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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 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 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]

r c a a d e t l

ttp://dx.doi.org/10.1016/j.qref.2014.04.004 062-9769/© 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- 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.

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iquidity as they raised market breadth, integration with nominal 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 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 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.

( F ( M i

w ( B

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 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- 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

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E p o t r c f u w 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.

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

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 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 X̃T 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

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 X̃T are deter- ined by the function X̃T = 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 X̃T − C̃T = P0 Q X0Ẽh,T ŨT − C0Ẽh,T (1)

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

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62 P. Koziol / The Quarterly Review of E

ealizes a cash flow of X̃T − F FX0,T only at T. Since it is assumed that the orward price is “fair” at initiation, the forward contract is 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 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 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

)

+ 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- 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

( 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 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.

.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 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.

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3

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H

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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

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- 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 B̃T + H �̃,h T

C̃T + H�̃,fT D̃T (6) ith

ÃT ≡ P0 Q X0ŨT − C0,

B̃T ≡ F FX0,T 1

Ẽh,T − X0

ŨT Ẽf,T

,

C̃T ≡ F �̃,h0,T 1

Ẽh,T − 1,

D̃T ≡ 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 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 B̃T , C̃T , D̃T has full rank, i.e., if none f the forward contracts is a redundant hedge instrument:

Cov[ÃT , B̃T ] + HFXT Var[B̃T ] + H �̃, h T

Cov[B̃T , C̃T ] + H�̃, fT Cov[B̃T , D̃T ] !=0

Cov[ÃT , C̃T ] + H�̃, hT Var[C̃T ] + HFXT Cov[C̃T , B̃T ] + H �̃, f T

Cov[C̃T , D̃T ] !=0

Cov[ÃT , D̃T ] + H�̃, fT Var[D̃T ] + HFXT Cov[D̃T , B̃T ] + H �̃, h T

Cov[D̃T , C̃T ] !=0

(8)

Solutions 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 B̃T , C̃T , D̃T ). 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 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[B̃T ] Cov[B̃T , C̃T ] Cov[B̃T , D̃T ]

Cov[C̃T , B̃T ] Var[C̃T ] Cov[C̃T , D̃T ]

Cov[D̃T , B̃T ] Cov[D̃T , C̃T ] Var[D̃T ]

⎞ ⎟⎠

−1

·

⎛ ⎜⎝

Cov[B̃T , ÃT ]

Cov[C̃T , ÃT ]

Cov[D̃T , ÃT ]

⎞ ⎟⎠ (9)

Since the optimal hedge positions depend on all covariances 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 =

⎛ ⎜⎜⎝

HRFX∗T

HR�̃, h∗ T

HR �̃, f ∗ T

⎞ ⎟⎟⎠ = 1P0 Q E(1 + �̃f,T )

⎛ ⎜⎜⎝

HFX∗ T

H�̃, h∗ T

H �̃, f ∗ T

⎞ ⎟⎟⎠ (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 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

4

4

g i i b c a i

o e j i i E w l a i h d t h

r o

r t t t t i a t S o t t t i 2 y a m a P S i a

o a v t c l r t u b

I

w r

o c c p U e p e I a a t i a g t o r a l A

4

m

�

e m 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

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, 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

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 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 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 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 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

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, . . ., T̂ } (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, . . ., T̂ }, 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 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 c d r

b i

h d a c a m o c h c a

Y

I m m t ( c g

t t d c o a d d

I t a o

b

t

t

r

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 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 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 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

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 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 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.

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 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.

. 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)

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

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

v g

�

T g b

5

w m e r T t f g t t t e

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 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 g l w C t t i o t

5

f r o h t u e e t s a c h

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

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 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 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, 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 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 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

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 h i

6

6

g a i o a i a ( t

b e

h a t i d 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

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-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 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, 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 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

6

a h w f p u h f

c a r f h E a

r o o f a o h b b b s t u e t s

7

f b p h d a r a i w s e i h b

h a r s t c f b

A

K p t R a w I a o

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, 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 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 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- 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, 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 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

a rterly

R eview

o f

E co

n o m

ics a

n d

Fin a n

ce 5

4 (2

0 1

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9 –

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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)

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] −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] �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

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] 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]

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

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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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