Currency futures hedging effectiveness in cme group by md rubel khondoker

CURRENCY FUTURES HEDGING EFFECTIVENESS IN CME GROUP
FIN 4430

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

Page 1

FIN 4430

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 :

Page 2

FIN 4430

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

Page 3

FIN 4430

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 .

Page 4

FIN 4430

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 .

Page 5

FIN 4430

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

Page 6

FIN 4430

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

Page 7

FIN 4430

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

Page 8

FIN 4430

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 .

Page 9

FIN 4430

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.

Page 10

FIN 4430

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 2 nd 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

Page 11

FIN 4430

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.,

Page 12

FIN 4430

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

Page 13

FIN 4430

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

Page 14

FIN 4430

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)

Page 15

FIN 4430

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 .

Page 16

FIN 4430

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 .

Page 17

FIN 4430

 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 d L 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 R 2 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 R 2 which is squire of the correlation

coefficient is been applied which is denoted as :

Page 18

FIN 4430

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:

Page 19

FIN 4430

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.

Page 20

FIN 4430

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

Page 21

FIN 4430

Coefficient Std. Error t-Statistic Prob.

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

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


C 0.001283 0.004117 0.311670 0.7553
_FUTURE_SWISS 0.920558 0.007953 115.7521 0.0000

Page 22

FIN 4430

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

coefficient of determination ; R2 is 0.850855which is also significant because previous study


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

Page 23

FIN 4430

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 ,


coefficient of determination ; R2 is 0.818409 which is also significant because previous study



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


Page 24

FIN 4430



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 ,


coefficient of determination ; R2 is 0.410741 which is insignificant and in previous study


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



Page 25

FIN 4430

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 ; R 2 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



Page 26

FIN 4430

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

coefficient of determination ; R2 0.884800 which is also significant because previous study



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



Page 27

FIN 4430

The Intercept (α) is 0.001434and the slope coefficient (β) is 0.932893.T-probability



is coefficient of determination ; R 2 0.861965which is also significant because previous study



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


Page 28

FIN 4430


is coefficient of determination ; R2 0.824373 which is also significant because previous

study suggest that R2 should be between 80% to 99% for hedging effectiveness.


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





Page 29

FIN 4430


is coefficient of determination ; R 2 is 0.427173 which is not significant.

So the slope coefficient hedge ratio β in not very effective and R 2 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.

Page 30

FIN 4430

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 coefficient of determination ; R 2 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):

Page 31

FIN 4430

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 coefficient of determination ; R 2 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):


Page 32

FIN 4430

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 ; R 2 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

Page 33

FIN 4430


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






coefficient of determination ; R2 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



Page 34

FIN 4430




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.

Page 35

FIN 4430

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 ; R 2 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.

Page 36

FIN 4430

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


coefficient of determination ; R2 is 0.860562 which is also significant because previous study



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):

Page 37

FIN 4430

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



coefficient of determination ; R2 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


Page 38

FIN 4430



The Intercept (α) is 0.002849 and the slope coefficient (β) is 0.891447 .T-probability is



coefficient of determination ; R 2 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 R 2 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

Page 39

FIN 4430

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.

Page 40

FIN 4430

Bibliography

1. Adams,j.& Montesi,C,J. (1995). "Major Issues Related to Hedging Accounting

,Financial Accounting". "Financial Accounting Standard Board",Newark,Connecticut .

2. Akin, R. M. (2003)." Maturity Effects In Futures Market:Evidence from Eleven

Financial Future Markets". Unpublished Article .

3. Allayannis,G,S and Ofek,Eli. (1997)." Exchange Rate Exposure, Hedging, And the Use

Of Foreign Currency Derivatives".

4. Allyayannis, G,S. & Weston,J. (1998)." The Use of Foreign Currency Derivatives and

Firm Market Value."

5. Apte, P. G. (2006)". International Financial Management,Fourth Edition. McGraw-

Hill."

6. Baillie,R, T.& Myers, R, J. (1991). "Bivariate Garch Estimation of the Optimal

Commodity Futures Hedge"." Journal Of Applied Econometrics" , 6 (2), 109-124.

7. Bodie,Z.,kane,A.,Marcus,A,J. (2008)." investments",Seventh Edition,International

Edition .

8. Bodnar,G,M.,Hayt,G,S.,Marston,R,C. (1998). "1998 Wharton Survey of Financial Risk

Management by US Non-Financial Firms"." Financial Management" , 27 (4).

9. Bollerslev, T. (1986)." Generalized Autoregressive Conditional heteroskedasticity"."

Journal Of Econometrics" , 31 (3), 307-327.

10. Brailsford,T ., Corrigan,K.,and Heaney,R. (2001)." A Comparison Of Measures Of

Hedging Effectiveness:A Case Study Using The Australian All Ordinaries Share Price

Page 41

FIN 4430

Index Futures Contract"." Journal Of Multinational Financial Management" , 11 (4-5),

465-481.

11. C.Hull, J. (1998). "Introduction to Futures and Option Market" ,third edition . prentice

–hall,inc.

12. Carbaugh, R,j. (2009). "International Economies",Twelfth Edition.

13. Cavanaugh,K,L. (1987). "Price Dynamics in Foreign Currency" ." Journal of

International Money and Finance ", 6 (3), 295-314.

14. Chang, J. S. K. and Shanker, L. (1986)." Hedging Effectiveness of Currency Options

and Currency Futures"." Journal of Futurers Market" , 6 (2), 289-305.

15. Clark, E. (2002). "International Finacne",Second edition. thomason.

16. Ederington, Louis H. (1979). "The hedging Performance of the New Futures

Market"." The Journal Of Finance" , 34 (1), 157-170.

17. Elliott,W,B.,Huffman,S,P.,Makar,S,D. (2003)." Foreign-denominated debt and foreign

currency derivatives: complements or substitutes in hedging foreign currency risk?".

"Journal of Multinational Financial Management" , 13 (2), 123-139.

18. Engle,R,F. (1982)." Autoregressive Conditional Heteroscedasticity With Estimaties Of

The Variance Of United Kingdom Inflation"." Econometrica" , 50 (4), 987-1007.

19. Floros C and Vougas D, V. (2006). Christos Floros and Dimitrios V.Vougas “Hedging

Effectiveness in Greek stock index future market ,1999-2001"." International Reearch

Journal of Finance and Economics" (5).

20. Geczy,C., Minton,B,A., and Schrand,C,. (1997). "Why firms Use Currency Derivatives.

The Journal of Finance" , 52 (4), 1323-1354.

21. Herbst,A,F.,Kare,D,D.,Marshall,J,F. (1997). "A Time Varying Convergence Adjusted

Hedge Ratio Model. Advances In Futures And Option Research ", Unpublished Article.

Page 42

FIN 4430

22. Johnson, L. (1960). "The Theory OF Hedging And Speculation IN Commodity Futures.

The Review Of Economic Studies" , 27 (3), 139-151.

23. Kenneth, F.K .,& Sultan ,J. (1993)." Time-Varying Distributions And Dynamic Hedging

With Foreign Currency Future. Jounral Of Financial And Quantitave Analysis" , 28 (4),

535-551.

24. Lien,D.,Yang,L. (2009)." Effects Of Omitting Information Variables On Optimal Hedge

Ratio Estimation:A Note."

25. Liouia,A., & Poncet,P. (2003)." Dynamic Asset Pricing With Non-Redundant

Forwards". "Journal of Economic Dynamics and Control" , 27 (7), 1163-1180.

26. Markowitz, H. (1952)." Portfolio Selection"." The Journal Of Finance" , 7 (1), 77-91.

27. Marmer, H, S. (1986). "Portfolio Model Hedging With Canadian Dollar Futures: A

Framework For Analysis"." Jounral Of Futures Market" , 6 (1), 83-92.

28. Moosa,I.A. (2003). "The sensitivity of the Optimal Hedge Ratio to Model

Specification". Financie Letters , 1, 15-20.

29. Moschinia,G. & Myers,R,J. (2002)." Testing For Constant Hedge Ratios In Commodity

Markets: A Multivariate GARCH Approach"." Journal Of Empirical Finance" , 9 (5),

589-603.

30. Myers,R.J. (1991)." Estimatin time-varying hedge ratios on futures market"." Journal

of Futures Market ", 11 (1), 39-53.

31. N.Gujarati, D. (2003)." Basic Econometrics", Fourth edition. McGraw-Hill.

32. Nguyen,H & Faff,R. (2003). "Can the use of foreign currency derivatives explain

variations in foreign exchange exposure?: Evidence from Australian companies.

Journal of Multinational" "Financial Management" , 13 (3), 193-215.

Page 43

FIN 4430

33. Nguyena,H.,Faff,R., Marshall,A. (2007). "Exchange Rate Exposure, Foreign Currency

Derivatives And The Introduction Of The Euro: French Evidence"." International

Review Of Economcs & Finance ", 16 (4), 563-577.

34. Pok ,W, C. , poshakwale,S,S., Ford,J,L. (2009). "Stock Index futures Hedging In The

Emerging Malaysian Market"." Global Finance Journal" , 20 (3), 273-288.

35. Terry, E. (2007)." Inverse Currency Futures Hedging". Unpublished Article .

36. Tingting Y., Zongye C. (2006)." The Hedging Effectiveness Of Currency Futures".

Unpublished Article .

37. Wang,C.,& Low,S,S. (2003)." Hedging With Foreign Currency Denominated Stock

Index Futures: Evidence From The MSCI Taiwan Index Futures Market. Journal of

Multinational" "Financial Management" , 13 (1), 1-17.

38. Wasendorf, R. R. (2001)." All about futures". Mc Graw-Hill.

39. Working, H. (1953). "Futures Trading And Hedging"." The American Economic

Review" , 43 (3), 314-343.

40. http://www.cmegroup.com/trading/fx/

41. http://www.jstor.org/

42. http://www.sciencedirect.com/

Page 44

Currency futures hedging effectiveness in cme group by md rubel khondoker

Recommandé

Recommandé

Contenu connexe

Tendances

Tendances (18)

En vedette

En vedette (20)

Similaire à Currency futures hedging effectiveness in cme group by md rubel khondoker

Similaire à Currency futures hedging effectiveness in cme group by md rubel khondoker (20)

Currency futures hedging effectiveness in cme group by md rubel khondoker