Analysis of Oil Seeds & Grain
Price Volatility in India:
A VEC-MVGARCH Approach
A Research Proposal by
Dr Alok Pandey, Ph.D.
Associate Professor (Finance)
IMT Ghaziabad
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.
Date: 2004-2007 (Feb)
06-02-2007
14-07-2006
22-04-2005
09-10-2004
30-08-2004
01-07-2004
25-06-2004
11-05-2004
03-06-2004
11-05-2004
16-03-2004
03-05-2004
06-04-2004
13-03-2004
03-04-2004
11-03-2004
01-03-2004
Spot Prices
Spot Price Volatility (Wheat)
Spot Prices Wheat
1200
1000
800
600
Series1
400
200
0
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.
Overview of Edible Oil Economy
• 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
(Quantity in Million Tonnes)
Crop
2-Jan
3-Feb
4-Mar
5-Apr
05-06 (F)
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
25.3
22.1
23.5
Major Oilseeds
Groundnut
15.1 *
Others
Cottonseed
5.1
4.5
5.5
6.6
8.5
Copra
0.9
0.7
0.7
0.7
0.6
26.7
20.3
31.5
29.4
32.6
Grand Total
* Reduced due to Drought.
Overview of Edible Oil Economy
• 80 per cent of India's domestic oil output
comes from the primary source that is nine
cultivated oilseeds and two major oilbearing materials (Cottonseed and Copra).
The secondary source comprises of
solvent extracted oils, Rice bran oil, oils
from minor and tree-borne oilseeds etc.
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
7
10.1
13.4
4.3
5.9
8.3
39.40%
38.10%
39.50%
Domestic supply of edible oils (Mln. tonnes)
Total edible oil imports - (Mln. tonnes)
Imports as share of demand
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.
Date: 2004-2007 (Feb)
06-02-2007
14-07-2006
22-04-2005
09-10-2004
30-08-2004
01-07-2004
25-06-2004
11-05-2004
03-06-2004
11-05-2004
16-03-2004
03-05-2004
06-04-2004
13-03-2004
03-04-2004
11-03-2004
01-03-2004
Spot Prices
Spot Price Volatility (Wheat)
Spot Prices Wheat
1200
1000
800
600
Series1
400
200
0
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
•
1.
2.
3.
The research methodology broadly is based on
following three steps:
Modeling the Mean and Volatility of Indian oilseeds
and wheat grain prices using ARCH, GARCH and
ARIMA models.
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).
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 sn 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)
m
1
s n2 
( un  i  u ) 2

m  1 i 1
1 m
u   un  i
m i 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
1 m 2
s  i 1 un i
m
2
n
Weighting Scheme
Instead of assigning equal weights to the
observations we can set
s  i 1  i u
m
2
n
where
m

i 1
i
1
2
n i
ARCH(m) Model
In an ARCH(m) model we also assign
some weight to the long-run variance rate,
VL:
s  VL  i 1  i u n2i
m
2
n
where
m
   i  1
i 1
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
s  s
2
n
2
n 1
 (1  )u
2
n 1
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
s  VL  u
2
n
2
n 1
 bs
Since weights must sum to 1
    b 1
2
n 1
GARCH (1,1) continued
Setting w  V the GARCH (1,1) model is
s  w  u
2
n
2
n 1
and
w
VL 
1   b
 bs
2
n 1
Example
• Suppose
s  0.000002  013
. u
2
n
2
n 1
 0.86s
2
n 1
• The long-run variance rate is 0.0002 so
that the long-run volatility per day is 1.4%
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
0.000002  013
.  0.0001  086
.  0.000256  0.00023336
The new volatility is 1.53% per day
GARCH (p,q)
p
s  w   i u
2
n
i 1
q
2
n i
  b js
j 1
2
n j
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
p(1  p)
9
• We maximize this to obtain a maximum
likelihood estimate. Result: p=0.1
Example 2
Estimate the variance of observations from a
normal distribution with mean zero
 1
  ui2 

exp 
Maximize :  
i 1  2v
 2v 
m
Taking logarithms this is equivalent to maximizing :
m

ui2 

 ln( v)  
v
i 1 
1 m 2
v   ui
Result :
m i 1
Application to GARCH
We choose parameters that maximize
m

i 1
 ui2
1
exp  
2vi
 2vi
or

ui2 

 ln( vi )  
vi 
i 1 
m



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 ui2/si2
Correlations and Covariances
Define xi=(Xi-Xi-1)/Xi-1 and yi=(Yi-Yi-1)/Yi-1
Also
sx,n: daily vol of X calculated on day n-1
sy,n: daily vol of Y calculated on day n-1
covn: covariance calculated on day n-1
The correlation is covn/(su,n sv,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, W, is
internally consistent if the positive semidefinite condition
w Ww  0
T
for all vectors w
Example
The variance covariance matrix
 1

 0

 0.9
0
1
0.9
0.9

0.9

1
is not internally consistent
Modelling Volatility
• Take a structural model
y t    bxt  u t
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.
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
s t2   0  1u t21
• This is Engle’s ARCH(1) model
AutoRegressive Conditional
Heteroscedasticity (ARCH)
• Easily generalisable to an ARCH(q) form
s t2   0   1u t21   2 u t2 2  ...   q u t2 q
• 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
Generalised ARCH (GARCH)
• Allow conditional variance to also depend on its
own lagged value:
2
st
2
  0  1ut 1
2
 b1s t 1
• This is a GARCH(1,1) model
• A GARCH(p,q) model follows:
s t2   0   1u t21  ...   q u t2 q  b 1s t21  ...  b p s t2 p
GARCH(1,1) Model
s t2   0  1ut21  b1s t21
s t21   0  1ut2 2  b1s t2 2
s t2 2   0  1ut23  b1s t23
s t2   0  1ut21  b1  0  1ut2 2  b1s t2 2 
  0  b1 0  1ut21  b11ut2 2  b12s t2 2
 constants  1ut21  b11ut2 2  b121ut23  ...
  0   1ut21   2ut2 2   3ut23  ...
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
0
var ut  
1  1  b1 
– This is defined α1+β1 < 1
– But not if α1+β1  1, in which case the process
is non-stationary in variance
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
s   0   u  b1s
2
t
2
1 t 1
I t 1  1 if u
2
t 1
2
t 1
 u I
2
t 1 t 1
0
 0 otherwise
– Leverage effect would suggest γ > 0
– Non-negativity constraint is α0>0, α1>0, β1>0
and α1+γ>0
News Impact Curves
• NICs plot this impact of a shock (“news”)
on conditional variance
0.14
GARCH
GJR
Value of Conditional Variance
0.12
0.1
0.08
0.06
0.04
0.02
0
-1
-0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1
0
0.1
0.2
Value of Lagged Shock
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
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)
rt    st 1  ut
s   0   u  b1s
2
t
2
1 t 1
2
t 1
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 variancecovariance matrix
h11t  c11  a11u12t  a12 u 22t  a13 u1t u 2 t  b11 h11t 1  b12 h22 t 1  b13 h12 t 1
h22 t  c21  a 21u12t  a 22 u 22t  a 23 u1t u 2 t  b21 h11t 1  b22 h22 t 1  b23 h12 t 1
h12 t  c31  a 31u12t  a 32 u 22t  a 33 u1t u 2 t  b31 h11t 1  b32 h22 t 1  b33 h12 t 1
– 21 parameters to estimate
Multivariate GARCH
• Diagonal VECH model
h11t   0   1u12t 1   2 h11t 1
h22t  b 0  b 1u 22t 1  b 2 h22t 1
h12t   0   1u1t 1u 2t 1   2 h12t 1
– Restricted version of VECH model
– only 9 parameters to estimate
– and works pretty well
Application
• Bollerslev, Engleand Wooldridge (1988)
• Multivariate diagonal VECH GARCH-inmean model
– US T-bills (asset 1)
– US T-bonds (asset 2)
– US equities (asset 3)
– 1959Q1-1984Q2
Application
 h1 jt    1t 
 r1t   0.07 
r    4.3  0.5 w h    
j jt1  2 jt   2t 
 2t  

 h3 jt   3t 
 r3t    3.1
 
 h11t   0.01  0.445 12t 1   0.466h11t 1 
 
 h  0.18 

0
.
598
h
12t 1 
 12t  
  0.233 1t 1 2t 1  
h22t  13.3   0.188 22t 1   0.441h22t 1 

 


h

0
.
362
h
0
.
02
13t 1 
 13t  
  0.197 1t 1 3t 1  
 h23t  5.14 0.165 2t 1 3t 1   0.348h23t 1 
 
  

 
2
 h33t  2.08  0.078 3t 1   0.469h33t 1 
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
s S ,t
Ht  
s F ,t
• Conditional CAPM betas
s im,t
b i ,t  2
s m ,t
VEC Models
The Chavas Holt Methodology
(1990)
Hansen’s Test of SPA (2001)
The MV GARCH Model
Sources of Data
Limitations of the Study