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8/12/2019 Tom Wilkinson - A Tenge Oil Tango
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CONTENTS
1 introduction 1
2 history and context 4
3 literature review 8
4 data sources and properties 18
5 structural and empirical models 23
6 results and conclusions 34
references 42
appendix 44
TABLES and FIGURES
figure3.1 portfolio composition as rational consumer choicepart 1 9figure3.2 portfolio composition as rational consumer choicepart 2 1figure3.3 spot to futures price convergence 12ta!le 4.1 unit root tests with trend and intercept 19ta!le 4.2 unit root tests with intercept only 2ta!le 4.3 second unit root tests with trend and intercept 21figure 4.1 price series over the sample period 22ta!le 5.1 cointegration tests 29ta!le 5.2 specification and residuals tests 33ta!le 6.1 static hedge ratio estimates and performance 34
ta!le 6.2 rolling estimation performance 35ta!le 6.3 static hedge ratio estimates and performance post break 35figure 6.1 time structure of conditional correlation 3"ta!le 6.4 GARCH estimates and hedging performance 38ta!le # rolling hedge ratio estimates 44
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1 INTRODUCTION
$ince its independence signalled the final dissolution of the $oviet %nion in
&ecem!er 1991' the (epu!lic of )a*a+hstan has made a cossac+ pursuit of economicli!eralisation' with a succession of ,uic+' !ut well advised' shifts towards its now
nota!ly mar+et !ased economy1. -ot least amongst these were the managed2float of
the )a*a+hstani tenge / 0 on 5th#pril 1999' the simultaneous relaxation of trade
!arriers' and the vast pensions overhaul detailed in chapter two. #nother motivator to
the float' !esides the demands on currency reserves of a fixed regime' was the
looming contagion of the (ussian financial crisis' which )a*a+hstan had successfully
fended off since the previous #ugust !ut which had all !ut eliminated demand for the
countrys metals their second great export sector after oil' itself suffering from low
world prices. ut' as a maor food and goods exporter to its smaller entral #sian
neigh!ours and to many eastern !loc countries' this freeing of the central !an+s hand
!rought with it the typical side effect of exposing )a*a+hstani international trade and
investment to currency ris+s. eyond these ris+s effect on entral #sian poverty' an
nternational 7onetary und almer' 240 report on the state of cumulative fund
pension schemes in )a*a+hstan made clear that institutional investors' starved of
domestic e,uity opportunities and heavily invested a!road' were woefully un:
insulated against exchange rate shifts. &espite the existence of a domestic dollar
futures mar+et on the )a*a+hstan $toc+ ;xchange3'the report4la!els this far too thin
to allow for effective hedging of the some 45< of institutional investors assets
denominated in or lin+ed to0 dollars. )a*a+hstani institutional investors are therefore
in dire need of alternative instruments with which to cross hedge tenge exchange ris+s
and this paper sets out to assess the potential for such a hedge !ased on more heavily
traded futures.
y definition cross hedges are !ased on assets different to the cash position they are
applied to' !ut some relationship must exist so that swings in the value of the spot can
!e offset !y associated swings in the hedging instruments value. ndeed' withouttheoretical ustification for such a relationship' past successes of a hedging instrument
cannot !e assumed to carry on into the future. =hus' following their preliminary
investigation into commodity>currency cross hedging one of the earliest conducted :
;a+er and ?rant 198"0 highlight that @there is a need to identify those economic
factors which ma+e a particular commodity a li+ely candidate to match a particular
17 ountry (eport -o. 4>33" and details in chapter 22ormal inflation targeting is not in place' !ut government intervention until Acto!er 2" has !eendescri!ed !y all sources as minimal3
$adly price series for these futures are not availa!le' ma+ing consideration of their potential hedgingperformance impossi!le.47 ountry (eport -o. 4>33"
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HEDGING TENGE with OIL FUTURES
currencyB. #s if in answer' hen and (ogoff 220 propose that' particularly for
developing countries' the maor determinant of exchange rate fluctuations
specifically those volatile !ut persistent shoc+s that seemingly contradict urchasing
ower arity and other traditional monetary models might !e price changes for a
primary export commodity5'or several such' on a countrys terms of trade. t is in lightof these o!servations and the predominance of oil "7iddle eastern
states' for which they do not' presenting an o!stacle against using a currency to
currency cross hedge' which further promotes a commodity to currency hedge.
=he wor+ of Cohnson 1960 suggests that hedgers will choose a proportion of hedged
to unhedged assets within their position' so as to reduce uncertainty on the return it
will yield !y a proportion consistent with their ris+ to return preferences. n a cross
hedge there is no reason to !elieve that changes in the value of a unit of the spot asset
should coincide with e,ual changes to a single futures contracts price' and so the
num!er of contracts needed for each cash asset to provide a desira!le return is !y no
means clear. n the literature eg $tein' 19610 this proportion is em!odied in the hedgeratio. =he arsenal of methods for determining such hedge ratios is extensive' with
each derived from the optimisation of one specific o!ective function Dien and =se'
22E hen' Dee and $hrestha' 220. =he most popular is inargua!ly the ;derington
7inimum Fariance hedge ratio' deployed among many others !y enet 1990 and
)roner and $ultan 19930 on whose wor+ shall !ase a large part of my study. #s
the name would suggest the 7F hedge ratio produces a portfolio with minimal
volatility' and it is estimated most simply !y choosing the ratio that minimises the
variance for an o!served sample of cash and futures prices. oth the 7F and its
analogue for commoving processes sometimes called the ;rror orrection 7odel(atio suffer from the criticism that their focus on volatility neglects to consider the
actual returns expected on a portfolio as Cohnson 1960 and the mean:variance
framewor+ would demand. #n answer to this criticism are the optimum mean:
variance and $harpe ratios' the former of which allows for an admittedly su!ective0
ris+ aversion parameter to tailor the !alance of variance reduction and speculative
return' and the latter maximising expected return relative to ris+ hen' Dee and
$hrestha' 220. -evertheless' employ the 7F>;7 ratio as a general test of ris+
5=o !orrow a term from enets 1990 informal attempt at a lin+
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HEDGING TENGE with OIL FUTURES
reduction capacity' and find no reason to investigate further with more realistic hedge
ratios to give a hint of my results.
=he estimation method ust descri!ed for the 7F ratio ,uite o!viously assumes that
the hedging period shares the same variance minimising futures position as theestimation sample. =o escape this assumption' at the penalty of statistical complexity
here and transaction costs in practice' also explore dynamic estimations of the
minimum variance hedge ratio that allow the futures position to change over time
with the relationship lin+ing cash and futures prices. =he first of these is little more
than a continually updating extension of thestatic method $ercu and Gu' 19990' !ut
follow this with a more sophisticated GARCHprocedure' advocated !y )roner and
$ultan 19930 and ha+ra!orty and ar+oulas 19990' which reflects widely held
!eliefs on the nature of exchange rate and oil futures price !ehaviour.
n contrast to much of the early literature on cross hedging' !ut in line with enet
1990' the more su!ective ex ante' or out of sample' assessment of each ratios
performance is used alongside the o!ective ex post' or in sampleappraisal. Ghile the
latter is a fair indication of the @relatednessB of cash and futures assets and the futures
potential to achieve a specific o!ective function' it is meaningless to actual hedgers'
who will select instruments !ased on their expected performance against future rate
shifts. =he former measure imitates the real world dilemma for a hedgerH predicting
the !est position to ta+e for the future' !ased only on currently availa!le information.
=his paper is divided into six chaptersH =he next provides some !ac+ground
information on )a*a+hstan' its currency' and oil' while expanding on the ustification
for exchange rate hedging in institutional investors dollar exposure. hapter three is
a literature review. hapters four and five detail the data used and the models tested
respectively. hapter six presents the results of the investigation and draws
conclusions.
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2 HISTORY and CONTEXT
=he reader could !e forgiven for !eing unfamiliar with the recent or otherwise
history of )a*a+hstan' and for !earing some scepticism on its worthiness as a topic ofstudy. ndeed' the worlds ninth largest country spent most of the last fifty years
hidden !etween curtain and veil. Iowever' with the recent economic changes coming
over (ussia and hina' and the political re:alignment of #fghanistan and a+istan' the
su!stantial proven oil and gas reserves at =engi* along with a potentially massive
reserve under the northern aspian have !rought the country !ac+ to the Gestern
conscious. n fact )a*a+hstan is expected to !ecome one of the words top 1 oil
producers over the next two decades though its long term proven reserves mean this
position will not !e sustained indefinitely -aman' omfret' (a!alland and $ourdin'
260. rom a glo!al perspective' )a*a+hstan is also critical to regional welfare as a
dominant goods and food supplier to the neigh!ouring fledgling repu!lics of
)yrgy*stan' =ai+istan' =ur+menistan' and %*!e+istan.
Iaving !een a (ussian possession since the time of the great game' )a*a+hstan had
!uilt up' particularly during the soviet era' a si*a!le ethnic (ussian population.
ollowing the declaration of independence in &ecem!er 1991' repatriation of these
ethnic (ussians led to a fall in the population from around 1" million to roughly 15
million6' leaving the (ussian and )a*a+h populations !etter !alanced' !ut the demand
collapsed along with that from (ussia0 and the economy initially contracted Dloyd et
al' 19940. =he dominance of primary commodities now among its exports might give
the illusion that the countrys economy had regressed to !eing extraction !ased' !ut
this is not the caseH =he general population has always !een well educated though
the advent of )a*a+hstani students in western universities is only a recent trend'
than+s to recent legislation ma+ing study a!road a via!le option and a healthy
services sector ma+es up some 5
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HEDGING TENGE with OIL FUTURES
provisions. u!lic expectations of financial support in old age' a legacy of the soviet
era8' made an effective pensions system an essential development to satisfy demand
while relieving the massive strain on current resources. =he scheme inherited from the
ormer $oviet %nion' which prevailed until 199"' awarded a standard fixed
component supplemented !y a varia!le element !ased on @years of serviceB and thenature of that service and clearly did not comply with the countrys sworn new
capitalist principals. 7oreover' the pre:1998 system was plagued !y inefficiency in
collection with planned inter:raion9payments often neglected !y the local collection
administrations' motivated only to collect enough for their local lia!ilities. Ghen this
pay-as-you-go system was finally itself retired in 1998 a new efined !inancial
Contribution scheme was implemented' com!ined with a transition version of the
pay:as:you:go for existing claimants. oth new systems sought to address the issue of
@fairB distri!ution of pension funds' !y ma+ing payments according to wage' and
hence contri!ution1 as in the & system this is a fixed 1< of an individuals
salary. Gor+ers under the & scheme can choose !etween a default state
administered fund' and fifteen private accumulation pension funds' !ut the declining0
maority still choose the former.
&espite the startling efficiency with which the new pensions system was !rought into
operation' with overhauled collection and distri!ution via !an+s unheard of in other
former soviet states0' the institutional investors of )a*a+hstan were still limited !y
one important factor' namely the lac+ of domestic opportunities for the investment oftheir funds a sad state of affairs when Devine and Jervos 19960 suggest a maor
contri!ution !y financial mar+ets development to growth. )a*a+hstans stoc+ mar+et
)#$; has existed under various names0 since 1993 in !ut according to the 7
almer' 240H
@&espite its name' the )a*a+hstan $toc+ ;xchange )#$;0 remains primarily an
organi*ed place for trade in government securities...B
Ghereas individuals may tie their accumulated capital into small scale privateinvestment proects' this is not an option for a large scale institution' and so the
pension funds state and private have !een forced to invest a!road in order to
achieve their target 5< real returns11. ndeed' in 24 some 4< of the funds assets
were denominated in dollars' while 85< of tenge denominated corporate !onds were8or wor+ers in dangerous or otherwise undesira!le wor+ing conditions' retirement was sometimespossi!le as young as 4. Ghile in 1996 over 32 percent of old age pensioners were younger than 6.almer' 2409# (aion is the local administrative unit of the repu!lic of )a*a+hstan' with A!lasts the regionaldivision.1
=hough the special privilege of early retirement remains availa!le to wor+ers in ha*ardousen!ironments.117 ountry (eport -o. 4>33" 240
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HEDGING TENGE with OIL FUTURES
dollar lin+edE which should hopefully !e evidence enough of )a*a+hstani pension
holders commitment to foreign assets.
oth the apital #sset and #r!itrage ricing 7odels suggest that there should !e no
incentive to ris+ elimination through hedging' either !ecause diversifia!le ris+ should!e eliminated !y holding a suita!ly mixed portfolio' or !ecause non:diversifia!le ris+
should award a premium on expected returns ;a+er and ?rant' 198"0. Iowever'
amendments to this theory' !ased around varia!le cash flows effects on agents
decisions through the threat of financial distress' can !e used to ustify hedging
!ehaviour in developed economies indeed one of the earliest models of hedging'
that of =elser 19550' was geared around financial distress. or pension funds in
general' financial distress occurs when the portfolio of assets falls into deficit relative
to the funds lia!ilities to those drawing their pensions. Gith so many of their assets
denominated in dollars and lia!ilities denominated in tenge0 the volatility of
exchange rates clearly represents a maor threat of deficit to )a*a+hstani pension
funds' and so it is of great interest to find a cost effective method of currency ris+
reduction.
&espite this incentive' the lac+ of domestic investment opportunities in )a*a+hstan is
sadly mirrored !y a lac+ of ris+ management professionals. n the entire country there
are only fifty chartered actuaries compare this to the 15" charted in the %)0' to
perform all those ris+ management functions re,uired !y the sixteen funds' as well asgovernment and corporate entities. %nder this evidence' and the 7s emphasis of
need for !etter ris+ management' it seems fair to consider ris+ management in general
underdeveloped in )a*a+hstan' and any research li+ely to improve the situation well
ustified.
n so far as the lia!ilities faced !y the pension funds are concernedE enough ara!le
land lies within )a*a+hstans !orders' and enough soviet industry was !ased there
and retained !y the repu!lic0' for it to remain relatively self sufficient. -evertheless'
the some 5< of )a*a+hstani ?- spent on imports is dominated !y (ussia 4< ofimports0' and more recently hina 1
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HEDGING TENGE with OIL FUTURES
Ail production in )a*a+hstan dates !ac+ to the first half of the twentieth century !ut
even though these stoc+s were increasingly tapped during the 19"s and 198s
agricultural produce remained the countrys principal export throughout the soviet era
omfret' 19950. Gith the 199s and independence came the interest of the glo!al oilmar+et' such as hevrons !uying into the proect soon to !e +nown as
=engi*hevroil . Iowever' the 9s oil !oom that could have !een was delayed a
decade !y the inevita!le maritime !order disagreements that followed the !rea+ up of
the %$$(' and !ureaucratic mechanisms hung over from that former era. t was
therefore hand in hand with the economic reforms alluded to a!ove that )a*a+hstans
oil industry too+ off' with the period of greatest growth around 14< p.a.0 starting in
1999 -aman' omfret' (a!alland' $ourdin' 250.
ecause of its landloc+ed nature' the principal o!stacle to the )a*a+hstani oil industry
has always !e transportation. %ntil the inauguration of the aspian ipeline
onsortiums line in #utumn 21' pipes out of )a*a+hstan were monopolised !y
(ussia and exporters had at times !een confronted with highly constraining practices
!y the transport giant =ransneft. (ecently competition !etween the still part (ussian0
and the western developed a+u:=!ilisi:eyhan has further alleviated
monopolistic activities for the aspian shore fields. $uch practices do still continue to
limit the expansion of central )a*a+hstani fields' !ut competition is li+ely to improve
further over the coming decade with recent hinese ownership of fields heraldingproects to pipe oil east through Kiniang -aman' omfret' (a!alland' $ourdin'
250.
=he largest and !est +nown of the countrys oil fields is =engi* on the north eastern
shores of the aspian sea' !ut since its discovery in 19"9 other maor sites have !een
found further inland at )um+ol and %*en. =he greatest future prospect though' and
the source of aforementioned !order disputes' is the )ashagan field found under the
northern aspian in 2' holding an estimated 45 !illion !arrels of oil -aman'
omfret' (a!alland' $ourdin' 250.
Gith no immediate limits on )a*a+hstans oil production' or any sign that world oil
prices will collapse it seems li+ely that the country will continue to reap massive
energy revenues' and until !etter financial infrastructure is in place this will mean
increasing foreign investment and increasing exposure to currency ris+s.
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3 LITERATURE REVIEW
n tal+ing of )a*a+hstani institutional investors see+ing to eliminate currency ris+'
may have suggested a very narrow view of hedging. n fact' where the 7s reports
have highlighted currency ris+s' the call is for !etter ris+ management ta+ing a
position which !etter represents the ris+ to return preference of pension holders not
necessarily ris+ elimination. =he traditional view of hedging12was indeed of a world
with distinct hedgers and speculatorsE unsophisticated hedgers hoping to pass off the
entire ris+ of a position they were forced to hold' and sophisticated speculators willing
to ta+e on that ris+ in exchange for an expected profit 13.=his position of the theorists
was challenged in the 195s !y Iol!roo+ Gor+ing 1953' 19620' who was then the
$tanford rofessor of rices and $tatistics !ut was familiar with actual mar+et
practices from his role as associate director of the ood (esearch nstitute. Gor+ingsgreat offensive came in a 1953 article in the #merican ;conomic (eviewH =hrough
interviews with mem!ers of the grain industry' he revealed that many of those with
positions in !oth the spot and futures mar+ets' who would usually have !een called
hedgers' were altering their spot positions' according to their expectations for
upcoming relative price changes' to earn returns and there!y ta+ing speculative ris+s.
Ie continued to term these mar+et participants hedgers' and called for an expansion
of the theory to allow for other !ehaviours' !esides ris+ elimination' which he
considered dominant among actual hedgers. ntuition should have !een enough to
ustify ta+ing Gor+ing seriously' as large specialised goods procurers could hardly !eexpected to !e wholly ignorant of their mar+ets !ehaviours' or willing to ta+e a
!ac+seat while pure speculators reaped higher expected returns.
Cohnson 1960 too+ up the challenge !ut' after his own surveys of -ew Lor+ offee
hedgers' sought to moderate Gor+ings position to one where ris+ reduction remained
the primary' !ut not sole' motivation for ta+ing positions in !oth mar+ets and where
actual' rather than only relative' expected price changes are the driver for speculation.
Iis insight was that the hedger and speculator of traditional theory were in fact polar
extremes on a scale of mar+et participants' all placing different values on relative
certainty' and therefore choosing a different com!ination of expected return and
uncertainty through different portfolios of hedged and unhedged cash positions.
=hrough a model !ased around individuals ris+:return utility functions' he laid the
foundations for the modernportfolio theory treatment of hedgingHHedge ratios the
12$ee for instance Iawtrey 194 Cohnson' 196013ertainly' if a higher expected return for speculators was not originally part of the conceived
structure' then it was introduced with =o!ins "heory of li#uidity preferenceand )eynes "reatise onmoney. =hat said' Gor+ings description of mar+ets viewed as speculators playgrounds only wouldsuggest ris+ loving as the conceived drive for speculation.
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HEDGING TENGE with OIL FUTURES
value of the hedging instrument adopted as a proportion of the cash position
minimising ris+ for a given expected return.
&espite his merging of hedging and speculation' Cohnsons model provides an
analytical solution through a derivation similar to that coming !elow for a purehedger only. =he underlying consumer choice style model does' however' extend to
speculation when the expected return for either the spot or the futures is non:*ero. n
that model the hedging decision revolves around two optimisation pro!lems'
illustrated !y the diagrams !elowE
=his first diagram fig.3.10 shows the plane of com!inations !etween the spot
assumed to always !e long' as per older hedging theory0 and a single hedging
instrument long or short0. Iere the points of tangency !etween elliptic iso:variance
sets and linear iso:expected return sets represent the locus of com!inations !etween
cash and futures that minimise ris+ for a given expected return.
ash >M
utures >M
;(0 N 3r;(0 N 2r
;(0 N r
Far(0 N O2
Far(0 N 4O2
Far(0 N 9O2
7in P Far(0>;(0 Q
Fi! 3!1
9
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HEDGING TENGE with OIL FUTURES
=his second diagram fig. 3.20 shows the plane of all possi!le com!inations !etween
expected return and variance. 7apped onto this we have indifference curves dictated
!y our agents ris+:return utility function' along with the set of pairs derived in the
first diagram. -ow the point of tangency !etween indifference curve and minimum
variance set gives the agents optimal choice of expected return and variance'
translating !ac+ to their optimal portfolio of cash and futures in the former diagram.
=here is one ,uite o!vious flaw to Cohnsons treatment' in that he ta+es the variance
of return as proxy for all the ris+ a portfolio represents to its holder. =elser 19550
concurrently al!eit independently of Gor+ings challenge developed a portfolio
!ased theory of hedging' !ut !ased his framewor+ around the avoidance of a@disasterB return threshold more realistically mirroring the financial distress
ustifications of hedging. =hrough the =che!ycheff ine,uality he shows variance
minimisation to !e sufficient for the avoidance of such a threshold and this !roadens
wor+ !ased on Cohnson to cover a more general mar+et participant 14. -onetheless'
minimising variance relative to expected returns' or simply minimising variance for a
pure hedge' assumes that the ris+:return utility function of the agent in ,uestion is
,uadratic that their perception of ris+ is limited to the second moment of the
portfolio returns distri!ution only or that portfolio returns have a symmetric
14=hough the ine,uality means there might !e a portfolio with higher expected return which alsoavoids disaster
Fi! 3!2
O(0 >M
;(0 >M
7in P Far(0>;(0 Q
%tility N u
%tility N 2u
1
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HEDGING TENGE with OIL FUTURES
distri!ution with ?aussian tails0. =his flaw was in fact not addressed until relatively
recently' with the advent of more sophisticated o!ective functions' li+e the maximum
utility and minimum semi:variance conditions hen' Dee and $hrestha' 220.
(eturning !riefly to Gor+ings 19530 wor+' there are two other points of noteH&espite their long history' Gor+ing descri!es some confusion prior to the 195s as to
the primary function of futures mar+ets. rior to statistical treatment' it seems that
they were viewed largely as vehicles for speculation' with hedging a minor ancillary
role15. Iowever' Gor+ing presents somewhat speculative0 evidence suggesting that
the activity of futures mar+ets is driven !y those with a position in the underlying
cash mar+et. $peculations role is deemed less significant for volume !ut of course
very necessary for the existence of hedging' which the author gives as one reason for
the existence of a few !road mar+ets restricted to a single grade for most commodities
rather than many thin mar+ets tailored to specific grades of produce. =he second
point' and another reason for the !road few' comes from the authors direct
investigation of whether hedging acific -orth Gestern wheat with hicago futures
held any advantage over futures on the thinner $eattle 7ar+et. =he results indicated
that hedging for ris+ reduction with more li,uid !ut less correlated futures was @R
compara!le with insurance that covers losses a!ove some stated minimumB' which
would !e more desira!le to those with concave ris+ aversion. f true' this point could
prove reassuring for my own study as it suggests that near:perfect parallel movement
of spot and futures prices is not necessary to ensure a desira!le hedge.
=hough it was Cohnson who provided an analytic solution to a @ris+B minimising
!alance of futures to cash' and also an in samplemeasure of hedging effectiveness'
;derington 19"90 is often credited with the so called$inimum %ariance hedge ratio
or even the &derington $inimum %ariance ratio' as it is sometimes called.
;deringtons great contri!ution is in fact in his application of that ratio and measure to
time series data for severalsimplehedges' where futures exist for the specific cash
position and are used as the hedging instrument. t is ,uite intuitive that as a futures
contract nears its expiration date' and comes closer to !eing a contract for immediatedelivery' its value should grow to !e e,ual to that of a spot position' while similarly
fluctuations in its value should grow to match the spots volatility. =his intuition
illustrated in fig.3 !elow0 has the o!vious result for hedging that futures with more
immediate delivery dates should serve as !etter hedges' and this is confirmed !y
;deringtons results' which show improved in sample0 ris+ elimination for @near!y
contractsB over @distant contractsB with longer times to expiry. =he implication for my
study is that the o!vious choices of hedging instrument' particularly when the
15=his would indeed !e consistent with the @casino hypothesisB descri!ed !y ry 1988' p230 asprevalent for much of the early 2thcentury
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HEDGING TENGE with OIL FUTURES
termination date of the hedge is uncertain' are those futures which are closest to
expiry often called @the near!yB.
-ot until #ndersons and &anthines 19810 wor+ is an analytic solution derived for a
hedge ratio which considers expected returns' as the portfolio !ased theory
ac+nowledged !y Cohnson and ;derington would demand. -aturally an optimum
hedge ratio must !e the result of an optimisation pro!lem' and so the authors criticalstep is to introduce an o!ective function incorporating returns. Iowever' here there
necessarily enters some su!ectivity into the pro!lem' as the portfolio theory of
hedging suggests agents adopt positions in !oth mar+ets according to their individual
ris+:return preferences. =he hedgers preference is introduced !y #nderson and
&anthine through a coefficient of ris+ aversion' S' in the o!ective function !elowH
( ) 0Tvar2
1T &
fppypyp ff
0T
TT
11 =
where y is the num!er of units of the cash asset held' fthe corresponding vector of0
num!ers0 of futures contracts' tp is the price of once unit of the spot at time t'f
tp is
the vector of0 futures prices0 at the same instant' and Tdenotes a random varia!le16.
7aximisation of this o!ective function yields the following optimal futures position1"
16
=hose parenthetical arguments reflect the situation of a composite hedge' allowed for !y #ndersonand &anthine in their model.1"n the case of hedging with a single instrument.
Fi! 3!3
rice >M
=ime >days
;xpiry
utures price
$pot price
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HEDGING TENGE with OIL FUTURES
0Tvar
0T'Tcov
0Tvar
0T1
1
11
1
1
f
f
f
ff
p
ppy
p
p&pf +
=
=his expression can !e !ro+en down' with the second term representing the variance
minimising position' identical to those derived !y Cohnson 1960 and ;derington19"90' and the first representing the adustment to this position necessary to provide
the preferred expected return. =he astute o!server might recognise the coefficient of y
in the second term as the expression for a linear estimator according to least s,uares
regression' and indeed one of the reasons that the speculative term is often ignored in
empirical studies is that the ris+ minimising term can !e easily computed and its
effectiveness measured according to the vast and well recognised AD$ framewor+.
=he earliest review of the effectiveness of hedging exchange rate ris+ with commodity
futures comes in ;a+er and ?rants 198"0 @ross hedging foreign currency ris+B.
=hough commodity cross hedging is admittedly an afterthought' the emphasis of their
wor+ !eing on using other currencies futures for the hedge' the mechanics of cross
hedging with any futures are largely the same indeed they are almost identical to
hedging with the spot assets own futures and their methodology is therefore of
great interest to my study. 7oreover' cross hedging with other currencies futures
could !e seen as the principal alternative to commodity:currency cross hedging and its
relative performance will have no small !earing on the interpretation of my results.
=he authors choose to loo+ only at the pure hedging potential of the commodity
futures and consider only the variance minimising part of #nderson and &anthines
decomposition' which is to say that they employ the minimum variance hedge ratio.
Af course !y effectively choosing an o!ective function which ignores expected
portfolio return' the authors leave their results inconsistent with the portfolio theory of
hedging' and incomplete as a measure of practical hedging potential. #n innovation
on previous wor+' however' is ;a+ers and ?rants testing of hedging effectiveness ex
ante' orout of sample' !y applying the hedge ratio computed for the first half of the
sample to the remaining period.
=he first %$ dollar exchange rates to !e considered are those for sterling' the
anadian dollar' and the yen. #s currencies with futures mar+ets' the authors are a!le
to compare the ris+ reduction !etween periods achieved through simple and cross
hedges. =hey find that' !oth ex post and ex ante' simple18hedges provide excellent
ris+ reduction for all three currencies as one would expect from theory while
currency:currency cross hedges perform at !est moderately' and at worst
detrimentally. =he results for composite hedges suggest that' with futures availa!le in
18=he ris+ reduction is not perfect !ecause the maturity of the instruments does not match that of thecash positions' ma+ing for basis risk
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HEDGING TENGE with OIL FUTURES
the spot currency' cross hedging with other currencies futures can only worsen out of
sample ris+ reduction. 7eanwhile' the opposite is implied when the spots own
futures are not used' with multiple cross hedging instruments generally outperforming
one alone.
=he authors ac+nowledge that testing cross hedging where a simple hedge is availa!le
is artificial and go on to test the effectiveness of the same futures' plus those for the
&eutschemar+' as hedging instruments for the talian lira' $panish peseta' ?ree+
drachma' and the $outh #frican rand. =his is more relevant to my own study than the
first control0 group' as =enge futures are not availa!le in the volumes needed for a
simple hedge. onsistently for the three ;uropean spots it is seen that the !est hedges
consist of ideally multiple0 ;uropean futures' and that useful ris+ reduction is
achieved. =he rand denominated cash position' however' !enefits from nothing !ut a
sterling:yen composite cross hedge. =he authors descri!e these findings as consistent
with the intuition that the economic significance of the hedging instruments economy
to the spots economy is the crucial factor in the effectiveness of a currency:currency
cross hedge.
inally' and most relevant to this paper' the authors follow a similar procedure testing
the ris+ reduction for cash positions in every currency using gold futures. =he authors
cite golds role as a @currency su!stituteB' and its intuitive importance to the rand' as
ustifications for its use' !ut the results are far more conclusive than these arguments.?old is overwhelmingly reected as a hedging instrumentE increasing the ris+ for cash
positions in seven of the nine currencies examined' and showing uselessly slim ris+
reduction for even the rand. =his would indeed !e discouraging for hopes of a
commodity hedge of the tenge' were it not for wor+ such as that of ashin' espedes'
and $ahay 20 which suggests that the $outh #frican real exchange rate is in fact
tied to other commodities' and that gold is generally uncorrelated with its producers
currencies. 7eanwhile' it should !e considered that the most heavily traded currency
futures cannot !e expected to share the same relationship to the tenge as ;uropean
currencies do to one another' ma+ing a currency:currency cross hedge a less via!leoption in my case.
#nother limitation to their research' ac+nowledged !y ;a+er and ?rant' is that they
ma+e little attempt at formal theoretical ustification for the relative ,uality of
different hedges. or currency:currency hedges' more recent wor+ may use no:
ar!itrage conditions to ustify a lin+' while for commodity currency hedges this detail
is improved upon to a degree !y enet 1990 and can !e fleshed out further for D&
economies' as owman forthcoming0 does' with hens and (ogoffs 220
extension of the alassa:$amuelson model.
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HEDGING TENGE with OIL FUTURES
Ghere for ;a+er and ?rant commodity:currency cross hedging was a curiosity' for
ruce # enet 1990 it is in itself the focus of his study' and where the former
authors tested for the trivial case of developed economies' enet investigates those
minor currencies where a commodity futures !ased hedge might fill the !reach of nocurrency futures. #s mentioned' he also attempts to provide theoretical ustification
for a lin+ !etween @primary export commodityB prices and the exchange rateH
=raditional flow theories of exchange rate determination argue thatexchange rates reflect underlying supply and demand characteristics forcurrencies. hanges in exchange rates should !e generated !y changes inthe demand supply0 for goods and services exported imported0. &emandchanges are influenced !y export price changes. $o a positive correlationshould exist !etween exchange rate movements and export commodity
and commodity futures0 price changes.
=he author sets out two strengths of verification for his modelH Ie deems that the
model would !e wea+ly confirmed should hedging a currency with itsprimary export
commodities futures those commodities representing a disproportionately large
share of the nations exports successfully reduce the exchange rate ris+ of holding
that currency. =he support for the model could !e termed strong' he argues' were there
indication that hedging performance was positively related to !oth the share of exports
represented !y the commodity and the mar+et share in a commodity held !y the
country. n the case of )a*a+hstan' the first of these conditions for strong supportmight !e seen when hedging with oil futures !eing easily the dominant export.
enet sets a!out testing his model with a set of thirteen countries all without
currency futures and sixteen primary export commodities. Af these countries
-orway is the only economy !earing much resem!lance to that of )a*a+hstan' with
oil and metals representing similar proportions of exports !ut !oth most li+ely priced
exogenously and a recently floated currency.
=he testing methodology is generally similar to that employed !y ;a+er and ?rant'
with tests of the hedging effectiveness of each primary export commodity for each
country' in sample to verify the model and then out of sample to measure the
practicality of hedging. Ane differentiating feature of enets investigation is the use
of a currency futures !as+et as a !enchmar+ for hedging effectiveness.
=he effectiveness of hedges is highly varia!le' with some even increasing portfolio
ris+. or -orway ex post hedging performance is encouragingly strong' !ut ex ante
effectiveness is alternately good and terri!le !etween periods' suggesting hedge ratiovaria!ility that might ma+e the practice unrealistic. =his hedge ratio varia!ility is a
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HEDGING TENGE with OIL FUTURES
# concern that might validly !e raised is that the author chooses to use the minimum
variance ratio over the error correction model ratio' on the strength of a finding in her
previous paper' without having tested for non:stationarity in the nominal exchange rate
series. # unit root in the nominal series' as might !e portended !y the unit root in the
real' should properly !e dealt with !y use of an error correction framewor+ to estimatethe hedge ratio' in order to allow for reversion !ehaviour to the assets prices long
term e,uili!rium relationship19.
=he extant !ody of literature on commodity:currency cross hedging is overtly lac+ing
in more technical treatments of the ratio estimation pro!lem. therefore loo+ to the
parallel li!rary on currency:currency cross hedging for improved estimators' where a
good source is )roner and $ultan 19930. =heir paper contrasts the performance the
AD$ estimator for the minimum variance hedge ratio' used in all the papers touched
upon a!ove' with the ;rror orrection augmented AD$ estimator' which was so
readily dismissed !y owman' and a dynamic hedging strategy which will !orrow
for my own study. =his dynamic estimator revolves around the assumption of
conditionally heteros+edastic errors in the relationship !etween cash and futures
where!y the volatility of !oth assets returns is a function of the immediately o!served
past volatility. =he authors note a significant improvement in performance under the
assumption of a ?#(I structure' with some 4.5< additional variance elimination
out of sample.
#nother vein of estimation procedures' outside the scope of this paper' are explored !y
$ercu and Gu 19990' who' noting the large errors inherent in regression !ased
estimation' choose to use simple predictors !ased only on the most recently o!served
price for each asset. =hey test !oth random wal+ and @un!iased expectationsB
!ehaviours for the prices' and find no small success in doing so. =hese price !ased
estimators considera!ly out perform regression derived estimates !ut are not easily
translated from currency:currency into commodity:currency hedging' due to the
greater complexity of models lin+ing exchange rate to currency prices through
overed nterest arity and a @triangular no:ar!itrageB condition price rules can !ederived relating one commodity with ust the instruments futures and the interest rate
differential.
19#s per hen Dee and $hrestha 220
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" DATASOURCES and PROPERTIES
=he aim of this study is to identify a li,uidly traded futures contract to serve in place
of the sparsely traded tenge futures. -aturally though' no specific futures exist for
)a*a+hstans own oils and must therefore su!stitute alternative crude oil futures.
#mong the current internationally traded !lends' that can !e assumed li,uid enough'
%rals would seem the most o!vious choice of su!stitute as )a*a+hstani oil was
transmitted !y (ussian pipes until the pipeline was inaugurated and geographic
proximity should imply similar transport costs since. Iowever' futures prices for %ral
oil are only availa!le from 26. 7y second choice then is rent oil futuresE rent
serves as the !enchmar+ for most oil moving west and also' as a light !orderline:
sweet !lend' most closely resem!les the ma+eup of lend #ssay andomposition' hevron0.
#lthough will assume !asis ris+ is negligi!le next to inter:asset price ris+' the
selection of contract maturities availa!le for futures contracts represents a
complication in that it ma+es for multiple futures prices at any one time. t is
reasona!le to assume that it is the near!y contract that will !e the most heavily traded
at any one time except perhaps for the last few wee+s !efore delivery )roner and
$ultan' 199300 while also closest to the underlying assets price !ehaviour' due to the
convergence effect descri!ed in the previous chapter. t is for these reasons that choose &atastreams ; continuous futures price series for rent crude' which
always ta+es the price of the near!y contract and there!y replicates the !ehaviour of a
hedger who always updates to the closest contract to maturity immediately !efore his
current contract expires @&atastream &ata the factsB' =hompson inancial' 230.
; rent futures are contracts for a single !arrel !!l0 and expire 16 to 2 days
!efore the !eginning of the delivery month. ontracts for the next seventy two
consecutive months are always availa!le' so the nearest contract will always have no
more than a month to expiry.
=he exchange rate series chosen is the G7 standardised (euters daily mean spot rate'
also from &atastream. =he period of the study is dictated !y the period over which the
=enge has !een free:floating2' and therefore initially consider this series from 4th
#pril 1999. =he financial crisis of last autumn' called a foreign speculative attac+ !y
)a*a+hstani authorities' forced a temporary pegging of the tenge' which the
government insists will come to an end in the first ,uarter of 29' and ma+es
Acto!er 2" the end of my study period. ?iven the governments commitment to
2=hough this in fact coincides with the ascendancy of oil among the countrys exports -aman'omfret' $ourdin' (a!alland' 260
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HEDGING TENGE with OIL FUTURES
mar+et economics thus far' and their trou!le with a fixed exchange rate in 1998' there
is every reason to !elieve the re:float will happen when stated.
=he model shall present in the next section proposes a linear relationship !etween
the logs of the exchange rate and oil price' rather than the prices themselves. =heseries actually wor+ with for the remainder of this paper are therefore the logs of the
; continuous and G7( datasets.
#s am loo+ing to control for errors in varia!les pro!lems' caused !y !id as+ noise
among other things' narrow the two daily series to produce wee+ly every fourth
o!servation0 and monthly every twentieth o!servation0 series.
=hough the daily data series is extensive and regression on many su!:samples should
!e effective' when the data is reduced to wee+ly and monthly fre,uencies one has to
!e careful' in conducting out of sample testing' to ensure that the division of the time
series is into su! samples that will give optimal performance for !oth the ratio
estimation procedure and the effectiveness testing. #s later find cause to also
estimate using data starting 1 Can 23' and must !e a!le to fairly compare
performance' choose an estimation period for ex ante tests which provides a
sufficient margin after this date for AD$ to !e effective while leaving enough of the
sample for effectiveness measures to !e effective.
aily 'eekly $onthly(ags A! )*+
+
(ags A! )*+
+
(ag
s
A! )*+
+
,.,/.00
0
-
12.,0.1,,
3
M > / 1 :2.26 1.2V :2.41 .54V :2.4 .29V
M > !!l :2."3 .9V :2.63 .41V :2.1" .2"V
,.,.1,,
4
-
12.,0.1,,
3
M > / 1 :2.3 .39V :2.3 .2V :2.38 .1V
M > !!l :2.6" .63V :2."2 .32V :3.11 .13V
T#$%& "!1shows the results of unit root tests' with a deterministic trend and intercept' for all the log:series
that will eventually wor+ with. V denotes reection at the 5< significance level. Dags for the #& tests
were selected automatically according to the #+ei+e criterion. andwidths for the )$$ tests' which were
configured with the artlett +ernel' were selected according to the -ewey Gest criterion.
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HEDGING TENGE with OIL FUTURES
aily 'eekly $onthly(ags A! )*+
+
(ags A! )*+
+
(ag
s
A! )*+
+,.,/.00
0
-
12.,0.1,,
3
M > / 1 .3 3.64V .18 1.59V :.23 ."1V
M > !!l :1.4 5.28V :1.3 2.32V :1.44 1.6V
,.,.1,,
4
-
12.,0.1,,
3
M > / 1 :1.64 4.V :1.65 1."5V .49 .9V
M > !!l :.93 4.3V :.82 1.85V :1.9 .92V
T#$%& "!2shows the results of unit root tests' with intercept only' for all the log:series that will eventually
wor+ with. V denotes reection at the 5< significance level. Dags for the #& tests were selected
automatically according to the #+ei+e criterion. andwidths for the )$$ tests' which were configured
with the artlett +ernel' were selected according to the -ewey Gest criterion.
or nominal price and exchange rate data' found the daily series running from the
!eginning of #pril 1999 to !e am!iguously non:stationary' with #ugmented &ic+ey
uller tests suggesting no:unit root and )wiat+ows+y hillip $chmidt $hin tests
reporting the opposite. =his could argua!ly !e due to an adustment period
surrounding the float causing the exchange rate to follow an exceptional processEindeed the exchange rates movement is visi!ly different for the #pril and 7ay of that
year visi!le in figure 4.1. therefore omit the first two months of the tenges
floating !ehaviour from the study' and start instead from 1 Cune 1999. %nit root tests
detailed in ta!le 4.1' followed !y those detailed in ta!le 4.2' show the existence of a
unit root now ro!ust to all standard tests21. choose to use !oth #& and )$$ as
these two esta!lished unit root tests have opposite null hypotheses' and serve as good
complements to one another Ia!i! and )almova' 2"0.
=hough my hedge ratio estimation procedures will !e !ased on the first differences of
these series' and might therefore !e safe from spurious regressions even in the case of
first order integration' +nowing whether the prices are 10 is important in that it leads
into the ,uestion of cointegration' which shall explore in the next chapter. Ghat is
important' if am to avoid spurious results' is that the series are not of higher
integrating order than 10' as this would imply that the differenced series were not
0. =a!le 4.3 shows unit root test' with deterministic trends and intercepts' and
confirms that the log:series are indeed 10.
21#s the series are logs' they cannot ta+e negative values' and the case of a random wal+ with nointercept neednt !e explored as this is e,uivalent to supposing a random wal+ around *ero0.
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HEDGING TENGE with OIL FUTURES
aily 'eekly $onthly(ag
s
A! )*+
+
(ag
s
A! )*+
+
(ag
s
A! )*++
,.,/.000
-
12.,0.1,,3
M > / :38.1V .11 :18.6V .8 :8.38V .8
M> !!l :48.6 .6 :21.3V .6 :12.1V .9
,.,.1,,4
-
12.,0.1,,3
M > / :28.V .6 :14.9V .4 :6.48V .4
M> !!l :3".5V .4 :16.V .5 :9."9V .1
T#$%& "!3shows the results of unit root tests' with intercept and deterministic trend' for the first differences
of all the log:series that will eventually wor+ with. V denotes reection at the 5< significance level. Dags
for the #& tests were selected automatically according to the #+ei+e criterion. andwidths for the )$$
tests' which were configured with the artlett +ernel' were selected according to the -ewey Gest criterion.
Gea+ as graphical inference is' returning to figure 4.1 one can see some encouraging
coincidences of each series pea+s with the others troughs' over the long run at least.
Iowever' the six month intervals on the time axes allow one to o!serve that the finer
movement' wee+:to:wee+ or month:to:month the timescale will !e hedging0' mayust as possi!ly !e disparate.
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HEDGING TENGE with OIL FUTURES
80
90
100
110
120
130
140
150
160
170
01/04/99 01/10/99 01/04/00 01/10/00 01/04/01 01/10/01 01/04/02 01/10/02 01/04/03 01/10/03 01/04/04 01/10/04 01/04/05 01/10/05 01/04/06 01/10/06 01/04/07
Fi'(& "!1Deft is shown the movement of the tenge dollar exchange rate over the free floating period.
An the right is the dollar price of a !arrel of oil over that same period.
0
10
20
30
40
50
60
70
80
90
01/04/99 01/10/99 01/04/00 01/10/00 01/04/01 01/10/01 01/04/02 01/10/02 01/04/03 01/10/03 01/04/04 01/10/04 01/04/05 01/10/05 01/04/06 01/10/06 01/04/07
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HEDGING TENGE with OIL FUTURES
or the demand side of the economy assume that households have a homogeneous
degree *ero0 o!!:&ouglas type utility function !ased on their consumption of the
trada!le and non:trada!le goods. t can !e shown that a unit of consumption then costs
the domestic price level*E
= 1"5***
n the same manner as for the developing countrys production' wages e,uate !etween
the non:traded -0 and intermediate 0 goods sectors of the foreign V0 economy'
givingH
8
5
85 *
a
a* V
V
VV =
oth countries then contri!ute symmetrically to the production of the trada!le good
=0 through a o!!:&ouglas production function' which can then !e manipulated togive the foreign unit price of the trada!le goodH
= 1VVV 87" ***
Gith the assumption that foreign consumers share the utility function of domestic
consumers a more realistic assumption for an $% country redefining its economy
than for developing economies with more su!sistence cultures' such as many of those
considered !y ashin et al 230. IenceH = 1VVV "5 ***
=he law of one price for !oth the trada!le good and export commodity' com!inedwith some simple alge!ra then yield a relationship !etween the real exchange rate and
world export priceH
=
8
7
5
5
8
7
*
*
a
a
a
a
*
&*
V
VV
VV
=a+ing the natural logarithm of !oth sides of this e,uation leaves a straightforward
linear relationship !etween the log of the exchange rate' &' and the log of the primary
exports price along with productivity and price differentials that shall assume arerelatively static over the eight year test period0.
Af course futures are not oil itself !ut contracts written upon it' contracts which are
rarely completed at that. -evertheless' even the possibility of delivery means that
ar!itrage should force the prices of future and underlying to converge on nearing the
expiry date' as discussed in hapter 3. %ntil full convergence' the difference !etween
the price specified !y a futures contract and its underlying asset is +nown as the !asis.
7y choice of futures price series assumes that the hedger always holds a contract with
at most one month until expiry' and as my assessment of out of sample hedgingperformance is for one month exposures the futures price will !e close to convergence
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HEDGING TENGE with OIL FUTURES
suppose that the !est hedge ratio estimate for that monthly hedge would come from
monthly data9 Iowever' previous wor+ $ercu and Gu' 23E among others0 has
shown that more fre,uent data can out:perform less fre,uent regardless of the hedging
period' which is consistent with my model of a single relationship !etween exchange
rate and oil price across all timescales. =he one potential pitfall of using denserestimation data is that any day:to:day noise errors:in:varia!les such as the !ouncing
of transaction prices !etween the different the !id and as+ sides of the mar+et0 over
the !asic signal !ecomes more prominent $ercu and Gu' 230. #longside my
investigation of the general cross:hedging potential of oil futures' therefore also loo+
to compare' for every estimator' the performance of the different fre,uencies of data
mentioned in the previous chapter.
=o derive a minimum variance hedge ratio for a single period' we loosely follow
Cohnson 1960 in considering a portfolio consisting of one unit =enge0 of the cash
position' with log:dollar value $' and :units of a single type and maturity of futures'
with log:dollar value . =he variance of the return for this portfolio is then given !y
0''cov20var0var0var 1112
11 ++= tttttttttt !!++!!++
ttt !+ +=
Ghile the expected return is given !y
000 111 += tttttt !!&++&&
#s the former expression is a variance' hence everywhere positive and infinite as
' optimisation !y setting its first derivative e,ual to *ero will yield a glo!al
minimum. =he value of:at this minimum will then !e
0var
0'cov
1
11
=tt
tttt$%
!!
!!++
Ghich is clearly the same pure hedge component seen in #ndersons and &anthines
analysis. =his of course means that under the correct assumptions our !est estimate of
the minimum variance hedge ratio': $%' is the same as the Ardinary Deast $,uares
estimator for a futures price regressor and spot price regressandH
tt
$%
t !+ ++= 5.10
Ghere is the difference operator.
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HEDGING TENGE with OIL FUTURES
-aturally' as my model has pushed me to wor+ in log:series' the a!ove does not
produce an optimal num!er of futures contracts to hold relative to cash' as might !e
expected of a literal hedge ratio' !ut rather a ratio of changes in log:price. ortunately
for values close to *ero0 differences in logs are e,uivalent to percentage returns onthe value of each unit of the asset held ma+ing: $%the exchange rates elasticity
with respect to oil futures price an alternative to dollar returns often chosen !y
hedging theorists . =his therefore ma+es:$%the ratio of the value of futures held to
the value of cash held. # repercussion of this o!servation often swept over !y authors
that wor+ in differenced log:prices or percentage returns for instance hen' Dee and
$hrestha' 220 is that this means:$%is not truly a @staticB hedge ratio' !ecause the
proportion of futures contracts to cash held must !e continually updated as their prices
change. =o see this' note that there is no initial outlay in ta+ing up a futures contract'
!ut that mar+ing to mar+et24 guarantees that futures price changes are felt !y the
hedger' so that the time t;0 return on a portfolio' xR ' o!eysH
( ) ( )
11
11
11
++
++
++
=
=
=
=
==
tt
f
ts
tf
s
ts
ftfsts
ts
ttftts
ts
tftstfts
x
!+
Rsc
fcR
sc
RfcRsc
sc
ffcssc
sc
fcscfcscR
=he a!ove also serves to simplify my statistical treatment of the hedges effects' as it
allows me to find the return of the portfolio through the linear com!ination of the
individual assets returns' as might with simple dollar returns.
=he only remaining aspect of the a!ove treatment which might seem ,uestiona!le inpractice is that have assumed:can ta+e any valua!le' when of course only integernum!ers of contracts can !e ta+en on. Iowever' dealing with a single tenge lia!ility isof course an idealisation and' when scaled up to the millions that the pension fundshold in assets' infinite divisi!ility of the futures contracts simply scales up toreflecting the divisi!ility of a near infinite num!er of contracts.
=hough !oth the nominal exchange rate and oil futures log:series were identified as
10 in the previous chapter' this estimation procedure is performed on the first24 shall ignore the time value effects related to instantaneously realised changes in portfolio value
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HEDGING TENGE with OIL FUTURES
differences of these series' eliminating any danger of spurious regression under AD$.
Iowever' for !oth the daily and wee+ly series' resuch:?odfrey tests suggest serial
correlation of the residuals and reusch:agan:?odfrey maximum li+elihood0 tests
show signs of heteros+edasticity seen in ta!le 5.2 at the end of this chapter.
therefore employ -ewey:Gest standard errors to ensure any inference is !ased onconsistent statistics.
Githin the @staticB hedging framewor+ initially use for the minimum variance ratio'
the standard measure of two securities relevance to one another is in sample or ex
post0 assessment via the goodness of fit of the regression Cohnson' 1960. =he
goodness of fit is of course of little relevance to a practicing hedger loo+ing to
eliminate perceived future ris+ using current information. therefore also ma+e use of
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HEDGING TENGE with OIL FUTURES
!e mirrored in the other due to some long run dependency. =hough one might still
expect a relationship !etween the price changes seen in !oth' a regression !ased only
on the inflations would !e neglecting any tendency to return to this long run
e#uilibrium relationshipas opposed to value0. =he resultant !ias towards *ero0 in
the hedge ratio would !e corrected !y the introduction of an &rror Correction "ermfor the long run relationship into the regression e,uation26)roner and $ultan' 19930'
however there is some de!ate as to the significance of this effect for overall hedging
performance $ercu and Gu' 19990.
=o assess whether cointegration could indeed !e affecting my various hedges
performance though it seems unli+ely it could erode an otherwise effective hedge to
the degree seen in the next chapter conduct a standard Cohansen style cointegration
test. =his test is asymptotic so the si*e of the daily dataset should ensure a ro!ust
result' though it does have its detractors and we cannot !e sure of its accuracy for the
wee+ly or monthly series Iu!richt' Dut+epohl' $ai+onnen' 210.
aily 'eekly $onthly
>un 00 ?
+ep ,3
>an ,4 ?
+ep ,3
>un 00 ?
+ep ,3
>an ,4 ?
+ep ,3
>un 00 ?
+ep ,3
>an ,4 ?
+ep ,3
=race test-NZ[0
.4 .268 .21 .24 .318 .5""
=race test
-\1Z[0.5"6 .1"6 .96" .293 ."2 .323
(an+ test-NZ[0
.26 .345 .12 .211 .253 .61
(an+ test-\1Z[0
.5"6 .1"6 .96" .293 ."2 .323
Dong run >$ :.252 : :.1913 : : :
T#$%& )!1 shows the p:values of Cohansen cointegration tests' with [ the set of o!servations for the
fre,uency and timeframe descri!ed in the column head' and - the num!er of cointegrating relationships
hypothesised to !e in the system. values are as per 7ac)innon:Iaug:7ichelis 19990. ottom row shows
futures coefficient of normalised cointegrating vector.
t can !e seen from =a!le 5.1 that Cohansen tests clearly support the cointegration of
!oth the daily and wee+ly time series' over the whole sample' with !oth trace and
eigenvalue tests reecting the null of no cointegrating relationships while neither can
reect the null of up to one cointegrating relationship. #lso reported in the ta!le is the
cointegrating vector' relating the two series in e,uili!rium' which will soon use
according to )roners and $ultans 19930 model.
26=he method is often +nown as &ynamic Ardinary Deast $,uares
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=heir treatment is identical to the approach already detailed for the minimum variance
hedge ratio up until the point of conducting a regressionH (ather than regressing the
return of the exchange rate against a constant and0 the futures return alone' the
current deviation from the long term relationship called the&rror Correction "erm is included as a second regressor' ma+ing the regression e,uation
tttt$%t b!+!+ +++= 0 5.20
Ghere is the difference operator' t is a normally distri!uted independent error
term' and bis a coefficient producing an 0 com!ination of +and!13.
#s with regression 5.1 will test the effectiveness of the ;rror orrection modifiedhedge ratio estimators with !oth ex post and ex ante measures. =echnically for the ex
ante assessment the cointegrating vector should !e re:estimated for the smaller data
set' !ut for the sa+e of simplicity will assume that the difference will !e negligi!le
a failure of the model will continue to have the same implications under this
assumption.
DYNA*IC ESTI*ATORS
Iaving seen that the introduction of an error correction term does little to improve the
minimum variance hedges performance' a!andon any hopes that the oil:tenge
relationship is uniform over time along with the simplicity of @staticB hedge ratios'
and instead assume that pension funds utility functions0 are time separa!le. #mong
the alternative' dynamic' hedging strategies the most easily implemented is the rolling
hedge' where!y the minimum variance ratio is re:estimated for every increment of the
hedging period' ta+ing into account more data on the returns distri!ution as the
information set grows.
erhaps the !est way to present an analysis is through Diens and =ses 220
framewor+' as the change from the previous regression is ,uite straightforward' !eing
no more than a simple generalisation of our previous model to incorporate the
conditionality of the variances to the information set t !asically the set of all
o!servations from time to time t:10 this treatment can also !e viewed as an
expansion on the ex ante measure descri!ed a!ove.
2" assume that this bwill !e effectively the same for this linear causal model as the non:causal vectorderived coefficient in ta!le 5.1
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HEDGING TENGE with OIL FUTURES
0Z'cov20Zvar0Zvar0Zvar 2 ttttttttt !+!+7 ++=
[ ] "t '
Deading to the new conditional minimum variance hedge ratio
0Zvar
0Z'cov
1
11
ttt
ttttt$%
t!!
!!++
=
5.30
=he futures position ta+en at time t is then !ased on this ratio rather than that used at
time t:1. =his means the method produces an out of sampleestimate for the hedge
ratio
=he advantage of this standard rolling hedge model is that if the structural relationship!etween exchange rate and oil price alters during the sample period' then this change
does not interfere with the estimation of the earlier relationship. Iowever' the o!vious
flaw in that logic is that if data from the earlier relationship is still !eing used then it
wi%% interfere with AD$ regressions estimation of a new relationships parameters.
Ane remedy might !e a rolling window of a fixed length' progressively ignoring early
data as it incorporates newer o!servations' !ut any theoretical ustification for a
specific window length would pro!a!ly !e ustification for a more detailed !rea+
point model. nstead ma+e a still speculative !ut more ustifia!le0 assumption a!out
the possi!le nature of the relationship' !y assuming conditional heteros+edasticity for
!oth series.
# lagrange multiplier test for the a!sence of conditional heteros+edasticity in the
residuals of regression 5.1 strongly reects the null ta!le 5.20' for daily data at least'
and instead favours the presence of some form of #uto(egressive onditional
Ieteros+edasticity. 7oreover' there is a growing !ody of evidence to ustify such an
assumption for !oth exchange rates and oil prices. articularly popular is my
proposed structure of conditional heteros+edasticity following an #(7#1'10 process ma+ing it a ?#(I1'10 model as per )roner and $ultan 19930 which is typified
!y persistent periods of high volatility interspersed with similar periods of low
volatility' a pattern often o!served in price data. choose this over other conditionally
heteros+edastic models' !ased on ?#(Is superior performance in the exchange
rate study of 7curdy and 7organ 19880 and the oil futures study of #drangi'
hatrath' &handa and (affiee 210.
=he ?#(I consistent error correction treatment employ is !ased on that of )roner
and $ultan 19930' !eing a !ivariate error correction model with structureH
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HEDGING TENGE with OIL FUTURES
tsttsst !++ ++= 0 11
tfttfft !+! ++= 0 11
0'T ttft
stH5
5.40
=
tf
ts
tf
ts
t h
h
h
hH
1
1
2
1
2
1
2
++= tsstsssts hcbah 2
1
2
1
2
++= tfftffftf hcbah
=his onstant onditional orrelation model28 is so called !ecause @ is assumed
constant over the sample period' with less than unit a!solute value' and represents the
correlation !etween the cash and futures assets deviations from their e,uili!rium
values. =he long run relationship !etween cash and futures prices is now captured !y
the ratio ' as derived from the Cohansen cointegration29while theBs represent the
systems speed of return to e,uili!rium after shoc+s. =a!le 5.1 shows that error
correction is not relevant !ehaviour for some of the series' in which cases !othBs will!e set to *ero. =his will not !e detrimental to the estimation procedure' as the !asic
vector e,uation will still remove any intercept present in the differenced series'
leaving error terms which the ?#(I system then see+s to explain !y comparison
with one another.
y the same optimisation procedure as !efore' this leads to a time:varying hedge ratio
!ased on the conditional second moments of the returnsH
2
tf
tfts$%
th
hh
=
=hough #(7# style forecasting of the a!ove ratio would !e relatively
straightforward' restrict my study to the in sampleeffectiveness of such a hedge' and
ma+e comparisons with the variance elimination achieved in sample !y the AD$
derived minimum variance ratio.
28
Gith unrestricted intercepts29#s this cointegrating vector was derived through a vector model' it will !e consistent with !oth cashand futures !eing treated as endogenous
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HEDGING TENGE with OIL FUTURES
+,B BG BPG Ch-w ARCH.1/
aily ,.,/.000 -
12.,0.1,,3
9541,9,,12>24. R2is the adusted0goodness of fit forf$%' while &is the proportion of the unhedged positions
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monthly variance removed' out of sample' !y ta+ing a relative position of fmv futures over the period16>1>23 to 13>9>2". VAr its wee+ly>four:wee+ly su!:sample for the corresponding regressions.
#ssuming that there issome underlying lin+ !etween the two varia!les unli+ely as
this may seem given the significance and fit of ta!le 6.1s hedge ratios the failure of
AD$ to identify this relationship must !e attri!uted to the violation of one of itsunderlying assumptions. #s discussed in the previous chapter' one feature of the
relationship neglected !y the previous treatment' !ut shown to !e relevant for daily
and wee+ly fre,uencies !y the Cohansen tests detailed in ta!le 5.1' is the cointegration
of those series. n the hope of retaining the simplicity of AD$ !ased estimation for
hedges !ased at least on high fre,uency data' introduce an error correction term into
the regression. =he results in the lower section of ta!le 6.1 are for this ;rror
orrection modified regression. or wee+ly data a consistent relationship !etween
exchange rate and oil price remains as ,uestiona!le as !efore' as the ratios remain
decidedly insignificant' !ut daily elasticity estimates' particularly over the first half of
the sample' are much more convincing. or !oth series there is enough improvement
in ex post ris+ reduction' over the regression that ignored the long run e,uili!rating
!ehaviour of the series' to !e compara!le with the wea+est of enets 1990 hedges.
7eanwhile' out of sample the previously o!served consistency of the daily estimates
performance is reinforced' while there is a mar+ed improvement in the predictive
power of AD$ on the wee+ly series. -evertheless' it should !e stressed that with such
insignificant wee+ly estimates' with and without the error correction term' no relia!le
inference on relative performance can !e made' and this result serves only as a remotehope that some further modification of my method will yield more practical results.
?iven the sound theoretical !asis for interaction !etween prices and exchange rates
discussed in previous chapters' it seems li+ely that the failures of static hedges are
!ecause other factors determining that interaction have varied too significantly across
the sample period' ma+ing the assumption of a constant !eta invalid. 7y first attempt
to mitigate this pro!lem ta+es the form of a rolling window hedge' where!y the
coefficient relating oil price to exchange rate is continually re:estimated throughout
the hedging period. n practice this would lead to greater transaction costs' !ut given
the poor performance of the static hedge' these costs would have to !e !ourn to gain
anything from cross hedging with oil futures. =he left hand side of ta!le 6.2 shows the
results of rolling window dynamic monthly hedges' estimated from daily' wee+ly' and
monthly four wee+ly0 data series. t is apparent from the low &values' for daily and
wee+ly fre,uencies' that the dynamic hedge at !est only matches the static procedure
for ris+ elimination. ndeed' for all series the tightly !anded variances hint that there
might !e no relationship at all !etween exchange rate and oil futures priceE perhaps
merely the results of insignificant and unsu!stantiated hedge ratios' li+e those of the
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HEDGING TENGE with OIL FUTURES
static hedge' generating random gains and losses in variance which cancel out over the
seventy six rolling regressions.
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HEDGING TENGE with OIL FUTURES
ata
!re#uenc
y
,.,/.000 - 12.,0.1,,3 ,.,.1,,4 - 12.,0.1,,3
Far]0 Far]S0 & Far]0 Far]S0 &&aily 3.236x1:4 3.248x1:4 .4 3.214x1:4 3.248x1:4 .1Gee+ly 3.251x1:4 3.248x1:4 :.1 3.23x1:4 3.248x1:4 .67onthly 3.242x1:4 3.248x1:4 .2 3.2"x1:4 3.248x1:4 .13
T#$%& !2 shows the dynamic performance for hedge ratios derived progressively from e,uation 5.3 over the
periods at the column heads. Iere is the log of the month t value of the portfolio 0'1 1$%
tf over the su!
period starting 6>1>25. S is the unhedged spot position over the same period. ] is the monthlydifference operator.
;xamination of the conditional correlation series produced in estimating the rollinghedge' as shown in figure 6.1' suggests a significant change in the structure of the
cross hedging relationship at the start of 23. =his shift in the structural relationship
cannot !e easily reconciled with any political or industrial change' as we would not
expect any marginal further0 relaxation of government controls to have so radical an
effect and the greatest industrial change in the period the opening of the aspian
ipeline onsortium pipeline0 should have ta+en effect in 21>2. -evertheless'
how rea+point tests strongly reect the null of no such change at every fre,uency
see ta!le 5.20' and as it would invalidate !oth the static and rolling estimates !ased on
all prior information' repeat the a!ove estimations for the su! period starting 1Canuary 23. =he static results are presented in ta!le 6.3 and the dynamic in the right
hand portion of ta!le 6.2.
ata
!re#uency
&x post &x ante
OLS f$% f$%NZ0 R2 fmv fmvNZ0 &
&aily .85 . .5 .125 . :.3Gee+ly .128 .18 .8 .28 .1" .31
7onthly .26 .26 .24 .88 .62 .15
T#$%& !3 for regression 5.1 and 5.2.Gheref$%is the minimum variance hedge ratio !ased on data !etween1>1>23 and 28>9>2"V' whilefmvis the minimum variance hedge ratio !ased on the su!:sample ending3>12>24. R2is thegoodness of fit forf$%' while &is the proportion of the unhedged positions varianceremoved out of sample' !y ta+ing a relative position of fmv futures over the period 1>1>25 to28>9>2"V. VAr its wee+ly>four:wee+ly su!:sample for the corresponding regressions.
3"
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HEDGING TENGE with OIL FUTURES
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
2000 Jan 2001 Jan 2002 Jan 2003 Jan 2004 Jan 2005 Jan 2006 Jan 2007 Jan
rho
Monthly
Weekly
Daily
Fi'(& !1 #$-4&0 shows the conditional correlations for the various data fre,uencies starting from Canuary2 and hence ignoring initial estimates insta!ility' caused !y small generating samples. #fter highlyvolatile movement until Canuary 21' which might simply !e caused !y estimation error' there is a cleartwo years of very sta!le correlation !etween the series. =his then collapses into something resem!ling arandom wal+ or highly correlated autoregressive process. B&%-w is shown the effect of this correlation
structure on the hedge ratio estimated.
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
2000 Jan 2001 Jan 2002 Jan 2003 Jan 2004 Jan 2005 Jan 2006 Jan 2007 Jan
KZT/BBL
Monthly
Weekly
Daily
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=a!le 6.3 shows improvements in the fit and significance of the hedge ratios relative to
their counterparts in ta!le 6.1' !ut the performance of the hedges in terms of ris+
reduction is still uselessly low. Aut of sample' the static hedges continue to show
potential for a detrimental effect on returns' !ut this fact' com!ined with low p:values
and the 1:6< ex post (2
s for these ratios not shown0' once again suggests that theremay !e a shift in the underlying nature of the exchange rate:oil relationship !etween the
estimation and hedging periods if any such relationship actually exists.Gith so rich a
daily data series could continue to isolate structural changes without further0 ris+ing
the integrity of AD$ estimation' !ut with no clear economic ustifications for the
changes' this would !e of no help to an actual hedger.=he results on the right hand side
of ta!le 6.2 on the other hand show improved ex ante performance for all fre,uencies.
Iowever' that !oth the wee+ly and monthly hedges are outperformed !y their static
rivals' again forces me to ,uestion the sta!ility of the relationship across this sample.
aily 'eekly $onthly
1>6>99: 1>1>3: 1>6>99: 1>1>3: 1>6>99: 1>1>3:
^s*EFs,
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