Tom Wilkinson - A Tenge Oil Tango

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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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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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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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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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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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

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=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

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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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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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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

13


15/46


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.

14


16/46


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

15


17/46


18/46


# 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

1"


19/46

" 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

18


20/46


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.

19


21/46


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.

2


22/46


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.

21


23/46


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

22


24/46


25/46


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

24


26/46


27/46


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.

26


28/46


-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

2"


29/46


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

an out of sample or ex ante


30/46


!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

29


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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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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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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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+,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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static hedge' generating random gains and losses in variance which cancel out over the

seventy six rolling regressions.

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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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-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,

Tom Wilkinson - A Tenge Oil Tango

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Transcript of Tom Wilkinson - A Tenge Oil Tango