Abstract This study examines the effectiveness of cross-currency hedging compared to that of forward hedging and money market hedging. It is demonstrated that cross-currency hedging is not only less effective than forward and money market hedging but also that it is totally ineffective unless the exchange rate of the exposure currency and that of the third currency are highly correlated. The results indicate that for an effective crosscurrency hedging a correlation coefficient of 0.50 is required. This kind of correlation reduces the variance of the rate of return on the unhedged position by about 25 per cent

Imad A Moosa

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Moosa, I 2004, 'The effectiveness of cross-currency hedging', Finance Letters, vol. 2, no. 1,
pp. 32-37.
https://researchbank.rmit.edu.au/view/rmit:16017
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2004 Global EcoFinance All rights reserved
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Finance Letters, 2003, 1,  
 
 
The Effectiveness of Cross-Currency Hedging 
 
 
Imad A. Moosa* 
 
La Trobe University, Australia 
 
 
Abstract 
 
This study examines the effectiveness of cross-currency hedging compared to that of forward hedging and 
money market hedging. It is demonstrated that cross-currency hedging is not only less effective than forward 
and money market hedging but also that it is totally ineffective unless the exchange rate of the exposure 
currency and that of the third currency are highly correlated. The results indicate that for an effective cross-
currency hedging a correlation coefficient of 0.50 is required. This kind of correlation reduces the variance of 
the rate of return on the unhedged position by about 25 per cent. 
 
Key words: Cross-Currency Hedging, Correlation, Foreign Exchange Exposure 
JEL classification: F30, G15 
 
 
 
1. INTRODUCTION 
It has been suggested that cross-currency hedging can be used to cover exposure to foreign exchange risk 
when it is not possible or costly to engage in forward and money market hedging. Forward contracts may not be 
available on the currency in which the exposure is denominated (the exposure currency), either because it is an 
exotic, thinly-traded currency or because the exposure is of a long-term nature for which there is no matching 
forward contract. It may also be the case that it is not possible to borrow or lend funds denominated in the 
currency of the exposure, which means that it is not feasible to engage in money market hedging. Or it could be 
that money market hedging is expensive because it involves lending and borrowing in two currencies. 
Cross-currency hedging is also related to the concept of a “natural hedge”, which arises when a firm has 
offsetting positions on two currencies whose exchange rates against the base currency are highly correlated. 
Brooks and Chong (2001) argue that although hedging currency risk with currency futures is more effective than 
cross-currency hedging, firms often obtain a natural hedge when they have opposite exposures to movements in 
two or more currencies. Jorion (2001, p 475) argues that hedging each source of risk (in this case the risk arising 
from each individual currency) separately is inefficient because it ignores exchange rate correlations. Brooks 
and Chong (2001) put forward the idea that cross-currency hedging can reduce volatility by around 15 per cent 
compared with 60-80 per cent when futures contracts are used. Siegel (1997) evaluates the effectiveness of 
cross-currency hedging by employing the cross-currency options listed on the Philadelphia Stock Exchange to 
extract the relationship between hedging effectiveness and the implied exchange rate correlations. 
Cross-currency hedging amounts to taking an offsetting position on a third currency, such that the exchange 
rates of the third currency and the currency of exposure against the base currency are highly correlated. If there 
is a long exposure then the hedger takes a short position on the third currency and vice versa. Thus, if the 
exposure currency appreciates against the base currency, the third currency also appreciates (by the same 
percentage if the exchange rates are perfectly correlated). And since the positions on the exposure currency and 
the third currency are opposite, any profit (loss) made on the exposure will be offset by the loss (profit) made on 
the third currency position. Although the position on the third currency may involve forward, futures or options 
contracts, this exercise is based on offsetting spot positions, which gives the study a distinguishing feature. 
The objective of this paper is to test the effectiveness of cross-currency hedging compared to that of 
* Email: i.moosa@latrobe.edu.au 
I am grateful to the editor of this journal and an anonymous referee for their comments. 
ISSN 1740-6242 © 2003 Global EcoFinance™ All rights reserved. 15 
                                                          
Moosa 16 
forward and money market hedging using four currency combinations. This empirical exercise starts with some 
estimates of the optimal hedge ratios, which are subsequently used to construct hedged positions consisting of 
the unhedged positions and opposite positions on the hedging instrument.  
  
2. METHODOLOGY 
The optimal hedge ratio is measured as the slope coefficient in a regression of the rate of return on the 
unhedged position on the rate of return on the hedging instrument. If Up  and Ap  are the logarithms of the 
prices of the unhedged position and the hedging instrument respectively, then the underlying regression is  
ttAtU php εα +∆+=∆ ,,                                                      (1) 
where h is the hedge ratio. In the case of foreign currency exposure Up  is the spot exchange rate between the 
base currency (x) and the exposure currency (y) measured in logarithmic form as )/( yxs . Ap , on the other 
hand, depends on the kind of hedging instrument used. If forward hedging is used, such that the offsetting 
position involves a forward contract, then 
)/( yxfpA =                                                              (2) 
 where f is the logarithm of the forward rate. If money market hedging is used, then the price of the hedging 
instrument is represented by the interest parity forward rate, f , which is the forward rate consistent with 
covered interest parity. Thus 
)/( yxfpA =                                                                       (3) 
where 
)1log()1log()/( yx iisyxf +−++=                                            (4) 
where xi  and yi  are the interest rates on currencies x and y respectively, such that the maturity of the 
underlying assets is identical to the maturity of the forward contract. 
Finally, if a cross hedge involving a third currency z is used the price of the hedging instrument is the spot 
exchange rate between x and z, in which case 
)/( zxspA =                                                               (5) 
Once the hedge ratios are calculated, three positions are constructed depending on the type of the hedge 
used. The rates of return on the unhedged position and the three hedged positions are calculated as 
)]/([100 yxsRU ∆=                                                           (6) 
)]/()/([100 yxfhyxsR FF ∆−∆=                                    (7) 
)]/()/([100 yxfhyxsR MM ∆−∆=                                      (8) 
)]/()/([100 zxshyxsR CC ∆−∆=                                        (9) 
where UR  is the rate of return on the unhedged position, FR  is the rate of return on a hedged position 
involving a forward hedge, MR  is the rate of return on a hedged position involving a money market hedge, and 
CR  is the rate of return on a hedged position involving a cross-currency hedge. Fh , Mh  and Ch  are the 
corresponding hedge ratios. 
Consider first the effectiveness of a hedge against the alternative of leaving the underlying position 
unhedged. In this case, testing hedging effectiveness amounts to testing the equality of the variance of the 
hedged position and that of the unhedged position. The null hypothesis and the alternative are respectively 
)()(: 220 HU RRH σσ =                                                           (10) 
Moosa 17 
)()(: 221 HU RRH σσ >                                                            (11) 
where [ ]CMFH RRRR =  and (.)2σ is the variance of the rate of return on the underlying position. The 
null is rejected if 
)1,1(
)(
)(
2
2
−−>= nnF
R
R
VR
H
U
σ
σ
 (12) 
where VR is the variance ratio and n is the sample size. This test can be complimented by the variance reduction, 
which is calculated as 






−=
)(
)(1100 2
2
U
H
R
RVD
σ
σ
                                                          (13) 
This methodology is applied to four combinations involving four currencies. Before we proceed further, it 
is noteworthy that the model used to estimate the hedge ratios (equation 1) may be inadequate because (i) it 
excludes the error correction term; and (ii) it implies a constant hedge ratio calculated from the unconditional 
moments (see, for example, Kroner and Sultan, 1993; Ghosh, 1993; Lien, 1996; Brooks and Chong, 2001). 
However, the objective of this paper is not to measure the sensitivity of the estimated hedge ratio to model 
specification, but rather to compare the performance of three hedging instruments, while using the same model 
specification to estimate the hedge ratio. Moreover, Moosa (2003) has demonstrated that the estimated hedge 
ratio is not that sensitive to model specification. 
 
3. DATA AND EMPIRICAL RESULTS 
This empirical exercise is based on a sample of quarterly data covering the period 1974:1-2000:4, involving 
four currencies: the U.S. dollar (USD), the Japanese yen (JPY), the British pound (GBP) and the Canadian 
dollar (CAD). The variables are the spot exchange rates, the three-month forward exchange rates, and the three-
month interest rates, all measured at the end of the quarter. All of the time series were obtained from the DX 
database (OECD Main Economic Indicators). The hedging period is taken to be one quarter, extending between 
the end of each quarter and the end of the subsequent quarter.1 The four currency combinations are described in 
Table 1. 
 
Table 1: Currency Combinations for Cross Hedging  
Combination Base Currency (x) Exposure Currency (y) Third Currency (z) 
1 USD GBP CAD 
2 GBP USD JPY 
3 CAD JPY USD 
4 JPY CAD GBP 
 
The results of estimating the hedge ratios are reported in Table 2. Money market and forward hedging 
produce close hedge ratios that are not significantly different from unity. The cross currency hedge ratios are 
significantly different from unity, ranging between 0.311 and 0.700. The best fit (which is also a measure of 
hedging effectiveness) is found in case 4. It is noteworthy that the almost-perfect fit in the case of forward 
hedging indicates that a perfect hedge is obtained when a forward contract on the same currency is used. The 
almost-perfect fit in the case of money market hedging is indicative of the validity of CIP, under which forward 
hedging and money market hedging are equally effective. 
 
 
1 The use of quarterly data may be questioned on the grounds that it results in the loss of important information, 
which may be provided by higher frequency data. While this argument is valid, the choice of this particular 
frequency is warranted by the practical consideration that the settlement period in trade finance is typically 
longer than one month. 
                                                          
Moosa 18 
Table 2: Estimated Hedge Ratios 
Case Forward  Money Market Cross Currency 
 h R2 h R2 h R2 
1 0.975 0.99 1.005 0.99 0.442 0.03 
2 0.975 0.99 1.005 0.99 0.311 0.13 
3 0.996 0.99 0.989 0.99 0.555 0.03 
4 0.996 0.99 0.999 0.99 0.700 0.41 
 
Table 3 reports the results of measuring hedging effectiveness. The table shows that higher risk arises from 
fluctuations in the exchange rate between the U.S. dollar and the pound than what arises from fluctuations in the 
exchange rate between the Canadian dollar and the Japanese yen. Forward and money market hedging lead to a 
significant reduction in the variance in all cases, with more or less similar effectiveness. But only in case 4, do 
we find a significant reduction in the variance resulting from cross-currency hedging, because this case shows 
the highest exchange rate correlation.  
 
Table 3: Variances and Hedging Effectiveness 
 Variance Variance Ratio Variance Reduction (%) 
Case 1               
UR  29.14   
FR  0.395 73.77* 98.6 
MR  0.195 149.43* 99.3 
CR  28.25 1.03 2.9 
    
Case 2    
UR  29.14   
FR  0.395 73.77* 98.6 
MR  0.195 149.43* 99.3 
CR  25.53 1.14 12.3 
    
Case 3    
UR  43.86   
FR  0.196 223.78* 99.6 
MR  0.630 69.62* 98.6 
CR  42.46 1.03 2.9 
    
Case 4    
UR  43.86   
FR  0.196 223.78* 99.6 
MR  0.154 284.81* 99.6 
CR  26.23 1.67* 40.1 
* Statistically significant. The 5 per cent and 1 per cent critical values are 1.39 and 1.59 respectively. 
 
4. SOME EXTENSIONS 
The results presented in Table 3 show that the correlation coefficient, the hedge ratio, the variance ratio and 
variance reduction are related to each other. In this section we derive these relationships analytically, then we 
present some results showing the dependence of hedging effectiveness on exchange rate correlation. We start 
Moosa 19 
with the definition of these variables, and for the purpose of simplifying notation, let ρ  and zy ,σ  be the 
correlation coefficient between and the covariance of )/( yxs∆  and )/( zxs∆  respectively. Also let 2yσ  and 
2
zσ  be their variances respectively. Thus, we have 
zy
zy
σσ
σ
ρ ,=                                                                  (14) 
2
,
z
zyh
σ
σ
=                                                                    (15) 
zyzy
y
hh
VR
,
222
2
2 σσσ
σ
−+
=                                            (16) 
VR
VD 11−=                                                                  (17) 
From equation (14) and (15), we obtain 






==
z
y
z
zyh
σ
σ
ρ
σ
σρσ
2                                                            (18) 
which shows the relationship between the hedge ratio and the correlation coefficient. If zy σσ = , then 
ρ=h , and for constant variances, the hedge ratio is proportional to the correlation coefficient.  
The relationship between the variance ratio and the correlation coefficient can be derived by combining 
equations (16) and (18) to obtain 
zy
z
y
z
z
y
y
yVR
σρσ
σ
σ
ρσ
σ
σ
ρσ
σ








−







+
=
222
2
22
2
                                     (19) 
which can be simplified to                               
21
1
ρ−
=VR                                             (20) 
Hence                                                               
211 ρ=−=
VR
VD                                      (21) 
which shows that variance reduction is equivalent to the coefficient of determination of the regression of  
)/( yxs∆  on  )/( zxs∆ . This is actually confirmed by the results presented in Tables 2 and 3. 
Finally, we can derive the relationship between the variance ratio and the hedge ratio by combining 
equations (18) and (20) to obtain  
( )
( ) 222
22
/
/
h
VR
zy
zy
−
=
σσ
σσ
                                                           (22) 
which shows that if zy σσ = , then )1/(1
2hVR −= . 
These equations can be used to demonstrate the importance of the correlation coefficient for hedging 
Moosa 20 
effectiveness. If we define an effective hedge to be a hedge that produces a statistically significant variance 
ratio, we can calculate the value of the correlation coefficient corresponding to the variance ratio. Table 4 shows 
the results for sample sizes ranging between 20 and 200, assuming that zy σσ = . For the sample size used in 
this study, a statistically significant variance ratio at the 5 per cent level requires a correlation coefficient of at 
least 0.50. A correlation coefficient of at least 0.60 is required if the variance ratio is to be significant at the 1 
per cent level. Thus, what matters is the availability of a third currency whose exchange rate against the base 
currency is highly correlated with the exchange rate of the exposure currency against the base currency. 
 
Table 4: Correlation Coefficients Corresponding to Significant Variance Ratios 
N VR (5%) ρ  VD VR (1%) ρ  VD 
20 2.12 0.73 52.8 2.94 0.81 66.0 
50 1.60 0.61 37.5 1.94 0.70 48.5 
100 1.39 0.53 28.1 1.59 0.61 37.1 
200 1.26 0.45 20.6 1.39 0.53 28.1 
 
5. CONCLUSION 
This study examined the effectiveness of cross-currency hedging compared to that of forward hedging and 
money market hedging. By using four currency combinations it was found that cross currency hedging is 
ineffective unless the exchange rates between the base currency and the exposure currency and that between the 
exchange rate and third currency are highly correlated. The results show that for effective cross-currency 
hedging, a correlation coefficient of at least 0.50 is required. In the absence of a third currency that satisfies the 
correlation requirement, there is no point in using cross-currency hedging, and the firm will be better off 
remaining unhedged if forward hedging and money market hedging are not possible. The results also mean that 
a natural hedge will not arise unless it involves two strongly correlated exchange rates. 
As a final remark it can be claimed that this paper makes some contribution to the literature because it deals 
with a topic that has not been dealt with extensively in the literature, particularly that it is based on offsetting 
spot positions. Moreover, the paper identifies the synthetic instrument used when a money market hedge is 
implemented. 
 
 
 
REFERENCES 
Brooks, C. and I. Chong. (2001) The Cross-Currency Hedging Performance of Implied versus Statistical Forecasting 
Models, Journal of Futures Markets, 21, 1043-1069. 
Ghosh, A. (1993) Hedging with Stock Index Futures: Estimation and Forecasting with Error Correction Model, Journal of 
Futures Markets, 13, 743-752. 
Jorion, P. (2001) Value at Risk: The New Benchmark for Managing Financial Risk (2nd edition), New York: McGraw-Hill. 
Kroner, K.F. and J. Sultan (1993) Time-Varying Distributions and Dynamic Hedging with Foreign Currency Futures, 
Journal of Financial and Quantitative Analysis, 28, 535-551. 
Lien, D. (1996) The Effect of the Cointegration Relationship on Futures Hedging: A Note, Journal of Futures Markets, 16, 
773-780. 
Moosa, I.A. (2003) The Sensitivity of the Optimal Hedge Ratio to Model Specification, Finance Letters, 1, 15-
20. 
Siegel, A.F. (1997) International Currency Relationship Information Revealed by Cross-Option Prices, Journal of Futures 
Markets, 17, 369-384. 
 


The Effectiveness of Cross-Currency Hedging

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The Effectiveness of Cross-Currency Hedging

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