1 PRICE DISCOVERY IN SPOT and FUTURE HARD COMMODITY MARKETS Isabel Figuerola-Ferretti Jesus Gonzalo Universidad Carlos III de Madrid Business Department.

1

PRICE DISCOVERY IN SPOT and FUTURE HARD COMMODITY

MARKETS

Isabel Figuerola-FerrettiJesus Gonzalo

Universidad Carlos III de MadridBusiness Department and Economic Department

Preliminary October 2006

2

Trading Places Movie

3

We are going to talk about …

• Introduction

• Theoretical Model

• Econometric Implementation (GG P-T decomposition)

• Data

• Results

• Conclusions

4

Price Discovery

• The process by which future and cash markets attempt to identify permanent changes in transaction prices.

• The essence of the price discovery function of future markets hinges on whether new information is reflected first in changed future prices or changed cash prices (Hoffman 1932).

5

Contribution

• We separately quantify the relative contribution

of future and spot prices to the revelation of the

underlying fundamentals.

• We demonstrate that for those metals with a

liquid futures market the future price is more

important in the price discovery process.

• The Gonzalo-Granger decomposition allows us to

do this more robustly than in Habroucks

alternative way.

6

Why these commodity markets?

• Commodities are traded in highly developed future markets.

• In the metals sector 90% of the transactions take place in the forward/future markets.

• The LME quoted price is the world wide reference price and the common.

• It is important to quantify the price discovery role of metals futures.

7

Fig 1: Volumes traded in commodity and index future markets

0

100000

200000

300000

400000

500000

600000

03

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/2005

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Date

vo

lum

es t

rad

ed

(in

$)

FTSE 100-LIFFE

al-LME

cu-LME

IPE crude-oil

8

Literature Review 1Literature on price discovery

• Garbade, K. D. & Silver W. L. (1983). Price movements and price discovery in futures and cash markets. Review of Economics and Statistics. 65, 289-297.

• Hasbrouck, J. 1995. One security, many markets: Determining the contributions to price discovery. Journal of Finance 50, 1175-1199.

• Harris F., McInish T. H. Shoeshmith G. L. Wood R. A. (1995) Cointegration, Error Correction, and Price Discovery on Informationally Linked Security Markets. Journal of Financial and Quantitative Analysis. 30, 563-579

9

Literature Review 2:Price discovery metrics

• Gonzalo, J. Granger C. W. J 1995. Estimation of common long-memory components in cointegrated systems. Journal of Business and Economic Statistics 13, 27-36.

• Hasbrouck, J. 1995. One security, many markets: Determining the contributions to price discovery. Journal of Finance 50, 1175-1199

10

Literature Review 3Comparing the two metrics of price

discoverySpecial Issue Journal of Financial Markets

2002• Baillie R., Goffrey G., Tse Y., Zabobina T. 2002. Price discovery and common factor models.

• Harris F. H., McInish T. H., Wood R. A. 2002. Security price adjustment across exchanges: an investigation of common factor components for Dow stocks.

• Hasbrouck, J. 2002. Stalking the “efficient price” in market microstructure specifications: an overview. Leathan Bruce N. (2002). Some desiredata for the measurement of price discovery across markets.

• De Jong, Frank (2002). Measures and contributions to price discovery: a comparison.

11

Theoretical Model: Garbade and Silber 1983

Equilibrium with infinitely elastic supply of arbitrage Assumptions:• No taxes or transaction cost

• No limitations on borrowing• No cost other than financing to

storing a long cash market position • No limitations on short sale of the

commodity in the spot market• The interest rate is flat and

stationary at continuously compounded rate of r per unit time.

12

• Return of investing S0 € in the spot market

• Alternatively investing S0 in a risk free asset and at the same time taking a long position in the future market (delivery in one year) produces the return

0

01

SSS

rSFS

0

01

Theoretical Model: Garbade and Silver 1983

13

• Under the previous assumptions

so

• Taking logs, at time t the equilibrium with infinitely elastic supply of arbitrage is

0

01

0

01

SSS

rSFS

)1(00 rSF

Theoretical Model: Garbade and Silver 1983

14

where St and Ft are in logs, and t is the number of days to the first delivery date of the underlying commodity (in our case, 15 months).

• The previous assumptions imply that the supply of arbitrage services will be infinitely elastic whenever eq (1) is violated

ttt rSF (1)

Theoretical Model: Garbade and Silver 1983

15

Equilibrium with finitely elastic supply of arbitrage services

• Lets define a cash-equivalent future price

• To describe the interaction between cash and future prices we must first specify the behavior of agents in the marketplace.

• There are Ns participants in spot market.• There are Nf participants in futures market.• Ei,t is the endowment of the ith participant immediately

prior to period t.• rit is the reservation price at which that participant is

willing to hold the endowment Ei,t.• Elasticity of demand, the same for all participants.

Theoretical Model: Garbade and Silver 1983

ttt rFF ´

16

Equilibrium with finitely elastic supply of arbitrage services

• Demand schedule of ith participant in spot market

where A is the elasticity of demand

• Aggregate cash market demand schedule of arbitrageurs in period t

where H is the elasticity of cash market demand by arbitrageurs. It is finite when the arbitrage transactions of buying in the cash market and selling the futures contract or vice-versa are not riskless

stitti NiArSAE ,.....,1 ,0 ,,,

0 , ́ HSFH tt

Theoretical Model: Garbade and Silver 1983

17

• The cash market will clear at the value of St that solves

• The future market will clear at the value of Ft such that

tt

N

ititti

N

iti SFHrSAEE

cc

´)(1

,,1

,

tt

N

ititti

N

iti SFHrFAEE

ff

´)´(1

,,1

,

Theoretical Model: Garbade and Silver 1983

18

Equilibrium with finitely elastic supply of arbitrage services

• Solving the clearing market conditions we get

• If there is no arbitrage H=0

• If H=∞

ANHANH

rANHrANHF

ANANH

rANHrANHS

sf

fts

stf

t

sf

ftc

stf

t

//1

)}/(1{)}/({

/1

)}/({)}/(1{

ftt

stt

rF

rS

)(fs

ftf

sts

tt NN

rNrNFS

Theoretical Model: Garbade and Silver 1983

19

Dynamic price relationships

• To derive dynamic price relationships, we need a description of the evolution of reservation prices.

Theoretical Model: Garbade and Silver 1983

eiww

wv

NjwvFr

NiwvSr

teti

itit

ftjtttj

ctittti

,0),cov(

,0),cov(

,....,1 ,´

,....,1 ,

,,

,

,1,

,1,

20

• And the mean reservation price

)/,0(

)/,0( ),,0(

,....,1 , ´

,....,1 ,

2

22

,1

,1

fft

cstt

ftjtttf

ctittts

NTwNw

NTwNwTvNv

NjwvFr

NiwvSr

Theoretical Model: Garbade and Silver 1983

21

Dynamic price relationships: VAR model

)/(/1

)/(

)/()/(1

)/(

1

1

1

1

ANHANH

ANHb

ANHANH

ANHa

e

e

F

S

bb

aa

F

S

fs

f

fs

s

ft

st

t

t

t

t

• When H=0, prices are independent random walks

• When H=∞ prices, will follow a common random walk (ets=et

f )

• When 0<H<∞: – If Futures market dominate– If Cash markets dominate

ab 0

ba 0

fs

f

NN

N

ba

a

Mensures the importance

of future markets relative

to cash markets

Theoretical Model: Garbade and Silver 1983

22

VECM Representation

t

t

ft

ct

t

t

t

t

F

Sab

e

e

F

S

b

a

F

S

´

111

1

fs

f

NN

N

baa

The ratio is used to

measure the importance of future

market relative to the cash market

in the price discovery process

baa /

Theoretical Model: Garbade and Silver 1983

23

• Alternatively substituting

ttt rFF ´

ft

ct

t

t

t

t

e

e

F

S

b

a

F

S

´11

´ 1

1

Theoretical Model: Garbade and Silver 1983

with =r

24

Incorporating Mean Backwardation/Contango

tt FS

)(S Contango 0

)(S dation Backwar0

t

t

t

t

FNormal

FNormal

)(S tion BackwardaStrong0

then,-

t tF

Let

Theoretical Model: Garbade and Silver 1983

25

The ‘Theory’ of Normal Backwardation

• Normal backwardation is the most commonly accepted “driver” of commodity future returns

• “Normal backwardation” is a long-only risk premium “explanation” for futures returns

– Keynes coined the term in 1923– It provides the justification for long-only commodity futures indices

• Keynes on Normal Backwardation

“If supply and demand are balanced, the spot price must exceed the forward price by the amount which the producer is ready to sacrifice in order to “hedge” himself, i.e., to avoid the risk of price fluctuations during his production period. Thus in normal conditions the spot price exceeds the forward price, i.e., there is a backwardation. In other words, the normal supply price on the spot includes remuneration for the risk of price fluctuations during the period of production, whilst the forward price excludes this.”

A Treatise on Money: Volume II, page 143

26

$36,00

$36,50

$37,00

$37,50

$38,00

$38,50

$39,00

$39,50

$40,00

$40,50

$41,00

$41,50

April-04 June-04 August-04 September-04

November-04 December-04 February-05 April-05 May-05 July-05

Oil

pri

ce (

$/ba

rrel

)

$396

$397

$398

$399

$400

$401

$402

$403

$404

$405

Gol

d pr

ice

($/T

roy

ounc

e)

Crude Oil Gold

Backwardation

Contango

Note: commodity price term structure as of May 30th, 2004

•Backwardation refers to futures prices that decline with time to maturity

•Contango refers to futures prices that rise with time to maturity

NearbyFuturesContract

27

VECM with Mean Backwardation/Contango

ft

ct

t

t

t

t

e

eF

S

b

a

F

S

1

11´ 1

1

Theoretical Model: Garbade and Silver 1983

28

Econometric Implementation

• We use the Gonzalo-Granger (GG) methodology as opposed to Hasbrouck´s because it is robust to the presence of correlations in the error terms (et).

• This is important for commodity price data with daily frequency.

• Both techniques impose a minimum structure in the dynamics of the price series.

29

Metodology: the GG Permanent-Transitory

30

31

Metodology: the GG Permanent-Transitory

1

2

11

)´(

´

´

´

A

A

Xz

Xf

tt

tt

k

jtjtjtt XXX

11'

ttt zAfAX 21

t

tt F

SX

P-T decomposition

where

32

Easy Estimation and Testing

33

34

The steps are…

1) Perform unit root test on price levels2) Estimate the VECM model3) Test the rank of cointegration r4) Estimate by finding the first r

eigenvectors of the following eigenvalue problem

5) Estimate the α vector by finding the last n-r eigenvectors of the following eigenvalue problem

0011

001011 SSSS

0101

110100 SSSS

35

The steps are…

6) Test the H0:

7) Test the H0 α = (1,0) and α = (0,1)

8) Set up the PT decomposition

)1,1(´

ttt zAfAX 21

12

11

)´(

´

´

´

A

A

Xz

Xf

tt

tt

36

Data

• Daily spot and future (15 months) for Al, Cu, Ni, Pb, Sn, Zi, quoted in the LME.

• Sample January 1990- July 2006.• Source Ecowin.• Copper: historically most important

contract traded in LME. Aluminium took over in terms of volume in 1997.

• Aluminium and Nickel trading introduced in 1979.

37

Descriptive Statistics al cu ni Pb Zi

(1-L) Spot Average ret 0.0000 0.0002 0.0000 0.0001 0.0001

Robust SE (0.0002) (0.0002) (0.0003) (0.0003) (0.0002)

(1-L) F15-month Average ret 0.0000 0.0002 0.0001 0.0001 0.0001

Robust SE (0.0001) (0.0002) (0.0003) (0.0002) (0.0002)

Spot- F15month Average ret -0.0252 0.0411 0.0312 -0.0202 -0.0095

Robust SE (0.0009) (0.0015) (0.0015) (0.0014) (0.0014)

38

Table 1: Cointegration test, common factor weights and hypothesis testing

Al Cu Ni Pb Zi

r ≤1 0.06 1.22 0.00 0.00 0.02

r = 0 19.73 15.72 23.37 19.33 15.20

1 1.00 1.00 1.00 1.00 1.00

2 -1.00 -1.00 -1.00 -1.00 -1.00

H0:=(1,-1) 0.1435 0.3553 0.1502 0.4638 0.8320

-0.0252 0.0411 0.0312 -0.0202 -0.0095

Robust Sd (0.0009) (0.0015) (0.0048) (0.0044) (0.0043)

This table presents results on the Trace test of r= 0 against r>0. and r ≤against r>1for the whole sample. The 95% critical values for rejecting the null are 19.99 and 9.13 respectively. The 90% critical levels are 17.79 and 7.50. We also present p values from testing the null hypothesis of unit cointegrating vector and average constant terms of cointegrating relations with corresponding and Wewey West Stadanrd errors

)( 2 tt FSmean

39

Table 2: Proportion of price discovery for spot and future markets

Al Cu Ni Pb Zi

1 -0.2934 0.8864 0.0053 0.7886 -0.3081

2 0.9560 0.4630 1.0000 0.6150 0.9514

H0: =(0,1) (0.1473) (0.0991) (0.1294) (0.0822) (0.2753)

H0: =(1,0) (0.0002) (0.4847) (0.0039) (0.2453) (0.0035)

H0: =(1,1) (0.7092) (0.8516)

We present the common-long memory factor weights for five LME spot and future markets,. Since we have two series and one cointegrating vector r=1 there is only one common factor orthogonal to the adjustment vector. We test the elements of this last eigen vector of the common factor matrix for significance using the methodology of Gonzalo and Granger (1995). In each the null hypothesis is that the factor weight for the indicated market is 0. We have also tested the null hypothesis that the common factor weight is 1 in both markets for copper and lead.The test statistic is distributed with a chi-squared with one degree of freedom. We report P values which are given in parenthesis and calculated from the likelihood ratio test statistics reported in table A2 estimated following the PT methodology.

40

Conclusions and implications

• For those metals with most liquid future markets the future price is the major contributor to the revelation of the common factor.

• Producers and consumers should rely on the LME future price to make their production and consumption decisions.

• The LME future price changes lead price changes in cash markets more often than the reverse.

• Future and spot prices are cointegrated implying that it is not possible to make profits in the long run trading futures and taking positions in the underlying commodity

41

Graphical Appendix

Figure 1:Aluminium spot 3-month and 15-month forward future offer prices

0

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03/0

1/1

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006

date

futu

res als

al3

al15

42

Figure 2:Copper spot 3-month and 15-month future offer prices

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

1000003

/01/

1989

03/0

1/19

90

03/0

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91

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92

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1/19

93

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94

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1/20

06

date

Pri

ces

(in

$)

cus

cu3

cu15

43

Fig 3: Nickel spot 3-month and 15-month future offer prices

0

5000

10000

15000

20000

2500003

/01/

1989

03/0

7/19

89

03/0

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90

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90

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06

date

pri

ces

(in

$)

nis

ni3

ni15

44

Figure 4: Lead spot settlement 3 month and 15 month lead prices

0

200

400

600

800

1000

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03/0

1/19

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06

date

pri

ces pbs

pb3

pb15

45

Fig 5: Zinc spot 3-month and 15-month offer future prices

0

500

1000

1500

2000

2500

3000

3500

4000

4500

03/0

1/19

89

03/0

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date

pri

ces zis

zi3

zi15

46

Figure 6: Backwardation in the aluminium market

-300.00

-200.00

-100.00

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

03/0

1/19

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05

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1/20

06

date

bac

kwar

dat

ion

(in

$)

backwardation15

47

Figure 7: backwardation in the copper market

-400

-200

0

200

400

600

800

1000

1200

1400

1600

03/0

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03/0

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date

bac

kwar

dat

ion

backwardation15

48

Figure 8: Backwardation in the nickel market

-2000

0

2000

4000

6000

8000

10000

12000

03/0

1/19

89

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1/19

90

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05

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1/20

06

date

Bac

kwar

dat

ion

(in

$)

backwardation15

49

Figure 9: Backwardation in the Lead Market

-200

-100

0

100

200

300

400

500

600

03/0

1/19

89

03/0

1/19

90

03/0

1/19

91

03/0

1/19

92

03/0

1/19

93

03/0

1/19

94

03/0

1/19

95

03/0

1/19

96

03/0

1/19

97

03/0

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98

03/0

1/19

99

03/0

1/20

00

03/0

1/20

01

03/0

1/20

02

03/0

1/20

03

03/0

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04

03/0

1/20

05

03/0

1/20

06

date

bac

kwar

dat

ion

backwardation15

50

Figure 10: backwardation in the zinc market

-200

0

200

400

600

800

1000

03/0

1/19

89

03/0

1/19

90

03/0

1/19

91

03/0

1/19

92

03/0

1/19

93

03/0

1/19

94

03/0

1/19

95

03/0

1/19

96

03/0

1/19

97

03/0

1/19

98

03/0

1/19

99

03/0

1/20

00

03/0

1/20

01

03/0

1/20

02

03/0

1/20

03

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1/20

04

03/0

1/20

05

03/0

1/20

06

date

bac

kwar

dat

ion

backwardation15

51

Spot versus 15month aluminium prices

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500

spot prices

15 m

on

th p

rice

s

al15

52

Spot versus 15 months copper prices

0

1000

2000

3000

4000

5000

6000

7000

8000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

spot prices

15 m

on

th p

rice

s

cu15

53

Nickel spot and 15 month prices

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0 5000 10000 15000 20000 25000

spot prices

futu

re p

rice

s

ni15

54

Lead spot and 15 month prices

0

200

400

600

800

1000

1200

1400

0 200 400 600 800 1000 1200 1400 1600

spot prices

futu

re p

rice

s

pb15

55

Zinc spot versus 15-month price levels

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500 4000 4500

spot prices

15 m

on

th p

rice

s

zi15