Currency futures hedging effectiveness in cme group

CURRENCY FUTURES HEDGING EFFECTIVENESS IN CME GROUP
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BY
MD RUBEL KHONDOKER
1. Introduction :
Currency hedging is a mechanism to reduce foreign currency risk exposure .Foreign currency
hedgers use various strategy to eliminate the risk in foreign currency market. For A
Optimum currency hedging, hedger can take delta hedge, cross hedge or delta cross hedge
.Currency Hedgers use financial derivative to reduce the risk from variations in the spot
market. Hedgers usually sort a currency futures contract when they take a long position on
underlying assets. Hedgers participate in futures market to reduce their risk for a premium
but in futures market there is mismatch maturity mismatch in currency so hedgers need to
know the optimal number of futures contract for taking a long or short position in futures
market .If hedger can estimate the optimum number of contract for short or long they can
significantly reduce their risk. The hedge ratio is the ratio of the size of the position taken in
futures contracts to the size of the exposure (C.Hull, 1998).
Currency risk:
Currency futures have become extremely popular after Bretton Wood agreement was
breakdown. The appearance of futures markets for foreign currency inspires hedger to
reduce their currency risk exposure. Since world is becoming smaller and international trade
is going up significantly, currency risk turn out to be a fundamental concern for many
international merchandiser and international investor. International investors diversify

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there portfolio internationally because domestic market potentially my not give the return
for the risk they take for so they invest in foreign country for compensate their risk but
currency risk appear in the middle and their profit can turn into sour . There for in order to
hedge this risk hedge seekers look for a approach that can eliminate there exposure. There
are many financial derivatives in the market to reduce this risk like such as ;currency futures,
currency options, currency swap etc. among them currency futures is prefer in case of
currency hedging . Adams,j.& Montesi,C,J.(1995) in their study find that currency futures are
more preferable to currency option for corporate managers because of considerable big
transaction cost. Chang, J. S. K. and Shanker, L.(1986) in their study also concluded that
currency futures are better hedging derivatives compare to currency options.
Empirical evidence in currency risk exposure:
Volkswagen is a German automobile manufacturer company in year 2002 to 2004 it was
facing problem because of their home currency EUROFX appreciation against foreign
currency dollar .it had to pay its labour cost and operating cost in EUROFX but it received
revenue in dollar for the cars that it sold in the USA. For foreign exchange risk exposure
between 2004 and 2005 it has increased hedging against foreign exchange risk by currency
derivative and it’s also expand some of its production facilities in USA .This way Volkswagen
was able to shield its revenue from foreign exchange volatility and eliminate the currency
mismatch between cost and revenue. (Carbaugh, R,j., 2009)
Currency hedging with futures :

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futures contract my not match the maturity or currency .when currency does not match but
maturity match in the futures contract it this case by doing a cross hedge hedgers can
eliminate their exposure . if there is maturity miss mass futures contract may not provide a
perfect hedge so When maturity dates does not match the exposure to be hedged then
delta hedge can be constructed and when both currency and maturity does not match delta
cross hedge can be constructed in order to minimize exposure that needed to be hedged.
Basis risk:
At one stage usually spot and futures price have a big spread specially when the settlement
time is long period but when the maturity or settlement time comes very close the spread
reduced significantly .Basis can be express like below:
Basis = (Futures price – Spot price)
Another way to express it is:
Basis= (spot price –futures price)
When basis is positive it called Contango and when basis Is negative it is Backwardation.
Another way to state it as premium or discount. Basis point is one hundredth of 1% or
0.01%.
Futures are closely compared to forward transaction which is usually priced by “COST OF
CARRY “ idea .If the market is efficient which means all the information is present in the
market, everyone got the same information about the market and there is no arbitrage then
determining the basis will be difference between domestic and foreign currencies interest
rate and the payout on the underlying asset but the relationship between the term and base

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interest rates may affect the basis in the interim. Determination of the basis in currency can
be found by following equation:
Ft,T=Ste(r-r*)τ (Clark, 2002) (1)
Where:
Ft,T =price of a future contract at time t for delivery at time T
T=delivery date of currency future contract (years)
t =current date (years)
τ =T-t
St =Spot price at time t
r =risk free rate on domestic currency
r*=risk free rate on foreign currency
1.2 Currency futures in chicago mercantile exchange group (CME) Group :
Currency futures was first launch in 1972 by Chicago Mercantile Exchange via International
Monetary Market (IMM) .when Bretton Wood agreement was been breakdown currency
futures my be considered as a direct respond .CME Group is the largest market for Foreign
exchange futures in the world .its makes transactions of more then $1.9 trillion a day and
foreign exchange market impact on all the countries economy .
Since its creation it had added many currency contracts among them British pound,
EUROFXFX, Japanese yen, Swiss franc, Canadian dollar, Australian dollar, Mexican peso,
Russian ruble, Swedish korna, Nowegian korne, Brazilian real are quite frequently used in
futures contract .

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Trade unit for EUROFXFX futures is 125,000 EUROFXs, Swiss franc Futures is 125,000 francs,
British pound future is 62,500 pounds, Japanese yen futures is 12,500,000 yean and Mexican
Peso Futures is 5,00,000 pesos .contract settlement are usually in the month of march, June,
September, December.
Chicago mercantile exchange group use U.S. central time ,the time in Chicago, where CME
Group headquartered situated. CME Group begins trading at 0720 hours and close out at
1400 hours and for Electronic Trading 17:00 to 16:00 hours next day all the currency futures
contract that we have used for our analysis was been traded between those hours .There is
no counter party risk involved and all the transaction goes through be clearing house. And
there is low transaction cost.
Traders notes:
The rapid growth of futures contracts in foreign currencies testifies to their usefulness and
popularity, but some of these markets are still somewhat thin. This can be very dangerous.
It is advisable to avoid Friday afternoon after the London markets close because of the lack
of liquidity at this time. (Wasendorf, 2001)
1.3 Statement for research problem:
Currency fluctuation can cause investors or merchandiser income in there base
currency .so to reduce there exposure they can hedge by taking long or sort position in
currency futures market .for hedging against exchange rate exposure they needs to find
optimal hedge ratio . By hedging through currency future they can significantly reduce
their amount of exposure and increase their gain .

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1.4 Objectives:
 Our objectives are to emphasize hedging effectiveness in currency futures contracts.
 Estimate the “Optimal hedge ratio” for hedging in march, June, September, December
settlement .
 Determining the relationship between changes in spot price and futures price.
1.5 Scope for this study:
Currency futures helps to reduce exposure from the currency movement such that
;income and profit can become sour if cash inflow is low because of an appreciation or
depreciation of currency .Spot and future exchange rate differ significantly before
maturity and infrequent maturity dates made it difficult for futures contact to
correspond perfect maturity of the cash flow that needs to be hedge. So this study is
constructive for the participant of futures market who wants to hedge against their cash
flow in certain period of time. By using the hedge ratio they can eliminate their
exposure against uncertain movement of currency exchange rate.
2. Literature Review:
Many researcher invented many new technique to come out with better estimation of
optimal hedge ratio for currency futures and many models like Ordinary Least squire,
Autoregressive integrated moving average, Autoregressive moving average, Generalized

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autoregressive conditional Heteroskedasticity, Vector Auto regression ,Exponential general
autoregressive conditional Heteroskedasticity etc
The review focuses on studies specifically conducted on currency futures but for estimation
of optimal hedge ratios other types of futures contracts ,farms value using currency
derivatives instrument , hedging in different market, hedging for different investors also
mentioned in order to understand the development of the research .
2.1 Farm Value Using Currency Derivatives Instruments:
Elliott,W,B.,Huffman,S,P.,Makar,S,D,(2003)in a study they investigate the implications of
foreign exchange derivatives use for the association between firm value changes and
exchange rate changes and they found a lagged firm value/exchange rate relationship and
foreign exchange derivatives plays an important role in understanding the lagged market
response to changes in exchange rate . They found that the lagged firm value effects of
exchange rate changes are particular to companies with low foreign exchange derivatives
use relative to their foreign sales and the level of foreign exchange exposure decreases
monotonically across all foreign exchange derivatives group. Terry,E(2007) hedging foreign
currency exposure when a future foreign currency does not exist but exist a futures
contract on the value of the local currency in terms of foreign currency exist . in comparison
of inverse hedging strategies they have examined five inverse hedging strategies using both
daily and weekly return . the inverse conintegrated hedge for daily return performed better
then all other strategy ,the inverse lognormal hedge performed little bit less and the inverse
CI-GARCH hedge performed most terrible average hedging strategy. On the other hand in

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comparison with direct hedging strategies using daily returns, the most effective direct
currency hedge performed better from the sample of “CME” contract than the
corresponding inverse currency futures hedge from the sample of “ICE “contract. Nguyen,H
& Faff,R.(2003) in a study with a sample of 469 non financial Australian companies with a
sample period of 1999 to 2000 and two levels of analysis (Logit and Tobit) found that
leverage and firm size are the two most important factors to use financial derivatives large
firms with more debt in its capital structure is likely to use foreign currency derivatives and
large firms with high levered ,high liquid and pays higher dividends use interest rate
derivatives. there result are reliable with existing hedging theories.
Nguyena,H.,Faff,R.,Marshall,A(2007) examine the impact of the introduction of the EUROFX
on foreign exchange exposures for French firms .they examine the post EUROFX exchange
rate exposure for those corporate use foreign currency derivatives to hedge .Their finding
signal that introduction of the EUROFX related with reduction in number of firms significant
exchange rate exposure and absolute size of exposure and French firms use foreign
currency derivative less intensively. Geczy,C., Minton,B,A., Schrand,C,M.(1997)in a paper
“why firms use currency Derivatives” they have examine the use of currency derivatives for
a sample of firms that have ex ante exposure to foreign exchange rate risk and the
magnitude of exchange rate risk exposure benefits that can be realized from reducing risk
and cost associated with risk reduction . in there sample 41% firms have used currency
futures ,currency option ,currency swap . All the firm that have greater growth
opportunities and tighter financial constraints are more likely to use currency derivatives.
Allayannis,G,S & Ofek,Eli(1997)In study analyses whether firms use currency derivatives for
hedging or for speculative reason and the impact of currency derivatives on firm exchange
rate exposure and all the factors for hedge and factors that cause their decision on how

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much they should hedge .by taking a sample of S&P nonfinancial firms for 1993 ,and using
weighted least squares and probit model they found strong negative relationship between
foreign currency derivative for hedging and speculate in the foreign exchange markets.
Allyayannis, G,S. & Weston,J.(1998)Examines the use of foreign currency derivatives
(FCDs)and its potential impact on farm value in large U.S non financial firms using sample
period of 1990 to 1995.Using Tobin’s Q as an proxy of a firms market valuation they found
relation ship between firm value and the use of foreign currency derivatives which means
hedging increase firm value overall . Bodnar,G,M.,Hayt,G,S.,Marston,R,C.(1998) in a study
,explained that Exchange rate risk management is combination of financial and operational
hedges as part of an integrated risk management strategy aimed at reducing exposure to
foreign exchange risk. and financial hedges via the use of derivative instruments mainly
target short-term ,observable exposures.
2.2 Hedging effectiveness in different Market :
Floros C and Vougas D, V,(2006)in there study investigate the hedging effectiveness of Greek
stock index future contracts on FTSE /ASE-20 and FTSE/ASE-40 and they have consisted the
methods of OLS,ECM,VECM and Bivariate GARCH(1,1)to obtain hedge ratio .the outcome of
OLS model for FTSE /ASE-20 provides large risk reduction and ECM produces the most
effective hedges and both contracts the OLS hedge ratio shows greater variance reduction
and BGARCH (1,1) hedge ratio provides greater variance reduction then other models and
generates better results in terms of hedging effectiveness .finally for hedging effectiveness
by considering the hedging performance for the post-sample periods, and using forecasting
statistics they found that Error Correction model outperforms the OLS model ,there for
the Error correction model(ECM)is superior to the OLS model .

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Pok,W,C.,poshakwale,S,S.,Ford,J,L(2009)examined the hedging performance of dynamic and
constant models in the emerging Malaysian market during the financial crises and found
that the General GARCH model outperforms other models like TGARCH and provides the
best hedging performance during the normal period, financial crisis period ,and in the
period after imposition of capital controls.
2.3 Hedging for different Expectation of investors:
Wang,C.,& Low,S,S.(2003) in their studies they have compare optimal hedging strategies for
two different types of investors .one is international investor and other is domestic
investors . they have investigate with MSCI Taiwan index future contracts from January
1997 to June 2000 , and daily closing price of MSCI Taiwan index future contracts and they
found that MSCI Taiwan index futures market is about fifty percent more volatile then the
spot market ,the average daily changes in the price of New Taiwan dollar is -0.022% so US
dollar was appreciating against Taiwan dollar on the sample period . they have used
GARCH(1,1)error correction model to estimate optimal hedge ratios for both the
international and domestic investors and reason behind it was that GARCH(1,1) adequacy
of characterizing the dynamics of the second moment of financial asset prices . and they
have compared four different hedging techniques such as Naïve ,OLS ,OLS-CI(spot and
future prices cointegration ) ,and GARCH error correction model . their result shows that
domestic and foreign both investors benefit from future contracts and international
investor benefit more then domestic investors and optimal hedge ratio in equity, futures
and currency markets tends to be large then the domestic inventors.

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2.4 Research for hedging effectiveness:
Herbst,A,F.,Kare,D,D.,Marshall,J,F.,(1997) in a study they have employed futures contracts
for British pound ,Canadian dollar, German mark, Japanese yen and Swiss franc and all this
contracts were traded on Chicago Mercantile Exchange and the data range was form 2nd
of
January 1985 to 17th
June 1985 and they have compared OHR and JSB and conclude that
JSB s minimum risk hedge ratios calculate as the slope coefficient in ordinary least squares
regression and the intercept term does not considered and do not take in to account for a
declining basis of a future contract and JSE Portfolio hedging technique do not take into
account of a direct hedge relationship of futures price to spot price restricted by cost of
carry and convergence of future price to spot price at maturity . they also mentioned that
OLS residuals form JSE estimation of minimum variance hedge ratio are serially correlated
and for that Box –Jenkins “Auto regressive integrated moving average (ARIMA) model could
be use for estimating the minimum risk hedge. And for the suggestion for hedgers they said
OHR hedge ratio is better for sort term and for long term JSE hedge ratio performs superior.
Tingting Y., Zongye C (2006) in their study they have compared with four different hedging
techniques; the OLS regression model, the autoregressive model (VAR), the vector error
correction model(VECM) and Multivariate GARCH with error correction model are
compared in expressions to minimize variance by using spot and future exchange rates of
British Pound from 18 July 1994 to 1st
march 2006 and they find that VAR and VECM
perfume the same and perfume little higher then the OLS regression model and the
Multivariate GACH model with error correction model that capture the time varying nature

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of hedge ratio do not make difference vary much . Marmer, H, S(1986) in his article
‘portfolio model hedging with Canadian dollar futures: A framework for analysis “ he
analysis the hedging effectiveness of Canadian dollar future from the sample period of July
1981 to September 1984 and found that time invariant Minimum Variance Hedge Ratio
has a limitation of expediency. Akin(2003) investigate the volatility of financial futures
return with Australian dollar ,British Pound, Canadian dollar, German mark, Japanese yen
,Swiss franc and the sample of future data form Chicago Mercantile Exchange for a period
of 4th
January 1982 to 31 December 2000 using GARCH model find evidence that time to
maturity play a big role in currency future .Liouia,A.,& Poncet,P.(2003)Currency forward
and currency future contracts are not substitutable when interest risk exists.
Brailsford,T.,Corrigan,K.,Heaney,R(2001) “A comparison of measures of hedging
effectiveness: a case study using the Australian all Ordinaries share price index futures
contract” the time period selected was 17th July 1990 to 9th June 1990 from AOI spot index
.the analyze the hedging effectiveness on reduction in portfolio standard division all the
measure they employed that falls under Markowitz Mean Variance structure. LIEN,D.,YANG,L
(2006) Investigates the effects of the spot-futures spread on the return and risk structure in
currency market of Australian dollar, British pound, Canadian dollar, Deutsche mark,
Japanese yen and Swiss. They found evidence of positive and negative return on spot and
future. And they found that in sample asymmetric effect model provides the best hedging
strategy for all currency except Canadian dollar and out of sample the asymmetric effect
model provides the best strategy for all currency and symmetric effect model provides
better strategy in Canadian dollar and Japanese Yen. Markowitz, H.(1952)”Portfolio
Selection “ mean variance framework was mentioned for hedging with basis risk ,which is
difference between future price and spot price .after that Working,H.(1953) , (Johnson, L.,

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1960) drive minimum variance framework and (Ederington, Louis H., 1979) suggest that
minimum variance hedge ration can be defined as the ratio of the covariance between spot
and future price to the variance of the future price and he mention that minimum variance
hedge ratio is the slope coefficient of Ordinary Least Squire regression .Kenneth, F.K .,&
Sultan ,J.(1993) have propose and estimate Bivariate error correction model(ECM) in ΔSt
and ΔFt with a GARCH error structure . The error correction term imposes the long run
relationship between St and Ft, and GARCH error structure allow the second moments of
the distribution to change through time and the time varying hedge ratio can be calculated
form the estimated covariance matrix from the model .for the risk minimizing futures hedge
ratio. They have employed British pound, Canadian dollar, German mark, Japanese yen and
Swiss franc for their analysis. They have argued that there is a potential problem in
conventional model first of all; if spot rates and futures rates are conintegrated then
conventional model will over difference data and ambiguous long run relationship between
spot and future rates .secondly spot and future markets is constant which is not right in
reality and difficult to produce risk minimizing hedge ratios. Engle,R,F.(1982) Suggested that
this unobservable second moment could be model by specifying a functional form for the
conditional variance and modelling the first and second moments jointly, giving what is
called in the literature the Autoregressive Conditional Heteroskedasticity (ARCH )model .he
also suggestion that the conditional variances depend on elements in the information set in
an autoregressive manner has become the most common perhaps . The linear ARCH model
was generalized by (Bollerslev, 1986) in a manner analogous to the extension from AR to
ARMA models in traditional times series by allowing past conditional variances to appear in
the current conditional variance equation .the resulting model is called Generalized ARCH
or GARCH .ARCH and GARCH materialize valuable for estimating time-varying optimal hedge

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ratio and number of Scholar given opinion that ,this ratios take in to considerations of
variability over time. Among all the scholar Baillie,R, T.& Myers, R, J.(1991) in there study
concluded that GARCH Model is more satisfactory.
But until now there is no convenience evidence that such time-varying hedge rations are
statistically desperate from a constant hedge ratio .a time-varying covariance matrix of cash
and futures prices is not adequate to establish that the optimal hedge ratio is time varying.
Moschinia,G. & Myers,R,J.(2003) in a studies with a sample of corn cash and futures prices a
sample period of 1996 to 1997 they have drive their new multivariate GARCH
parameterization to see optimal future ratio is constant over time and it is flexible form time
varying volatility even in constant hedge ratio and found that optimal hedge ratios does not
vary only systematically with seasonality and time to maturity effects and optimal hedge
ratio for weekly storage hedging of corn in the Midwest are time varying and can not be
explained by seasonality and time to maturity .Myers,R.J(1991) suggest that empirical ARCH
models performance is not better than OLS model and there is no significant hedging
performance between them .
Moosa,I.A.(2003)in his studies with a sample period of 1987 to2000with a sample of spot
exchange rates of British Pound and Canadian Dollar in opposition to United States Dollar
and with a sample of monthly data for cash and futures prices and he analyzed with a first
difference model, a simple error correction model and a general error correction model .
after analyzing model he did not find significant difference for hedging effectiveness with
both sample and he concludes that “Although the theoretical arguments for why model
specification does matter are elegant, what really matters for the success or failure of a

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hedge is the correlation between the prices of the unhedged position and the hedging
instrument”
In other words, low correlation make poor hedging position and high correlation make a
good hedging performance
3. Research Methodology :
We have applied Minimum variance delta hedge because there is basis risk for
asymmetrical or infrequent maturity and its not likely to maturity of futures contract will
match up and it will mismatch with its cash flow that needs hedged.. And when it occurs
basis risk appear and make it imperfect hedging rather the perfect hedging.
So if a hedger want to hedge against its portfolio risk the value of the port folio will be like:
St1C-N(ft1,t2-ft0,t2)Q (Apte, 2006) (2)
Where :
st1 = spot price at time 1
Ft1,t2 = futures price of 1 foreign currency at time t1 for settlement at time’t2’
Ft0,t2 = futures price of 1 foreign currency at time ‘t0’ for settlement at time’t2’
N= number of futures contract
C=Cash amount to be hedge
Q= Size the contract
If we divide equation (2) by C ,we can find hedge ratio like:
β=
and the equation (2) can be written like: - β ( - ) (3)

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and variance of equation(3) will be like below:
Var ( ) - 2 βCov ( , )+ Var ( ) (4)
so the hedge ratio for sorting future contract which is beta coefficient defined as :
β= (5)
so once we have estimate beta or hedge ratio hedgers can find optimal contract number by:
N= β (6)
Regression model :
Our Autoregressive model or AR(1)which can be express like below:
ΔSt1=α+βΔFt1,t2+ ut (Apte,P,G ,2006) (7)
Where ΔSt1=change in spot exchange rate at time 1,Alpha α= intercept or constant ,
ΔFt1,t2= change in future exchange rate at time t1 of future contract maturing at t2
β= slope coefficient for minimum variance hedge ratio, and the
first order Autoregressive scheme in here ,
ut= ρut-1+ εt , -1<ρ<1 (8)
there for E(ut)= ρE(ut-1)+E(εt)=0
var(ut)= ρ2 var(ut-1)+var(εt)
(N.Gujarati, 2003)
the u’s and ε’s are uncorrelated and εt it the normal error term in regression model .

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Historical data has been collected for the time series regression although theory says this
model should be estimated as forecast but the data need to forecast above equation is not
available. So our dependent Variable is Change in Spot Price which is denoted as ΔS and
our Independent Variable Change in Futures Price which is denoted as ΔF.Null hypothesis is
there is no relationship between ΔSpot price and ΔFutures Price. And the Alternative
hypothesis is there is relationship between ΔSpot price and ΔFutures Price.
In order to examine whether there is serial correlation between the error terms, we have
applied Durbin- Watson test because many a times regressions of time series data have the
problem of positive autocorrelation, the hypotheses in Durbin-Watson test is in below :
Null hypothesis : ρ=0
Alternative hypothesis: ρ>0
Durbin-Watson statistic is in below:
(9)
(N.Gujarati, 2003)
Decision Criteria
 If t-probability value is more then 5% we accept the null hypothesis.
 If t-probability value is less than 5% we reject the null hypothesis.
 R2
coefficient of determination .

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 Probability (F-Statistic)or test statistic which is rusticated and unrestricted regression
if it is more then 5% we accept the null hypothesis if less we reject the null
hypothesis.
 Durbin-Watson statistics or ‘D’test decision rules are below:
Null hypothesis Decision if
There is No positive autocorrelation reject 0<d<dL
There is No positive autocorrelation no decision dL<d<dU
There is No negative correlation reject 4-dL<d<4
There is No negative correlation no decision 4-dU<d<4-dL
There is no autocorrelation positive or negative do not reject dU<d<4-dU
Where du is devaluated upper value and dL is devaluated lower value(N.Gujarati, 2003) .We
will follow Durbin-Watson d statistic table for level of significance points of dL and dU at 5%
level.
We have used this model because there are some drawback with simple regression model .
Measurement of Hedging effectiveness :
Ederington(1979)suggested that hedging effectiveness is equal to R2
of the OLS regression in
other words R2
of the regression line explaining the data if high then hedging is effective
,so the higher the R2
the higher the minimum variance hedge . so we can measure hedging
effectiveness by R2 in our regression model .Change in spot price to the change in future
measured by the correlation coefficient .in our analysis R2
which is squire of the correlation
coefficient is been applied which is denoted as :

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R2
= = 1 -
if R2
80% or 0.80 then it would mean the variation in dependent variables which is ΔS
has been explained be the independent variable which is ΔF .when R2 is low for instance
less then 50% or .50 then for hedgers it would be not wise to use that currency futures
contract to hedge . if it is less then 80% or .80 the hedging effectiveness is inefficient .
3.1 Data Description :
We have collected data from ‘DATASTREAM TOMASON REUTERS’ and USD is the base
currency. We have collected USD/EUROFX, USD/SWISS-FRANC, USD/GBP,USD/MEXICAN
PESO,USD/YEN. Five days a week basis daily Futures contracts settlement price and spot
exchange rate of those futures. We have been taken direct quote which means units of USD
for one unit of foreign currency (EUROFX, SWISS FRANC, GBP, MEXICAN PESO and YEN). For
YEN however units of USD for 100 Japanese yen is been taken into consideration .Because
compare to other currency one unit of foreign currency Japanese yen is too low against
USD. For March settlement from 16th March, 2001 to
16th March, 2009 .for June settlement form 15th June, 2001 to 15th March, 2009 .for
September
Settlement from 14th September, 2001 to 14th September 2009 .for December settlement
from
14th December, 2001 to 14th December, 2009.The Number of observation table below:

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Number of observation in our sample:
Quotation March settlement June settlement August settlement December settlement
USD/EUROFX 2086 2086 2086 2085
USD/SWISS FRANC 2086 2086 2086 2086
USD/GBP 2082 2086 2086 2086
USD/MEXICANPESO 2086 2086 2086 2086
USD/YEN 2086 2086 2086 2086
We have used daily data because of currency fluctuation in spot and futures and futures
market
Participant re equilibriums their position daily basis also in currency futures market there is
marginal cost involved daily basis.
For technical reason due to problems of stationary or nonstationarity in mean and variance
of price level in data series effect futures price unpredictability that’s why we have
estimated hedge ratio(β) based on natural logarithm changes in the spot market rather than
on the actual rate. Stationarity and related problem such as cointegrastion can be overcome
be using this method . Cavanaugh,K,L(1987) mention that raw price and natural logarithm
of future is big issue for convenience. Logarithm of first difference of futures prices or price
change or returns in a sample will have a better distribution then the first difference of the
raw series and its more convenient to base hypothesis testing on the first difference of
natural logarithm of prices .
Moreover the futures prices are quoted in terms of units of USD for per foreign currency or
per USD unit to foreign currency units will not significantly affect the analysis.

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All the currency we have taken to analysis play a vital role in currency and other financial
futures market as well as in global economy. That’s why we have chosen all this currency.
4. Empirical Result and Analysis:
we have used ‘EViews 6 ‘ statistical software to calculate our regression all the result below
is the out put of EViews 6.
From our regression model we have found that USD/EUROFX,USD/SWISS FRANC and
USD/GBP All this futures contracts in four different settlement date are significant except
December settlement for USD/EURO is not significant when we measure with R2
for good
hedging effectiveness and also we also found that there is relationship between spot and
future price changes .One the other hand USD/Mexican Peso and USD/YEN futures
contracts non of the four different settlement dates are insignificant when we measure the
hedging effectiveness with R2
. So we can not measure hedging effectiveness because R2 is
low for We have the out put form EView 6 and we have interpreter the result below.
Appendix No-1 :March Settlements:
March Settlement(USD/EUROFX):
Dependent Variable: _SPOT_EUROFX
Method: Least Squares
Date: 04/29/10 Time: 16:41
Sample (adjusted): 3 2087
Included observations: 2085 after adjustments
Convergence achieved after 6 iterations

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The Intercept (α)is 0.000706 and the slope coefficient (β) is 0.951744.T-probability is 0.0000,
Probability (F-Statistic)is 0.0000000 which means both are significant at 5% level , Durbin-
Watson statistics implies there is no autocorrelation and the test of over all model which is
coefficient of determination ; R2
is 0.880260which is also significant because previous study
suggest that R2
should be between 80% to 99% for hedging effectiveness.
So if a investor wishes to hedge a long position by using a sort position in future contract
the hedge ratio is 0.951744.which implies that 0.951744 units of the future asset to sell
1unit of the spot asset held.
March Settlement(USD/SWISS FRANC)
Dependent Variable: _SPOT_SWISS
Date: 04/29/10 Time: 16:43
Coefficient Std. Error t-Statistic Prob.
C 0.001283 0.004117 0.311670 0.7553
_FUTURE_SWISS 0.920558 0.007953 115.7521 0.0000
C 0.000706 0.003404 0.207372 0.8357
_FUTURES_EUROFX 0.951744 0.007177 132.6172 0.0000
AR(1) -0.408963 0.020278 -20.16787 0.0000
R-squared 0.880260 Mean dependent var 0.017567
Adjusted R-squared 0.880145 S.D. dependent var 0.632154
S.E. of regression 0.218852 Akaike info criterion -0.199403
Sum squared resid 99.72005 Schwarz criterion -0.191284
Log likelihood 210.8773 Hannan-Quinn criter. -0.196428
F-statistic 7652.842 Durbin-Watson stat 2.252983
Prob(F-statistic) 0.000000
Inverted AR Roots -.41

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AR(1) -0.419374 0.019997 -20.97210 0.0000
S.E. of regression 0.266671 Akaike info criterion 0.195832
Sum squared resid 148.0576 Schwarz criterion 0.203951
Log likelihood -201.1552 Hannan-Quinn criter. 0.198807
The Intercept (α) is 0.001283 and the slope coefficient (β) is 0.920558. T-probability is
0.0000 ,Probability (F-Statistic)is 0.0000000 which means both are significant at 5% level,
Durbin-Watson statistics there is no autocorrelation and the test of over all model which is
is 0.850855which is also significant because previous study
suggest that R2
So if a investor wishes to hedge a long position using a sort position in future contract the
hedge ratio is 0.920558.which implies that 0.920558 units of the future asset to sell 1unit
of the spot asset held.
March Settlement(USD/GBP)
Dependent Variable: _SPOTPOUND
Date: 04/29/10 Time: 16:45
C -0.000389 0.004197 -0.092556 0.9263
_FUTURES_POUND 0.896710 0.008657 103.5836 0.0000
AR(1) -0.295938 0.021332 -13.87291 0.0000

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R-squared 0.823281 Mean dependent var -0.000910
The Intercept (α) is -0.000389 and the slope coefficient (β) is 0.896710. T-probability is
0.0000 ,Probability (F-Statistic)is 0.0000000 which means both are significant at 5% level ,
is 0.818409 which is also significant because previous study
suggest that R2
hedge ratio is 0.896710.which implies that 0.896710units of the future asset to sell 1unit of
the spot asset held.
March Settlement(USD/MEXICAN –PESO )
Dependent Variable: _SPOT_PESO
Date: 04/29/10 Time: 16:48
C -0.007364 0.009429 -0.780915 0.4349
_FUTURE_PESO 0.612525 0.015878 38.57706 0.0000
AR(1) -0.300972 0.021192 -14.20226 0.0000

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The Intercept (α) is -0.007364 and the slope coefficient (β) is 0.612525.T-probability
is,0.0000 ,Probability (F-Statistic)is 0.0000000 which means both are significant at 5% level ,
is 0.410741 which is insignificant and in previous study
suggest that R2
So the slope coefficient hedge ratio β in not very effective because it is far form unity and
R2
is very low which indicates our model outcome is insignificant
March Settlement(USD/YEN)
Dependent Variable: _SPOT_YEN
Date: 04/29/10 Time: 16:46
C 0.003241 0.005070 0.639132 0.5228
_FUTURE_YEN 0.873119 0.009910 88.10775 0.0000
AR(1) -0.337895 0.020797 -16.24696 0.0000

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The Intercept (α) 0.003241is and the slope coefficient (β) 0.873119 isT-probability is 0.0000
and Probability (F-Statistic)is 0.0000000 which means both are significant at 5% level ,
Durbin-Watson statistics there is no autocorrelation and the test of over all model which
is coefficient of determination ; R2
is 0.776680which is close to significant level .
hedge ratio is 0.873119.which implies that 0.873119 units of the future asset to sell 1unit
of the spot asset held ,which Is the slope estimate in our regression. but it is just about
efficient because of R2
,which is bit less
Appendix No-2 :June Settlements:
June Settlement (USD/EUROFX)
Date: 04/29/10 Time: 16:49
C 0.000640 0.003428 0.186731 0.8519
_FUTURES_EUROFX 0.962152 0.007126 135.0245 0.0000
AR(1) -0.398660 0.020390 -19.55219 0.0000

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The Intercept (α) is 0.000640and the slope coefficient (β) is 0.962152.T-probability is,0.0000
,Probability (F-Statistic)is 0.0000000 which means both are significant at 5% level,Durbin-
Watson statistics there is no autocorrelation and the test of over all model which is
0.884800 which is also significant because previous study
suggest that R2
the hedge ratio is 0.962152.which implies that 0.962152units of the future asset to sell
June Settlement(USD/SWISS)
Date: 04/29/10 Time: 16:51
C 0.001434 0.004057 0.353393 0.7238
_FUTURE_SWISS 0.932893 0.007723 120.7896 0.0000
AR(1) -0.410216 0.020082 -20.42700 0.0000

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The Intercept (α) is 0.001434and the slope coefficient (β) is 0.932893.T-probability
0.861965which is also significant because previous study
suggest that R2
the hedge ratio is 0.932893.which implies that 0.932893units of the future asset to sell
June Settlement(USD/GBP)
Date: 04/29/10 Time: 16:50
C 0.000569 0.004378 0.129977 0.8966
_FUTURES_POUND 0.899715 0.008708 103.3246 0.0000
AR(1) -0.267868 0.021465 -12.47951 0.0000
The Intercept (α) is 0.000569 and the slope coefficient (β) is 0.899715.T-probability

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0.824373 which is also significant because previous
study suggest that R2
the hedge ratio is 0.899715.which implies that 0.899715 units of the future asset to sell
June Settlement(USD/MEXICAN-PESO)
Date: 04/29/10 Time: 16:50
C -0.006908 0.009620 -0.718114 0.4728
_FUTURE_PESO 0.617963 0.015545 39.75266 0.0000
AR(1) -0.301190 0.021237 -14.18252 0.0000

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is 0.427173 which is not significant.
So the slope coefficient hedge ratio β in not very effective and R2
is very low which point
towards insignificancy of our model.
June Settlement(USD/YEN):
Date: 04/29/10 Time: 16:52
C 0.003458 0.006097 0.567235 0.5706
_FUTURE_YEN 0.819059 0.011938 68.60764 0.0000
AR(1) -0.377284 0.020352 -18.53782 0.0000
The Intercept (α) is 0.003458 and the slope coefficient (β) is 0.819059 . T-probability is
coefficient of determination ; R2 is 0.666950 .so our model is not very significant although it
is more then 60%.
So the slope coefficient hedge ratio β in not very effective and R2 is low which point
towards insignificancy in our model.

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Appendix No-3 :September Settlements:
September Settlement(USD/EUROFX)
Date: 04/29/10 Time: 16:54
C 0.000853 0.003289 0.259382 0.7954
_FUTURES_EUROFX 0.966677 0.006920 139.6919 0.0000
AR(1) -0.401376 0.020409 -19.66685 0.0000
is 0.892258 which is highly significant .
hedge ratio is 0.966677which implies that 0.966677units of the future asset to sell 1unit of
the spot asset held.
September Settlement(USD/SWISS):

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Date: 04/29/10 Time: 16:57
C 0.001729 0.003946 0.438024 0.6614
_FUTURE_SWISS 0.932900 0.007483 124.6627 0.0000
AR(1) -0.396373 0.020039 -19.77989 0.0000
0.0000 ,Probability (F-Statistic)is 0.0000000 which means both are significant at 5% level ,
is 0.870832is significant its more then 80%.
hedge ratio is 0.932900.which implies that 0.932900units of the future asset to sell 1unit of
the spot asset held
September Settlement(USD/GBP):

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Date: 04/29/10 Time: 16:56
C 0.000587 0.003811 0.154039 0.8776
_FUTURES_POUND 0.916809 0.007831 117.0692 0.0000
AR(1) -0.343561 0.021039 -16.32949 0.0000
0.0000 ,Probability (F-Statistic)is 0.0000000 which means both are significant at 5%
level,Durbin-Watson statistics there is no autocorrelation and the test of over all model
which is coefficient of determination ; R2
is 0.853040 Which is significant at 80% level .
hedge ratio is 0.916809 .which implies that 0.916809 units of the future asset to sell 1unit
of the spot asset held .
September Settlement(USD/MEXICAN PESO):
Date: 04/29/10 Time: 16:55

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C -0.005475 0.008889 -0.615883 0.5380
_FUTURE_PESO 0.693300 0.014785 46.89230 0.0000
AR(1) -0.313061 0.020970 -14.92922 0.0000
is 0.503494 and its not significant for effective hedging .
September Settlement(USD/YEN):
Date: 04/29/10 Time: 16:57
C 0.002894 0.005018 0.576863 0.5641
_FUTURE_YEN 0.881168 0.009734 90.52467 0.0000
AR(1) -0.349288 0.020634 -16.92803 0.0000

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coefficient of determination ;R2
is 0.785546. Which is very close to be significant at 80%
level but its not significant for effective hedging .
Appendix No-4 :December Settlements:
December Settlement(USD/EUROFX):
Date: 04/29/10 Time: 16:59
C 0.001196 0.005745 0.208236 0.8351
_FUTURES_EUROFX 0.843212 0.012067 69.87884 0.0000
AR(1) -0.421089 0.019974 -21.08237 0.0000
coefficient of determination R2
is 0.655401. which implies insignificance and of hedge ratio
is not effective.

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December Settlement (USD/SWISS):
Date: 04/29/10 Time: 17:01
C 0.001694 0.003861 0.438840 0.6608
_FUTURE_SWISS 0.927912 0.007334 126.5233 0.0000
AR(1) -0.413676 0.020056 -20.62558 0.0000
The Intercept (α) is 0.927912and the slope coefficient (β) is 0.927912 . T-probability is
0.0000 ,Probability (F-Statistic)is 0.0000000 which means both are significant at 5% level
and the test of over all model which is coefficient of determination ; R2
is 0.872995 .which is
also significant because previous study suggest that R2
should be between 80% to 99% for
hedging effectiveness.
hedge ratio is 0.927912.which implies that 0.927912 of the future asset to sell 1unit of the
spot asset held.

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December Settlement(USD/GBP):
Date: 04/29/10 Time: 17:01
C 0.000553 0.003754 0.147249 0.8829
_FUTURES_POUND 0.924250 0.007641 120.9631 0.0000
AR(1) -0.343212 0.021017 -16.33005 0.0000
0.0000 ,Probability (F-Statistic)is 0.0000000 which means both are significant at 5% level
is 0.860562 which is also significant because previous study
suggest that R2
hedge ratio is 0.924250 .which implies that 0.924250 units of the future asset to sell 1unit
of the spot asset held.
DECEMBER SETTLEMENT(USD/MEXICAN PESO):

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Date: 04/29/10 Time: 17:00
C -0.004643 0.009139 -0.508060 0.6115
_FUTURE_PESO 0.700378 0.015305 45.76281 0.0000
AR(1) -0.301254 0.021154 -14.24123 0.0000
The Intercept (α) is -0.004643 and the slope coefficient (β) is 0.700378 . T-probability is
is 0.495637 which is not significant for effective hedging.
DECEMBER SETTLEMENT(USD/YEN):
Date: 04/29/10 Time: 17:02
C 0.002849 0.004999 0.569973 0.5688
_FUTURE_YEN 0.891447 0.009596 92.90117 0.0000
AR(1) -0.337976 0.020802 -16.24764 0.0000

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The Intercept (α) is 0.002849 and the slope coefficient (β) is 0.891447 .T-probability is
value 0.794859which is almost good fit and effective
hedging .
5. CONCLUSION :
In this study hedging effectiveness obtained form regression model and March, June,
September, December settlement for USD/EUROFX, USD/SWISS FRANC, USD/GBP we have
found satisfactory result for hedging effectiveness which we measured by R2
and
USD/MEXICAN PESO and USD/YEN currencies all the settlements hedging effectiveness is
not satisfactory . we have applied minimum variance delta hedge for all the settlements
which is for mismatch in maturity in futures contracts but hedgers should keep in mind that
for currency mismatch they should concern about minimum variance cross hedge and when
none of them match with the contract they should concern with minimum variance delta
cross hedge. Its very important for hedger to up-to-date there knowledge about all the
information about currency they are hedging, what’s the interest rate going to prevail in the
time when the amount is payable and receivable ,balance of payment, supply and demand

FIN 4430
Page 40
for foreign currency etc. if a hedger or investor manage to follow above mentioned issue
there is greater chance that he or she will be able to perfectly eliminate the foreign currency
risk exposure and add value to their firm and themselves .
5.1 Further suggestion for research :
Further study can be conducted for minimum variance cross hedge and minimum variance
delta cross hedge and also by using different models like Vector auto regression model,
Vector error correction model ,Autoregressive moving average model ,Generalized
autoregressive conditional Heteroskedasticity model etc.
In our regression model we have used historical data for analysis which can be biased
because historical data or past can not always predict futures and any model can become
meaningless or valueless recent credit crunch is the best example to illustrate this issue.

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