Econometric Modeling in relation to Foreign Exchange Risk

Econometric Modeling
and the Effectiveness
of Hedging Exposure
to Foreign Exchange
Risk
Does Model Specification Matter?
For decades, the debates on unconditional and conditional econometric models for
estimating the optimal hedge ratio have been extensive. However, there is still no
consensus to date on the optimal hedge ratio model. This paper argues that optimal
hedge ratio is inconsequential to model specification – whether conditional or
unconditional, what is important is the correlation coefficient between the
underlying unhedged position and the hedging instrument. Four different models;
(i) Levels (ii) First Difference (iii) Non-Linear (iv) Error Correction Model, have
been employed in the estimation of hedge ratio and applied to two hedging
instruments; Money Market and Cross Currency Hedge. The empirical evidence
indicate that due to the strong correlation between the price of the unhedged
position with money market hedge, all four models exhibited similar hedge ratio
and hedging effectiveness. When correlation is weak as evident by cross currency,
the hedging effectiveness in all four models becomes inefficient. The discussion
highlighted in this paper is in reference to three major developed currencies: Swiss
Franc (CHF), British Pound ( GBP) and Hong Kong Dollar (HKD) with data
spanning from 2001 to 2009.
2015
Matthew Au De Jian
RMIT University
5/28/2015

1 BAFI 2085: Research Project in Finance
Section 1: Introduction
The existence of foreign exchange risk management can be traced back to the
shortfall of Bretton Wood system and also the end of U.S dollar pegged to the gold. Foreign
exchange risk relates to the effect of unexpected exchange rate changes to the value of the
firm. Many multinational companies (MNCs) are strongly susceptible to foreign exchange
risk by virtue of their international operations. The management of foreign exchange risk for
these companies represents an integral part of their daily operations (Papaioannou, 2006).
Prudent management of these multinational companies (MNCs) requires currency hedging
for their foreign transactions to avoid potential adverse currency effect on their profitability,
market valuation and long term sustainability. The measurement of foreign exchange risk on
companies can be done through the use of Value at Risk (VaR) or Expected Shortfall (ES)
methods. According to Geczy et al (1997) multinational companies tend to hedge their
foreign exchange risk exposure through financial hedging such as forward and money market
rather than internal hedging strategies. Also, Wong & Broll (1999) documented other
multinational companies (MNCs) tend to hedge their foreign exchange risk exposure through
cross currency hedge techniques.
When MNCs ultimately decides to hedge against their foreign exchange risk
exposure, another important question typically arises. The question here remains as to what is
the hedging proportion and how the choice of model specification to derive the optimal hedge
ratio affects the hedging effectiveness. Many researches have surfaced over the decade on the
optimal hedge ratio derivation from a stock and futures contract perspective. Dale (1981) first
documented that hedge ratio should be derived from a price level model. He found that using
a hedge ratio derived from price level model leads a futures hedging effectiveness of
approximately 97 percent. Following his work, Hill and Schneeweis (1981) analysed the
same data set and found that the hedging effectiveness based on price levels model tend to be
overspecified due to the autocorrelation problem. They argued that the hedge ratio was
unreliable in the sense that it violates the Ordinary Least Square (OLS) assumption.
Although, the hedge ratio estimate may still be unbiased, it longer contains a minimum
variance. Therefore, they highlighted the importance of price change models when estimating
the optimal hedge ratio.

Broll et al (2001) then discussed the importance of non-linearity of financial time series. He
proposed that spot-futures exchange relationship are nonlinear, thus it is important to model
the effects of nonlinearity through the use of quadratic models when deriving the optimal
hedge ratio. Later on, Ghosh (1993) and Lien (1996) argued the importance of optimal hedge
ratio estimation through error correction model (ECM) when cointegration relationship
exists. They highlighted that suppose the spot and futures price are cointegrated, an errant
hedger who omits cointegration relationship will tend to adopt a smaller than optimal futures
positions ultimately resulting in a relatively poorer hedge performance. Thus, the use of ECM
is the true indispensable component when forming hedging strategies. The paper discussed up
to this point for model specification and hedge ratio are based on the view that the variance of
and covariance with are constant over time. Though, in reality they are time varying thus
must be modelled using dynamic statistical hedge model such as put forth by Kroner &
Sultan (1993), Park and Switzer (1995) and Chen et al (2014).
Despite of clear existence of evidence documenting the superiority of conditional
models over unconditional models, there is still no consensus no date. This is because there is
existing evidence such as Myers (1991) who suggests that transaction costs as a consequence
to portfolio rebalancing outweighs the benefit of dynamic hedging.
Here, rather than contributing to the endless debate of unconditional or conditional hedge
ratio models, this paper differentiates from the rest in the sense that its objective is to evaluate
the fundamental correlation coefficient between the unhedged position and hedging
instrument as discussed by Ederington (1979). He documented that the optimal hedge ratio
and hedging effectiveness is inconsequential to model specification but rather dependent the
relationship between the spot position and hedging instrument. Law and Thompson (2005)
also documented that when correlation coefficient between the price of spot position and
futures contract are weak, the risk reduction capabilities for various hedge ratio models tend
to be generally lower. Also, Ghosh & Clayton (1996) highlighted that fundamental
correlation between the price movement of spot instrument and futures contract is an
important factor to driving the hedging effectiveness. Third, Moosa (2003) whom analysed
similar proposition employed four different models in estimating the hedge ratio and found
that there was no significant difference in the hedging effectiveness produced by one model
compared to another. He commented:

“Although there are many theoretical arguments on which model specification suits
best for deriving the optimal hedge ratio, the topic is still elegant. Though, what determines
the success or failure of a hedge depends on the correlation coefficient between the price of
the unhedged position and the hedging instrument. (Moosa, 2003)”
Thus, the objective of this paper follows in spirit of Ghosh & Clayton (1996), Law &
Thompson (2005) and Moosa (2003) to ascertain whether model specification matters in
respect to deriving an optimal hedge ratio under the context of money market and cross
currency hedge. Four unconditional models are used to calculated the hedge ratio: (i) Levels
(ii) First Difference (iii) Quadratic and (iv) Error Correction Models (ECM) . Following that,
the hedging effectiveness will be measured by the hedging instrument to reduce the variance
on the underlying unhedged foreign exposure position through the use of variance ratio and
variance reduction. This paper entails the use of three developed currencies: Swiss Franc
, British Pound and Hong Kong Dollar with its data spanning from
1998 to 2009.
Following a series of robustness checks, the empirical results concluded that all four
models under money market hedge exhibit similar hedge ratios, hedging effectiveness and
variance reduction capabilities as a consequence to high correlation to the underlying
unhedged foreign currency exposure. The hedging effectiveness and variance reduction for
all four models under money market were approximately 99 percent. In contrast to cross
currency hedge, low correlation coefficient between the underlying unhedged foreign
currency exposure with the third currency led to all four models exhibiting different hedge
ratio, inefficient hedging effectiveness and variance reduction capabilities compared to
money market hedge. The results from an out-sample test with ex-ante hedge ratio illustrated
similar conclusion on the hedging effectiveness of ex-post money market and cross currency
hedge ratios.
The remainder of the paper proceeds as follows. In Section 2, the related literatures
are reviewed. Section 3 presents the basic concepts of financial hedging. The methodology or
research designs are discussed in Section 4. In Section 5, the data and empirical results on the
relationship between optimal hedge ratio and hedging effectiveness are presented. Section 6
provides the concluding remarks.

Section 2: Literature Review
For decades, there have been an extensive range of studies which have been
conducted on the calculation of optimal hedge ratio. Various approaches have been proposed
and used in many financial and non-financial market settings such as wheat, soybean and
even electricity. The optimal hedge ratio is defined as the quantity of the spot instrument and
hedging instrument which ensures that the total value of the hedged portfolio does not
change. The hedge ratio proposes the portion of hedging instrument in which minimizes the
variance of the underlying unhedged position.
2.1 Early Research Studies
The history behind hedge ratio can be traced back to Johnson (1960) who extended
the theory of hedging using Markowitz (1952) portfolio theory. Ederington (1979) who
examined the hedging performance of the New Futures Market (GNMA and T-Bills) then
further formalized Johnson „s theory and derived the minimum variance hedge ratio (MVHR)
which minimizes the variance of the spot portfolio. He explained that a minimum variance
hedge ratio can be defined as the ratio of the covariance between the spot and futures price to
the variance of the futures price. The objective of the hedge ratio is to determine the hedging
ability of the financial instrument to minimize the price risk associated with holding a pre-
determined spot portfolio.
The MVHR or can be shown as follows:
Where is the value of the hedged portfolio during period ; and are the log of the
spot and futures prices during period ; is the hedge ratio; and corresponds to
the covariance between the log spot and futures price during period . The minimum variance
hedge ratio can be obtained by differentiating with respect to the hedge ratio and solving the
first order conditions, which can be written as
( )
( )
While solving the first order conditions lead to
[1]
[2]

Where, denotes the minimum variance hedge ratio. The MVHR can also be obtained from
an ordinary least square (OLS) regression where the spot and futures prices are the dependent
and independent variable respectively. The estimated slope coefficient is then multiplied by -
1 to obtain the hedge ratio. The negative hedge ratio reflects that when a long spot position is
taken, the opposite will be a short futures position. When this is done the coefficient of
determination, is an appropriate measure of hedging effectiveness ( . The measure for
hedging effectiveness can be defined as the percentage reduction of the variance on the
underlying unhedged position . Equation [4] shows the degree of hedging effectiveness:
Where is also the square of the correlation between the spot and futures price.
Thus, here it can be seen that the hedging effectiveness of futures contract is a function of the
relationship with the underlying unhedged spot position.
Subsequently to Ederington‟s theory, there have been numerous studies which followed suit
such as those developed by Dale (1981), Hill & Schneeweis (1981) and Witt et al (1987).
These studies first tried to analyse in particular the question of whether the hedge ratio should
be estimated from a price levels or price change model. For instance, Dale (1981) who first
studied the hedging effectiveness of three foreign currencies futures with hedge ratio derived
from a price level model. His results concluded that all three currency futures documented
significant hedging effectiveness of approximately 97 percent for both two week hedge and
four week hedge during the period of mid-1974 to mid-1980. Here, Dale‟s price level
regression can be expressed as follows:
Similarly to Ederington (1979), and denotes the spot and futures prices at time ;
represents the hedge ratio and signifies the residual term for the regression at time .
Correspondingly, Hill & Schneeweis (1981) who studied a common set of data with a price
changes regression found the hedging effectiveness to differ significantly to that of Dale
(1981) findings. H&S criticised that autocorrelation problem was evident when using price
levels model and that it violates the OLS regression assumption. They find that although the
[3]
[4]
[5]

hedge ratio estimated by Dale (1981) was still unbiased, it becomes an inefficient estimate
such that it does not contain a minimum variance. Also, they found that when estimating at
price levels, either price series often contains a unit root or non-stationarity. Hence, an errant
hedger who overlooks these issues will eventually be under hedged due to the upward bias on
the hedging effectiveness of price level model. H&S then suggest that the regression should
be estimated from a price change perspective such as:
Where and represents the spot and futures price changes at time ; represents the
hedge ratio and is the residual term for the regression.
Consequently to Dale (1981) and Hills & Schneeweis (1981) findings, Witt et al (1987) then
studied the theoretical and practical differences among the two frequently used specifications
to estimate a hedge ratio in the context of hedging agricultural commodities such as sorghum,
barley and cash price with corn futures price. Their findings concluded that the hedge ratio
derived from a price level perspective was as statistically significant as price changes in terms
of hedging effectiveness. They argued that the proper hedge ratio model estimation is a
function of the hedger‟s objective and the type of hedging instrument being used.
Following that, Broll et al (2001) provided some empirical evidence of nonlinear spot futures
exchange rate relationships. Their research were based on 6 major currencies over the period
of 1993 to 1999 found that five out of six currencies of developed countries do have spot-
future exchange rates relationship which are either convex or concave shaped. Moreover,
they believe more significant nonlinear spot futures exchange rates relationship would exist
for emerging market and transition economies currency because of illiquidity issues. Thus,
they suggest that hedge ratio should be derived from the following:
Where , , and are similar to that of Dale (1981) and Hill & Schneeweis (1981) while
represents the quadratic term on the futures prices to model the non-linear relationship
between and .
[6]
[7]

2.2 Evolvement on Early Research Studies
Later on, Ghosh (1993) who analysed several stock portfolios hedged to the S&P 500
Index Futures found that hedge ratio derived from traditional models as in the earlier pages to
be misspecified due to the ignorance of cointegration relationship. Such that, the short run
dynamics and long run relationship embodied within the error correction term are not taken
into account. The cointegration theory was first developed Engle & Granger (1987) who
illustrated that if two price series are integrated at the same order, there must exist an error
correction representation. According to Lien & Luo (1993), they favoured the use of ECM
when deriving the hedge ratio for spot stock and futures index hedging effectiveness due to
its clear relationship between spot and future prices. Lien (1996) then demonstrated that an
errant hedger who omits the cointgration relationship when using first difference model (eq
6) will result to a relatively poorer hedging performance compared to a hedger who takes into
account the cointegration relationship. Thus the hedge ratio regression under ECM should be
estimated as follows:
∑ ∑
Where and represents the spot and futures price changes at time ; signifies the
hedge ratio derived from ECM; denotes speed of adjustment parameter from
disequilibrium; is the residual term on the ECM regression.
Other research findings that support the cointegration relationship for S&P 500 Index Futures
to that demonstrated by Ghosh (1993) include Wahab & Lasgari (1993) and Arshanapalli &
Doukas (1997). Also, Quan (1992) found cointegration relationship between the spot and
short term futures prices in crude oil market as well. Chou et al (1996) who studied numerous
Nikkei spot index portfolios with NSA index futures, agreed with the ECM model being
more superior over conventional models such as price changes. They documented that ECM
does a better job in reducing the risk associated with the underlying cash position by on
average 2 percent in contrast to price changes with data spanning from 1989 to 1993. Also,
Lim (1996) who studied similar Nikkei stock and futures data confirmed the superiority of
ECM method. Ghosh & Clayton (1996) who applied the cointegration theory in estimating
the hedge ratio using stock index futures for CAC 40, FTSE 100, DAX and Nikkei also found
that ECM hedging effectiveness to be superior over those estimated by conventional models.
[8]

Despite of the clear existence of evidence pointing to the superiority of hedge ratios
estimated with the use of ECM over those calculated from price levels and price changes,
many other researchers have criticized the assumption of constant variance of and covariance
between the spot and futures instrument when OLS regression is used. They highlighted that
homoscedasticity or non-constant variances are evident when using OLS regression to
estimate the price level, price change and error correction model (ECM). They underlined
that in reality, inherent structural changes or shocks in economic conditions are bound to
occur such that the hedge ratio changes over time upon receiving new information. Such that,
the hedge ratio is time-varying over time (Grammatikos & Saunders, 1983)(Brooks & Chong,
2001). Thus, more sophisticated alternative hedging models such as ARCH and GARCH
framework developed by Engle (1982) and Bollerslev (1986) should be used. While the
ARCH model received considerable attention as it models heteroscedasticity, GARCH model
were more frequently used since it permits more parsimonious description over ARCH
conditional variance equation with arbitrary linear declining lag structure as a result of Box
Jenkins ARMA terms.
In accordance to the use of GARCH, Kroner & Sultan (1993) compared the hedging
effectiveness of hedge ratio derived from a bivariate error correction model (ECM) fitted
with a GARCH error structure found to have a higher hedging effectiveness and variance
reduction compared to that of conventional models. Their research documented that within in
sample test, conditional hedge tend to outperform conventional OLS hedge by 2.5 percent.
While in an out-sample test, conditional hedge outperforms conventional OLS hedge by 1.5
percent. Their study was performed using five different currency spot and futures data over
the period of 1985 to 1990.
Similarly, Bailie & Myers (1991) applied the use of multivariate GARCH specification to
model the conditional the conditional covariance matrix for six commodities futures contract.
They illustrate the superiority of dynamic models over unconditional OLS models in terms of
hedging effectiveness. Additionally, Park & Switzer (1995) provided support for the
superiority of GARCH hedge ratio over OLS models in their study of hedging performance
using S&500 index futures and Toronto 35 index futures data. They commented that though
GARCH model is the most preferred, the potential utility gain from portfolio rebalancing
must outweight the losses arising from transaction cost.

2.3 Recent work in Hedge Ratio Estimation
Following the development of dynamic hedging models, recent researches have put
forth much more complex estimation methods some of which have yet to be proved of their
severe improvements. For example, Also, Lypny & Powalla (1998) examined the hedging
effectiveness of dynamic hedging strategy of an Error Correction Model fitted with a
GARCH (1,1) for German Index DAX futures found statistically and economically
superiority of the model over error correction model fitted with no GARCH and GARCH
fitted with no error correction term. They explain the adoption of ECM-GARCH delivers the
highest utility for both in and out sample periods even when transaction costs related to
rebalancing were included.
Also, Lien & Tse (1999) applied the price change, vector autoregrssive model (VAR), ECM
and ARFIMA-GARCH approaches using Nikkei Stock Average (NSA) index over the period
of 1989 to 1997 concluded that price change hedge ratio performed the worst as compared to
the other models. Couple with that, Floros & Vougas (2004) estimated the hedge ratio using
daily data on Greek stock and futures market from August 1999 to August 2001 over the debt
crisis period based on price change, ECM, Vector ECM (VECM) and multivariate GARCH
model (M-GARCH). They found to be most superior over other models.
Another paper who examined conditional hedge ratio modelling includes Laws &
Thompson (2005) who compared the hedge ratio obtained through OLS, GARCH, EGARCH
in mean and exponential weighted moving average (EWMA) models using FTSE 100 and
FTSE 250 stock index futures data. Their findings highlighted that EWMA to be superior
over others methods throughout the period from January 1995 to December 2001. Also,
Pradhan (2011) who focused on the impact of asymmetries on the hedging of S&P CNX
Nifty Index and its futures index using OLS, VAR, VECM and MGARCH. The outcome of
her research, based on 1871 daily observation spanning the period of June 2000 to April
2007, shows that asymmetric models such as MGARCH to provide the greatest portfolio risk
reduction and generates the highest portfolio return.

Other recent findings include Hou & Li (2013) who studied the hedging performance
of newly established CSI 300 stock index futures using wavelet analysis, price change, ECM,
constant conditional correlation (CCC), dynamic conditional correlation (DCC) and
BGARCH. Their empirical result concludes that short-run hedging horizon favours the use of
BGARCH while long run hedging horizon favours unconditional price change model. In the
same year, Kostika & Markellos (2013) who analysed the hedging performance of optimal
hedge ratio derived from an autoregressive conditional density (ARCD) which allows four
moments of conditional distribution of normalized error to be have higher hedging
effectiveness and variance reduction in contrast to GARCH, price changes and ECM models.
2.4 Inconclusive debates on Model Specification
To date, the debate on which method is really the best option is still ongoing. This is
because there are conflicting evidences which can be found from other literatures. For
instance, Kroner & Sultan (1991) applied the use of bivariate GARCH model for Japanese
Yen spot and futures return found it to be inferior to that of unconditional OLS based model
in term of risk reduction. In the same year, Myers (1991) who studied extensively on
Michigan‟s wheat commodity futures found only marginal improvement of GARCH model
in terms of hedging effectiveness over constant unconditional covariance hedge approach
estimated by OLS models. His findings concluded that GARCH hedging will not be
appropriate for risk adverse hedger due to the extra expenses arising from portfolio
rebalancing and complexity of using GARCH model.
Another prominent paper is from Holmes (1996) who analysed the ex-post hedging
effectiveness for UK FTSE 100 contract. He found that the risk reduction of a hedge strategy
based on hedge ratio estimated by unconditional OLS models outperforms advanced and
sophisticated techniques such as ECM and GARCH. Chakraborty & Barkoulas (1999) agrees
on the non-importance of utilizing sophisticated techniques such as GARCH (1,1) in
estimating hedge ratio as transaction cost associated with portfolio rebalancing will outweigh
the benefits. Their arguments were based on the empirical application to five leading
currencies spot and futures market data. The paper offered by Sim & Zurbrruegg (2001)
offers similar arguments on conditional and unconditional models on the FTSE-100 spot and
futures contract found that the latter shows significant advantage in hedging effectiveness
compared to the former.

Another paper by Lien, et al. (2002) explained that if conditional heteroscedasticity is a
characteristic of many financial time series, there is no clear superiority of conditional
models. They applied the use OLS, constant correlation model and GARCH in relevance to
ten spot and futures market covering currency, commodity and stock index futures and found
that the latter do not outperform the classical OLS and also constant correlation model. The
use of GARCH was further questioned as a result of expensive transaction cost due to
portfolio rebalancing. Other more recent papers which found no evidence that complex
econometric models have significant improvement over simple ordinary least square hedge
ratio includes Boystrom (2003), Alexander & Barbosa (2007), Harris, et al (2010), Chen, et al
(2014) and Wang, et al (2015).
Here, rather than contributing to the endless debate on conditional or unconditional
optimal hedge ratio model, this paper looks into the fundamental correlation coefficient
between the price of unhedged position with the price of the hedging instrument as discussed
by Ederington (1979). He highlighted that the optimal hedge ratio with hedging effectiveness
is a function of the correlation coefficient between the price of the spot and futures contract
eq [4]. Also, Ghosh & Clayton (1996) highlighted that the fundamental correlation between
the price movement of the spot instrument and futures contract is an important factor to
determine the hedging effectiveness. Moreover, Law & Thompson (2005) documented that
the reduction in risk for various hedge ratio models were generally lower as attributed to the
low correlation coefficient between the return on the investment portfolio and the hedging
indices. Additionally, .Moosa (2003) who analysed similar proposition employed four
different models found that hedge ratio and hedging effectiveness to be inconsequential to
model specification. He commented:
“Although there are many theoretical arguments on which model specification suits best for
deriving the optimal hedge ratio, the matter is still elegant. Though, what determines the
hedging success rate depends on the correlation coefficient between the unhedged and
hedging instrument (Moosa, 2003)”
Thus, the objective of this paper follows in spirit of Ghosh and Clayton (1996), Law
and Thompson (2005) and Moosa (2003) to ascertain whether hedge ratio is indeed
inconsequential to model specification using four constant unconditional models; (i) Levels
(ii) First Difference (iii) Quadratic and (iv) Error Correction Model (ECM).

The methodology entailed the estimation of the hedge ratio with the use of money market and
cross currency hedge as the hedging instrument instead of futures contract which have been
widely discussed by many researchers. Here, we will use Swiss Franc (CHF), British Pound
(GBP) and Hong Kong Dollar (HKD) to discuss the paper‟s objective. Prior to discussing the
methodology, it is important to understand the basic principles of financial hedging. Thus, the
next section highlights the concept of financial hedging techniques.
[Next page for Section 3 on the concepts of financial hedging]

Section 3: The Concepts of Financial Hedging
3.1 Forward Market Hedge
A forward contract is an agreement between two parties to exchange a specified
amount of a currency at a specified exchange rate on a specified date in the future. When a
corporation anticipate future need for or future receipt of a foreign currency, they can set up
forward contract to lock in the rate at which they can purchase or sell a particular foreign
currency.
An example from a receivables point of view, a corporation enters into a forward
hedge when it decides to insulated its foreign receivables from possible depreciation.
Thus, it will locks itself into a predetermine exchange rate known as forward rate at
which it can sell a specific foreign currency and exchange it to home currency ,
therefore allow it to hedge the foreign receivables due at time . By locking into a
forward contract, the uncertainty which lies within the future home currency value ultimately
changes to a certain home currency value since the forward rate is known a time . This can
be illustrated as follows:
( )
( ) ( ) [ ( )
]
Where
( )
( )
[9]
[10]

3.2 Futures Market Hedge
`Currency futures contracts are standardized contracts specifying a standard volume
of a specific currency to be exchange for another currency on a specific settlement date in the
future. Thus, currency futures contract are similar to forward contracts in terms of their
obligation, though differ from forward contracts in several ways. Firstly, currency futures
contracts are traded on an exchange, therefore are standardized. Forward contracts on the
other hand are private agreement between two parties, thus the agreement can be tailored to
individual needs. Since forward contracts are private agreements, there is a possibility a party
may default on its side of agreement. The default risk for futures contracts are close to zero
due to the existence of clearing house. Secondly, futures contract are marked to market
(MTM) hence settlements are on a daily basis until the end of the contract. In the case of
forward contract, settlement only occurs at the end of the contract. Third, futures markets are
more liquid than forward market. Therefore, futures hedger can close their position if their
contract timing fails to match the underlying exposure.
3.3 Money Market Hedge
Another alternative hedging technique is money market hedge. To hedge in the
money market, the corporation will have to borrow the present value of the foreign
receivables in the foreign country at time . The present value is calculated by
discounting the future value of the foreign receivables with the foreign interest rate (
applicable from to . Immediately after that, convert the borrowed present value of
foreign currency into home currency based on the current spot exchange rate between and
. Following that, invest the proceeds based on the home currency interest rate (
applicable from to . The borrowed foreign currency will be repaid with the proceeds
from the receivables ( paid by its foreign counterpart at . Here, the money market
hedge creates a foreign denominated liability (loan) to offset the foreign denominated asset
(receivables) (Eiteman, et al., 2013). A money market hedge involves the use of a contract
and a source of funds to fulfil the respective contract. In the above instance, the contract is a
loan agreement. The corporation seek the use of money market hedge to borrow in one
currency and exchange the proceeds to another currency. Funds to fulfil the contract – that is
to repay the loan are generated from the business operation or receivables.

The discussed can be written as:
( )
( )
Money market hedge can also be considered as a synthetic forward hedge or a
hedging technique of which mimics the characteristic of a forward hedge (Butler, 2012). This
is particularly true only when covered interest parity condition holds (Al-Loughani & Moosa,
2000). According to the theory of covered interest parity condition, the variation in exchange
rate between two currencies is mainly caused by the differential in the national interest rates
for securities of similar risk and maturity. Thus, arbitrage opportunities from interest rate
differential do not exist. As a consequence, the receivables will be the same for both
forward and money market when interest parity condition holds. As a result, the outcome
from equation [10] will be the same as equation [13]1
or as follows:
( ) ( )
3.4 Cross Currency Hedge
While Al-Loughani & Moosa (2000) proposed that money market hedging is an
effective hedging technique as forward hedging when covered interest parity (CIP) holds.
Chang & Wong (2003) highlighted that some currencies particularly less developed countries
(LDCs) may not be easily available due to its less matured or heavily controlled capital
markets. While this restricts the use of money market hedging, there are, however, alternative
options such as cross currency hedge where a third currency is introduced to act as a
hedge against the base and exposure currency.
The general idea behind this hedging technique is for any profit (loss) made on the
exposure to be offset by the loss (profit) made on the third currency position. For this
technique to work, the exposure and third currency must be highly correlated to the base
1
Appendix 1 illustrates an example of synthetic forward hedge when CIP holds
[12]
[13]
[14]
[11]

currency. The cross hedge can be in the form of forward, futures or options. According to
Eaker & Grant (1987) whom analysed the use of cross currency hedge between EMS
currencies, he presented that a third currency which belong to the European Monetary System
(EMS) will be an effective hedge to an exposure currency which also belong to the EMS.
Additionally, Moosa (2004) documented that the correlation of the third and exposure
currency to the base currency should be equal or more than 0.50 in order for the hedging
technique to be effective. Furthermore, Aggarwal & Demaskey (1997) concluded that
Japanese Yen to be an effective third currency to hedge against investment in Asian newly
industrialized countries (AIC) due it‟s to close economic integration. Brooks & Chong (2001)
also found that cross currency hedge between USD/DEM and USD/GBP are effective in
reducing portfolio risk due to the high correlation as a result of close economic relationship
between Germany and United Kingdom.
[Next page explains Section 4 methodology applied in this paper]

Section 4: Methodology
4.1 Optimal Hedge Ratio Estimation
The present study employs the regression discussed by Dale‟s (1981), H&S (1981),
Broll et al (2001) and Ghosh (1996) to estimate the optimal hedge ratio. Here, let and
represent the logarithmic prices of the unhedged position and the hedging instrument
respectively such that and denotes the rates of return on their prices. Thus, the
underlying regression for price levels, price changes and quadratic regression are written as
Where , and are the estimated hedge ratio while the represents the hedging
effectiveness or based on Ederington (1979) model. In the case of foreign currency
exposure, is the logarithmic spot exchange rate on the exposure currency expressed in
base currency or . On the other hand, the hedging instrument position will be
represented by money market and cross currency hedge instead of futures contract that have
been widely documented by many researchers. If money market hedge is used, such that the
offsetting position involves an interest parity forward rate (̅) consistent with covered
interest parity. Therefore
̅ ( )
Where
̅ ( ) *
( )
+
Where and represents the interbank interest rate for currency and .
[16]
[17]
[18]
[19]
[15]

If the hedging instrument is represented by a cross currency hedge, then a third currency
will be introduced. With the use of a third currency , a second exchange rate between
and or will be formed and used as a hedging instrument. Similarly, will be in
logarithmic form. Thus, can also be represented as:
( )
An alternative method to estimating the hedge ratio for equation 16 and 17 is through
(Markowitz, 1952) portfolio theory. At first the representation to minimize the variance of the
portfolio value for equation [16] and [17] can be represented by:
Following that, the minimum hedge ratios can be derived by differentiating both equations
with respect to their hedge ratios and solve the first order conditions,
( )
( ) ( )
( )
( ) ( )
In which later will gives
As highlighted in the literature review, Ghosh (1993) and Lien (1996) documented
that an errant hedger who omits the cointegration relationship but uses price levels or price
changes model will result to a smaller than optimal position on the hedging instrument
ultimately leading to a poorer hedging performance compared to a hedger who takes into
account the cointegration relationship.
[20]
[21]
[22]
[23]
[24]
[25]
[26]

Thus, the hedge ratio from an ECM perspective should be estimated as follows:
∑ ∑
( )
Where and represents the logarithmic rate of return on the unhedged foreign
exposure position and hedging instrument at time ; signifies the hedge ratio derived from
ECM; denotes speed of adjustment parameter as a function of disequilibrium between the
unhedged position and hedging instrument while is the residual term on the ECM
regression.
Lien (1996) then provided a theoretical analysis on equation [28] and suggests when the two
price variables adjust from disequilibrium then it can be written as follows:
Such that the ECM hedge ratio can be calculated as
( )
( ⁄ )
Where represents the correlation coefficient between the residual terms and .
[27]
[28]
[29]
[30]
[31]
[32]

4.2 Rate of Return Estimation
In the above, four unconditional hedging models have been discussed to derive the
optimal hedge ratio. Using the estimated hedge ratios, the rate of return on the unhedged and
the hedged position are then calculated as follows:
( ̅( ))
Where represents the rate of return on the unhedged position, is the rate of return on
money market hedge and expressed as rate of return on cross currency hedge.
4.3 Variance Ratio (VR) and Variance Reduction (VD) Estimation
The null hypothesis focused in this paper will be to determine the hedging
effectiveness of money market and cross currency hedge on an underlying unhedged foreign
exchange exposure. To do these, the rate of return variance of the unhedged foreign exchange
exposure will be compared with the hedging instrument rate of return variance. This can be
formally written as follows:
H0: = [Null Hypothesis]
H1: > [Alternative Hypothesis]
Where, represents the rate of return on the unhedged position and is a function on the
rate of and . The represents the variance of the respective hedging instrument rate
of return. The null hypothesis will be rejected if:
Where VR is the variance ratio of the variance of , under no hedge case to the variance
obtained from a hedged case or while n is the sample size. If the ,
this indicates that the respective hedging instrument is effective in the sense that it reduces
the variation of the underlying foreign exposure position. The VR test can be complemented
with the variance reduction (VD) which is calculated as
* +
[33]
[34]
[35]
[36]
[37]

Section 5: Data and Empirical Results
5.1 Data
The empirical analysis discussed in this paper is performed using monthly exchange
rates and interest rates sourced directly from Bloomberg. The data spans over the period of 29
May 1998 to 30 September 2009, a length of time approximately twelve years with a total of
137 monthly observations. There is no significance in either the choice of exchange rates or
sample period. The exchange rates employed for this study will be the Swiss Franc ,
British Pound and Hong Kong Dollar .
The exchange rates obtained were directly quoted in terms of per unit of U.S Dollar. For the
purpose of this study, the direct exchange rate for or must be calculated.
This can be done by dividing ⁄ with ⁄ . also represents the underlying
unhedged position. Other than that, the cross exchange rate for or must be
determined. Similarly, this involves dividing ⁄ with ⁄ . Here,
represents one of the hedging instruments. The second hedging instrument will be
represented by the interest parity forward rate ̅ between and using monthly
interbank interest rate belonging to those currencies, and .The interest rates are
deannualised and expressed in decimals. Following that, , ̅ and are then measured in
logarithmic form before it being used to estimate the hedge ratio via ordinary least square
(OLS) method under the four different models in eViews 8.
Table 1: The Variables – Definition and Specifications
Variables Definition and Specification
Exchange Rate for [Foreign Exposure]
̅ Interest Parity Forward Rate for [ Hedging Instrument]
Exchange Rate for [ Hedging Instrument]
Switzerland one Month Interbank Interest Rate
United Kingdom one Month Interbank Interest Rate

Table 2: Descriptive statistics for , ̅, and
̅ iCHF iGBP
Mean 2.282 2.275 0.175 1.433 4.742
Median 2.310 2.304 0.168 1.188 4.805
Minimum 0.221 0.220 0.027 0.999 1.426
Maximum 1.895 1.863 -0.986 -1.021 1.970
Standard Deviation (SD) -1.306 -1.292 0.361 0.445 -1.028
Skewness 1.560 1.557 0.128 0.125 0.475
Kurtosis 2.679 2.670 0.231 3.410 7.563
No. of Observations 137 137 137 137 137
Figure 1: Switzerland and United Kingdom one month Interbank Interest Rate
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
1/5/1998
1/11/1998
1/5/1999
1/11/1999
1/5/2000
1/11/2000
1/5/2001
1/11/2001
1/5/2002
1/11/2002
1/5/2003
1/11/2003
1/5/2004
1/11/2004
1/5/2005
1/11/2005
1/5/2006
1/11/2006
1/5/2007
1/11/2007
1/5/2008
1/11/2008
1/5/2009
InterestRate(%)
iCHF iGBP

Figure 2: Graphical illustration for , ̅ and
1.4
1.6
1.8
2
2.2
2.4
2.6
1/5/1998
1/10/1998
1/3/1999
1/8/1999
1/1/2000
1/6/2000
1/11/2000
1/4/2001
1/9/2001
1/2/2002
1/7/2002
1/12/2002
1/5/2003
1/10/2003
1/3/2004
1/8/2004
1/1/2005
1/6/2005
1/11/2005
1/4/2006
1/9/2006
1/2/2007
1/7/2007
1/12/2007
1/5/2008
1/10/2008
1/3/2009
1/8/2009
Swiss Franc (CHF) Per British Pound (GBP)
1.5
1.7
1.9
2.1
2.3
2.5
2.7
1/5/1998
1/10/1998
1/3/1999
1/8/1999
1/1/2000
1/6/2000
1/11/2000
1/4/2001
1/9/2001
1/2/2002
1/7/2002
1/12/2002
1/5/2003
1/10/2003
1/3/2004
1/8/2004
1/1/2005
1/6/2005
1/11/2005
1/4/2006
1/9/2006
1/2/2007
1/7/2007
1/12/2007
1/5/2008
1/10/2008
1/3/2009
1/8/2009
Interest Parity Forward Rate for Swiss Franc (CHF) per
British Pound (GBP)
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
1/5/1998
1/10/1998
1/3/1999
1/8/1999
1/1/2000
1/6/2000
1/11/2000
1/4/2001
1/9/2001
1/2/2002
1/7/2002
1/12/2002
1/5/2003
1/10/2003
1/3/2004
1/8/2004
1/1/2005
1/6/2005
1/11/2005
1/4/2006
1/9/2006
1/2/2007
1/7/2007
1/12/2007
1/5/2008
1/10/2008
1/3/2009
1/8/2009
Swiss Franc (CHF) Per Hong Kong Dollar (HKD)

5.2 Preliminary Checks
5.2.1 Unit Root Tests
Table 3: ADF and KPSS Unit Root Tests
Augmented Dickey Fuller
(ADF)
Kwiatkowski Pihllips Schmidt Shin
(KPSS)
Variable t-statistics P value LM Statistics
Levels With Intercept
-0.137494 0.9420 0.782206
̅ 0.157667 0.9397 0.780912
-0.621351 0.8610 1.199675
First Difference
-13.08219 0.0000 0.233972
̅ -13.12556 0.0000 0.233247
-12.14207 0.0000 0.131748
Critical Values
Test Models 1% 5% 10%
ADF -3.479 -2.882 -2.578
KPSS 0.739 0.463 0.347
Source: Appendix 2
Note: The null hypothesis for ADF test is by the presence of unit root while the null hypothesis for
KPSS test is by the presence of stationarity.
In order to avoid spurious regression results, it is necessary to first test whether the
variables are stationary or non-stationary. To test for stationarity, the Augmented Dickey
Fuller test proposed by Dickey Fuller (1979) and KPSS test proposed by Kwiatkowski et al
(1992) are used. The KPSS test is used as a complement to ADF test as the credibility of
ADF were questioned by Schwert (1987). The null hypothesis for ADF test is that the series
contains a unit root. While the null hypothesis for KPSS test is that the series is stationary.
Table 3 reports the unit tests on the logarithmic levels and first difference of , ̅ and 2.
The results indicate that all three variables are non-stationary at levels since ADF and LM-
statistics indicate insignificance of p value and LM statistics. To solve for non-stationary, the
2
The variables are in logarithmic form

variables are differentiated once. As expected, both ADF and KPSS test indicate that all
variables are stationary or an I(1) process.
5.2.2 Autocorrelation
Table 4: Autocorrelation Test using Durbin Watson and Breusch Godfrey LM Test
Variable DW test
(AR (1))
LM test Chi-Sq
Probability
Money Market Hedge
0.101 -
2.186 -
0.226 -
2.007 0.0263 (Lag 3)
Cross Currency Hedge
0.083 -
1.832 -
0.093 -
1.995 0.0134 (Lag 9)
Source: Appendix 3 and 4
Note: The DW statistic is always between 0 to 4. A value of 2 indicates no autocorrelation of order
one, AR (1), in the sample. The Breusch-Godfrey LM test null hypothesis represents no higher order
of autocorrelation.
For practical learning purpose, I have modelled for autocorrelation problems even
though it might not have substantial effects on the hedging effectiveness.. Based on Table 4
above, AR (1) was imminent in both levels and quadratic model for money market and cross
currency hedge as exhibited by their low Durbin Watson. As highlighted by Hill &
Schneweeis (1981) presence of autocorrelation will overstate the hedging effectiveness.
Moreover, although the hedge ratio estimate will still be unbiased, it longer contains a
minimum variance (no longer BLUE3
). As a consequence, the variables required differencing
to solve for autocorrelation problem. After differencing the variables once, both first
3
Gauss Markow Best Linear Unbiased Estimate Theorem

difference and error correction model (ECM) show no evidence on any significant
autocorrelation of first order, AR (1), based its Durbin Watson that is close to 2.
Since the error correction model (ECM) for both money market and cross currency
hedge uses two lag dependent variables, I further tested for serial correlation beyond AR(1)
using the correlogram Q statistics and Breusch-Godfrey (1986) LM test. In reference to the
correlogram Q statistics for money market ECM, there appears to be a significant
autocorrelation at lag 3. To confirm this, I performed the Breusch-Godfrey LM test on the
lag, the result concluded that autocorrelation exist for lag 3. As a consequence, I reestimated
the model with an MA(3) term to correct the autocorrelation problem. For cross currency
ECM model, it was found to contain a significant serial correlation at lag 9 hence I
reestimated the model with an MA (9) term. After that, the LM test confirmed that there was
no significant autocorrelation at lag 9.
Table 5: Variance Reduction comparison for ECM models with and without MA terms
Type Variance Reduction (VD)
Money Market Hedge
ECM without MA(3) term 0.9999
ECM with MA(3) term 0.9999
ECM without MA(9) term 0.3838
ECM with MA(9) term 0.3868
Source: Appendix 5
Note: VD is calculated based on equation [37]
To check for any significant differences between the ECM models which does and
does not take into account of autocorrelation beyond lag one, I compare their variance
reductions (VD) for both money market and cross currency hedge. Table 5 documents the
results. As suggest by Moosa (2015), there is indeed not much difference between models
with and without MA terms. Both models were found to portray similar results. The
difference for cross currency was mainly attributed to the differences in hedge ratio estimate.
For the purpose of isolating the autoccorelation effects on the optimal hedge ratio coefficient
estimate, I will proceed with the ECM models with the autoregressive (AR) terms.

5.2.3 Normality Tests
Table 6: Jarque Bera Test
Type JB Skewness Kurtosis
Money Market Hedge
0.722 0.1444 3.208
169.342 -1.012 8.078
15.120 0.616 4.062
122.881 -0.621 7.523
71.132 -1.277 5.435
194.153 -1.337 8.206
54.888 -1.144 5.091
42.521 -0.794 5.255
Source: Appendix 6
Note: The null hypothesis for Jarque Bera test is by the presence of normal distribution in the errors.
The null hypothesis is rejected when JB-calc > 5.99.
Another important error testing to consider is normality test using the Jarque-Bera
(1980) test. The results shown in Table 6 for both money market and cross currency hedge
using four different models illustrated that the errors are not normally distributed. Except for
levels under money market hedge, others have non symmetrical error distribution While this
may affect the inference made on the hedge ratio, central limit theorem holds in this case
since the sample size is sufficiently large enough ( >50). Central limit theorem (CLT)
suggests that the coefficient to have approximately normal distribution even if the residuals
are not normal under the circumstances of large sample set (Stuart, 2014).

5.2.4 Cointegration Relationship
Table 7: Engle-Granger test for unit root in the residual of the cointegration equation
Type t statistics P-value
Money market: ̅ regression -12.745 0.000
Cross Currency: regression -6.065 0.000
Significance level 1% 5% 10%
Critical Values -3.479 -2.882 -2.578
Source: Appendix 7
Note: The null hypothesis of the test presented is by the presence of unit root in the residual of the
cointegrating equation using ADF test.
Cointegration relationship must be necessarily proven before estimating the hedge
ratio under error correction model (ECM) for both money market and cross currency hedge.
There are two commonly used way to test for cointegration. The Engle & Granger (1987)
methodology seeks to determine whether the residuals of the equilibrium relationship are
stationary, while Johansen (1988) methodology determines the rank of matrix consisting of
the cointegrating vectors in the error correction model.
In this paper, I will proceed with Engle & Granger‟s two step estimation
methodology. The first step is to ensure that both price series are difference stationary in the
same order. The second step then hinges on the results from the first step. The residual )
from the regression with the same order difference stationary of with ̅ and with are
then tested for stationarity at levels or process. The golden rule is that if the residual of
the regression ) is found to be stationary, than a cointegrating relationship exist.
Under money market hedge, the regression between and interest parity forward
rate, ̅, was first tested for stationarity. As shown in Table 3, the unit root test concludes that
both variables are non-stationary at levels but stationary at first difference. Since both are
integrated of the same order, there might exist a linear combination between the two series.
To test for that, a regression was run between the first difference of and interest parity
forward rate, ̅.

Following that, the residual from the regression ) was then tested for unit root.
Based on Table 7 above, the results concluded that the residual series from the regression was
found to be stationary thus a cointegrating relationship exists. The same inference was made
for the residual series between the first difference of and . Overall, error correction
models do exist for both money market and cross currency hedge.
[Next page for Section 5.3 Empirical Results]

5.3 Empirical Results
Money Market Hedge: Rate of Return Comparison
Figure 3: Rate of Return between Unhedged Position and Money Market Hedge based
on Levels Model
on First Differences Model
-17
-12
-7
-2
3
8
1/5/1998
1/11/1998
1/5/1999
1/11/1999
1/5/2000
1/11/2000
1/5/2001
1/11/2001
1/5/2002
1/11/2002
1/5/2003
1/11/2003
1/5/2004
1/11/2004
1/5/2005
1/11/2005
1/5/2006
1/11/2006
1/5/2007
1/11/2007
1/5/2008
1/11/2008
1/5/2009
RateofReturn(%)
Levels
Rate of Return on Unhedged Position (RU) Rate of Return on Hedge Position (RH)
-17
-12
-7
-2
3
8
1/5/1998
1/11/1998
1/5/1999
1/11/1999
1/5/2000
1/11/2000
1/5/2001
1/11/2001
1/5/2002
1/11/2002
1/5/2003
1/11/2003
1/5/2004
1/11/2004
1/5/2005
1/11/2005
1/5/2006
1/11/2006
1/5/2007
1/11/2007
1/5/2008
1/11/2008
1/5/2009
RateofReturn(%)
First Differences

on Quadratic Model
on Error Correction Model (ECM)
-17
-12
-7
-2
3
8
1/5/1998
1/11/1998
1/5/1999
1/11/1999
1/5/2000
1/11/2000
1/5/2001
1/11/2001
1/5/2002
1/11/2002
1/5/2003
1/11/2003
1/5/2004
1/11/2004
1/5/2005
1/11/2005
1/5/2006
1/11/2006
1/5/2007
1/11/2007
1/5/2008
1/11/2008
1/5/2009
RateofReturn(%)
Quadratic
-17
-12
-7
-2
3
8
1/5/1998
1/11/1998
1/5/1999
1/11/1999
1/5/2000
1/11/2000
1/5/2001
1/11/2001
1/5/2002
1/11/2002
1/5/2003
1/11/2003
1/5/2004
1/11/2004
1/5/2005
1/11/2005
1/5/2006
1/11/2006
1/5/2007
1/11/2007
1/5/2008
1/11/2008
1/5/2009
RateofReturn(%)
Error Correction Model (ECM)

Cross Currency Market Hedging: Rate of Return Comparison
Figure 7: Rate of Return between Unhedged Position and Cross Currency Hedge based
on Levels Model
on First Differences Model
-20
-15
-10
-5
0
5
10
1/6/1998
1/12/1998
1/6/1999
1/12/1999
1/6/2000
1/12/2000
1/6/2001
1/12/2001
1/6/2002
1/12/2002
1/6/2003
1/12/2003
1/6/2004
1/12/2004
1/6/2005
1/12/2005
1/6/2006
1/12/2006
1/6/2007
1/12/2007
1/6/2008
1/12/2008
1/6/2009
RateofReturn(%)
Levels
-20
-15
-10
-5
0
5
10
1/6/1998
1/12/1998
1/6/1999
1/12/1999
1/6/2000
1/12/2000
1/6/2001
1/12/2001
1/6/2002
1/12/2002
1/6/2003
1/12/2003
1/6/2004
1/12/2004
1/6/2005
1/12/2005
1/6/2006
1/12/2006
1/6/2007
1/12/2007
1/6/2008
1/12/2008
1/6/2009
RateofReturn(%)
First Differences

on Quadratic Model
Figure 10: Rate of Return between Unhedged Position and Cross Currency Hedge
based on Error Correction Model (ECM) Model
-50
-40
-30
-20
-10
0
10
20
30
40
1/6/1998
1/12/1998
1/6/1999
1/12/1999
1/6/2000
1/12/2000
1/6/2001
1/12/2001
1/6/2002
1/12/2002
1/6/2003
1/12/2003
1/6/2004
1/12/2004
1/6/2005
1/12/2005
1/6/2006
1/12/2006
1/6/2007
1/12/2007
1/6/2008
1/12/2008
1/6/2009
RateofReturn(%)
Quadratic
-20
-15
-10
-5
0
5
10
1/6/1998
1/12/1998
1/6/1999
1/12/1999
1/6/2000
1/12/2000
1/6/2001
1/12/2001
1/6/2002
1/12/2002
1/6/2003
1/12/2003
1/6/2004
1/12/2004
1/6/2005
1/12/2005
1/6/2006
1/12/2006
1/6/2007
1/12/2007
1/6/2008
1/12/2008
1/6/2009
RateofReturn(%)
Error Correction Model (ECM)

Figure 3 to Figure 10 illustrates a graphical comparison between the returns on the
unhedged position with returns from money market and cross currency hedge under four
different unconditional models. For money market hedge, Figure 3 to Figure 6 shows that the
return variances on the hedged positions are significantly reduced when using the hedge
ratios derived from the four different models. All four models depict a similar low volatility
over the sample period. Thus, this may suggest that money market is an effective hedging
instrument for the underlying unhedged foreign currency exposure.
In contrast to cross currency hedge, Figure 5, 6 and 8 illustrates that the return
variances on the hedged position still remains volatile as compared to the unhedged position.
Also, an interesting observation in Figure 7 shows that the variance of the returns of the
hedged position using hedge ratio derived from quadratic model has a higher foreign
exchange risk exposure compared to the unhedged position. Thus the higher degree of
hedging using the optimal hedge ratio derived from quadratic model, the higher the foreign
exchange risk exposure. Overall, cross currency hedge may not be an effective hedging
instrument to hedge the underlying unhedged position.
Table 8: The Estimated Hedge Ratios for H1 and H2
Hedging Method Estimated Hedge Ratio (h) t statistics
Money Market
Levels 1.0044 1519.210 0.999
First Differences 1.0003 1421.846 0.999
Quadratic 1.0372 175.629 0.999
Error Correction Model 1.0007 1372.820 0.999
Cross Currency Market
Levels 0.4699 11.054 0.475
Quadratic -2.4265 -2.531 0.509
Note: Esimated (h) is the coefficient derived from regressing the logarithmic return on the unhedged
position with the hedging instrument following the use of four models. measures the hedging
effectiveness between the unhedged and hedging instrument.

Table 9: The Estimated VD and VR for H1 and H2
Hedging Method Variance
(RU)
Variance
(RH)
VD (%)
Money Market
Levels
7.397
0.001 11353.150 99.991
Quadratic 0.011 692.602 99.856
Cross Currency Market
Levels
7.397
4.559 1.622 38.365
Quadratic 85.608 0.086 -1057.369
Note: Estimated VR statistical significance is determined by comparing with f- distribution critical
value of 1. 327 (probability of 0.5 and d.f of 136).Whereas, VD measures the variance reduction
capability of the hedging instrument on the unhedged position.
Coupled with Figure 3 to 10, Table 8 and 9 depicts the descriptive results on the
hedge ratio , the hedging effectiveness ( ), the variances, variance ratio and
variance reduction for both money market and cross currency hedge using the four
different models Firstly, by looking at the variance of the unhedged position in contrast to the
hedged position regardless of money market or cross currency, it is no surprise that a no
hedge position has the highest volatility. Except for cross currency quadratic model, all
hedged position has a lower return variance as compared to a no hedge case. Thus the hedged
portfolios perform better than the unhedged position.
Secondly, the hedge ratios under money market hedge using four different models do not lead
to a vast dissimilarity and that the variance reductions are not all that different. In all cases,
hedging is effective and is approximately 99 percent throughout the sample period.
Also, all four models are statistically significant since their variance ratio far exceeds
the f distribution critical value of 1.327. Thus, the null hypothesis which stems that the
variance of the unhedged position is the same as the variance of the hedging instrument is
rejected. Also, the variance reductions appeared to be significant high or approximately
99 percent. Thus it is effective to hedge the unhedged position with money market hedging.
The strong hedging effectiveness and significant variance reduction (VD) here can be mainly
attributed to the strong correlation coefficient between the unhedged position and interest

parity forward rate between and . Here, the hedge ratios estimated under money
market are optimal.
Third, when the correlation coefficient between the unhedged position and hedging
instrument weakens, the hedging effectiveness ultimately declines. This can evident
based on cross currency hedge. Although, three out of four models under cross currency
hedge are statistically significant since VR exceeds the f-distribution critical value of 1.327.
The variance reductions (VD) for levels, first difference and error correction model (ECM)
are only approximately 39 percent throughout the sample period. This result is far from the
variance reduction obtained under money market hedge even though the null
hypothesis is rejected in this case. As a result, the hedge ratios under cross currency
hedge are suboptimal. Although the results here suggest that cross currency hedge may not be
suitable for the underlying unhedged position, it is not generalize across other cross currency
hedges. As highlighted by Eaker and Grant (1987), cross currency hedge may be effective
when a third and base currency are part of the same region such as the European Monetary
System (EMS).
Fourth, although the quadratic model under cross currency hedge remains as statistically
insignificant an interesting finding is that an increase in hedge position
actually leads to higher foreign exchange risk exposure. This argument is similar to what was
illustrated in Figure 9 which encompasses the comparison between the returns of unhedged
position with the return of the cross currency quadratic model.
Fifth, the results illustrated for money market hedge tend to mirror as what was documented
by Hill and Schneeweis (1981). As a consequence of serial correlation or autocorrelation of
order one, AR (1), the hedge ratio and hedging effectiveness of levels and quadratic model
tend to be higher than the first difference and error correction model (ECM). Thus, ultimately
an errant hedger whom ignores the serial correlation problem tend to be under hedged and
faces a maturity mismatch which requires him or her to regularly update their hedge position.
Overall, it can be concluded that the selection of models used to determine the
optimal hedge ratio are not that of significance and can be negligible here. Though, what
matters the most is the correlation coefficient ( ) between the price of the unhedged position
with the price of hedging instrument. High correlation invariably produces effective hedge

irrespective to how the hedge ratio is modelled while low correlation typically produces
ineffective hedge as evident by cross currency hedge.
5.4 Out of Sample Hedging Effectiveness
Figure 11: Outsample hedging effectiveness simulation
Table 10: Comparison of Out-of-Sample Hedging Effectiveness
Money Market Hedge Cross Currency Hedge
Variance
(RH)
Variance
Ratio (VR)
Variance
Reduction
(VD) %
Variance
Return (RH)
Variance
Ratio (VR)
Variance
Reduction
(VD) %
Levels 0.000 21103.942 99.995 6.302 1.522 34.281
First
Difference
0.000 22402.040 99.996 6.216 1.543 35.173
Quadratic 0.001 17912.153 99.994 62.053 0.155 -547.118
ECM 0.000 22576.245 99.996 6.226 1.540 35.068
Note: Estimated VR statistical significance are determined by comparing with f- distribution
critical value of 1.4944 (probability of 0.05 and d.f of 68).
Here, both the theoretical and empirical results on hedging effectiveness are explained
with an in-sample approach. In such an approach it is assumed that the optimal hedge ratio
and the hedging effectiveness can be determined in the same period. However, this is highly
unrealistic in practice and practitioner are concern is which method provides the greatest out-
of-sample hedging performance (Geppert, 1995)(Jong, et al., 1997).
May 29
1998
December
30, 2003
September
30, 2009
Sample for the
calculation of
the hedge ratio
68 months 68 months
Hedge

To conduct an out-sample hedging effectiveness test, the whole data set which spans
from 29 May 1998 to 30 September 2009 with 136 observations are separated into two
periods. The first period (29 May 1998 to December 30, 2003) is used as a specific period to
calculate the hedge ratio. After this period, the estimated hedge ratio is then applied onto the
underlying unhedged position over the second period (January 30, 2004 to September 30,
2009). In other words, the ex-ante hedge ratio calculated over the period of 68 months is then
applied over the remaining 68 months to simulate the hedge.
The ex-ante hedge ratio will be determined similarly to the ex-post hedge ratio with equation
[15], [16], [17] and [28]. The measure of hedging effectiveness will be based on the variance
of the returns on the unhedged position over the variance of the returns on the hedging
instrument given by equation [36] and equation [37].
Based on Table 10, the results concluded that all four models under money market are
effective in reducing the variance of the return on the underlying unhedged position by
approximately 99 percent throughout the second sample period (January 30, 2004 to
September 30, 2009). All four models‟ variance return are close to zero and are statistically
significant since their variance ratio far exceeds the f-distribution critical value of 1.494.
Similarly to in-sample hedging effectiveness, both first difference and error correction model
(ECM) have the highest variance reduction (VD) among the four models.
In contrast to money market hedge, the out-of-sample hedging effectiveness of cross currency
hedge for all four hedge ratio models is inefficient. The variance returns for all four models
are far from zero. Even though three out of four models are statistically significant, variance
reduction measured in percentage are only approximately 35 percent. The cross currency
hedge variance reduction ability is far from those obtained from money market hedge.
Correspondingly to ex-post hedging effectiveness results showed in Table 9, the ex-ante
hedging effectiveness here exhibit similar results for both money market and cross currency
hedge.

Section 6: Limitations
The initial focus of the paper was to include conditional ECM-GARCH models into
the discussion. However, money market ECM-GARCH was found to be statistically
insignificant while cross currency ECM-GARCH was found to have convergence issue
(Appendix 8). Thus, the recommendation here for future research is to include other forms of
conditional model for discussion even though optimal hedge ratio is inconsequential to model
specification.
Section 7: Conclusion
There have been a considerable number of studies on deriving the optimal hedge ratio
model, yet there is no consensus to date. Instead of contributing to the endless pit of
conditional and unconditional model specification debate, this paper revisits the issue by
investigating the fundamental correlation coefficient between the price of the unhedged
position and hedging instrument and then determines whether model specification does in
fact matter when deriving the optimal hedge ratio. Four unconditional minimum variance
hedge ratio models have been applied to two hedging instruments to determine its hedging
effectiveness in minimizing the variance of the unhedged position returns. Rather than futures
contract, the hedging instruments adopted here were represented by money market and cross
currency. The underlying unhedged position was represented by a foreign currency exposure.
The empirical results concluded that high correlation coefficient between the price of
the unhedged position with the interest parity forward rate ( ̅) or money market hedge
invariably produces effective hedges in all four unconditional models. When the correlation
coefficient weakens, the hedging effectiveness typically produces an inefficient hedge as
evident by cross currency hedge case. Furthermore, it have been found that ex ante hedge
ratio derived from all four models under money market hedge are as effective as ex-post
hedge ratio. First difference and error correction model (ECM) documented higher variance
reduction (VR) out of the four models. In contrast to ex-ante hedge ratio for cross currency
hedge, the variance reduction (VR) were bare minimal as compared to money market hedge.
Overall, the findings here is line with what was documented by Ghosh & Clayton, Law and
Thompson (2002) and Moosa (2003) who suggest that hedge ratio is inconsequential to
model specification but what is important is the correlation coefficient or the relationship
between the price of unhedged position with the price of the hedging instrument.

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Appendices

Appendix 1: Forward and Money Market Hedge Illustration
Swiss firm expects to receive £50,000 receivables from its British counterpart
CHF1.65/ £1
1.75 % GBP annual interest rate
2.50% CHF annual interest rate
Forward Market Hedging
⁄
⁄
⁄
Money Market Hedging
⁄

Appendix 2: Augmented Dickey Fuller (ADF) test
Null Hypothesis: S1 has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.137494 0.9420
Test critical values: 1% level -3.478911
5% level -2.882748
10% level -2.578158
Null Hypothesis: F has a unit root
Exogenous: Constant
t-Statistic Prob.*
5% level -2.882748
10% level -2.578158
Null Hypothesis: S2 has a unit root
Exogenous: Constant
t-Statistic Prob.*
5% level -2.882748
10% level -2.578158

Null Hypothesis: D(S1) has a unit root
Exogenous: Constant
t-Statistic Prob.*
5% level -2.882910
10% level -2.578244
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: D(F) has a unit root
Exogenous: Constant
t-Statistic Prob.*
5% level -2.882910
10% level -2.578244
Null Hypothesis: D(S2) has a unit root
Exogenous: Constant
t-Statistic Prob.*
5% level -2.882910
10% level -2.578244

Kwiatkowski – Phillip – Schmidt – Shin (KWSS) test
Null Hypothesis: S1 is stationary
Exogenous: Constant
Bandwidth: 9 (Newey-West automatic) using Bartlett kernel
LM-Stat.
Kwiatkowski-Phillips-Schmidt-Shin test statistic 0.782206
Asymptotic critical values*: 1% level 0.739000
5% level 0.463000
10% level 0.347000
*Kwiatkowski-Phillips-Schmidt-Shin (1992, Table 1)
Null Hypothesis: S2 is stationary
Exogenous: Constant
LM-Stat.
5% level 0.463000
10% level 0.347000
Null Hypothesis: F is stationary
Exogenous: Constant
LM-Stat.
5% level 0.463000
10% level 0.347000

Null Hypothesis: DS1 is stationary
Exogenous: Constant
LM-Stat.
5% level 0.463000
10% level 0.347000
Null Hypothesis: DS2 is stationary
Exogenous: Constant
LM-Stat.
5% level 0.463000
10% level 0.347000
Null Hypothesis: DF is stationary
Exogenous: Constant
LM-Stat.
5% level 0.463000
10% level 0.347000

Appendix 3: eViews Regression Output
Money Market Hedge
(i) Levels
Dependent Variable: S1
Method: Least Squares
Date: 04/25/15 Time: 23:00
Sample: 1998M05 2009M09
Included observations: 137
Variable Coefficient Std. Error t-Statistic Prob.
C -0.000848 0.000545 -1.557770 0.1216
F 1.004404 0.000661 1519.210 0.0000
R-squared 0.999942 Mean dependent var 0.819730
Adjusted R-squared 0.999941 S.D. dependent var 0.105052
S.E. of regression 0.000806 Akaike info criterion -11.39352
Sum squared resid 8.78E-05 Schwarz criterion -11.35089
Log likelihood 782.4561 Hannan-Quinn criter. -11.37620
F-statistic 2307998. Durbin-Watson stat 0.100645
Prob(F-statistic) 0.000000
(ii) First Difference
Dependent Variable: DS1
Date: 04/25/15 Time: 23:05
Sample (adjusted): 1998M06 2009M09
Included observations: 136 after adjustments
C -3.30E-05 1.96E-05 -1.681662 0.0950
DF 1.000261 0.000703 1421.846 0.0000
R-squared 0.999934 Mean dependent var -0.002785

(iii) Quadratic
Date: 04/25/15 Time: 23:06
Sample: 1998M05 2009M09
C -0.012465 0.002141 -5.822877 0.0000
F 1.037165 0.005905 175.6289 0.0000
F2 -0.022331 0.004005 -5.576154 0.0000
(iv) Error Correction Model
Date: 05/24/15 Time: 14:06
C 2.08E-05 6.67E-05 0.311192 0.7562
DS1(-1) -0.103970 0.090345 -1.150809 0.2520
DS1(-2) -0.010251 0.089815 -0.114133 0.9093
DF 1.000691 0.000741 1350.906 0.0000
DF(-1) 0.105880 0.090426 1.170898 0.2438
DF(-2) 0.010868 0.089895 0.120893 0.9040
E(-1) -0.018205 0.022865 -0.796186 0.4274
F-statistic 335415.1 Durbin-Watson stat 2.006296

(i) Levels
Date: 04/25/15 Time: 23:09
Sample: 1998M05 2009M09
C 1.643820 0.074834 21.96618 0.0000
S2 0.469944 0.042512 11.05434 0.0000
Sum squared resid 0.787800 Schwarz criterion -2.248791
Date: 04/25/15 Time: 23:10
C -0.001255 0.001869 -0.671135 0.5033
DS2 0.580414 0.061570 9.426880 0.0000

(iii) Quadratic
Date: 04/25/15 Time: 23:11
Sample: 1998M05 2009M09
C -0.859893 0.831070 -1.034682 0.3027
S2 -2.426546 0.958653 -2.531204 0.0125
S22 -0.831183 0.274842 -3.024223 0.0030
Date: 05/24/15 Time: 13:06
C -0.000247 0.003631 -0.067929 0.9459
DS1(-1) 0.065799 0.086395 0.761611 0.4477
DS1(-2) 0.222903 0.082525 2.701020 0.0079
DS2 0.551906 0.058373 9.454852 0.0000
DS2(-1) -0.237324 0.075637 -3.137659 0.0021
DS2(-2) -0.133976 0.077606 -1.726356 0.0867
E2(-1) -169.6698 380.6605 -0.445725 0.6566

Appendix 4: Breusch-Godfrey LM Test
Money Market ECM
Before adding MA(3) term
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 3.060139 Prob. F(3,124) 0.0308
Obs*R-squared 9.236912 Prob. Chi-Square(3) 0.0263

After adding MA(3) term

Cross Currency Hedge ECM
Before MA (9) term

After adding MA (9) term

Appendix 5: Money Market and Cross Currency ECM
Date: 05/24/15 Time: 13:00
Convergence achieved after 9 iterations
MA Backcast: 1998M05 1998M07
C 4.11E-05 7.95E-05 0.516665 0.6063
DS1(-1) -0.096056 0.091898 -1.045236 0.2979
DS1(-2) -0.005874 0.092328 -0.063618 0.9494
DF 1.000664 0.000729 1372.820 0.0000
DF(-1) 0.097986 0.091974 1.065364 0.2887
DF(-2) 0.006081 0.092431 0.065792 0.9476
E(-1) -0.025380 0.027341 -0.928278 0.3550
MA(3) 0.219810 0.092347 2.380271 0.0188
Date: 05/24/15 Time: 13:33
MA Backcast: 1997M11 1998M07
C 0.002979 0.004363 0.682806 0.4960
DS1(-1) -0.000833 0.084713 -0.009834 0.9922
DS1(-2) 0.251557 0.079397 3.168327 0.0019
DS2 0.484070 0.053898 8.981247 0.0000
DS2(-1) -0.214646 0.068171 -3.148653 0.0020
DS2(-2) -0.217685 0.070080 -3.106226 0.0023
E2(-1) -583.8781 443.3917 -1.316845 0.1903
MA(9) 0.455770 0.091644 4.973259 0.0000

Appendix 6: Jarque Bera Normality Test
Money Market Hedge
(i) Levels
0
4
8
12
16
20
24
-0.001 0.000 0.001 0.002
Series: Residuals
Sample 1998M05 2009M09
Observations 137
Mean -7.98e-17
Median 9.94e-05
Maximum 0.002463
Minimum -0.001698
Std. Dev. 0.000803
Skewness 0.144080
Kurtosis 3.208605
Jarque-Bera 0.722404
Probability 0.696838
0
5
10
15
20
25
30
-0.0010 -0.0005 0.0000 0.0005
Series: Residuals
Sample 1998M06 2009M09
Observations 136
Mean 1.12e-18
Median 7.33e-06
Maximum 0.000760
Minimum -0.001032
Std. Dev. 0.000227
Skewness -1.012003
Kurtosis 8.078130

(iii) Quadratic
0
4
8
12
16
20
-0.001 0.000 0.001 0.002
Series: Residuals
Sample 1998M05 2009M09
Observations 137
Mean -1.13e-16
Median -6.25e-05
Maximum 0.002203
Minimum -0.001612
Std. Dev. 0.000724
Skewness 0.616351
Kurtosis 4.062685
0
4
8
12
16
20
24
-0.0005 0.0000 0.0005
Series: Residuals
Sample 1998M08 2009M09
Observations 134
Mean -1.42e-06
Median 7.33e-06
Maximum 0.000752
Minimum -0.000920
Std. Dev. 0.000215
Skewness -0.595014
Kurtosis 7.277815

(i) Levels
0
2
4
6
8
10
12
14
-0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10
Series: Residuals
Sample 1998M05 2009M09
Observations 137
Mean 6.40e-17
Median 0.012122
Maximum 0.128882
Minimum -0.268331
Std. Dev. 0.076109
Skewness -1.277650
Kurtosis 5.435478
0
4
8
12
16
20
24
-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06
Series: Residuals
Sample 1998M06 2009M09
Observations 136
Mean 9.18e-19
Median 0.000665
Maximum 0.063802
Minimum -0.104426
Std. Dev. 0.021638
Skewness -1.337753
Kurtosis 8.206153

(iii) Quadratic
0
2
4
6
8
10
12
14
16
-0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10
Series: Residuals
Sample 1998M05 2009M09
Observations 137
Mean -3.85e-17
Median 0.006459
Maximum 0.129768
Minimum -0.247331
Std. Dev. 0.073638
Skewness -1.144578
Kurtosis 5.091726
0
4
8
12
16
20
-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08
Series: Residuals
Sample 1998M08 2009M09
Observations 134
Mean -5.27e-05
Median 0.001064
Maximum 0.075191
Minimum -0.064799
Std. Dev. 0.018890
Skewness -0.280145
Kurtosis 5.067134

Appendix 7: Engle-Granger Cointegration test
Money Market
Null Hypothesis: M_RESID has a unit root
Exogenous: Constant
t-Statistic Prob.*
5% level -2.882910
10% level -2.578244
Cross Currency
Null Hypothesis: CC_RESID has a unit root
Exogenous: Constant
t-Statistic Prob.*
5% level -2.883073
10% level -2.578331

Appendix 8 Invalid ECM GARCH
Money Market Hedge
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 05/29/15 Time: 00:28
Presample variance: backcast (parameter = 0.7)
GARCH = C(8) + C(9)*RESID(-1)^2 + C(10)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob.
C 4.35E-05 5.03E-05 0.865790 0.3866
DS1(-1) -0.178046 0.114602 -1.553597 0.1203
DS1(-2) -0.023720 0.098481 -0.240855 0.8097
DF 1.001371 0.000655 1528.940 0.0000
DF(-1) 0.178275 0.114673 1.554635 0.1200
DF(-2) 0.022908 0.098568 0.232413 0.8162
E(-1) -0.028378 0.016487 -1.721217 0.0852
Variance Equation
C 9.68E-09 3.69E-09 2.625780 0.0086
RESID(-1)^2 0.714328 0.224319 3.184424 0.0015
GARCH(-1) 0.245870 0.145005 1.695593 0.0900
Durbin-Watson stat 1.796215

Method: ML - ARCH (Marquardt) - Normal distribution
Date: 05/29/15 Time: 00:26
Convergence not achieved after 500 iterations
Presample variance: backcast (parameter = 0.7)
GARCH = C(8) + C(9)*RESID(-1)^2 + C(10)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob.
C 0.001799 0.003786 0.475119 0.6347
DS1(-1) -0.036657 0.122071 -0.300295 0.7640
DS1(-2) 0.105959 0.122128 0.867608 0.3856
DS2 0.501022 0.049486 10.12448 0.0000
DS2(-1) -0.073020 0.091664 -0.796599 0.4257
DS2(-2) 0.023119 0.080749 0.286305 0.7746
E2(-1) -254.2845 369.9638 -0.687323 0.4919
Variance Equation
C 2.46E-05 4.56E-05 0.539195 0.5898
RESID(-1)^2 0.139319 0.088195 1.579673 0.1142
GARCH(-1) 0.816629 0.208638 3.914103 0.0001
Durbin-Watson stat 1.737479

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