Corn Future Spreads - Zentraler Informatikdienst ...homepage.univie.ac.at/robert.kunst/seas2010_pres_lehecka.pdfIntroduction Futures Spread A futures spread is a technique in which

Corn Future SpreadsEconometric Analysis of Seasonality

Georg Lehecka

June 8, 2010

Georg Lehecka Corn Future Spreads

Table of Content

1 Introduction: Futures and Futures Spreads

2 Description of Data

3 Application of Seasonal ModelsDeterministic ModelLinear Stationary Seasonal ModelSeasonal Unit-Root Non-Stationary Model

4 Results and Discussion


Introduction

Aim of this empirical analysis

Estimation and forecast of corn futures spreads based on thefact of seasonal time series

Application of different seasonal models to the time series


Introduction

Futures Contracts

A futures contract is an agreement between two parties to buy orsell an asset at a certain time in the future for a certain price.

Suppose that, on June 8, the July futures price of corn at theChicago Merantile Exchange (CME) is quoted as 350 $Cents perbushel (contract size is 5,000 bushels ∼127 t.). This is the price,exclusive of commissions, at which traders can agree to buy or tosell Corn for December delivery.


Introduction

220

230

240

250

260

270

280

July and December Corn Futures Prices 2006

2006

Fut

ure

Pric

es

Sep Nov Jan Mär Mai Jul

July Corn ContractDecember Corn Contract


Introduction

200

300

400

500

Corn Futures Prices

1989 − 2006

Cor

n F

utur

es P

rices

1990 1995 2000 2005

July Corn ContractDecember Corn Contract


Introduction

Futures Spread

A futures spread is a technique in which a trader buys one contractand sells another contract of the same commodity with anotherdelivery date.

Suppose that, on June 8, the July futures price of corn at theChicago Merantile Exchange (CME) is quoted as 350 $Cents perbushel and the December futures price of corn is quoted as 360$Cents per bushel. A trader sells July Corn and buys DecemberCorn. The spread has as value 360− 350 = 10 $Cents per bushel.The goal for the trader is that the July contract declines and thatthe December contract increases in order to increase the spreadvalue.


Introduction

−15

0−

100

−50

050

Corn Futures Spreads Dec−Jul (every Spread beginning with 0)

Last 250 days of both legs1989 − 2006

Spr

ead

(beg

inni

ng w

ith 0

) D

ec−

Jul i

n po

ints

1990 1995 2000 2005


Introduction

Economic Reasons for Seasonality in Agricultural Markets

There is obviously seasonality in the underlying agriculturalbusiness. For example the bulk of the US corn crop is plantedApril/May and harvested October/November.The seasonal patternfor the corn market should assume therefore a specific path. Priceand perceptions of supply tend to be inversely related, with priceoften lowest when supply is greatest, at harvest and with priceoften highest in May when the market is anxious about thepotential for new production.


Description of Data

Data are the July and December Corn Futures Contracts

At the Chicago Merantile Exchange (CME)

During the years 1989 - 2006

Unit of measurement: $Cents per bushel (contract size is5,000 bushels ∼127 t.)

Relevant time series are the last 250 days of the Dec - JulySpread


Description of Data

0 50 100 150 200 250

−15

0−

100

−50

050

Corn Futures Spreads Dec−Jul (in absolute numbers)

1989 − 2006Last 250 Days

Spr

eads

Dec

−Ju

l in

poin

ts


Description of Data

0 50 100 150 200 250

−15

0−

100

−50

050

Corn Futures Spreads Dec−Jul (in absolute numbers)

1989 − 2006Last 250 Days

Spr

eads

Dec

−Ju

l in

poin

ts

mean of spreadsmedian of spreads


Description of Data

0 50 100 150 200 250

05

10Mean/Median of Corn Futures Spreads Dec−Jul (in absolute numbers)

1989 − 2006Last 250 Days

Mea

n/M

edia

n of

Spr

eads

Dec

−Ju

l in

poin

ts

mean of spreadsmedian of spreads


Description of Data

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

−10

0−

500

Average Spreads over Time Classes

Days until maturity

Ave

rage

spr

ead

in ti

me

clas

ses:

mea

n(sp

read

[x[i−

1]=

>D

ays<

x[i]]

)

> 250 > 225 > 200 > 175 > 150 > 125 > 100 > 75 > 50 > 25


Description of Data

●

●

●

●●

●

●

●●

●

24

68

Mean of average Spread over Time Classes

Days until maturity

Mea

n of

ave

rage

spr

ead

over

tim

e cl

asse

s

> 250 > 225 > 200 > 175 > 150 > 125 > 100 > 75 > 50 > 25


Description of Data

−10

0−

500

Average Spreads over Time Classes

Ave

rage

spr

eads

ove

r tim

e cl

asse

s

1989 1991 1993 1995 1997 1999 2001 2003 2005

> 250> 225> 200> 175> 150> 125> 100> 75> 50> 25


Application of Seasonal Models

Discussion on useful Seasonal Model ClassesData follow a ’deterministic’ seasonality (’summer remainssummer’) and are non-stationary.

Deterministic model class: non-stationary → maybe a goodmodel for data

Linear stationary model class: stationary → not such a goodmodel for data

Unit-root model class: non-stationary but ’summer maybecome winter’ → maybe only a good model withdeterministic parts


Application of Seasonal Models: Deterministic Model

Simple Model for Deterministic Seasonality

yt =S∑

s=1

δstms + εt

δst = 1 if t falls to season s, and δ = 0 otherwise; ms is the meanfor season s; S is the numer of seasons and in the example 250; εt

is zero-mean stationary; t = 1, ...,T = 4500

Estimation:SSE 1.508 · 106


Application of Seasonal Models: Deterministic Model

−15

0−

100

−50

050

Corn Futures Spreads Dec−Jul

Last 250 days of both legs1989 − 2006 ( 2007 estimate)

Spr

ead

Dec

−Ju

l in

poin

ts

1990 1995 2000 2005

Seasonality Estimation


Application of Seasonal Models: Linear Stationary Model

Simple Stationary Seasonal Model

yt = φSyt−S + εt , |φS | < 1

S is the numer of seasons and in the example 250; εt is zero-meanstationary; t = 1, ...,T = 4500

Estimation:Estimate t value p-value

φ̂S 0.10872 −6.846 < 10−3

AIC 37, 197 SSE 1.642 · 106



−15

0−

100

−50

050



Spr

ead

Dec

−Ju

l in

poin

ts

1990 1995 2000 2005




Another Stationary Seasonal Model

yt =5∑

i=1

φiSyt−iS + εt

S is the numer of seasons and in the example 250; εt is zero-meanstationary; t = 1, ...,T = 4500; |φiS | < 1 for each i



Another Stationary Seasonal Model


φ̂1S 0.22493 −11.808 < 10−3

φ̂2S 0.11821 −6.039 < 10−3

φ̂3S 0.09586 −5.007 < 10−3

φ̂4S 0.01669 −0.865 0.387

φ̂5S −0.01464 0.790 0.429

AIC 28, 957 SSE 1.695 · 106



−15

0−

100

−50

050



Spr

ead

Dec

−Ju

l in

poin

ts

1995 2000 2005



Application of Seasonal Models: Unit-Root Model

Seasonal Unit-Root Model (SWR)

yt = yt−S + εt

S is the numer of seasons and in the example 250; εt is zero-meanstationary; t = 1, ...,T = 4500

Estimation:SSE 3.376 · 106



−15

0−

100

−50

050



Spr

ead

Dec

−Ju

l in

poin

ts

1990 1995 2000 2005




Another more general seasonal unit-root model

yt = φyt−S +S∑

s=1

δstms + εt ,

assuming φ to be well behaved (all roots outside unit circle). S isthe numer of seasons and in the example 250; ms is the mean for

season s; εt is zero-mean stationary; t = 1, ...,T = 4500


φ̂ 0.19682 −13.11 < 10−3

AIC 36, 721 SSE 1.632 · 106



−15

0−

100

−50

050



Spr

ead

Dec

−Ju

l in

poin

ts

1990 1995 2000 2005




A third general seasonal unit-root model

yt =5∑

i=1

φiSyt−iS +S∑

s=1

δstms + εt ,

assuming φiS to be well behaved (all roots outside unit circle). S isthe numer of seasons and in the example 250; ms is the mean for

season s; εt is zero-mean stationary; t = 1, ...,T = 4500



A third general seasonal unit-root model


φ̂1S 0.30125 −16.678 < 10−3

φ̂2S 0.20608 −11.104 < 10−3

φ̂3S 0.19126 −10.535 < 10−3

φ̂4S 0.12277 −6.708 < 10−3

φ̂5S 0.07595 −4.325 < 10−3

AIC 28, 612 SSE 1.920 · 103



−15

0−

100

−50

050



Spr

ead

Dec

−Ju

l in

poin

ts

1995 2000 2005



Results and Discussion

Model comparisonModel AIC SSE

Simple Deterministic Model

yt =∑S

s=1 δstms + εt - 1.508 · 106

Simple Stationary Seasonality Model

yt = φSyt−S + εt 37, 197 1.642 · 106

Another Stationary Seasonality Model

yt =∑5

i=1 φiSyt−iS + εt 28, 957 1.695 · 106

Seasonal Unit-Root Model(SRW)

yt = yt−S + εt - 3.376 · 106

Another Seasonal Unit-Root Model

yt = φyt−S +∑S

s=1 δstms + εt 36, 721 1.632 · 106

A third Seasonal Unit-Root Model

yt =∑5

i=1 φiSyt−iS +∑S

s=1 δstms + εt 28, 612 1.920 · 106


End

Thank you for the attention!


Documents

Corn Future Spreads - Zentraler Informatikdienst ...homepage.univie.ac.at/robert.kunst/seas2010_pres_lehecka.pdfIntroduction Futures Spread A futures spread is a technique in which