pecific situations, since it gives information about an “average”
rm behavior. The uncertain future exchange rates X̃ T are deter-
ined by the function X̃ T = X0(Ẽh,T /Ẽf,T )ŨT , where X0 is the
current
xchange rate and the fraction of Ẽh,T to Ẽf,T determines the
level of
he relative price changes of the domestic country. The part of
the
elative exchange rate changes that is not determined by relative
rice changes is covered by the random variable ũT . This
variable
mplies the deviations from the PPP for the time horizon T and,
ence, the uncertain future exchange rates growth is written as
actor ŨT = (1 + ũT ). For instance, if ŨT ≡ 1 the relative PPP
would
old since the exchange rate would exactly adjust in the sense
that
here is no change in the relative prices between the two
countries.
ince the future exchange rate is a function of random variables
nd the distribution of ŨT is not further specified, no restrictions
re made on the distribution of the future exchange rates.
Merging
hese components, the nominal operative profit of the exporting
rm ˜̆ T without any hedging strategy can be defined as:
˜
T = P̃T Q X̃ T − C̃T = P0 Q X0Ẽh,T ŨT − C0Ẽh,T (1)

25. q. (1) shows that the nominal profit of the exporting firm is
inde-
endent of the foreign price risk Ẽf,T as this term is canceled
out. In
rder to consider the hedging of exchange rate risk, it is assumed
hat the firm can enter into foreign exchange forwards with
matu-
ity T at time zero. Let HFX
T
denote the number of units of foreign
urrency sold for delivery at time T and F FX0,T the
corresponding
orward price. Due to the covered interest rate parity relationship
nder standard assumptions, no-arbitrage prices of currency for-
ard contracts are defined by F FX0,T = X0(Rh,T /Rf,T ). The
factors Rh,T
nd Rf,T are thus determined by Rh,T = (1 + rh,T) and Rf,T = (1
+ rf,T), at
2 Note that the interest rates rh/f,t are Svensson interest rates
(Svensson, 1993).
hey are only used for the calculation of the FX forward prices.
Furthermore, they
4 conom
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27. F
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62 P. Koziol / The Quarterly Review of E
ealizes a cash flow of X̃ T − F FX0,T only at T. Since it is
assumed that the
orward price is “fair” at initiation, the forward contract is

29. value-
ess and contains no default risk. The following total nominal
profit
f the considered firm, including only the FX hedging strategy, is
eceived as:
˜ FX
T = ˜̆ T + HFXT
(
F FX0,T − X0
Ẽh,T
Ẽf,T
ŨT
)
(2)
q. (2) serves as a foundation for extending the approach
proposed
y Korn and Koziol (2011) of adding inflation or interest rate
for-
ards to the hedging strategy. To do so, forward contracts are
ssumed to be quoted in the home currency, so that no additional
xchange rate risk is added by using these contracts. In the
follow-
ng the derivation of the model is exhibited by applying inflation
orwards. The usage of interest rate forwards is technically
equiv-
lent and only the resulting equations are shown in the paper.
The
otal nominal profit, including the considered inflation rate
hedge

30. nstruments, becomes:
˜ �̃
T = P0 Q X0Ẽh,T ŨT − C0Ẽh,T + HFXT
(
F FX0,T − X0
Ẽh,T
Ẽf,T
ŨT
)
+ H�̃,h
T
(
F �̃,h0,T − Ẽh,T
)
+ H�̃,f
T
(
F
�̃,f
0,T − Ẽf,T
)
(3)
here HFX/�̃,h/�̃,f

31. T
is the number of FX and inflation forwards sold
n each case and F FX/�̃,h/�̃,f0,T are the respective forward
prices. Those
ill be described in Subsection 3.2 and different hedging
strategies
re considered in Subsection 3.3.
As investors are ultimately interested in consumption, Eq. (4)
akes this into account and provides the real profit, i.e. the
firm’s
rofit in its home currency, measured in prices at time zero. The
otal real profit ˜̆ �̃
real,T
of the considered firm is equal to Eq. (3)
ivided by Ẽh,T and can therefore be expressed as:
˜ �̃
real,T
= P0 Q X0 ŨT − C0 + HFXT
(
F FX0,T
1
Ẽh,T
− X0
ŨT
Ẽf,T

32. )
+ H�̃,h
T
(
F �̃,h0,T
1
Ẽh,T
− 1
)
+ H�̃,f
T
(
F
�̃,f
0,T
1
Ẽh,T
−
Ẽf,T
Ẽh,T
)
(4)
t turns out that the inflation forward on the home prices only
rep-

33. esents a contract with additive basis risk in real terms, since the
nderlying has been canceled out. When using inflation forwards,
ajor improvements in the hedging strategy are expected due to
heir very strong correlation with the basis risks.
Moreover, interest rate forwards are applied to improve the
X hedge. The underlying interest rates with maturity T in the
ome or foreign market are denoted as ĩh/f,T . Ĩh/f,T = (1 +
ĩh/f,T )
etermines the interest rate factor. Eq. (5) shows the real profit
of
he considered firm, including all considered interest rate
hedging
ransactions:
˜ ĩ
real,T
= P0QX0ŨT − C0 + HFXT
(
F FX0,T
1
Ẽh,T
− X0
ŨT
Ẽf,T
)
+ Hĩ,h
T
(

34. F ĩ,h0,T
1
Ẽh,T
− Ĩh,T
Ẽh,T
)
+ Hĩ,f
T
(
F
ĩ,f
0,T
1
Ẽh,T
−
Ĩf,T
Ẽh,T
)
(5)
re different from the interest rates ih/f,t , which are the
underlyings of the interest
ate forwards and are specified in the cointegrated VAR model.
t
i

35. w
a
t
0
p
ics and Finance 54 (2014) 459–472
qs. (4) and (5) illustrate that the risk of the FX forward depends
n the random variable ŨT and the development of the price lev-
ls Ẽh,T and Ẽf,T whereas the original risk of the considered
firm
epends only on the random variable ŨT . The second line of Eq.
(5)
hows that the FX forward exhibits both additive and
multiplicative
asis risks. The additive basis risk is caused by the domestic
price
evel (Ẽh,T )
−1
and the multiplicative basis risk by the foreign price
evel (Ẽf,T )
−1
. Furthermore, the correlation of these two factors also
mpacts on the total basis risk of the FX hedge. Thus, inflation
as
ell as interest rate forwards are included in the hedging strategy
o increase hedge efficiency on the basis of the correlation struc-
ure of all risk factors. As the basis risks are created by both the
omestic and the foreign price levels, instruments capturing both
isks have to be applied.

36. .2. Hedge instruments
In this subsection we specify the properties of the applied hedge
nstruments. For the purposes of our study, we need derivative
ontracts whose payoff is highly correlated with the additive and
ultiplicative basis risks of the FX forwards. As they are caused
by
rice changes, derivatives based on inflation rates are
appropriate.
ccording to the earlier discussions, synthetic inflation forwards
re examined where the profit is proportional to the difference
etween the underlying price index at contract maturity and the
ontract price index level entered into at contract inception. This
ype of contract draws on the Euro Inflation Futures traded on
UREX, which have the same properties as the Euribor futures. It
is
ssumed that the contracts are quoted in Euros and that the
under-
ying of the contracts is either the price change Ẽh,T or Ẽf,T .
The
orward price at time 0 to hedge inflation risks until time T in
the
ome or foreign country, respectively, equals the expected value
f the respective inflation rate in period T with the assumption of
nbiased forward markets. The maturities of the inflation
forwards
t the hedge horizons exactly.
In addition to the inflation forwards, a synthetic interest rate
orward is applied for our study where the profits are propor-
ional to the difference between the underlying interest rate
t contract maturity and the contract rate entered into at con-
ract inception. This sort of contract is based on properties that
re typical, for example, of Eurodollar or Euribor futures (e.g.,
ernoth & von Hagen, 2004; Hull, 2006). For instruments like

37. hese, large trading volumes are observed even for contract
matu-
ities of up to ten years (Bank for International Settlements,
013; Gyntelberg & Upper, 2013). Since the OTC market for
inter-
st rate forwards is very large and liquid, we also apply these
orwards.
The simplifying assumption is made that forward markets
f interest rates are unbiased, i.e. the forward price equals the
xpected future interest rate, which is a common assumption
ccording to the expectations hypothesis (e.g., Cox, Ingersoll,
onathan, & Ross, 1981, 1985). Whether unbiasedness holds or
ot is an empirical question. Recent studies on the interest rate
arket show that the hypothesis is not easy to reject statistically
e.g., Bulkley, Harris, & Nawosah, 2011; Jitmaneeroj & Wood,
2013;
udebusch & Wu, 2007). This seems to be a reasonable assump-
ion as the underlying firm in the considered model has no
special
nformation on interest rate and inflation movements compared
ith other market participants. In the context of the model, unbi-
sedness in the interest rate market means that the forward price
of
he interest rate in the home country and foreign country in
period
is equal to the expected value of the respective interest rate in
eriod T.

38. conom
s
t
3
o
a
f
T
S
m
c
1
t
i
r
e
t
a
t
p
w
h
u
r
˘
w
T
H

39. A
o
o
T
v
o
p
t
m
a
p
o
(
f
p
n
e
t
p
p
⎛
⎝
b
f
H
p
p
a
t
t

40. r
H
H
c
c
i
s
a
p
i
h
p
ward strategy is used in all cases and is the baseline strategy in
our
analysis. Additionally, the baseline FX strategy is
complemented by
combinations of all other hedge instruments. The hedging
strate-
gies are composed with respect to the region of the underlyings
Table 1
Overview of hedging strategies.
Abbreviation Forwards
HRFXT HR
�̃, h
T
HR
�̃, f
T

41. HRĩ,h
T
HR
ĩ,f
T
Only FX X 0 0 0 0
P. Koziol / The Quarterly Review of E
This specification of the applied hedge instruments guarantees
ymmetry between the two types of hedge instruments regarding
he chosen maturity matched hedging strategies.
.3. Hedging Strategies
Before starting with the empirical analysis, we discuss the
ptimal hedging strategy in our theoretical model and provide
n overview of the applied hedging strategies. The number of
orward positions is determined by the firm’s hedging problem.
hese hedging decisions are discussed in detail in the literature.
everal authors analyze the firm’s hedging strategies as a maxi-
ization problem of the expected utility of profits according to a
oncave utility function (e.g., Benninga et al., 1984; Feder et al.,
980; Holthausen, 1979). The profit Eqs.(4) and (5) show
similarity
o a hedging problem with various hedge instruments contain-
ng additive and multiplicative basis risks. By implementing
some
estrictions on the decision criterion, the difficulty of obtaining
gen-
ral results in these cases is reduced to some extent.3 Because of
its
ractability and popularity in practice, the variance minimization
pproach is applied in this study as the hedging objective func-

42. ion. The minimum-variance hedge has no effect on the expected
rofit; it only serves to reduce risk. Any assumptions on the for-
ard prices of the hedge instruments do not influence the optimal
edging strategy.
To formulate the firm’s decision problem, the case of Eq. (4)
sing inflation forwards is considered and real profits including
the
epresentations of the inflation forward prices are rewritten as:
˜ �̃
real,T
= ÃT + HFXT B̃ T + H
�̃,h
T
C̃T + H�̃,fT D̃ T (6)
ith
ÃT ≡ P0 Q X0ŨT − C0,
B̃ T ≡ F FX0,T
1
Ẽh,T
− X0
ŨT
Ẽf,T
,
C̃T ≡ F �̃,h0,T
1

43. Ẽh,T
− 1,
D̃ T ≡ F �̃,f0,T
1
Ẽh,T
−
Ẽf,T
Ẽh,T
he firm’s decision problem then becomes:
min
FX
T
,H
�̃, h
T
,H
�̃, f
T
Var
[
˜̆ �̃
real,T
]
for each hedge horizon T (7)
ccording to the setting, variance minimization is a standard

44. ptimization problem that leads to the necessary conditions for
ptimal forward positions given in the normal Eqs. (8) below.
hese conditions are also sufficient for a unique minimum if the
ariance–covariance matrix of B̃ T , C̃T , D̃ T has full rank, i.e., if
none
f the forward contracts is a redundant hedge instrument:
Cov[ÃT , B̃ T ] + HFXT Var[B̃ T ] + H
�̃, h
T
Cov[B̃ T , C̃T ] + H�̃, fT Cov[B̃ T , D̃ T ]
!=0
Cov[ÃT , C̃T ] + H�̃, hT Var[C̃T ] + HFXT Cov[C̃T , B̃ T ] + H
�̃, f
T
Cov[C̃T , D̃ T ]
!=0
Cov[ÃT , D̃ T ] + H�̃, fT Var[D̃ T ] + HFXT Cov[D̃ T , B̃ T ] + H
�̃, h
T
Cov[D̃ T , C̃T ]
!=0
(8)

45. Solution
s to the system of linear Eq. (8) can easily be com-
uted numerically if the necessary variances and covariances are
3 See Briys et al. (1993) for qualitative results for different
specifications of addi-
ive basis risk and Adam-Mueller and Nolte (2011) for results of
independent
ultiplicative basis risk.
T
c
ics and Finance 54 (2014) 459–472 463
vailable. As seen from the optimality conditions, the hedge
ositions depend on all covariances between the profits from
perations (ÃT ) and the payoffs of different forward contracts
B̃ T , C̃T , D̃ T ). Moreover, all covariances between the payoffs
of dif-
erent forward contracts enter into the calculation of the forward
ositions. Note, however, that these optimal forward positions do

46. ot depend on the initial cost C0, but do depend on the initial
xchange rate X0. The cost C0 is an additive non-random term in
he profit function, which does not influence the variance of
total
rofits. Solving for the HTs yields the following optimal forward
ositions:
HFX∗
T
H�̃, h∗
T
H
�̃, f ∗
T
⎞
⎠ =
⎛
⎜⎝
Var[B̃ T ] Cov[B̃ T , C̃T ] Cov[B̃ T , D̃ T ]

47. Cov[C̃T , B̃ T ] Var[C̃T ] Cov[C̃T , D̃ T ]
Cov[D̃ T , B̃ T ] Cov[D̃ T , C̃T ] Var[D̃ T ]
⎞
⎟⎠
−1
·
⎛
⎜⎝
Cov[B̃ T , ÃT ]
Cov[C̃T , ÃT ]
Cov[D̃ T , ÃT ]
⎞
⎟⎠
(9)
Since the optimal hedge positions depend on all covariances

48. etween the profits from operations and the payoffs of different
orward contracts, it is difficult to obtain an insight into the
optimal
∗
T
s (e.g., Timm, 2002, p. 188f). Hedge ratios are used for better
com-
arison and easier interpretation. While absolute values of
forward
ositions depend on variables such as price and quantity, which
re not our main interest, hedge ratios are normalized quantities
hat make comparisons easier. These hedge ratios are defined as
he ratios of the optimal forward positions H∗
T
and the expected
evenues at time T in foreign currency:
R∗ T =
⎛
⎜⎜⎝

49. HRFX∗ T
HR�̃, h∗
T
HR
�̃, f ∗
T
⎞
��� = 1P0 Q E(1 + �̃f,T )
⎛
⎜⎜⎝
HFX∗
T
H�̃, h∗
T
H
�̃, f ∗
T

50. ⎞
⎟⎟⎠ (10)
R∗ T reflects the optimal hedge ratio regarding inflation
forwards. In
ase of additional interest rate forwards, a firm’s decision
problem
an be formulated by rewriting Eq. (5) using the home and
foreign
nterest rate forwards. Then the real profits including the repre-
entations of the interest rate forward prices can be expressed in
n equivalent way to how it is done in Eq. (10). The
mathematical
rocedure to calculate the hedge ratios is equivalent to the case
of
nflation forwards.
In order to identify the optimal hedge design over different
edge horizons, several hedging strategies are considered. Table
1
rovides an overview of all analyzed hedging strategies. The FX
for-
Home PPI X X 0 0 0
For PPI X 0 X 0 0

51. All PPI X X X 0 0
Home IR X 0 0 X 0
For IR X 0 0 0 X
All IR X 0 0 X X
his table describes different forward combinations. X indicates
the usage of the
orresponding hedge instrument, 0 implies no usage.
4 conom
f
t
i
a
h
o
r
w
o

52. 4
4
g
i
i
b
c
a
i
o
e
j
i
i
E
w
l
a
i
h
d
t

53. h
r
o
r
t
t
t
t
i
a
t
S
o
t
t
t
i
2
y
a
m
a
P

54. S
i
a
o
a
v
t
c
l
r
t
u
b
I
w
r
o
c
c
p
U

55. e
p
e
I
a
a
t
i
a
g
t
o
r
a
l
A
4
m
�
e
m

56. s
t
{
T
pendent cointegration equations. Therefore, the long-run matrix
̆ is defined as ̆ = ˛ˇ′ . The matrix consists of the two p × r coef-
ficient matrices ̨ and ˇ, which both have full column rank and
r ≤ p. The first difference �Yt is stationary, since Yt is assumed
to
64 P. Koziol / The Quarterly Review of E
or inflation and interest rate forwards. For each hedge horizon
hey exhibit the same structure but the value of the correspond-
ng hedge ratios changes accordingly. This set of hedging
strategies
llows us to thoroughly investigate the impact of the considered
edge instruments both individually and simultaneously.
The purpose of this study is to empirically analyze the influence
f different sorts of underlyings on the hedging performance with
espect to the time horizon. We obtain an intuition on how and
to
hat extent new hedge instruments, which either base on inflation

57. r interest rates, are useful.
. Empirical study
.1. Study design and dataset
In the empirical study, optimal hedge ratios for different hed-
ing strategies, i.e. different combinations of available hedge
nstruments, are estimated. To obtain data to estimate the
theoret-
cal moments derived in Eq. (10), a cointegrated VAR model and
a
ootstrap algorithm are applied (e.g., Lien, 2004). In the second
step
onducted in Section 5, the performances of all hedging
strategies
s well as the relative improvement of the hedging performances
n comparison to the baseline strategy are evaluated.
As the hedge ratios depend particularly on the joint distribution
f the random variables Ẽh,T , Ẽf,T , ŨT as well as the chosen
inter-
st rates of Ĩh,T and Ĩf,T , an econometric model which captures
this
oint distribution is required. A VAR model can achieve this,

58. because
t is able to express the dynamics of prices, exchange rates, and
nterest rates. The required moments of the random variables
Ẽh,T ,
˜f,T , ŨT , Ĩh,T and Ĩf,T , are determined using a bootstrap
algorithm,
hich allows us to resample residual vectors and generate simu-
ated paths of the corresponding variables. These simulated paths
re constructed for a time horizon of up to ten years. The real-
zed moments can be calculated based on these paths. Then, the
edge ratios according to Eq. (10) are estimated. In this way, the
ynamic cointegrated VAR specifies the moments of the risk fac-
ors, which are then used to calculate the hedge ratios for
different
edge horizons in a one-period framework.
In the case of the interest rates, it is not feasible to add interest
ates for each maturity to the cointegrated VAR model;
therefore,
nly one short-term interest rate is
h/f
and one long-term interest

59. ate il
h/f
for each country are included. To model the term struc-
ure from these bootstrapped interest rates we use a simple linear
erm structure model. There are several reasons for employing
his approach in our analysis. The real nature of the term struc-
ure is difficult to specify because modeling the term structure of
nterest rates demands further assumptions, i.e. it requires bal-
ncing the trade off between the smoothness and the flexibility
o display the shape of the term structure (Bank for International
ettlements, 2005; Dai & Singleton, 2000; Schich, 1997). The
shape
f the yield curve depends on three common factors: the level,
he slope and the curvature (Litterman & Scheinkman, 1991).
Even
hough a higher degree of flexibility achieves a better
approxima-
ion of the term structure, it is not clear whether the term
structure
s concave or convex (e.g. Afonso & Martins, 2012; Diebold &
Li,
006). The above mentioned three factors explain the shape of
the
ield curve on the basis of different factor loadings. The level

60. thus
ccounts for the main part of the total explained variance across
aturities. Moreover, the slope and the curvature capture only
smaller part of the variation across maturities (e.g. Cochrane &
iazzesi, 1995; Driessen, Melenberg, & Nijman, 2003; Litterman
&
cheinkman, 1991) and accordingly play a minor role. In captur-
ng the two factors level and slope an average yield curve
without
bnormalities in the term structure and high robustness against
S
t
b
ics and Finance 54 (2014) 459–472
utliers is assumed to be appropriate for our analysis.
Furthermore,
n average term structure model fits to the purpose of this study
ery well as the considered exporting firm has no special
informa-
ion on the behavior of interest rates (See also Section 3.2). We

61. thus
alculate the interest rate for the hedge horizon T by linear
interpo-
ation between each simulated short-term and long-term interest
ate pair from the bootstrap algorithm. Thus, the term structure
of
he interest rates in Germany and the US is obtained for each
sim-
lation run k and the interest rate factor Ij,T,k with maturity T
can
e written as:
j,T,k = 1 +
[
T − Tl
Ts − Tl
is
j,T,k
−
(
1 − T − Tl

62. Ts − Tl
)
il
j,T,k
]
(11)
here j = {h, f}. Tl determines the maturity of the long-term
interest
ate il
h/f
and Ts the maturity of the short-term interest rate ish/f .
The cointegrated VAR model is estimated using a dataset
btained by the International Monetary Fund’s International
Finan-
ial Statistics database and Thomson Financial Datastream. It
ontains price levels, interest rates and exchange rates during the
eriod from January 1976 to December 2012 for Germany and the
S. Covering 37 years, the dataset provides 444 observations in
ach data series, including the latest financial crisis. The starting
oint is set at the year 1976 to avoid any potential distortion of

63. the
xchange rates due to the collapse of the Bretton Woods system.
nstead of consumer price indices, the producer price indices
(PPI)
re used as an approximation for product prices and costs as they
re more appropriate. Pf denotes the prices in the foreign coun-
ry (USA) and Ph the domestic prices (Germany), while pf and
ph
ndicate logarithmic values. The exchange rate between the Euro
nd the US Dollar, X, is defined as end-of-month rates and is
also
iven in logarithmic values, x. To calculate exchange rates
before
he introduction of the Euro, i.e. before 1999, the introductory
rate
f the Euro to the Deutsche Mark is used and a synthetic
exchange
ate is defined. As proxies, the long-term government bond
yields
nd the three-month Treasury bill rates are used to determine the
ong-term and short-term interest rates respectively.4 Fig. A.3 in
ppendix shows the time series used in our econometric model.
.2. Specification of the VAR model

64. A p-dimensional cointegrated VAR model with l lags is used.
The
odel is specified in vector error correction form (VECM):
Yt = �1�Yt−1 + . . . + �l−1�Yt−l+1 + ˘Yt−1 + ˚Dt + �t ,
with t = {1, . . ., T
̂ } (12)
The variables Yt denote a p-dimensional random vector of
ndogenous variables, ̆ and �1, . . ., �l−1 are p × p coefficient
atrices, Dt is a b-dimensional vector of deterministic
components,
uch as a constant, a linear time trend, seasonal or interven-
ion dummies etc., ̊ is a p × b coefficient matrix and �t, t =
1, . . ., T
̂ }, are p-dimensional vectors of i.i.d. Gaussian error
terms.
he cointegrated VAR model has the degree I(1) and r linearly
inde-
4 Since the time series of German three-month Treasury bill
rates ends in
eptember 2007 in the IMF database, we completed it by adding
growth rates of
he German six-month yield curve according to the Svensson
procedure provided

65. y the Deutsche Bundesbank.
P. Koziol / The Quarterly Review of Economics and Finance 54
(2014) 459–472 465
Table 2
Rank determination tests (trace test).
p − r r Eig. value Trace Trace* Frac95 p-Value p-Value*
7 0 0.366 461.277 448.739 133.317 0.000 0.000
6 1 0.284 260.522 253.833 102.653 0.000 0.000
5 2 0.108 113.011 110.218 76.688 0.000 0.000
4 3 0.073 62.780 60.157 53.184 0.007 0.012
3 4 0.048 29.411 24.886 34.795 0.158 0.341
2 5 0.011 7.756 6.953 19.293 0.686 0.758
1 6 0.007 3.087 2.604 5.904 0.210 0.268
This is a likelihood ratio test for cointegration rank, where p − r
denotes the num-
ber of unit roots (as null hypothesis) and r the number of
cointegrating relations.
Asterisks denote trace test statistics and p-values based on the
Bartlett small-sample

66. c
d
r
b
i
h
d
a
c
a
m
o
c
h
c
a
Y
I
m
m
t

67. (
c
g
t
t
d
c
o
a
d
d
I
t
a
o
b
t
t
r

68. d
d
Table 3
Misspecification tests (p-values given).
Tests for autocorrelation
LM(1) 0.084
LM(2) 0.086
Test for Normality 0.000
Tests for ARCH
LM(1) 0.019
LM(2) 0.000
This table shows the results of three tests: (i) Test of residual
autocorrelation of first
and second lagged VAR residuals (approximately distributed as
�2 with p2 degrees
of freedom). (ii) Test of residual normality by Hansen and
Doornik (calculated as
the sum of the p univariate Shenton–Bowman normality tests).
(iii) Test of residual

69. heteroscedasticity (first and second order ARCH test;
approximately distributed as
�
e
t
t
o
t
a
t
I
o
o
t
t
w
w
e
i
H
fi
v
T

70. m
s
5
i
h
r
d
a
i
orrection. Since the models contain level shifts that create shifts
in the asymptotic
istributions, the critical values of the test statistics were
simulated using 1000
andom walks and 10,000 replications.
e integrated of order one. Therefore, the non-stationary process
s converted into a stationary one by the matrix ˘.
In the model developed for specifying the hedge ratios and
edge efficiencies for various horizons, the vector time series Yt
is
etermined by seven different variables. Firstly, the variables
�ph

71. nd �pf giving the monthly inflation rates at home and abroad
over the uncertainty of revenues and costs. Secondly, the vari-
ble ppp = ph − pf − x, where x is the logarithmic exchange rate,
easures the deviation from absolute PPP and provides that part
f uncertainty in exchange rates which is not explained by price
hanges. Finally, the long- and short-term interest rates for the
ome country, il
h,t
and is
h,t
, and the foreign country, il
f,t
and is
f,t
, are
onsidered. Adding up the seven variables, the vector Yt is
defined
s

72. t =
(
pppt , �ph,t , �pf,t , i
l
h,t
, il
f,t
, is
h,t
, is
f,t
)
′ (13)
n order to ensure the optimal specification of the general VECM
odel described above, several tests are conducted.5 The Aug-
ented Dickey Fuller (ADF) test (Dickey & Fuller, 1979, 1981)
and
he test developed by Kwiatkowski, Phillips, Schmidt, and Shin

73. 1992) (KPSS) support the hypothesis of non-stationarity; I(1)
pro-
esses describe the time series best, which is also confirmed by
raphical examination (Fig. A.3).
The lag length of the VAR model is determined using informa-
ion criteria. In keeping with Hannan–Quinn and Schwarz
criteria,
wo lags are chosen. Furthermore, the normality assumption for
the
istribution of the differenced variables is examined. The graphi-
al analysis indicates that the assumption does not hold for
several
f the marginal processes. Including an unrestricted constant,6
few additive outliers,7 innovational dummies,8 and level shift
ummies9 leads to valid statistical implications, since potential
istortions can be controlled.
Thereafter, the trace test is used to identify cointegration of the
(1) processes. The results in Table 2 indicate that the cointegra-
ion rank r is at least three, since the three largest eigenvalues
re significantly different from zero. The fourth eigenvalue is
nly marginally significant, although the rank test provides

74. partial
5 Centered seasonal dummies are used to apture the seasonal
effects of the data
ecause the time series re not seasonally adjusted.
6 In this way, a trend in levels, but not in differences, is
allowed, which matches
he behavior of the underlying processes.
7 Additive outliers strongly indicate measurement errors and
were applied to the
ime series of the inflation rates.
8 Unrestricted permanent and transitory intervention dummies
are used if a
esidual larger than |4 �� | can be related to a known
intervention.
9 The level shift dummies are included in the cointegration
space and in first
ifferences outside the cointegration relations. In the model,
there are level shift
ummies in January 1982 and March 1999.

75. F
1
J
w
h
s
r
m
i
s
2 with one and two degrees of freedom, respectively).
vidence for four cointegration relations. Therefore, the
cointegra-
ion rank is further examined by inspecting the number of roots
of
he companion matrix (Juselius, 2006, p. 50f) and the time series
f the cointegration relations, which finally leads to the choice of
hree cointegration relations.
Table 3 presents the results of misspecification tests. The

76. ssumption of the standard I(1) approach is validated by means
of
hese tests. Autocorrelation is tested using multivariate LM tests.
nsignificant values are found at the 5% level for first and sec-
nd order residual autocorrelation, which supports the
assumption
f no autocorrelation. Testing for multivariate normality reveals
he rejection of this property indicated by the highly significant
est statistic. This violation of the normality assumption can be
eakened by the results of the univariate misspecification tests,
hich are not reported here, since non-normality is achieved by
xcess kurtosis, not skewness. Furthermore, a test for ARCH
effects
ndicates robustness against ARCH effects, as shown by Rahbek,
ansen, and Dennes (2002). Moreover, several statistical tests
con-
rm the constancy of the coefficients. The misspecification tests
erify the econometric accuracy of the model. As can be seen in
able A.6, the estimated coefficients support the plausibility of
the
odel and most of the coefficients have economically expected
igns.

77. . Empirical results
In order to identify the appropriate hedge instruments to
mprove FX hedging performance, the hedge effectiveness of the
edging strategies using additional forwards is analyzed. With
espect to the chosen data set in Section 4, the home country is
efined as Germany and the foreign country as the US. To evalu-
te the hedge efficiency, the measure suggested by Johnson
(1960)
s used, which is commonplace in the hedging literature (e.g.,
erguson & Leistikow, 1998; Martinez-Garmendia & Anderson,
999). It is defined as:
MT,i =
�2
UT,i
− �2
HT,i
�2
UT,i
(14)

78. here �2
UT,i
and �2
HT,i
denote the variance of the unhedged and
edged position applying hedging strategy i. Since the John-
on measure captures the hedge effectiveness in terms of risk
eduction, it fits well into the framework of variance mini-
ization. As the key figure for our analysis we calculate the
mprovement of the hedge efficiency for the considered hedging
trategy (JMT,i − JMT,onlyFX) in relation to the non-hedged
part of the
466 P. Koziol / The Quarterly Review of Economics and
Finance 54 (2014) 459–472

79. Table 4
Improvements in hedging performances �T,i for inflation
forward strategies.
Hedge horizon Strategies
Only FX GER PPI US PPI All PPI
0.5 years 0.944 +1.31% +76.15% +98.99%
1 year 0.936 +3.54% +72.42% +97.48%
2 years 0.924 +7.06% +68.82% +92.96%
3 years 0.912 +10.09% +64.07% +85.99%
4 years 0.899 +12.74% +57.70% +76.71%
5 years 0.885 +14.16% +50.56% +65.44%
10 years 0.799 +9.07% +12.00% +12.04%
The first column outlines the absolute hedging performance
using the Johnson mea-
sure for the baseline forward strategy. The values for the
hedging strategies GER PPI,
US PPI and all PPI in the second to fourth column sketch the
corresponding relative
improvement �T,i achieved by the respective strategy.
Furthermore, the results are
s

80. v
g
�
T
g
b
5
w
m
e
r
T
t
f
g
t
t
t
e

81. h
t
b
h
d
i
t
t
T
p
U
r
c
t
a
m
i
b
b
w
r
p
Table 5
Improvements in hedging performances �T,i for interest rate

82. forward strategies.
Hedge horizon Strategies
Only FX GER IR US IR All IR
0.5 years 0.944 +0.82% +0.05% +1.49%
1 year 0.936 +1.64% +4.16% +5.34%
2 years 0.924 +2.30% +15.03% +15.50%
3 years 0.912 +3.15% +23.08% +23.23%
4 years 0.899 +3.78% +27.20% +27.29%
5 years 0.885 +5.83% +30.17% +30.25%
10 years 0.799 +9.91% +27.07% +29.83%
The first column outlines the absolute hedging performance
using the Johnson mea-
sure for the baseline FX forward strategy. The values for the
hedging strategies GER
IR, US IR and all IR in the second to fourth column sketch the
corresponding relative
improvement �T,i achieved by the respective strategy.
Furthermore, the results are
s
l

83. g
l
w
C
t
t
i
o
t
5
f
r
o
h
t
u
e
e
t
s
a
c
h

84. l
r
c
V
o
A
b
i
rates depend heavily on inflationary components (e.g., Ang et
al.,
2008; Ivanova, Lahiri, & Seitz, 2000).10 This effect is also
caused by
the behavior of the real rates, since they are quite variable for
short
10 Considering interest rates regarding risk aversion would also
require an inflation
risk premium to be accounted for (Benninga & Protopapadakis,
1983; Cox, Ingersoll,
hown for hedge horizons from half a year to ten years.
ariance (1 − JMT,onlyFX). Thus, the relative improvement of
the hed-
ing performance is determined as

85. T,i =
JMT,i − JMT,onlyFX
1 − JMT,onlyFX
(15)
his relative improvement �T,i values 100% if the applied hed-
ing strategy i is able to eliminate the total risk which remains
y applying the baseline hedging strategy “only FX”.
.1. Hedging strategies using inflation forwards
The results in Table 4 show that the application of inflation for-
ards can significantly enhance FX hedging from a short-term
and
id-term perspective. The simultaneous use of domestic and for-
ign inflation forwards is capable of eliminating the variance of
the
eal profit for hedge horizons of up to two years for the most
part.
he use of a one-country strategy performs significantly less well
han a strategy hedging both the domestic and foreign price
risks. In

86. act, the single usage of one US inflation forward improves the
hed-
ing performance considerably, but it ignores an important part
of
he improvement potential. For hedge horizons of up to five
years,
wo thirds of the remaining risk can still be eliminated by
applying
he hedging strategy “all PPI”. For long-term hedge horizons, the
nhancement potential declines substantially.
The main drivers of a substantial hedge improvement is the
igh correlation of the underlyings in the hedge instruments with
he risk factors as the risk factors are induced in the FX forwards
y domestic and foreign inflation risk. Furthermore, the optimal
edging performance benefits from the simultaneous use of the
omestic and foreign inflation forwards, even though this effect
s of limited importance. The two-country strategy works better
han the single-country strategies as the difference between these
wo strategy types decreases with an increasing hedge horizon.
he two price risks affect the FX contract differently: the
German
rice risk has an effect in the form of additive basis risk while
the

87. S price risk reduces the multiplicative basis risk. These two
basis
isks interact and have to be hedged simultaneously in the
optimal
ase. RIP provides the economic explanation for the performance
of
he two-country strategy. The fact that the inflation contracts
have
lmost no effect on real FX hedging for longer hedge horizons is
ainly due to the characteristics of the FX forward and the
foreign
nflation forward in the long run. Even for short hedge horizons,
oth the FX forward and the US inflation forward face basis
risks,
ut the level is rather small, since the revenue and cost risks as
ell as the correlation between foreign revenue risk (ẼUS,T )
−1
and
eal exchange rate risk (ŨT ) are rather small. On the one hand,

88. the
rices underlying the revenue and cost risks follow I(2)
processes,
&
o
a
S
s
hown for hedge horizons from half a year to ten years.
eading to a disproportionably large increase in these risks with
a
rowing hedge horizon (Fig. 1(a)). On the other hand, the corre-
ation between revenue risk and real exchange rate risk increases
ith the hedge horizon, reaching values of almost 40% (Fig.
1(b)).
ombining these two effects, the two basis risks rise strongly
over
he hedge horizons. As a result, the dependence between the
mul-
iplicative basis risk of the FX forward and the payoff of the
foreign
nflation forward is no longer perfect. Furthermore, the interplay

89. f the risk factors inside the foreign inflation forward accelerates
he overall risk.
.2. Hedging strategies using interest rate forwards
Table 5 shows clearly that the introduction of interest rate
orwards enhances FX hedging for certain combinations and
matu-
ities. For short hedge horizons, the impact of interest rate
forwards
n the FX hedging strategy is negligible. The enhancement of the
edging performances clearly increases with the hedge horizon.
In
he case of 10 years, the relative improvement of the FX hedge
adds
p to 30% using the hedging strategy “all IR”. However, the
strat-
gy applying US interest rate forwards also generates significant
nhancements with 27%. This hedging strategy reduces the mul-
iplicative basis risk caused by the US price risk. The alternative
trategy “GER IR” with respect to the additive basis risk does
not
chieve a significant impact. Adding only US forwards, the FX
hedge
an be improved significantly and, at the same time, the whole

90. edging strategy is simplified and transaction costs are reduced.
The results are mainly driven by the information content of the
ong-term interest rates. In our approach, the underlying interest
ates of the applied forwards are linear combinations of the fore-
asted short-term and long-term interest rates in the cointegrated
AR model. Thus, with an increasing hedge horizon, the impact
f the long-term interest rate rises and becomes more important.
ccording to the Fisher equation, the nominal interest rates can
e described by real interest rates and inflation. While short-term
nterest rates are dominated by real rates, the long-term interest
Ross, 1985) according to the extended Fisher equation. In the
literature the effect
f the inflation risk premium on the nominal interest rate is
mixed. Evans (1998)
nd Buraschi and Jiltsov (2005) state that the risk premium is
time varying while
home, Smith, and Pinkerton (1988) cannot confirm the presence
of a statistically
ignificant risk premium. As the significance of the inflation risk
premium cannot

91. P. Koziol / The Quarterly Review of Economics and Finance 54
(2014) 459–472 467
Fig. 1. Behavior of risk factors. The figure illustrates the
behavior of the risk factors over time. This is achieved by
plotting the variances and correlations against the hedge
horizon. In part (a) the dashed line stands for the home cost
risk (ε̃)−1GER,T , the solid line stands for the foreign revenue
risk (ε̃)
−1
US,T , and the dotted line for the real exchange
rate risk ŨT . In part (b) the solid line stands for the
correlation of home cost risk and foreign revenue risk, the
dashed line stands for the correlation of home cost risk and
r nue r
m
T
s
m
t
a

92. h
i
6
6
g
a
i
o
a
i
a
(
t
b
e
h
a
t
i
d

93. a
g
H
r
i
2
(
&
a
e
t
t
m
i
t
eal exchange rate risk, and the dotted line stands for the
correlation of foreign reve
aturities but smooth for longer maturities (e.g., Ang et al.,
2008).
hus, the long-term interest rates possess a much stronger
relation-
hip with inflation than short-term interest rates do, and perform
uch better than the corresponding inflation forward strategies in

94. his instance.
In contrast to the inflation derivatives, the simultaneous cover-
ge of both price risks is of limited importance as for longer
hedge
orizons the strategy based on the US forwards captures almost
all
mprovements in the FX hedge.
. Discussion
.1. Implications for risk management theory
The results of our investigations complement the existing hed-
ing literature as we have conducted a comprehensive empirical
nalysis on enhancing FX risk management with inflation and
nterest rate forwards. The related literature so far has focussed
n theoretical investigations (See Section 2). Furthermore, there
re only a limited number of studies that look at the hedging of
nflation risk. The fundamental studies in this field, such as
Briys
nd Schlesinger (1993), Adam-Mueller (2000), and, Adam-

95. Mueller
2002), assume that inflation risk is untradable. These studies
show
hat the presence of inflation risk can have a strong impact on
e fundamentally proven regardless of the degree of risk
aversion, the basic Fisher
quation is a reasonable approximation in practice.
t
c
i
B
a
a
e
isk and real exchange rate risk.
edging strategies and the optimal hedge positions change
ccordingly. The size of this effect depends on the firm’s produc-
ion, the hedging criterion, and the chosen model assumption. If
t is assumed that inflation risk is tradable, the general results
for
eriving optimal hedging strategies in the presence of price risk

96. re valid and our results are in line with the fundamental hed-
ing literature (Benninga, Eldor, & Zilcha, 1985; Feder et al.,
1980;
olthausen, 1979). Under non-perfect market assumptions, hedge
atios of lower than one are obtained due to certain
imperfections
n derivatives contracts such as basis risks (Adam-Mueller &
Nolte,
011; Briys et al., 1993), liquidity needs with futures contracts
Mello & Parsons, 2000; Zhou, 1998), and default risk (Cummins
Mahul, 2008). However, in this study we run a detailed
empirical
nalysis to explain why and how additional hedge instruments
can
nhance FX risk management for different hedge horizons.
In a recent study Brière and Signori (2011) analyze the infla-
ion hedging properties of assets in different regimes and find
hat the optimal hedging strategies depend significantly on the
acroeconomic regime. In more stable economic environments
nvestors should invest in nominal bonds, i.e. interest rate
products,

97. o hedge inflation risk for longer hedge horizons, which supports
he findings of our study. In the case of a volatile regime marked
by
ountercyclical inflation, investors should increase their portion
of
nflation-linked bonds, which contradicts our obtained results.
As
rière and Signori (2011) analyze inflation hedging with respect
to
sset management and there are several differences in the applied
pproaches, the results differ to some extent. Applying vector
rror correction models Attie and Roache (2009) also confirm the
468 P. Koziol / The Quarterly Review of Econom
Fig. 2. Hedging performances for major hedging strategies. The
figure compares
the hedging performances according to the Johnson measure.
The lower solid line
stands for the basis “only FX” strategy, the dashed line stands
for the usage of all

98. interest rates, the dotted line stands for the strategy using all
considered inflation
derivatives, and the upper solid line stands for the strategy
using both all interest
r
h
e
p
l
r
r
h
f
J
B
(
2
c
H
p
a
F

99. 6
a
h
w
f
p
u
h
f
c
a
r
f
h
E
a
r
o
o
f
a
o

100. h
b
b
b
s
t
u
e
t
s
7
f
b
p
h
d
a
r
a
i
w
s
e

101. i
h
b
h
a
r
s
t
c
f
b
A
K
p
t
R
a
w
I
a
o

102. Appendix A.
ate derivatives and all inflation derivatives. The x-axis
represents different hedge
orizons from one year up to ten years. The y-axis denotes the
Johnson measure for
ach hedging strategy and hedge horizon.
revious results even though the adjustment process lasts
onger. Bekaert and Wang (2010) reveal a sub-optimal hedging
elationship for interest rate products. However, in line with our
esults they find that these instruments perform better for longer
edge horizons than for shorter hedge horizons.
The hedging literature also considers alternative instruments
or hedging inflation risk, such as stocks (e.g., Bodie, 1976;
Reilly,
ohnson, & Smith, 1970; Schotman & Schweitzer, 2000), gold
(e.g.,
eckmann & Czudaj, 2013; Bernard & Frecka, 1987), and real
estate
e.g., Hoesli, Liu, & Hartzell, 1997; Hoesli, Lizieri, &
MacGregor,
008). Although there are reasons to apply such assets, the
empiri-
al evidence for their usefulness is weak (e.g., Ely & Robinson,

103. 1997;
ess & Lee, 1999; Hoesli et al., 1997; Taylor, 1998) and the
hedging
erformance lies below the results of our study. These
instruments
re not suitable for our purpose of enhancing an already fairly
good
X hedging strategy.
.2. Implications for risk management practice
The findings of Section 5 demonstrate that the impact of the
dditional instruments on the FX hedge depends crucially on the
edge horizon (Fig. 2). For shorter hedge horizons, inflation for-
ards are very useful, but for longer hedge horizons, interest rate
orwards perform best. This is because, due to the integration
roperties of the prices, the inflation forwards contain additional
nhedgeable risks which increase exponentially with the hedge
orizon, which means that the FX hedging strategy cannot benefit
rom their use in the case of longer hedge horizons.
These results have important practical risk management impli-
ations which can be applied easily. A firm which faces revenue

104. nd cost risks in addition to exchange rate risk can improve its
FX
isk management significantly by using more than the standard
FX
orward. To do so, inflation contracts should be chosen for
shorter
edge horizons and interest rate forwards for very long horizons.
specially for longer hedge horizons, interest rate forwards are
very
ppropriate for significantly enhancing the performance of the
FX
A
A
ics and Finance 54 (2014) 459–472
isk management. It is important to note that these outcomes are
btained in a framework without trading frictions. In the
presence
f market frictions, the dependence structure of the underlying
risk
actors may change, but the fundamental behavior of the interest

105. nd inflation rates is maintained. It can be expected that the level
f enhancement will be adjusted, but not the overall impact of
the
edging strategies. In this case, dynamic hedging strategies can
be
eneficial. As a firm wishes to hedge the long-term exposure on
the
asis of a dynamic hedging strategy, the short-term hedges have
to
e rolled over into longer-dated contracts. In general, this kind of
trategy is beneficial if, for instance, long-term derivatives are
not
raded or at least not sufficiently liquid. However, if the prices
of the
nderlying contracts do not match at the time of rollover,
hedging
rrors occur and the efficiency of the dynamic hedge decreases.
It
hen has to be analyzed on a case by case basis whether the
hedging
trategy is still profitable.
. Conclusion
This paper investigates hedging strategies to improve the per-

106. ormance of an FX hedge in real terms using hedge instruments
eyond FX forwards. For an exporting firm which is exposed to
roduct price, cost, and exchange rate risks variance-minimizing
edge ratios are derived for many hedging strategies. The pro-
uction quantity is not stochastic in our model, because a more
ggregated approach is chosen that abstracts from firm-specific
isks. This is also reflected in the use of the PPI as a proxy for
price
nd cost risks. Using this methodology, we can provide
instructive
nsights into optimal hedging procedures for a whole economy,
hile it would be interesting to study firm-, product-, or sector-
pecific quantity risks for future research. By quantifying the
hedge
fficiencies for the considered hedging strategies, important
empir-
cal insights can be gained on how and to what extent certain
edging strategies based on either inflation or interest rates are
eneficial.
The results of our study can help firms to design optimal FX
edging strategies. An FX hedge, in real terms, warrants a
careful
nalysis of the integration properties of the revenues, costs,

107. interest
ates, and exchange rates in order to design the optimal hedging
trategy, which is not obvious at first sight. This paper finds that
he impact of the additional instruments on the FX hedge
depends
rucially on the hedge horizon. Inflation derivatives are very
useful
or shorter hedge horizons but interest rate derivatives perform
est for longer hedge horizons.
cknowledgements
We have benefited from comments by Olaf Korn, Christian
oziol, Markus Rudolf, Tilman Sayer, Klaus Schaeck, and
partici-
ants of the WHU Campus for Finance Research Conference and
he Annual Conference of the Swiss Society for Financial Market
esearch (SGF). We thank Ricardo Peña Hoepner, Timo Reinelt,
nd Madlen Sode for their excellent research assistance. This
study
as previously circulated as “Enhancing FX Risk Management
with
nflation and Interest Rate Derivatives”. This paper represents
the

108. uthor’s personal opinion and does not necessarily reflect the
views
f the Deutsche Bundesbank or its staff.
.1. Tables
.2. Figures
P
.
K
o
zio
l
/
Th
e
Q
u

109. a
rterly
R
eview
o
f
E
co
n
o
m
ics
a
n
d
Fin
a
n

110. ce
5
4
(2
0
1
4
)
4
5
9
–
4
7
2

111. 4
6
9
Table A.6
Long-run and short-run structure of the VECM for the US.
Long-run structure
ˇ′ pppt �pf,t �ph,t i
l
f,t
il
h,t
is
h,t
is
f,t
C(99:03) C(82:01)

112. ˇ(1) 0.699 −0.596 1.000 0.604 −0.045 −0.390 −0.198 0.002
−0.001
ˇ(2) 0.547 −0.168 −0.777 1.000 −0.528 0.260 −0.109 0.004
−0.003
ˇ(3) 0.320 −0.002 −0.005 1.000 −0.867 0.253 −0.269 0.001
−0.001
˛ �pppt �2 pf,t �
2 ph,t �i
l
f,t
�il
h,t
�is
h,t
�is
f,t
˛(1) 0.000 [0.039] 0.935[11.152] − 0.236[− 5.901] − 0.007[−
2.540] −0.003[− 1.579] −0.002[− 0.908] 0.001 [0.243]
˛(2) 0.004 [0.831] 0.850 [8.555] 0.569 [12.018] 0.001 [0.426]

113. −0.001[− 0.300] −0.003[− 1.048] −0.000[− 0.160]
˛(3) − 0.042[− 2.080] −0.328[− 0.825] 0.020 [0.105] 0.029
[2.066] 0.015 [1.606] −0.012[− 1.164] 0.098 [8.333]
˘ pppt �pf,t �ph,t i
l
f,t
il
h,t
is
h,t
is
f,t
C(99:03) C(82:01)
�pppt −0.011[− 1.447] −0.001[− 0.277] −0.003[− 0.495]
−0.037[− 1.799] 0.034 [1.931] −0.010[− 1.737] 0.011 [1.957]
−0.000[− 0.329] 0.000 [1.249]
�2 pf,t 1.013 [6.738] − 0.700[− 13.281] 0.276 [2.422] 1.087
[2.628] −0.206[− 0.591] − 0.227[− 2.077] −0.189[− 1.737]
0.005 [9.571] − 0.003[− 5.626]

114. �2 ph,t 0.153 [2.131] 0.045 [1.781] − 0.678[− 12.482] 0.446
[2.266] −0.307[− 1.846] 0.245 [4.715] −0.021[− 0.403] 0.002
[8.504] − 0.001[− 5.845]
�il
f,t
0.005 [0.914] 0.004 [2.250] − 0.009[− 2.195] 0.026 [1.781] −
0.025[− 2.079] 0.011 [2.771] −0.006[− 1.688] 0.000 [0.720]
−0.000[− 1.569]
�il
h,t
0.002 [0.637] 0.002 [1.574] −0.003[− 0.988] 0.013 [1.281]
−0.013[− 1.525] 0.005 [1.886] −0.003[− 1.309] 0.000 [0.137]
−0.000[− 0.930]
�is
h,t
−0.007[− 1.718] 0.002 [1.207] 0.000 [0.064] −0.016[− 1.484]
0.012 [1.318] −0.003[− 1.052] 0.004 [1.387] −0.000[− 1.679]
0.000 [1.664]
�is
f,t

115. 0.032 [7.096] −0.000[− 0.275] 0.000 [0.130] 0.098 [8.016] −
0.085[− 8.217] 0.025 [7.590] − 0.026[− 8.215] 0.000 [4.051] −
0.000[− 6.804]
�1 �pppt−1 �2 pf,t−1 �2 ph,t−1 �i
l
f,t−1 �i
l
h,t−1 �i
s
h,t−1 �i
s
f,t−1 Constant
Short-run structure
�pppt −0.041[− 0.841] −0.001[− 0.698] 0.000 [0.011] −0.114[−
1.303] 0.240 [1.882] 0.006 [0.064] 0.017 [0.343] 0.000 [0.557]
�2 pf,t 2.272 [2.368] −0.017[− 0.429] −0.051[− 0.584] 0.739
[0.426] 2.133 [0.841] 0.155 [0.087] 0.069 [0.069] 0.001 [3.571]
�2 ph,t − 2.017[− 4.412] −0.003[− 0.160] − 0.182[− 4.344]
−0.119[− 0.144] 0.318 [0.263] 2.127 [2.503] 0.081 [0.170]

116. 0.000 [0.051]
�il
f,t
− 0.101[− 3.021] 0.001 [0.530] 0.006 [2.030] 0.221 [3.643]
−0.019[− 0.210] 0.033 [0.535] −0.053[− 1.518] −0.000[− 0.467]
�il
h,t
− 0.079[− 3.394] 0.001 [1.304] 0.003 [1.198] 0.048 [1.149]
0.255 [4.155] 0.021 [0.479] 0.000 [0.000] −0.000[− 0.876]
�is
h,t
− 0.080[− 3.097] 0.001 [1.291] −0.000[− 0.194] −0.014[−
0.305] 0.379 [5.571] 0.048 [1.006] 0.027 [0.998] −0.000[−
0.729]
�is
f,t
− 0.079[− 2.770] 0.001 [0.645] 0.002 [0.728] −0.060[− 1.166]
0.147 [1.953] −0.046[− 0.870] 0.387 [13.100] 0.000 [1.730]

117. This table shows the short-run and the long-run structure of the
estimated VECM; significant test statistics on the 5% level are
given in bold face. The coefficient matrix ˛ hereby measures the
speed of adjustment to long-run
equilibrium relations, and the coefficient matrix ˇ defines the
weights of the stationary linear combinations of the I(1) vector
time series. �1 is the coefficient matrix of the first Y-lag. For
totality reasons we distinguish between
long-run and short-run structure, even though the short-term
does not impact the estimates that much. The t-statistics are
provided in brackets.
470 P. Koziol / The Quarterly Review of Economics and
Finance 54 (2014) 459–472
Fig. A.3. Time series of the input variables in the VAR model.
Plots of logarithmic producer price index (log PPI), absolute
purchasing power parity (absolute PPP), and interest
rate time series from 1976 to 2012 are presented. Short-term
and long-term interest rates correspond to three-month as well
as ten-year maturities. The graphs underline
the fact that the interest rate time series are I(1) and PPI are
I(2). In (a) the logarithmic PPI developments in the US and in

118. Germany both exhibit a strong increase in the late
1 fter th
l (d) a
e
R
A
A
A
A
A
A
A
A
A

119. A
B
B
B
B
B
B
B
B
B
B
B
B

120. B
B
B
970s and the early 1980s. Plot (b) shows absolute PPP values
fluctuating heavily a
ong-term interest rates in the US and in Germany are presented
in figures (c) and
arly years and low values by expansionary monetary policy for
the latest values.
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