Analysis of Oil Seeds & Grain Price Volatility in India:

A VEC-MVGARCH ApproachNitesh Kumar Pandey

England

Background

• Oilseeds and wheat grains have witnessed unprecedented volatilities and price fluctuations in the recent past.

• Extreme volatility in commodity prices, particularly of food commodities, affects producers, consumers, traders, exporters & food procurement agencies of the central and state Government.

Commodities Under Study

• Wheat

• Selected Edible Oil seeds and Oil

Wheat & Edible Oil Price Forecast World Bank.xls

Wheat Price Volatility

• Who plays the biggest role in pushing the global wheat prices now?

• It is India.

• Following India’s plan to buy more wheat for buffer stock, the commodity’s prices soared across the world with the World Food Programme (WFP) expressing concern over the impact of dwindling stocks of the cereal.

Wheat Price Volatility

• After India invited tenders for an unspecified quantity of wheat from the international market, the price of wheat crossed record levels on commodity exchanges on Thursday.

• As grain traders reacted to urgent tenders from grain importers and the lowest global stock levels for 25 years, the prices shot up across the globe.

• India is the world’s second-largest wheat producer after China, but orders from Delhi to build up buffer stocks pushed price of a bushel climbing 30 cents to $7.88 a bushel on the Chicago Board of Trade.

Wheat Price Volatility

• In France, the price of November milling wheat also soared.

• Natural calamities like droughts and floods and production shortfalls, burgeoning demand and dwindling stocks also created a harvest season panic that again pushed the prices of wheat further.

• Since April, it has risen 75 per cent on both sides of the Atlantic after recent tenders from Egypt and India.

Wheat Price Volatility

• India last year suffered a weak harvest and entered the world market aggressively to import wheat. The International Grains Council expects India to import more than three million tonnes this year, despite an improved harvest.

Analysts believe that there is growing anxiety that the country had benefited from a succession of good monsoons.

Wheat Price Volatility

• The International Grain Council cut its forecast of world grain production by seven million tonnes this month to 607 million tonnes, as it assessed the impact of a wet summer in Northern Europe, weak output in Ukraine and drought in Argentina and Australia.

• Chicago Board of Trade wheat Futures contract set a new all-time high this week as crop concerns roil the market again. The December contract took out last week’s previous all-time high of $7.54.

Wheat Price Volatility

• Paris wheat Futures settled just shy of their all-time high and London-based wheat Futures surpassed their previous top.

More talk of Australian drought conditions and wheat crop woes there was another reason for bulls to buy.

Spot Price Volatility (Wheat)

Spot Prices Wheat

0

200

400

600

800

1000

1200

01

-03

-20

04

 

11

-03

-20

04

 

03

-04

-20

04

 

13

-03

-20

04

 

06

-04

-20

04

 

03

-05

-20

04

 

16

-03

-20

04

 

11

-05

-20

04

 

03

-06

-20

04

 

11

-05

-20

04

 

25

-06

-20

04

 

01

-07

-20

04

 

30

-08

-20

04

 

09

-10

-20

04

 

22

-04

-20

05

 

14

-07

-20

06

 

06

-02

-20

07

 

Date: 2004-2007 (Feb)

Sp

ot

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Series1

Oil & Oilseeds

Oil & Oilseeds Caster Seed /  Caster Oil  Coconut Oil / Copra  Cotton Seed / Cottonseed Oil  Crude Palm Oil  Ground Nut / Groundnut Oil  Kapasia Khalli  Linseed /  Linseed Oil  

Oil & Oilseeds

Mustard Oil / Mustard Seed  /Mustard Seed Oil

 RBD Palmolein / Refined Soy Oil  

Refined Sunflower Oil  

Rice Bran Refined Oil  

Safflower / Safflower Oil  

Sesam Oil  

Soy Meal  /Soybean / Soyabean Oil / Sunflower Oil/ Sunflower Seed

Oil & Oil Seeds

• India is the world’s fourth largest edible oil economy with 15,000 oil mills, 689 solvent extraction units, 251 Vanaspati plants and over 1,000 refineries employing more than one million people.

• The total market size is at Rs. 600,000 Mln. and import export trade is worth Rs.130,000 Mln.

Oil & Oil Seeds

• India being deficient in oils has to import 40% of its consumption requirements.

• With an annual consumption of about 11 mln. Tonnes, the per capita consumption is at 11.50 kgs, which is very low compared to world average of 20 kgs.

• China is currently at 17 kg.

Overview of Edible Oil Economy

• Indian vegetable oil is world's fourth largest after USA, China and Brazil.

• Oilseed cultivation is undertaken across the country in two seasons, in about 26 million hectares; mainly on marginal lands, dependent on monsoon rains (un-irrigated) and with low levels of input usage.

• Yields are rather low at less than one ton per hectare.

• Three oilseeds - Groundnut, Soybean and Rapeseed/ Mustard - together account for over 80 per cent of aggregate cultivated oilseeds output.

• Mustard seed alone contributes Rs.120,000 Mln. turnover out of Rs.600,000 Mln. oilseed based Sector domestic turnover.

• Cottonseed, Copra and other oil-bearing material too contribute to domestic vegetable oil pool

Overview of Edible Oil Economy

• Currently, India accounts for 7.0% of world oilseeds output; 7.0% of world oil meal production; 6.0% of world oil meal export; 6.0% of world veg. oil production; 14% of world veg. oil import; and 10 % of the world edible oil consumption

• With steady growth in population and personal income, Indian per capita consumption of edible oil has been growing steadily.

• However, oilseeds output and in turn, vegetable oil production have been trailing consumption growth, necessitating imports to meet supply shortfall.

Overview of Edible Oil Economy

Overview of Edible Oil Economy(Quantity in Million Tonnes)

Crop 2-Jan 3-Feb 4-Mar 5-Apr 05-06 (F)

Major Oilseeds

Groundnut 7 4.4 8.2 6 6.4

Rape/Mustard 5.1 3.9 6.2 6.6 7

Soybean 5.6 4.6 7.9 5.8 6.5

Other Six 3 2.2 3 3.7 3.6

Sub-Total 20.7 15.1 * 25.3 22.1 23.5

Others

Cottonseed 5.1 4.5 5.5 6.6 8.5

Copra 0.9 0.7 0.7 0.7 0.6

Grand Total 26.7 20.3 31.5 29.4 32.6

* Reduced due to Drought.

• 80 per cent of India's domestic oil output comes from the primary source that is nine cultivated oilseeds and two major oil-bearing materials (Cottonseed and Copra). The secondary source comprises of solvent extracted oils, Rice bran oil, oils from minor and tree-borne oilseeds etc.

Overview of Edible Oil Economy

Market Potential

• The per capita consumption of oil in India is 11.5 kg/year is way below the world average of 18 kg. Even china is at 17 kg. By 2010 the per capita consumption of oil in India is likely to be 15.6 kg. There is huge potential of growth.

• The demand for edible oils is expected to increase from Oil Year 2004-05 levels of 10.9 Mln. tonnes to 12.3 Mln. tonnes by 2006-07 (two years). This assumes a per capita consumption increase of 4% and a population growth of 1.9% which translates to an overall growth in demand @ 6% p.a. Based on the above assumptions, edible oil demand in the year 2015 is expected to be 21.3 million tonnes.

Demand Projection Edible Oil

2004 2010 2015

Total Demand (Mln. Tonnes) 10.9 15.6 21.3

Total Area under Oilseeds (Mln. Hectares) 23.4 28 32

Yield (Tonnes/hectare) 1.07 1.2 1.4

Production of Oilseeds (Mln. tonnes) 25.1 33.6 44.8

Domestic supply of edible oils (Mln. tonnes) 7 10.1 13.4

Total edible oil imports - (Mln. tonnes) 4.3 5.9 8.3

Imports as share of demand 39.40% 38.10% 39.50%

Demand Projection (Contd.)

• India will continue dependence on imports to the extent of 40% of its consumption requirements. The improvement in yields and the increase in area under cultivation will ensure that the domestic oilseed production is sufficient to meet 60% of consumption requirements.

Increased support from the Government

Year Minimum support Price Rs. per

MT

FY2001 11,000

FY2002 12,000

FY2003 13,000

FY2004 16,000

FY2005 17,000

FY2006 17,250

Increased support from the Government

• The government is increasing its focus on the edible oil industry, given that it has the second largest import bill after crude petroleum. The supported price of mustard seed, which was Rs 11,000 per MT in 2001, was increased to Rs 17,250 per MT by 2006. Consequently, mustard seed cultivation also increased from 5 MMT to 7.0 MMT in 2006. The main emphasis of the government is on reducing the import bill, and this step has helped to a certain extent.

Spot Price Volatility (Wheat)

Spot Prices Wheat

0

200

400

600

800

1000

1200

01

-03

-20

04

 

11

-03

-20

04

 

03

-04

-20

04

 

13

-03

-20

04

 

06

-04

-20

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03

-05

-20

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16

-03

-20

04

 

11

-05

-20

04

 

03

-06

-20

04

 

11

-05

-20

04

 

25

-06

-20

04

 

01

-07

-20

04

 

30

-08

-20

04

 

09

-10

-20

04

 

22

-04

-20

05

 

14

-07

-20

06

 

06

-02

-20

07

 

Date: 2004-2007 (Feb)

Sp

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Series1

Spot Price Volatility (RM Seed Oil)

Spot Price Volatility (Refined Soy Oil)

Objectives

• This paper proposes a multivariate vector error-correction generalized autoregressive conditional heteroscedasticity model to investigate the effect of oilseeds and wheat grain prices in neighbouring countries of Asia on its Indian equivalents.

• We propose to test whether in the long run the law of one price holds and whether in the short run the model captures the salient features of Indian commodity prices (oilseeds and wheat grain).

Objectives (Contd.)

• This model will be used to compute rolling forecasts of the conditional means, variances and covariance of the prices of oilseeds and wheat grain one year ahead.

• We expect that this model will produce superior forecasts compared to those based on a commonly used methodology of an autoregressive conditional mean model where the second moments are estimated using a fixed weight moving average.

Objectives

• To measure the degree of price instability of important agricultural commodities in the major international and domestic markets. The commodities selected for the study are wheat, palm oil, groundnut oil, soybean oil and coconut oil.

• To Compare the patterns of variability in Asian markets and understand its implications for Indian producers and consumers.

Objectives (Contd.)

• To examine whether the conditional mean relationship between Asian and Indian grain and oilseed prices can be characterized by a vector error correction (VEC) model.

• To examine how well do the one-year ahead forecasts of the conditional first and second moments from the VEC-MVGARCH model compare with those generated using the Chavas and Holt (1990) methodology and whether there is a significant difference in these forecasts using Hansen’s (2001) recently developed test of superior predictive ability (SPA).

Methodology

• The research methodology broadly is based on following three steps:

1. Modeling the Mean and Volatility of Indian oilseeds and wheat grain prices using ARCH, GARCH and ARIMA models.

2. Testing the data to examine whether the conditional mean relationship between Asian (few select countries independently) and Indian oilseed and wheat grain prices can be characterized by a vector error correction (VEC) model based on short and long run theory of Law of One Price (LOP).

3. Expanding the VEC model to allow for the modeling of the time varying second moments of domestic oilseeds and grain prices using a MVGARCH model.

Standard Approach to Estimating Volatility

• Define n as the volatility per day between day n-1 and day n, as estimated at end of day n-1

• Define Si as the value of market variable at end of day i

• Define ui= ln(Si/Si-1)

n n ii

m

n ii

m

mu u

um

u

2 2

1

1

1

1

1

( )

Simplifications Usually Made

• Define ui as (Si-Si-1)/Si-1

• Assume that the mean value of ui is zero

• Replace m-1 by m

This gives

n n ii

m

mu2 2

1

1

Weighting Scheme

Instead of assigning equal weights to the observations we can set

n i n ii

m

ii

m

u2 2

1

1

1

where

ARCH(m) Model

In an ARCH(m) model we also assign some weight to the long-run variance rate, VL:

m

ii

m

i iniLn uV

1

1

22

1

where

EWMA Model

• In an exponentially weighted moving average model, the weights assigned to the u2 decline exponentially as we move back through time

• This leads to

21

21

2 )1( nnn u

Attractions of EWMA

• Relatively little data needs to be stored• We need only remember the current

estimate of the variance rate and the most recent observation on the market variable

• Tracks volatility changes• RiskMetrics uses = 0.94 for daily

volatility forecasting

GARCH (1,1)

In GARCH (1,1) we assign some weight to the long-run average variance rate

Since weights must sum to 1

21

21

2 nnLn uV

GARCH (1,1) continued

Setting V the GARCH (1,1) model is

and

1LV

21

21

2 nnn u

Example

• Suppose

• The long-run variance rate is 0.0002 so that the long-run volatility per day is 1.4%

n n nu21

21

20 000002 013 0 86 . . .

Example continued

• Suppose that the current estimate of the volatility is 1.6% per day and the most recent percentage change in the market variable is 1%.

• The new variance rate is

The new volatility is 1.53% per day0 000002 013 0 0001 0 86 0 000256 0 00023336. . . . . .

GARCH (p,q)

n i n i jj

q

i

p

n ju2 2

11

2

Maximum Likelihood Methods

• In maximum likelihood methods we choose parameters that maximize the likelihood of the observations occurring

Example 1

• We observe that a certain event happens one time in ten trials. What is our estimate of the proportion of the time, p, that it happens?

• The probability of the event happening on one particular trial and not on the others is

• We maximize this to obtain a maximum likelihood estimate. Result: p=0.1

9)1( pp

Example 2

Estimate the variance of observations from a normal distribution with mean zero

m

ii

m

i

i

m

i

i

um

v

v

uv

v

u

v

1

2

1

2

1

2

1

)ln(

2exp

2

1

:Result

:maximizing to equivalent is this logarithms Taking

:Maximize

Application to GARCH

We choose parameters that maximize

m

i i

ii

i

im

i i

v

uv

v

u

v

1

2

2

1

)ln(

2exp

2

1

or

Variance Targeting

• One way of implementing GARCH(1,1) that increases stability is by using variance targeting

• We set the long-run average volatility equal to the sample variance

• Only two other parameters then have to be estimated

How Good is the Model?

• The Ljung-Box statistic tests for autocorrelation

• We compare the autocorrelation of the

ui2 with the autocorrelation of the ui

2/i2

Correlations and Covariances

Define xi=(Xi-Xi-1)/Xi-1 and yi=(Yi-Yi-1)/Yi-1

Also

x,n: daily vol of X calculated on day n-1

y,n: daily vol of Y calculated on day n-1

covn: covariance calculated on day n-1

The correlation is covn/(u,n v,n)

Updating Correlations

• We can use similar models to those for volatilities

• Under EWMA

covn = covn-1+(1-)xn-1yn-1

Positive Finite Definite Condition

A variance-covariance matrix, is internally consistent if the positive semi-definite condition

for all vectors w

w wT 0

Example

The variance covariance matrix

is not internally consistent

1 0 0 9

0 1 0 9

0 9 0 9 1

.

.

. .

Modelling Volatility

• Take a structural model

with ut N(0,σ2)• typically assumes homoscedasticity• if the variance of the errors is not constant this

would imply that standard error estimates could be wrong.

• Is the variance of the errors likely to be constant over time? – Not for financial data.

ttt uxy

Modelling Volatility• So can we model time-varying volatility of the errors?

• Recall the definition of the variance of ut:

σt2 = Var(ut ut-1, ut-2,...) = E[(ut-E(ut))

2 ut-1, ut-2,...]

= E[ut2 ut-1, ut-2,...]

• since E(ut) = 0

• What might variance of u depend on?– Lagged squared errors

• This is Engle’s ARCH(1) model2110

2 tt u

AutoRegressive Conditional Heteroscedasticity (ARCH)

• Easily generalisable to an ARCH(q) form

• Often large values of q required to capture volatility processes

• Comes with problems– many coefficients to estimate– non-negativity constraints

• variance cannot be negative so estimated alphas all need to be positive to ensure definitely positive variance for all errors

2222

2110

2 ... qtqttt uuu

Generalised ARCH (GARCH)

• Allow conditional variance to also depend on its own lagged value:

• This is a GARCH(1,1) model• A GARCH(p,q) model follows:

211

2110

2 ttt u

2211

22110

2 ...... ptptqtqtt uu

GARCH(1,1) Model

...

...constants2

332

222

110

231

21

2211

211

22

21

2211

211010

221

22101

2110

2

231

2310

22

221

2210

21

211

2110

2

ttt

ttt

ttt

tttt

ttt

ttt

ttt

uuu

uuu

uu

uu

u

u

u

GARCH(1,1) Model• GARCH(1,1) is a restricted infinite order ARCH

model• yet only needs three parameters to be estimated

– α0 is the constant– α1 is the effect of last period’s error– β1is the effect of last periods variance– α1 + β1 gives the persistence of the volatility:

• α1 + β1 < 1 implies volatility decays• α1 + β1 1 implies very slow decay• α1 + β1 > 1 implies volatility explodes

More about GARCH

• Conditional variance is time-varying and can be modelled by GARCH

• Unconditional variance is constant, and is given by

– This is defined α1+β1 < 1– But not if α1+β1 1, in which case the process

is non-stationary in variance

11

0

1var

tu

Estimation of GARCH Models

• The GARCH-class of models are not like simple linear ones we have encountered until now

• Hence OLS cannot be used– essentially, OLS minimises RSS which only depends

on parameters in the conditional mean equation– we want to optimise parameters in the conditional

variance term so OLS is not useful

• Instead, maximum likelihood techniques are used

Maximum Likelihood

• The parameters of the model are chosen which are most likely to have produced the observed data

• First, specify the likelihood function– an equation that states how likely it is that the

observed data came from the data generating process

• Then search for the maximum of this (very complex) function– local versus global maxima

Extensions

• Asymmetric GARCH– In a basic GARCH model, the conditional

variance is determined by last period’s variance and last period’s error squared

– So a positive error has the same effect on variance as a negative error

– This need not always be a good assumption

Leverage Effects

• Suppose there is a negative shock to the equity return of a company

• This increases the leverage of the firm (equity value down, debt unchanged)

• So the risk of the equity has risen• A positive shock to the equity reduces

leverage and has a negative impact on risk (other things ignored)

• A negative error has a larger effect than a positive error

GJR Model

• Glosten, Jagannathan and Runkle proposed

– Leverage effect would suggest γ > 0– Non-negativity constraint is α0>0, α1>0, β1>0 and

α1+γ>0

otherwise 0

0 if 1 211

12

12

112

1102

tt

ttttt

uI

Iuu

News Impact Curves

• NICs plot this impact of a shock (“news”) on conditional variance

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Value of Lagged Shock

Val

ue

of

Co

nd

itio

nal

Var

ian

ce

GARCH

GJR

Extensions

• GARCH-in-mean– Finance suggests that expected returns

depend on expected risk– Today’s returns should depend on today’s

(sometimes yesterday’s) conditional standard deviation (or sometimes variance)

211

2110

2

1

ttt

ttt

u

ur

GARCH-in-Mean

• An increase in risk, given by the conditional standard deviation leads to a rise in the mean return

• The value of δ gives the increase in returns needed to compensate for a give increase in risk

• So is a measure of risk aversion

Extensions

• Multivariate GARCH– Univariate GARCH models capture the

evolution of conditional variances– Multivariate GARCH models also capture

movements in conditional covariances– These look quite complicated and use a lot of

matrix algebra– But are really quite simple (honest)

Multivariate GARCH

• VECH model, 2 asset case– we here model the conditional variance-

covariance matrix

– 21 parameters to estimate

11233122321113121332232

21313112

11223122221112121232222

21212122

11213122121111121132212

21111111

tttttttt

tttttttt

tttttttt

hbhbhbuuauauach

hbhbhbuuauauach

hbhbhbuuauauach

Multivariate GARCH

• Diagonal VECH model

– Restricted version of VECH model– only 9 parameters to estimate– and works pretty well

112212111012

12222

121022

11122

111011

tttt

ttt

ttt

huuh

huh

huh

Application

• Bollerslev, Engleand Wooldridge (1988)• Multivariate diagonal VECH GARCH-in-

mean model– US T-bills (asset 1)– US T-bonds (asset 2)– US equities (asset 3)– 1959Q1-1984Q2

Application

133

123

113

122

112

111

213

1312

1311

212

1211

211

33

23

13

22

12

11

3

2

1

3

2

1

1

3

2

1

469.0

348.0

362.0

441.0

598.0

466.0

078.0

165.0

197.0

188.0

233.0

445.0

08.2

14.5

02.0

3.13

18.0

01.0

5.0

1.3

3.4

07.0

t

t

t

t

t

t

t

tt

tt

t

tt

t

t

t

t

t

t

t

t

t

t

jt

jt

jt

jjt

t

t

t

h

h

h

h

h

h

h

h

h

h

h

h

h

h

h

w

r

r

r

Interpretation

– Coefficient of risk aversion was 0.5, in line with theory– Persistence of shocks to conditional variance high for T-

bills (0.445+0.466) but low for bonds (0.188+0.441) and stocks (0.078+0.469)

– But stock variances not well captured (no element statistically significant)

– unconditional covariance between bills and bonds positive(h12). Negative between bills and stocks (h13) and bonds and stocks (h23)

• since lagged conditional covariances negative and larger than error cross-products

Practical Uses

• Time-varying optimal hedge ratio Ht

• Conditional CAPM betas

tF

tStH

,

,

2,

,,

tm

timti

VEC Models

The Chavas Holt Methodology (1990)

Hansen’s Test of SPA (2001)

The MV GARCH Model

Sources of Data

Limitations of the Study