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Hedging With Futures Contract: Estimation and Performance Evaluation of
Optimal Hedge Ratios in the European Union Emissions Trading Scheme
John Hua Fan, Eduardo Roca and Alexandr Akimov
No. 2010-09
Series Editor: Dr. Alexandr Akimov
Copyright © 2010 by author(s). No part of this paper may be reproduced in any form, or stored in a retrieval system,
without prior permission of the author(s).
Hedging With Futures Contract: Estimation and Performance
Evaluation of Optimal Hedge Ratios in the European Union
Emissions Trading Scheme
John Hua Fan, Eduardo Roca and Alexandr Akimov
Department of Accounting, Finance and Economics, Griffith University,
Queensland, Australia 4111
Abstract
Following the introduction of the European Union Emissions Trading Scheme, CO2 emissions
have become a tradable commodity. As a regulated party, emitters are forced to take into
account the additional carbon emissions costs in their production costs structure. Given the
high volatility of carbon price, the importance of price risk management becomes
unquestioned. This study is the first attempt to calculate hedge ratios and to investigate their
hedging effectiveness in the EU-ETS carbon market by applying conventional and recently
developed models of estimation. These hedge ratios are then compared with those derived for
other markets.
In spite of the uniqueness and novelty of the carbon market, the results of the
study are consistent with those found in other markets – that the hedge ratio is in the range of
0.5 to 1.0 and still best estimated by simple regression models.
Key words: hedging, conditional hedge ratio; carbon market; CO2; emissions trading; risk
management
JEL classification: G32, G19, Q54, C32
1
1. Introduction
Following the introduction of the European Union Emissions Trading Scheme
(EU-ETS) in early 2005, emissions trading has officially become a reality. One
of the major objectives of the scheme is to reduce CO2 levels by tightening
the allowance cap over time, which makes CO2 scarcer, therefore more
expensive. Thus, eventually emitters will be forced to switch to alternative or
“cleaner” energy that will produce less or zero carbon dioxide emissions.
There are several market participants in the carbon market, the major ones
being emitters, financial institutions, investors, clearing houses and the EU
commission. Each participant plays a different role, where the EU
commission is the regulator/policy maker and emitters are the regulated
parties. Trading is not limited to the emitters; investors (usually large
corporate or financial institutions) are also permitted to take part. The clearing
houses and financial institutions are there to facilitate the operation of the
market. Accordingly, the impact on the introduction of emissions trading is
expected to vary among these parties. The short and long term uncertainty for
each party arising from ETS also differs.
From the policy markers’ perspective, the risk they need to manage is to
ensure compliance of the proposed trading scheme with the target set in the
Kyoto Protocol. This can be done by clear planning and monitoring,
continuous review and other rigorous controls. From an investor’s point of
view, the uncertainty will be their portfolio risk and return after incorporating
the carbon allowances.
Undoubtedly, the emitters, as the regulated, are more affected than other
market participants. Therefore, carbon market related risks should be
appropriately assessed and managed. There is short and long run emphasis
on risk management. In the short run, wise decisions towards risk
management seem to be based on hedging because no substitutes are
available. Over the long run, the significance of hedging remains in order to
2
provide more certainty to alternative energy investing. Besides, the transition
from conventional means of power generation to any future substitutions are
not expected to be immediate and in fact will take considerably longer to
achieve. Of course the speed of transition may accelerate if more inputs and
resources are devoted to it; however current practice or focus is on the
hedging of the price risk of carbon credits (referred to as EUA, European
Union Allowance).
This paper aims to calculate the optimal hedge ratio in the EU-ETS carbon
market using conventional and recently developed models of estimation.
Based on variance reduction and utility improvement capabilities, the
effectiveness of each estimated hedge ratio is going to be evaluated. The
novelty of the paper rests in two areas: firstly, this is an original estimation of
minimum variance hedge ratio as applied in the EU-ETS carbon market;
secondly, this is the first study to compare carbon market hedge ratios with
other markets. As discussed in the literature review section of this paper, the
hedge ratio has already been estimated using a variety of models in different
markets – financial as well as agricultural markets; however, it has not been
estimated yet in relation to carbon markets. Given the novelty, uniqueness
and distinctiveness of the carbon market from other markets, there is a need
for a separate estimation of the hedge ratio for this market. The estimated
hedge ratio for the carbon market can then compared with those obtained for
other markets. This will offer further insights into the distinctiveness of the
carbon market and the applicability of certain finance concepts, such as the
hedge ratio, into such a new market as the carbon market.
The main
motivation of this paper is therefore to estimate hedge ratio in the carbon
market given that it has not been done yet in this important market rather than
to prove which model works best in estimating the hedge ratio.
This paper consists of six main sections. Section 2 provides an institutional
setting for the EU-ETS carbon market. In Section 3 we review existing
literature on hedge ratios and methods of their estimation while in Section 4,
we introduce our methodology of the estimation of hedge ratios in the carbon
3
market. Section 5 provides estimation results accompanied by extensive
discussion. This is followed by a comparison of estimated hedge ratios in the
carbon market to other markets. The paper is concluded in Section 6.
2. Institutional Setting
The European Union Emissions Trading Scheme is the world’s largest
multi-country, multi-sector mandatory greenhouse gas emissions trading
regime. There are 27 member states currently under the scheme. It covers
CO2 emissions from electricity generation and the main energy-intensive
industries including power stations, refineries and offshore oil and gas
production, iron and steel, cement and lime, paper, food and drink, glass,
ceramics, engineering and the manufacture of vehicles (Directive 2003/87/EC,
2003). Fundamentally, as a cap-and-trade program, EU-ETS operates by
placing a cap or limit on the amount of CO2 companies can emit every year.
Each company is awarded an annual quota of carbon dioxide emission units
where 1 unit of allowance = 1 tonne of CO2 (officially as European Union
Allowances). Firms that emit more than their allocated allowance can choose
to pay the non-compliance penalty or purchase surplus allowance from
companies that manage to stay below their limit. The system is designed to
cut CO2 emissions in the most cost effective way. In addition, over time, the
total number of quotas/allowances is to be reduced, which will lead to an
increase in the price of carbon emissions allowances due to the scarcity of
supply.
One unit of CO2 allowance is officially referred to as one European Union
Allowance (EUA). The allocation of EUA is determined by each individual
country’s Nation Allocation Plan (NAP). Each country designs its own NAP
according to its emissions produced from different sectors and other relevant
characteristics.
Before
distributing
these
allowances
to
firms
and
organizations, the NAP has to be reported to the EU Commission for
approval.
Commencing operation in January 2005, there are three phases set out in
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EU-ETS, Phase I (2005-2007), Phase II (2008 – 2012) and Phase III
(2013-2020). Phase I is an experimental scheme; it started with six key
industrial sectors, namely energy activities production and processing of
ferrous metals, mineral industry and pulp, paper and board activities. In
Phase II, coverage is broadened, so that in addition to Phase I, CO2
emissions from glass, mineral, wool, gypsum, flaring from offshore oil and gas
production, petrochemicals, carbon black and integrated steel works are
included. In Phase III, an EU-wide cap is proposed to replace the current
system of NAPs set by each member state, and the overall cap will be further
tightened on an annual basis.
In phase II of the EU-ETS, trading in so called certified emission reduction
(CER) credit contracts was launched. CER credits are issued to countries that
undertake emission-reduction or emission-limitation projects in developing
countries under the Clean Development Mechanism of Kyoto Protocol (Annex
B Party).
Banking of allowances means the carrying forward of the unused emission
allowances from the current year for use in the following year. The banking of
allowances is permitted within Phases (except for France and Poland),
however it was prohibited from 2007 to 2008 (inter-phase). This had
significant implications for the pricing of emission allowance and its
underlying derivatives. Nevertheless, industries are allowed to bank the
unused permit from Phase II to Phase III. Financial penalties apply when
emitters do not meet their compliance requirements. In Phase I 2005-2007,
the penalty was 40 Euro/t CO2, from 2008 it has been increased to 100 Euro/t
CO2 which provides more incentives for carbon trading. Meanwhile, all credit
deficiencies must be purchased in addition to fines paid. All the reported
emissions must be audited by an independent third party.
3. Literature Review
Hedging is an investment made to mitigate the price risk (unfavourable
fluctuation) of the underlying assets at maturity. Fundamentally, it involves
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taking an opposite position to the spot market so that a portfolio consisting of
both spot and futures contracts is formed. It is generally accomplished
through the trading of financial derivatives such as forward contracts, futures
contracts, swaps and options, along with other over-the-counter instruments
and derivatives. A futures contract is a dominant instrument in reality, mainly
because of its transparency and liquidity advantages over the others. The
hedging is primarily implemented by using a hedge ratio, which determines
the portions of the spot that need to be hedged in order to achieve a minimum
level of unfavourable price fluctuation (Ederington, 1979, Johnson, 1960;
Myers and Thompson, 1989).
According to Hatemi-J and Roca (2006), the optimal hedge ratio is defined as
the quantities of the spot instrument and the hedging instrument that ensure
that the total value of the hedged portfolio does not change. It can be formally
expressed in terms of the following:
Vh = Qs S − Q f F
∆Vh = Qs ∆S − Q f ∆F
Where Vh is the value of the hedged portfolio, Qs and Q f are the quantity
of spot and futures instrument respectively, S and F are the price of spot and
futures instrument respectively,
If ∆Vh = 0 , then
Let h =
Qf
Qs
Qf
Qs
⇒h=
=
∆S
∆F
∆S
∆F
where h gives the hedge ratio.
Therefore, the hedge ratio can be demonstrated as the slope coefficient in a
regression of the price of the spot instrument on the price of the future
(hedging) instrument.
However, this also depends on the objective function of the hedger. Minimum
variance is the most popular and widely used approach, although this has
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been criticized for not taking into account the expected return which is
inconsistent with the mean-variance framework. Since the selection of a
hedge ratio is dependent on the hedgers’ objective in the hedging position,
this will be different for various participants in the carbon market. For example,
investors not only desire to protect the investment portfolio from carbon price
risk but also need to ensure their returns at the same time. Therefore, the
objective function of hedging under such circumstances should not be solely
based on minimum variance. However, the objective of risk management for
emitters in the market does not necessarily have to be the same as investors’
objectives. Because of its compulsory participation, the priority of risk
management should be given to hedging of the carbon price risk. Accordingly,
the objective function for them can be (but not limited to) the achievement of a
minimum variance of the hedged portfolio.
Optimal hedge ratio estimations have been conducted extensively since the
introduction of futures contracts. There are various techniques suggested by
many researchers and studies in a majority of markets not limited to
traditional financial markets. For example the more recent ones are those of
Ghosh & Clayton (1996) and Kenourgios, Samitas & Drosos (2008) for the
stock index, Copeland & Zhu (2006) for the foreign exchange rate, Yang &
Awokuse (2003) for agricultural and livestock and Cecchetti et al. (1988) for
fixed-income securities. Moreover, there are a large number of studies in this
area which consider the hedge ratio across financial, agricultural, livestock,
interest rates, foreign exchange, metal and energy markets, etc. By contrast,
research on hedging in the carbon market is very limited. This could be
explained by the immaturity of the market since it started trading only in early
2005. Given the young age of the market, arguments of market efficiency,
liquidity and data availability are commonly cited barriers (Daskalakis and
Markellos 2008, Daskalakis, Psychoyios and Markellos 2009, Paolella and
Taschini 2008, and Uhrig-Homburg 2008). Chevallier’s PhD thesis (2008)
researched Phase I of the EU-ETS extensively with the emphasis on banking,
pricing and risk hedging strategies. However, under the section relating to risk
7
hedging, the possible use of the optimal hedge ratio has not been discussed.
This paper sets out to fill the gap in the existing literature.
The methodology applied to hedge ratio estimations can be generally
classified into three categories, the Ordinary Least Squares (OLS), the error
correction mechanism (ECM) and GARCH (Generalised Autoregressive
Conditional Heteroscedasticity). Witt, Schroeder, Hayenga (1987) applied
OLS methodology to estimate optimal hedge ratios in sorghum and barley
spot markets cross hedged with corn futures. The shortcomings of the OLS
method is that it does not take into consideration time varying distributions,
serial correlation, heteroscedasticity and cointegration (Poterba and
Summers, 1986; Bollerslev, 1986; Baillie and De Gennaro, 1990).
To overcome the problems encountered by the Ordinary Least Squares
model of OHR estimation, Ghosh (1993), Chou, Fan and Lee (1996), Ghosh
and Clayton (1996), Lien (1996), Sim and Zurbruegg, (2001) among many
other researchers, adopted the Error Correction Model (ECM). Ghosh (1993)
adopted the ECM to calculate OHR on S&P futures, S&P index, Dow Jones
industry average and the NYSE composite index. Later Ghosh & Clayton
(1996) expanded the previous study to an international context which
includes CAC 40 (France), FTSE 100 (UK), DAX (Germany) and the Nikkei
(Japan) index. In both of the studies, they found improved performance
compared to the traditional OLS model. Kenourgios, Samitas and Drosos
(2008) confirmed the conclusion made by previous studies about the
superiority of ECM. They investigated the hedging effectiveness of the S&P
500 futures contract for the period July 1992 - June 2002 and concluded that
ECM was still proven to be the best model and better at forecasting. The
problem with ECM is that the heteroskedasticity problem remains. Moreover,
it cannot be used for a stationary time series despite the ability to capture
both long and short-term dynamics in a single statistical model (Keele and De
Boef, 2004).
Furthermore, as can be seen from markets throughout the world, financial
8
time series exhibit conditional volatility. In other words, over time, these series
do not fluctuate constantly at an unchanged rate; instead they vary over
diverse time periods. To reflect the problem of heteroskedasticity, Kroner and
Sultan (1993) combined the Bivariate VECM with a GARCH error structure.
Baillie & Myers (1991) employed the Bivariate GARCH model for hedging six
different commodities, namely beef, coffee, corn, cotton, gold and soybean.
Park and Switzer (1995) tested the S&P 500 and Toronto 35 index futures.
They both found that the performance is far superior to a constant hedge ratio.
More recently, Yang and Awokuse (2003) examined corn, soybean, wheat,
cotton and sugar (as storable commodities) and lean hogs, live cattle and
feeder cattle (as non storable commodities), and found that BGARCH is
strong for all storable commodities but weak for non storable commodities.
Kroner and Sultan (1993) implemented the combined methodology on
currency risk hedging of the British pound (BP), the Canadian dollar (CD), the
German mark (DM), the Japanese yen (JY), and the Swiss franc (SF) using
International Monetary Market (IMM) futures contracts. They concluded that
both within-sample and out-of-sample tests demonstrated that the proposed
methodology was superior compared to the conventional methods in currency
hedging. Yang and Allen (2004) and Kenourgios, Samitas and Drosos (2008)
adopt
the
VECM-GARCH
model
with
BEKK
(positive
definite)
parameterization. The all ordinary stock index in Australia and the S&P 500
stock index in the U.S. are hedged using respective futures contracts.
Findings in these studies are in line with Kroner and Sultan (1993).
Nevertheless, like every other model in the world, the GARCH model is
criticized by researchers like Myers (1991), Lien and Luo (1994), Fackler and
McNew (1994). The main arguments are that the GARCH model in reality
only performs slightly better than the constant hedge ratio, despite its
complex theoretical superiority. However the GARCH model may have taken
into account the price behaviour of the hedging instrument, cointegration,
while the most import element should be the error correction term. Also,
GARCH is criticized because of the inequality restrictions on model
9
parameters and the use of nonlinear optimization algorithms.
As mentioned earlier, the EU ETS market is relatively young and new
compared to other ordinary financial markets such as the stock market and
commodities market which have existed before the introduction of the carbon
market. Accordingly, the number of research in this particular area may not be
as rich as it would be in other markets. The EU ETS market has generated a
brand new research area that differs from other pre-existing areas. As pointed
out in Convery (2009, p123), the current literature may be classified into a
number of sub issues.
Context and history, emissions reduction and
allocation, competitiveness, distributional issues, new entrants, markets,
finance and trading have been the topics of focus
Unfortunately, in spite of
its importance in hedging of price risk in this market, the optimal hedge ratio,
has not been investigated yet. The PhD thesis by Chevallier (2008) studied
the Phase I of EU ETS extensively with the emphasis of banking, pricing and
risk hedging strategies. However, under the risk hedging section, the possible
use of the optimal hedge ratio is yet to be discussed. Cetin and Verschuere
(2009) propose hedging formulas using a local risk minimisation approach,
but again, hedging with carbon futures contracts or other derivatives are not
considered. Thus, given the importance of the issue, this paper investigates
the estimation of optimal hedge ratio and evaluates the hedging effectiveness
on those estimated hedge ratios in the EU-ETS market. This is then
compared to hedge rations obtained for other markets, particularly financial
markets.
4. Methodology
4.1 Hedge Ratio Estimation
This paper applies hedge ratio estimation models which have been widely
used in calculating hedge ratios in other markets. These are the naive
approach, the ordinary least squares, the error correction, and the
generalised autoregressive conditional heteroscedasticity models. Each of
these is discussed below.
10
Naïve approach
The most naïve approach to futures hedging is a one-to-one hedge ratio. In
this approach for any given spot position, an equal amount of futures
positions are undertaken. Therefore, the hedge ratio will always be 1 where
each spot is offset by exactly one futures contract. In other words, there is no
basis, because the spot and futures prices do not change or move by an
exact amount. Despite perceived low value of the naive model in practice, the
naive model is included in this paper for later comparisons.
Ordinary Least Squares (OLS)
We estimate the hedge ratio using the OLS method based on the following
equation:
∆St = α + β∆Ft + ε t
(1)
where ε t is the error term from OLS estimation, and ∆S t and ∆Ft represent
changes in the spot and futures prices; β gives the minimum variance hedge
ratio
Two-step Error Correction Model
We also estimate the hedge ratio using the two-step error correction model a
shown below:
m
n
i =1
j =1
∆S t = αµ t −1 + β∆Ft + ∑ δ i ∆Ft −i + ∑θ i ∆S t − j + ε t
(2)
where µ t −1 = S t −1 − [α + bFt −1 ] and β is the optimal hedge ratio.
This is based on the cointegration equation: S t = a + bF t + ε t . To ensure ε t is
a white noise, enough lags will need to be introduced into the equation. In this
model, changes in spot price are no longer only explained by changes in
futures but also by past changes in futures and past of itself as well as the
11
long-run cointegrating relationship between price level of spot and futures
also affects the changes in spot price.
Vector Error Correction Model
We further provide an estimate of the hedge ratio based on the vector error
correction model as expressed below:
n
m
j =1
i =1
∆S t = α s + α11εˆt −1 + ∑ ϕ s1i ∆S t − j + ∑ ϕ s 2i ∆Ft −i + vts
n
(3)
m
∆Ft = α f + α 21εˆt −1 + ∑ ϕ f 1i ∆S t − j + ∑ ϕ f 2i ∆Ft −i + vt
j =1
where α 10 α 20
f
i =1
are intercept, and ϕ , α 11 α 21 and are parameters, vts vtf are
white-noise disturbance terms. εˆ t −1 is the error correction term which
measures how the dependent variable (in the vector) adjusts to previous
long-term disequilibrium.
The coefficient α11 α 21 is the speed of adjustment parameters; the greater the
α11 or α 21 , the greater the response of spot to εˆ t −1 , the previous periods
disequilibrium. If Var(vts ) = σ ss , Var (vt f ) = σ ff
and Cov(vts , vtf ) = σ sf , the
minimum variance hedge ratio is calculated as:
h* =
σ sf
σ ff
Vector Error Correction Model (VECM) with GARCH Error Structure
We allow for GARCH effects in the estimation of the hedge ratio through the
sue of the VECM with GARCH error structure, as specified below:
n
m
j =1
i =1
∆S t = α 10 + α 11 Z t −1 + ∑ ϕ s1i ∆S t − j + ∑ ϕ s 2i ∆Ft −i + ε ts
n
m
j =1
i =1
∆Ft = α 20 + α 21 Z t −1 + ∑ ϕ f 1i ∆S t − j + ∑ ϕ f 2i ∆Ft −i + ε t f
(4)
12
ε 
ε t =  t  | Ω t −1 ~ D (0, H t )
ε t 
H t = C ' C + A ' ε t −1ε 't −1 A + B ' H t −1 B , which is expanded to the following:
 h s,t 
 C ss ,t   a 11 a12 a13   ε 2s,t -1   b11 b12 b13   h ss,t -1
 
 

 



H t =  h sf,t  = C sf ,t  +  a 21 a 22 a 23  ε s,t -1 ε f,t -1 + b 21 b 22 b 23   h sf,t -1 
 b31 b32 b33   h 
 h f,t 
C ff ,t   a 31 a 32 a 33   ε 2
  ff,t -1 
f,t -1
 



 
or written in equations as:
hss ,t = c ss + α ss ε s2,t −1 + β ss hss ,t −1
hsf ,t = c sf + α sf ε st −1ε ft −1 + β sf hsf ,t −1
h ff ,t = c ff + α ff ε 2f ,t −1 + β ff h ff ,t −1
where the mean equation is drawn from equation 1 with a couple of
modifications in parameter representations. The error correction term is
amended to Z, and the error term of the VAR is now ε t . This is for the
purpose of comparability with the existing hedge ratio studies. In addition, the
error term is now conditionally normally distributed with a mean of 0, and a
covariance matrix is time-varying. The h* optimal hedge ratio is computed as:
h* =
hsf
h ff
Conditional covariance between spot return and futures is divided by the
conditional variance of futures return. Thus the minimum variance hedge ratio
has now become time-varying; it varies with the changes in conditional
covariance matrices.
4.2 Evaluation of Hedging Effectiveness
The effectiveness of each estimated hedge ratio is assessed based on two
criteria: (a) variance reduction, and (b) utility maximization.
Variance Reduction
To calculate the percentage variance reduction, the difference in variance of
the unhedged portfolio and each hedged portfolio (constructed using different
hedge ratios resulted from diverse models) is divided by the variance of the
13
unhedged portfolio, as follows:
VR =
VAR (∆S t ) − VAR (∆S t − h * ∆Ft )
VAR (∆S t − h * ∆Ft )
= 1−
VAR (∆S t )
VAR (∆S t )
(5)
VAR ( ∆S t − h * ∆F ) = σ s2 + h *2 σ 2f − 2h * σ sf
where h * is the computed hedge ratios derived from different hedge ratio
estimation models discussed in section 4.
∆ S t = S t − S t −1 is the return of the unhedged portfolio, ∆ Ft = Ft − Ft −1 , is the
return on futures, σ s is the standard deviation of spot price, σ f is the standard
deviation of the futures price, σsf is the covariance of spot and futures price,
VAR ( ∆ S t − h * ∆ Ft ) is the variance of the hedged portfolio, VAR ( ∆ S t ) is the
variance of the unhedged portfolio.
This above equation provides the variance reduction in percentage from
hedging and
VAR ( ∆ S t ) − VAR ( ∆ S t − h * ∆ Ft ) gives the variance reduction in a natural number.
Utility Maximization
The utility maximization method incorporates the risk aversion of investors.
Using this method, the level of investors’ utility that computed differently from
the hedged portfolio is compared and ranked by the degree of utility
improvement from the unhedged portfolio. This method now satisfies the
mean-variance framework because it does not assess the minimum variance
but also takes into consideration the return of the hedged portfolio. The
objective function that maximises the utility is given as:
1
MAX[ E ( Rh | Ωt −1 ) − φVar( Rh | Ωt −1 )]
2
(6)
where R h is the hedged portfolio ( ∆ S t − h * ∆ F ), E ( R h ) is the return of the
hedged portfolio, Var ( R h ) is the variance of the hedged portfolio, φ is the
14
investors’ level of risk aversion, Ω t −1 is the information set at time t-1.
The utility level for the hedged and unhedged portfolio is computed from the
portfolio’s mean and variance of return.
4.3 Data and Diagnostic Tests
The data used in this study consists of spot (cash) and futures contracts of
the respective carbon trading instruments. One tonne of carbon dioxide
permit equals one unit of EUA - the spot EUA data is drawn from BlueNext
exchange. In line with Phases set by policy makers, our data is divided into
two periods which are referred to as BNS EUA 05-07 (Phase I BlueNext Spot
EUA 05-07) from 24/06/2005 to 25/04/2008 and BNS EUA 08-12 (Phase II
BlueNext Spot EUA 08-12) from 26/02/2008 to 18/12/2009. Another type of
data used in this paper is spot BNS CER (BlueNext Spot CER) contracts. The
time span for CERs is from 12/08/2008 to 18/12/2009, with the same cut-off
point as for BNS EUA. To match the hedging horizon and the maturity of the
futures contract, the spot EUA dataset is subdivided into a number of periods.
Data on the futures contract is drawn from the ECX (European Climate
Exchange), known as the ICE/ECX EUA futures contract and the ICE/ECX
CER futures contract. ECX offers futures contracts on EUA and CER for
different maturities; they are sorted as Dec-05, Dec-06, Dec-07, Dec-08,
Dec-09, etc. To match the spot EUA data, this paper uses the ECX futures
contract up to Dec09 maturity. Note that future contracts on CERs became
available in 2008, thus in this paper, Dec-08 and Dec-09 contracts are used.
All spot and futures data mentioned above are historical daily closing prices.
To distinguish contracts between EUA and CER, this paper uses EUA Dec-xx
for EUA futures contract and CER Dec-xx for CER futures contract.
Various diagnostic tests are carried out before modelling. This paper uses
Augmented Dickey Fuller (ADF) and Phillips & Perron test for stationarity.
Subsequently, if data series are found to have non-stationarity, Engle and
Granger procedure and Johansen’s technique are used to test for possible
15
cointegration between series.
5. Empirical Results and Discussion
In this section, we report findings of our empirical analysis. Firstly, descriptive
statistics are provided followed by the application of diagnostic tests.
Secondly, estimations of optimal hedge ratios are conducted. Thirdly, we
present the effectiveness of the application of hedging ratios. Lastly, we
undertake the comparative analysis of hedging ratios in various markets.
5.1 Descriptive statistics and diagnostic tests
Table 1 provides the descriptive statistics for spot and futures of both EUA
and CER. There are two panels in the table, panel A reports the results on the
original price level and panel B reports the returns level. To test for stationarity,
Augmented Dickey-Fuller (ADF) and Philips-Perron (PP) stationarity tests
were applied. The test results revealed that the data series are non-stationary.
Then, the two-step Engle and Granger method was used to test for
cointegration of spot/futures price combinations. All combinations show
cointegration.
16
Table 1. Descriptive statistics
Obs.
EUA
Dec-05
EUA
Dec-06
EUA
Dec-07
EUA
Dec-08
EUA
Dec-09
CER
Dec-08
CER
Dec-09
EUA
Dec-05
EUA
Dec-06
EUA
Dec-07
EUA
Dec-08
EUA
Dec-09
CER
Dec-08
CER
Dec-09
120
237
246
206
244
89
244
119
236
245
205
243
88
243
Mean
Median
22.619
22.628
17.618
17.960
0.675
0.695
22.671
22.908
13.158
13.365
17.493
17.479
11.919
11.815
22.140
22.200
16.000
16.300
0.120
0.140
23.370
23.610
13.510
13.725
18.800
18.770
12.205
12.120
-0.018
-0.021
-0.064
-0.067
-0.022
-0.023
-0.027
-0.030
-0.001
-0.005
-0.071
-0.073
-0.001
-0.001
0.050
0.050
0.010
0.000
0.000
0.000
0.000
0.010
0.000
-0.020
-0.025
-0.055
0.000
0.000
Max.
Min. Std. Dev. Skewness
Panel A: Price Level
28.930 18.850
2.012
1.490
29.100 19.500
2.060
1.532
29.750 6.400
6.606
0.269
30.450 6.400
6.837
0.273
5.480 0.030
1.096
2.443
5.600 0.010
1.107
2.411
28.730 13.700
3.476
-0.817
29.330 13.720
3.559
-0.824
15.490 7.960
1.599
-1.145
15.870 8.200
1.567
-1.142
20.900 13.180
2.550
-0.322
21.200 12.820
2.681
-0.302
13.900 7.600
1.308
-0.869
13.820 7.390
1.371
-0.974
Panel B: First Difference
2.350 -3.450
0.697
-1.062
2.350 -3.300
0.690
-1.573
3.510 -8.600
0.885
-3.843
5.800 -7.150
0.891
-1.589
0.280 -0.960
0.106
-4.210
0.350 -0.850
0.111
-3.698
1.220 -1.660
0.521
-0.596
1.100 -1.720
0.521
-0.562
0.990 -0.940
0.363
-0.003
1.130 -0.970
0.371
0.095
0.950 -1.470
0.457
-0.552
0.880 -1.460
0.452
-0.658
0.820 -0.910
0.299
-0.214
1.000 -1.000
0.315
-0.150
Kurtosis
J-B
Prob.
5.645
5.697
1.840
1.842
8.435
8.283
2.956
3.018
3.827
4.009
1.506
1.512
3.370
3.515
79.369
83.302
16.150
16.188
547.537
524.459
22.919
23.306
60.254
63.421
9.815
9.571
32.091
41.268
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.007
0.008
0.000
0.000
8.443
10.836
41.273
28.602
32.388
25.129
3.837
3.422
2.931
3.109
3.817
3.662
3.514
3.827
169.275
353.520
14984.830
6544.883
9539.924
5557.353
18.118
12.302
0.049
0.485
6.921
7.950
4.531
7.835
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.002
0.976
0.785
0.031
0.019
0.104
0.020
Following these tests, Johansen’s cointegration procedure was applied to
identify the number of cointegration relationships between spot and future
series. The results are presented in Table 2. The second column of the table
represents the number of cointegration relationships of each hedging
combination. From the third column through to the second last column,
and
λtrace
λmax statistics of each combination are reported respectively, with the
5% critical level attached to the last column. The lag length used for each
combination is also reported in the last row of the table. The lag length is
selected by SIC based on unrestricted VAR with spot and futures being the
endogenous variable and the intercept being the exogenous variable. The
maximum lag length is set to be 10.
17
Table 2. Results of Johansen’s Cointegration Test
2005
2006
2007
2008
2009
2008
2009
No. of
EUA
EUA
EUA
EUA
EUA
CER
CER
Critical
Test
cointegration
vs.
vs.
vs.
vs.
vs.
vs.
vs.
5%
Statistics
Equation
Dec-05
Dec-06
Dec-07
Dec-08
Dec-09
Dec-08
Trace
MaxEigen
Eigenvalue
Dec-09 Statistics
None
84.0411
85.5215
89.9540
26.8420
28.3065
17.0891
24.3685
At most 1
6.3236
1.4710
24.8160
0.0582
2.7429
0.2287
3.4869
3.8415
None
11.1756
84.0506
65.1381
26.7839
25.5636
16.8603
20.8816
14.2646
At most 1
1.7905
1.4710
24.8160
0.0582
2.7429
0.2287
3.4869
3.8415
None
0.4824
0.3028
0.2351
0.1230
0.1006
0.1762
0.0830
At most 1
0.0522
0.0063
0.0971
0.0003
0.0113
0.0026
0.0144
1,1
1,3
1,2
1,1
1,2
1,1
1,2
Lag Length
15.4947
Based on Johansen’s technique, there are two test statistics: the trace and
the maximum eigen. According to the results reported in Table 2, hedging
combinations EUA vs. Dec-05 and EUA vs. Dec-07 exhibit more than one
cointegration equation as the null hypothesis of the “none” and “r”
cointegration equations are both rejected. In this case, there are two
cointegration equations (cointegrated one way or another) because there
cannot be more than two cointegration equations in the two endogenous
variable VAR. There is only one cointegration equation in all other
combinations as null value of no cointegration is rejected while the null of at
most one cointegration is not rejected.
Table 3 below summarizes the results discussed where “Yes” represents
cointegration and “No” represents no cointegration between spot and futures.
The number of cointegration relationships is also attached.
Table 3. Summary of Cointegration Based on Johansen’s technique
2005
EUA
vs.
Dec-05
Yes
2
Max-Eigen Yes
2
Test
Statistics
Trace
2006
2007
2008
2009
2008
2009
EUA
vs.
Dec-06
Yes
1
Yes
1
EUA
vs.
Dec-07
Yes
2
Yes
2
EUA
vs.
Dec-08
Yes
1
Yes
1
EUA
vs.
Dec-09
Yes
1
Yes
1
CER
vs.
Dec-08
Yes
1
Yes
1
CER
vs.
Dec-09
Yes
1
Yes
1
5.2 Hedge Ratios by different models in EU-ETS carbon market
Sorted by models, the following Table 4 contains a summary of hedge ratios
for all hedging combination. Each hedging combination consists of a spot
contract and a futures contract. For all Phase I hedging combinations, the
18
starting point is 24th June, 2005. Therefore, every following combination
comprises the entire horizon of the previous combination. This applies to all
combinations in Phase II as well, except for Phase II EUA hedging
combinations, the starting point is 24th February 2008, and 12th August 2008
for CER combinations. Treating Phase I and II separately for hedge ratio
application implies the exclusion of inter-phase hedging of EUA. In addition,
hedge ratios computed using Naive, OLS, ECM and VECM models are fixed,
in other words time-invariant hedge ratios. All of them remain unchanged
throughout the entire hedging horizons (i.e. Phase I and II). By contrast, since
VECM-GARCH produces conditional hedge ratio, results of VECM-GARCH
reported in Table 4 are the averaged value of the dynamic, time-varying
hedge ratio at each point in time. The purpose of presenting the averaged
dynamic hedge ratio is solely comparative, since it cannot be used in practice.
Table 4. Calculated Hedge Ratios
Phase Hedging
Horizon
I
II
2005
2006
2007
2008
2009
2008
2009
Hedging
Combination
Naive
Simple Two-stage
Apporch
OLS
ECM
One Year Hedging Horizon
EUA vs Dec05 1.0000
0.8556
0.7683
EUA vs Dec06 1.0000
0.8533
0.7016
EUA vs Dec07 1.0000
0.8962
0.9331
EUA vs Dec08 1.0000
0.9557
0.9666
EUA vs Dec09 1.0000
0.8794
0.9444
CER vs Dec08 1.0000
0.9431
0.8928
CER vs Dec09 1.0000
0.8325
0.8679
Vector
ECM
VECM
GARCH*
0.7743
0.6801
0.9099
0.9666
0.9384
0.8929
0.8636
0.7157
0.8740
0.5565
0.9792
0.9379
0.9293
0.8732
* note that hedge ratios listed in table are averaged values
As can be seen from Table 4 hedge ratios (OHR) vary from model to model
and period to period. Firstly, the calculated hedge ratio for two-stage ECM
and VECM are extremely close to each other in most cases. This is not
surprising given that they share the same error correction fundamentals.
However, this minor difference may generate implications for hedge ratio
performance evaluations as OHR is one of the inputs for performance
calculation. Secondly, in Phase II, all OHRs for both EUA and CER decline in
2009, compared to the 2008 hedging horizon. Thirdly, Phase II OHRs are
generally greater than Phase I; this can be explained by the lowered overall
19
variance of futures price changes in Phase II as compared to Phase I.
However, in Phase I of the one year hedging horizon, OHR derived by OLS
and ECMs decreased in 2006 compared to 2005 and increased again in 2007.
Meanwhile, the averaged OHR derived by VECM-GARCH increased in 2006
and decreased again in 2007.
In order to better understand the changes in calculated hedge ratios, recall
the basic formula for hedge ratio estimation,
h=
σ
Cov ( ∆s, ∆f )
=ρ s
Var ( ∆f )
σf
Fundamentally, the minimum variance optimal hedge ratio in this study is
calculated as dividing the covariance between spot and futures returns by the
variance of the futures return. Accordingly, any factors that have an effect on
the changes of covariance and variance become the objects for investigation
towards the changes of hedge ratios. Therefore, the question has essentially
become the behaviour of both spot and futures prices since changes in price
levels contribute to variations in covariance and variances. To demonstrate
the
discussion,
Figure
1
Phase I EU-ETS
Spot EUA
Dec-05
Dec-06
Dec-07
EUR 35.00
Before the Break
After the Break
EUR 30.00
02/2006
to
10/2006
EUR 25.00
10/2006
to
12/2007
EUR 20.00
EUR 15.00
EUA vs Dec-05
EUR 10.00
EUA vs Dec-06
EUR 5.00
EUA vs Dec-07
EUR 0.00
Figure 1revises the historical price of EUA and futures in Phase I, however,
20
this time the full period is divided into three sub-periods1. By doing so, we are
able to identify the different sub period volatility that contributes to the high full
period volatility. It also indicates the hedging horizons of each phase I
hedging combinations in addition to the prices.
Phase I EU-ETS
Spot EUA
Dec-05
Dec-06
Dec-07
EUR 35.00
Before the Break
After the Break
EUR 30.00
02/2006
to
10/2006
EUR 25.00
10/2006
to
12/2007
EUR 20.00
EUR 15.00
EUA vs Dec-05
EUR 10.00
EUA vs Dec-06
EUR 5.00
EUA vs Dec-07
EUR 0.00
Figure 1. Phases I EU ETS and Hedging Combinations (Sub-phases)
The EUA and futures price exhibit massive price changes in Phase I. Starting
from early 2005, EUA and futures price increased to around 30 euro in July
2005, bouncing within 20-25 euro during the following six months, then rose
to 30 euro until the end of April 2006. In the last week of April 2006 EU
officials
disclosed
2005
verified
emissions
data
and
reported
the
over-allocation of free permits. In the following four days, prices went down by
54%, and after about a week, EUA prices slightly recovered and fluctuated
within the range of 15 to 20 euro until October 2006. Approaching the end of
Phase I, since the unused allowances are not allowed to be carried forward,
the Phase II companies tried to sell out all their allowances. From this date,
Phase I prices were declining towards zero and eventually fell to one euro
cent. As can be seen in Figure 1, Phase I EUA futures and spot prices are
strongly correlated, which is what was expected based on the cointegration
1
This study adopts the breaks carried out in Alberola, Chevallier and Che`ze (2008)
21
test results. These events created substantial volatility to the market in Phase
I. The following Table 5 reports the sub-periods variance and standard
deviation of EUA.
Table 5. Phase I EUA Variance and Standard Deviation (Break up)
Before the Break
24/06/200521/04/2006
During the Break
After the break
24/04/200620/06/2006
20/06/2006-28/12/2007
Variance
6.5147
16.5169
10.0839
Standard Deviation
2.5524
4.0641
6.1525
2/05/2006- 20/10/200719/10/2007 28/12/2007
3.0633
37.8538
Variance
Standard Deviation
1.7502
3.1755
Complete Period 24/06/2005-28/12/2007
Variance
104.7334
Standard Deviation
10.2339
in
Demonstrated
Figure
1,
Phase I EU-ETS
Spot EUA
Dec-05
Dec-06
Dec-07
EUR 35.00
Before the Break
After the Break
EUR 30.00
02/2006
to
10/2006
EUR 25.00
10/2006
to
12/2007
EUR 20.00
EUR 15.00
EUA vs Dec-05
EUR 10.00
EUA vs Dec-06
EUR 5.00
EUA vs Dec-07
EUR 0.00
Figure 1 the compliance break happened within EUA vs Dec-06 hedging
horizon, the sudden excessive variance of EUA as seen in Table 5
contributed to the lower optimal hedge ratios calculated by OLS, ECM and
VECM. This also applies to EUA vs Dec-07 hedging combination as futures
contracts over the full period exhibit extremely high variance (104.73) due to
the incorporation of both the compliance break and the price collapse in late
22
Phase I.
In Phase II, despite the impact of the GFC on the market, the overall volatility
has largely decreased. Similarly with Phase I, in Figure 2, Phase II (up to
20/12/09) is subdivided into three sub-phases in relation to Phase II hedging
combinations.
Phase II EU-ETS
Spot EUA
Dec-08
Dec-09
Spot CER
CER Dec-08
CER-Dec-09
EUR 35.00
EUR 30.00
Before the worst period in
GFC
Worst period in
GFC
After the worst period in GFC
EUR 25.00
EUR 20.00
EUR 15.00
EUA vs. Dec09
EUA vs. Dec08
EUR 10.00
CER vs. Dec09
EUR 5.00
CER vs. Dec08
EUR 0.00
Figure 2. Phases II EU ETS (up to 20/12/09) and Hedging Combinations
(Sub-phases)
This was done to accommodate the impact of the global financial crisis on the
EU-ETS market. A contracted production caused by a drop in demand led to
a lower emissions output. Meanwhile, the price of EUA and CER fell
consecutively during the worst period of the GFC. To take into account the
effect of the GFC, there are three sub-periods shown in Figure 2. The worst
period during the GFC was from September 2008 to February 2009, when
global stock markets suffered enormous losses due to uncertainty about bank
solvency, credit availability and damaged investor confidence (particularly in
the U.S.). This period was separated from “before the worst period” and “after
the worst period” in the GFC for analytical purposes. Table 6 provides
statistical evidence on sub period and full period volatility of Phase II EUA
measured by variance and standard deviation.
23
Table 6. Phase II EUA Variance and Standard Deviation (up to 20/12/09)
Before the worst During the worst
time in GFC
time in GFC
26/02/20081/9/200829/08/2008
13/2/2009
After the worst
time in GFC
16/2/200920/12/2009
Variance
4.3876
22.1292
1.9582
Standard Deviation
2.0947
4.7042
1.3994
Whole period 26/02/2008-20/12/2009
Variance
28.7482
Standard Deviation
5.3617
If the results in Table 6 and Table 5 are compared, it can be observed that the
full period variance of Phase II EUA (28.74482) is substantially lower than in
Phase I (104.7334), which explains the higher overall level of Phase II hedge
ratio compared to Phase I.
A critical point to note here is that the covariance of spot and futures returns
and variance of futures returns for OLS and ECMs hedge ratio estimation are
assumed to be constant. In other words, the constant OHRs derived using
OLS and ECMs are designed to minimise the unconditional variance in a
particular hedging horizon. By contrast, covariance and variance used in the
VECM-GARCH framework is conditional, which means it varies over the
hedging horizon. Therefore, it is important to note that the VECM-GARCH
hedge ratio minimises the dynamic variance of futures returns. The following
Table 7 provides the decomposition of OHR derived using VECM as an
example of the constant covariance and variance.
Table 7. Unconditional Covariance and Variance for VECM Hedge Ratio
Asset
EUA
CER
2
Hedging
Cov( ∆s, ∆f )
Var ( ∆f )
OHR2
2005
0.3431
0.443
0.7743
2006
0.4362
0.641
2007
0.0071
2008
Cov Change
Var Changes
0.6801
0.093
0.1982
0.008
0.9099
-0.429
-0.6335
0.2632
0.272
0.9666
2009
0.1145
0.122
0.9384
-0.1487
-0.1503
2008
0.1773
0.199
0.8929
2009
0.0827
0.096
0.8636
-0.0947
-0.1029
horizon
Taken from Table 4
24
From Table 7, changes in OHR can be clearly seen. In 2006, OHR decreased
because variance has increased more than covariance due to the compliance
break. At the end of 2007, the price of EUA quickly fell to its technical
minimum. This led the variance and covariance to decrease accordingly. As a
result, OHR increased as variance decreased by larger proportion than
covariance. Similar behaviour can be observed in 2009 (Phase II). OHR for
both EUA and CER decreased compared to the previous year. The
decreasing variance was expected as the worst period in GFC had passed.
As one may notice, OHR derived by the VECM-GARCH model in Table 4
does not follow the general rule discussed, as such. Apart from the
inconsistency of the results, the presented OHRs were averages of all the
time-varying OHRs. Therefore, it is necessary to observe the full dynamics of
these hedge ratios from time to time in order to investigate the possible
explanations of such inconsistencies. The conditional hedge ratios derived by
VECM-GARCH are fully graphed in Figure 3 (Phase I), Figure 4 (Phase II)
against the conventional OLS and VECM hedge ratios in each graph. Each
figure consists of four sections, starting with the price level of EUA/CER and
futures contract, which is followed by the spot and futures returns. Based on
the return, the conditional variance of futures returns and covariance between
the returns are calculated using the GARCH framework. Finally, the dynamic
OHR is plotted against the fixed OHR derived by OLS and VECM. With the
OHR section of each figure, the horizontal axis dedicates the hedging horizon
and the vertical axis represents the level of hedge ratios. The fluctuating line
is the conditional hedge ratio at each point in time derived by the
VECM-GARCH model and the straight lines represent the constant hedge
ratios with the solid straight line being the conventional OLS hedge ratio and
the broken straight line being the VECM hedge ratio. All sections in each
sub-figure share the same timeline, which provides a comprehensive
visualization of the dynamic hedge ratio in relation to its determinative
elements. It is also important to note that each section in the figure includes
not only one futures contract, but all available contracts within the phase. For
25
every year, the graph uses a respective futures contract. This is because EUA
and CER futures contracts with different maturities are completely different
assets that are simultaneously traded in the market.
Phase I Spot and Futures Price
EUA
Dec-05
Dec-06
Dec-07
EUR 35
EUR 30
EUR 25
EUR 20
EUR 15
EUR 10
EUR 5
EUR 0
EUA & Futures Returns
8.0000
6.0000
4.0000
2.0000
0.0000
-2.0000
-4.0000
-6.0000
-8.0000
-10.0000
25
Dec05 Return
Dec06 Return
Dec07 Return
Dynamic Optimal Hedge Ratio
Dynamic Covariance and Variance
Dec05 Returns Variance
Dec07 Returns Variance
Dec06 Covariance
EUA
Dec06 Returns Variance
Dec05 Covariance
Dec07 Covariance
1.4
20
1.2
VECM-GARCH05
VECM-GARCH06
VECM-GARCH07
OLS05
OLS06
OLS07
VECM05
VECM06
VECM07
1
15
0.8
10
0.6
5
0.4
0
0.2
-5
0
Figure 3. Phase I Conditional Hedge Ratio with Determinative Elements
Most notably from Figure 3, the Phase I compliance break generated large
return variations, which caused the conditional variance and covariance to
surge to an extreme height for the 2006 hedging horizon. The conditional
variance and covariance in all three hedging horizons (2005-2007) generally
appears to be very close. However, OHRs are very sensitive to changes in
prices since the hedged portfolio is calculated on a daily basis. Despite the
extremely low level of several OHRs, such as during the compliance break,
most of the dynamic OHRs throughout the hedging horizon appear to be
larger than the lower-end extremes. It is reasonable that one may expect the
26
averaged OHR in 2007 to be higher than in 2006. However, because of the
price collapse at the end of Phase I, when both spot and futures price fell to
virtual zero, the covariance and variance became extremely small.
Accordingly, the dynamic OHR are forced to become lower until they
eventually become meaningless at the end. This has been the major factor
that contributes to the much lower averaged OHR derived by VECM-GARCH
in the hedging horizon of 2007 compared to 2005 and 2006. A number of
studies cut out the data from a few days after the price fell to near zero.
However for the purpose of completeness, this study incorporated the full
Phase I data.
Similarly with Figure 3, Figure 4 provides the complete set of dynamic optimal
hedge ratio for Phase II EUA.
Phase II Spot and Futures Price
EUA
Dec-08
EUA & Futures Returns
1.5
Dec-09
EUR 35
0
EUR 20
EUR 15
-0.5
EUR 10
-1
EUR 5
-1.5
EUR 0
-2
Dynamic Optimal Hedge Ratio
Dynamic Covariance and Variance
Dec08 Covariance
Dec-09
0.5
EUR 25
0.5000
0.4500
0.4000
0.3500
0.3000
0.2500
0.2000
0.1500
0.1000
0.0500
0.0000
Dec-08
1
EUR 30
Dec08 Returns Variance
EUA
Dec09 Returns Variance
Dec09 Covariance
1.2000
1.0000
0.8000
0.6000
0.4000
0.2000
0.0000
27
VECM-GARCH08
OLS08
VECM08
VECM-GARCH09
OLS09
VECM09
Figure 4. Phase II Conditional Hedge Ratio with Determinative Elements (EUA)
As can clearly be seen in Figure 4, the dynamic OHR in 2008 presents a
relatively stable trend over the hedging horizon which in other words, is very
close to the fixed hedge ratio derived by OLS and VECM. One of the most
obvious explanations for such a “calm” dynamic hedge ratio is primarily stable
price levels in that year. The price level and returns in the 2008 hedging
horizon created a series of dynamic variances and covariances that are fairly
stable. Since Phase II is a more ”mature” phase after “learning” the lessons
from Phase I when massive volatility took place, such calm conditional OHRs
are expected. Accordingly, the use of conditional optimal hedge ratio in this
hedging horizon may not be necessary. In 2009, the conditional variance and
covariance returned to the volatile form as seen before. However, compared
to Phase I hedging horizons, there are no sudden extreme jumps in variance
and covariance after taking into account the worst period in the GFC. As a
result, the dynamic OHR does not vary substantially as happened in Figure 3.
Figure 5 below provides the dynamic hedge ratio for CER:
28
CER and Futures Price
CER
CER Dec08
CER & Futures Returns
CER Dec09
2
EUR 25
CER
CER Dec08
CER Dec09
1.5
1
EUR 20
0.5
EUR 15
0
EUR 10
-0.5
-1
EUR 5
-1.5
EUR 0
-2
Dynamic Covariance and Variance
0.6
CER Dec08 Returns Variance
CER Dec09 Returns Variance
CER Dec08 Covariance
CER Dec09 Covariance
Dynamic Optimal Hedge Ratio
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.5
0.4
0.3
0.2
0.1
0
CER VECM-GARCH07
CER OLS08
CER VECM08
CER VECM-GARCH09
CER OLS09
CER VECM09
Figure 5. Phase II Conditional Hedge Ratio with Determinative Elements (CER)
Figure 5 illustrates dynamic hedge ratios of CER. For 2008 hedging horizon
the pattern similar to the one seen in Figure 4 is observed. The dynamic
covariance between spot and futures returns and variance of futures returns
are relatively stable as is the conditional OHR, particularly with the covariance
of futures returns, which has been almost flat over that entire hedging horizon
except for slight changes at the beginning. CER started trading only from
August 2008; therefore, the hedging horizon 2008 in Figure 5 is the shortest
hedging horizon in this study. Again, for the 2009 hedging horizon, the results
are similar to the 2009 EAU hedge. The dynamic variance and covariance as
well as conditional OHR for the CER vs Dec-09 hedging combination exhibits
a very close relationship with the EUA vs Dec-09 hedging combination.
Despite a different commencement date, they share similar trends in dynamic
29
covariance, variance and OHR. Most notably during May 2009, both OHRs
experienced a sudden drop caused by divergence variance of future returns
from covariance between spot and futures returns, which can be observed
from the conditional variance and covariance section of both figures. Based
on such similarities, the cointegration relationship between EUA and CER is
likely.
5.3 Hedging Effectiveness
This section reports on two aspects of the performance of the estimated
hedge ratios. The first part of this section reports the results of the variance
reduced by employing different models over the unhedged position. The
second part adopts the maximum utility technique. The utility improvements
of each model over the unhedged position are reported separately for each
hedging combination.
Variance Reduction
The following table reports the results of variance reduction for each hedging
combination achieved using Naive, OLS, ECM, VECM and VECM-GARCH
models. There are two rows for variance reduced for each hedging
combination. The first row represents the variance reduction in natural
numbers, where the second row shows percentage variance reduction over
the unhedged position.
30
Table 8. Variance Reduction Based on Different Models
Phase
Hedging
Horizon
2005
2006
I
2007
2008
2009
II
2008
2009
Hedging
Combination
Variance
Hedged Portfolio Variance Based On
Unhedged
Naive
OLS
ECM
VECM VECM-GARCH
One Year Hedging Horizon
EUA vs Dec05
0.4862 0.14801 0.13809 0.14171
0.14123
0.19013
0.33820 0.34812 0.34450
0.34498
0.29609
Variance Reduced
69.56% 71.60%
70.85%
70.95%
60.90%
EUA vs Dec06
0.7927 0.22498 0.20767 0.22616
0.23177
0.28203
0.56093
0.51068
0.56772 0.58503 0.56655
Variance Reduced
71.62% 73.80%
71.47%
70.76%
64.42%
EUA vs Dec07
0.0112 0.00141 0.00130 0.00174
0.00185
0.00101
0.00984 0.00995 0.00950
0.00939
0.01024
Variance Reduced
87.49% 88.48%
84.50%
83.52%
91.01%
EUA vs Dec08
0.2705 0.02469 0.02415 0.02419
0.02419
0.02435
0.24582 0.24635 0.24632
0.24632
0.24616
Variance Reduced
90.87% 91.07%
91.06%
91.06%
91.00%
EUA vs Dec09
0.1316 0.02720 0.02520 0.02578
0.02568
0.02614
0.10440 0.10640 0.10581
0.10592
0.10545
Variance Reduced
79.33% 80.85%
80.41%
80.49%
80.14%
CER vs Dec08
0.2062 0.02713 0.02647 0.02699
0.02698
0.02869
0.17902 0.17969 0.17917
0.17917
0.17746
Variance Reduced
86.84% 87.16%
86.91%
86.91%
86.08%
CER vs Dec09
0.0895 0.02347 0.02090 0.02193
0.02179
0.02123
0.06601 0.06858 0.06756
0.06769
0.06825
Variance Reduced
73.77% 76.64%
75.50%
75.64%
76.27%
As evident from Table 8, all models have suggested significant variance
reduction over the unhedged position across the entirety of Phases I and II
hedging horizons. The smallest reduction is greater than 60 percent of the
unhedged position. Meanwhile, the largest reduction (91 percent) indicates a
variance reduction of nearly a hundred percent. These results are consistent
with the conceptual framework, whereas hedging with futures contracts as a
financial risk management avenue, has significantly reduced the risk
(variance, in this case) of unhedged trading in spot EUAs or CERs. However,
the performance of individual hedge ratio estimation models is mixed, thus a
single conclusion on the superiority of a certain model cannot be drawn with
confidence. Instead, a generalised result which attempts to consolidate the
results will be discussed. The following frequency distribution table is
designed to pool the output. The performance of each model in terms of
variance reduction is ranked within the seven hedging horizons (see Table 9).
31
Table 9. Frequency Distribution Chart for Ranking of Variance Reduction.
Rank 1
Rank 2
Rank 3
Rank 4
Rank 5
Overall rank
Naive
0
0
2
2
3
Fifth
OLS
6
1
0
0
0
First
ECM
0
2
2
3
0
Third
VECM
0
3
3
0
1
Second
VECM-GARCH
1
1
0
2
3
Fourth
In contrast to some existing research, this study does not support superiority
of the VECM-GARCH model. VECM-GARCH has been ranked the worst on
three occasions. On the other hand, the conventional OLS is ranked as the
best performing model in six cases, clearly outperforming all other models in
overall ranking. Moreover, it is not surprising to see that frequency rankings
and variance reduction of ECM and VECM are close to each other since they
share the same foundation of error correction mechanisms. Also notable is
that the difference in variance reduction between OLS and ECMs is relatively
small (within 0.8 percent). The naive model, with no rank 1, hangs together
with the VECM-GARCH model as the worst performer in the overall ranking.
Despite the difference in overall result, variance reductions achieved using
Naive, OLS, ECMs are very close to each other, with differences of less than
3.5 percent in all hedging combinations. Most notably, although the Naive
model provides near-worst results, variance reduction is not too far away from
OLS and ECMs. This can be used as an argument for full hedge, as the
easiest and cheapest hedging strategy. However, variance reduction
achieved by the VECM-GARCH model in all Phase I hedging combinations
appears to be much lower than the others (over 10 percent difference). In
Phase II hedging combinations, such difference becomes much smaller, and
eventually VECM-GARCH outperforms the rest in the CER vs Dec09 hedging
horizon. In addition, unlike a fixed OHR where the hedged portfolio remains
unchanged across the hedging horizon, the VECM-GARCH derived
conditional optimal hedge ratio changes over time. Thus, the explicit
transaction cost of rebalancing the hedged portfolio will be added if applied in
practice. Therefore, based on the result in this study (worst variance
reduction) and taking into account transaction costs, the utility of
32
VECM-GARCH in the EU-ETS market over the studied period is seriously
questioned. Such findings are in line with Bystrom (2003), Copeland and Zhu
(2006), Lien et al. (2002) and Moosa (2003), where OLS was found to
outperform the more complex and sophisticated models. Later in Lien (2007),
it is shown that, in large sample cases, the conventional hedge ratio provides
the best performance, whereas for small sample cases a sufficiently large
variation in the dynamic variance of the futures return is required in order to
produce favourable variance reduction by dynamic models. It is also worth
noting that the hedging effectiveness measure is based upon the
unconditional variance. The conventional hedge ratio aims to minimize the
time-invariant variance while the conditional hedge ratio attempts to minimize
the dynamic variance. The pure variance reduction approach of performance
evaluation is criticized for not taking into account the utilities. Therefore the
next section incorporates the utilities factor into the modelling.
Maximum Utility
Adopting the procedures discussed in the methodology section, the following
Table 10 provides the utility improvements which have resulted from using
different models with a risk aversion ranging from 1 to 3. Results of each
hedging horizon are reported separately in chronological order. Similarly with
variance reduction, the utility improved over the unhedged position is
presented both in natural numbers and percentages.
33
Table 10. Utility Improvement Based on Different Models
Hedging
Horzion
Hedging
Combination
2005
EUA vs Dec05
2006
EUA vs Dec06
2007
EUA vs Dec07
2008
EUA vs Dec08
2009
EUA vs Dec09
2008
CER vs Dec08
2009
CER vs Dec09
2005
EUA vs Dec05
2006
EUA vs Dec06
2007
EUA vs Dec07
2008
EUA vs Dec08
2009
EUA vs Dec09
2008
CER vs Dec08
2009
CER vs Dec09
2005
EUA vs Dec05
2006
EUA vs Dec06
2007
EUA vs Dec07
2008
EUA vs Dec08
2009
EUA vs Dec09
2008
CER vs Dec08
2009
CER vs Dec09
Utiltiy
Utiltiy Improvement Based On
Unhedged
Naive
OLS
ECM
VECM
Risk Aversion=1
-0.2608
-0.0702 -0.0684 -0.0720 -0.0717
Utility Imporved 0.1905 0.1924 0.1887 0.1891
73.07% 73.78% 72.37% 72.51%
-0.4623
-0.1102 -0.1116 -0.1312 -0.1354
Utility Imporved 0.3521 0.3507 0.3311 0.3269
76.16% 75.87% 71.63% 70.70%
-0.0278
-0.0001 -0.0034 -0.0071 -0.0076
Utility Imporved 0.0277 0.0244 0.0208 0.0202
99.67% 87.84% 74.60% 72.64%
-0.1618
-0.0094 -0.0105 -0.0102 -0.0102
Utility Imporved 0.1524 0.1514 0.1517 0.1517
94.18% 93.54% 93.73% 93.73%
-0.0669
-0.0099 -0.0095 -0.0095 -0.0094
Utility Imporved 0.0571 0.0575 0.0575 0.0575
85.22% 85.84% 85.88% 85.91%
-0.1738
-0.0109 -0.0148 -0.0187 -0.0188
Utility Imporved 0.1628 0.1590 0.1551 0.1549
93.72% 91.51% 89.25% 89.16%
-0.0460
-0.0116 -0.0105 -0.0109 -0.0108
Utility Imporved 0.0344 0.0356 0.0351 0.0352
74.86% 77.27% 76.36% 76.48%
Risk Aversion=2
-0.5039
-0.1442 -0.1374 -0.1429 -0.1423
Utility Imporved 0.3596 0.3665 0.3610 0.3616
71.38% 72.73% 71.64% 71.76%
-0.8587
-0.2227 -0.2154 -0.2442 -0.2513
Utility Imporved 0.6360 0.6433 0.6144 0.6073
74.06% 74.91% 71.55% 70.73%
-0.0335
-0.0008 -0.0040 -0.0079 -0.0085
Utility Imporved 0.0327 0.0294 0.0255 0.0249
97.63% 87.95% 76.26% 74.47%
-0.2971
-0.0218 -0.0225 -0.0222 -0.0222
Utility Imporved 0.2753 0.2746 0.2748 0.2748
92.68% 92.42% 92.51% 92.51%
-0.1327
-0.0235 -0.0221 -0.0223 -0.0223
Utility Imporved 0.1093 0.1107 0.1104 0.1105
82.30% 83.37% 83.17% 83.22%
-0.2768
-0.0243 -0.0278 -0.0320 -0.0323
Utility Imporved 0.2525 0.2490 0.2448 0.2445
91.21% 89.95% 88.43% 88.32%
-0.0908
-0.0233 -0.0209 -0.0218 -0.0217
Utility Imporved 0.0675 0.0698 0.0689 0.0690
74.32% 76.96% 75.93% 76.07%
Risk Aversion=3
-0.7470
-0.2182 -0.2064 -0.2138 -0.2129
Utility Imporved 0.5287 0.5405 0.5332 0.5341
70.78% 72.36% 71.38% 71.50%
-1.2550
-0.3352 -0.3193 -0.3573 -0.3672
Utility Imporved 0.9198 0.9358 0.8977 0.8878
73.29% 74.56% 71.53% 70.74%
-0.0391
-0.0015 -0.0047 -0.0088 -0.0095
Utility Imporved 0.0376 0.0344 0.0303 0.0296
96.17% 88.02% 77.45% 75.77%
-0.4323
-0.0341 -0.0346 -0.0343 -0.0343
Utility Imporved 0.3982 0.3977 0.3980 0.3980
92.11% 91.99% 92.06% 92.06%
-0.1985
-0.0371 -0.0347 -0.0352 -0.0351
Utility Imporved 0.1614 0.1639 0.1633 0.1634
81.32% 82.53% 82.25% 82.32%
-0.3799
-0.0377 -0.0409 -0.0454 -0.0458
Utility Imporved 0.3422 0.3390 0.3346 0.3341
90.07% 89.23% 88.06% 87.94%
-0.1355
-0.0350 -0.0314 -0.0328 -0.0326
Utility Imporved 0.1005 0.1041 0.1027 0.1029
74.14% 76.86% 75.79% 75.93%
34
VECM
GARCH
-0.1189
0.1418
54.39%
-0.1771
0.2852
61.68%
-0.0021
0.0258
92.62%
-0.0094
0.1524
94.16%
-0.0152
0.0517
77.27%
-0.0245
0.1493
85.92%
-0.0155
0.0306
66.42%
-0.2140
0.2899
57.53%
-0.3182
0.5405
62.95%
-0.0026
0.0309
92.35%
-0.0216
0.2755
92.72%
-0.0283
0.1045
78.69%
-0.0386
0.2382
86.04%
-0.0261
0.0647
71.28%
-0.3090
0.4379
58.63%
-0.4592
0.7959
63.41%
-0.0031
0.0360
92.16%
-0.0338
0.3985
92.18%
-0.0414
0.1572
79.17%
-0.0528
0.3271
86.09%
-0.0367
0.0988
72.93%
As can be seen in Table 10, under different level of investor’s risk aversion the
results of utility improvement achieved by different models are mixed. Table 11
reports the frequency distribution of the utility improvement rankings under the
risk aversion ranging from 1 to 3.
Table 11. Frequency Distribution Chart for Ranking of Utility Improvement
Risk Aversion =1
Rank 1
Rank 2
Rank 3
Rank 4
Rank 5
Overall rank
Naive
4
1
1
1
0
First
OLS
2
2
2
0
1
Second
ECM
1
1
3
2
0
Third
VECM
1
1
1
3
1
Fourth
VECM-GARCH
0
2
0
0
5
Fifth
Risk Aversion =1
Rank 1
Rank 2
Rank 3
Rank 4
Rank 5
Overall
Naive
2
2
0
3
0
Second
OLS
4
1
1
0
1
First
ECM
0
0
6
1
0
Fifth
VECM
0
3
0
3
1
Third
VECM-GARCH
1
1
0
0
5
Fourth
Risk Aversion =3
Rank 1
Rank 2
Rank 3
Rank 4
Rank 5
Overall
Naive
2
2
0
3
0
Second
OLS
4
1
1
0
1
First
ECM
0
0
6
1
0
Fifth
VECM
0
3
0
3
1
Third
VECM-GARCH
1
1
0
0
5
Fourth
As observed in Table 11 with risk aversion set at 1, the model which most
frequently produces the highest utility improvement over the unhedged
position is the Naïve model. Under risk aversions 2 and 3, OLS demonstrated
the best overall performance. This result confirms findings based on variance
reduction capabilities, which in turn suggests robustness of the findings. At all
levels of risk aversion, OHR derived by VECM GARCH most frequently
produces the lowest utility improvement. As the risk aversion level increases
from 1 to 3, utility improvement based on OLS decreases. This is in line with
the in-sample results in Yang and Allen (2004). By contrast, utility improvement
35
achieved by VECM-GARCH presents a mixture of results when the risk
aversion increases gradually. In some cases it increases, while it decreases in
other cases.
5.4 Comparisons of Carbon Hedge Ratios to Those in Other Markets
Table 12 lists hedge ratios derived using OLS, ECM and GARCH models in
various existing markets. It should be noted here that, the hedge ratios in the
GARCH column are presented as averages. These ratios are then compared
with EUA vs. Dec-09 hedge ratios with the hedging horizon from 2008 to 2009
up to 20/12/2009.
36
Table 12. Comparisons of Carbon Hedge Ratio with other markets
Category
Currency3
Stock Index
Agriculture
Fixed-income
Power
Commodity
OLS
ECM
British Pound
0.9520
0.9690
Canadian Dollar
0.8750
0.8910
Japanese Yen
0.9910
0.9990
Swiss Franc
0.9740
0.9760
S&P 5004
0.9473
0.9558
NIKKEI5
0.7993
0.8297
FTSE1009
0.7495
0.8015
All ordinaries6
0.6740
0.7290
Beef7
0.0700
Corn11
0.6100
Wheat8
0.9600
Canola12
0.5800
GARCH*
ECM+GARCH
0.9481
0.9526
0.7920
0.9800
0.9200
T-Bond (U.S.)9
0.4400
G-Bond (Italian)
Electricity
Crude Oil
0.9676
Metal
Gold11
0.5000
Emission
Carbon
0.9143
0.9403
0.9548
It can be observed that all ratios lie within the range of 0.5 to 1 with the
exception of some of the GARCH conditional hedge ratios - an OLS hedge
ratio for beef. In Baillie and Myers (1991), the hedge ratio for beef was found to
have zero variance reduction, which in other words is not recommended for
hedging application. This was later confirmed in Yang & Awokuse (2003),
where the hedge ratio for live cattle did not produce much variance reduction
compared to no hedge at all. Hedge ratios for carbon emissions are listed last
in the table. Despite its special features, the size of carbon hedge ratios is not
3
Kroner and Sultan (1993)
4
Kenourgios, Samitas and Drosos (2008)
5
Ghosh and Clayton (1996)
6
Yang and Allen (2004)
7
Baillie and Myers (1991)
8
Sephton (1993a)
9
Ahmed (2007)
37
so different from the other markets.
6. Conclusion
This paper has investigated a number of approaches towards the estimation of
the optimal hedge ratios in the EU-ETS carbon market, including Naïve, OLS,
ECM, VECM and VECM-GARCH.
Significant reduction of volatility can be
attained if spot positions are hedged in futures market independently on what
hedge ratio estimation method is applied. However, performance of models
was not uniform. For example, findings presented in this paper have
discouraged the use of the VECM-GARCH model for the hedging of EUA and
CER price risk. If the emitter chooses the minimum variance as the objective,
the hedge ratio calculated by OLS estimation should be the one to select as it
provides the greatest variance reduction compared to other models. However,
if the hedger (not limited to emitters) expects to incorporate the return as well
as minimum variance, a choice between OLS, Naive and ECM can be made.
As suggested by findings of this research, the results in terms of utility
improvement are quite mixed in different hedging horizons. Nevertheless, the
use of VECM-GARCH is also not recommended as it produces the lowest level
of utility improvement overall. Comparing values of hedge ratios with hedge
ratios obtained in other markets, no significant differences were found. Inspite
of the uniqueness and novelty of carbon markets, the estimated hedge ratios
also fall in the range of 0.5 to 1 in line with those of other markets.
However, due to various limitations of this study, future research is encouraged
to further assess the performance of these models in the EU-ETS market
environment. There are a number of issues which need to be considered: the
availability of phase II spot and futures data have restricted the analysis and
testing. Once more data becomes available, a more accurate estimation will be
forthcoming.
The structural break in phase I of the EU-ETS is not represented in modelling
38
and testing of this paper. To incorporate this, other studies have used dummy
variables to represent such phenomenon. Again, these issues have not been
studied in terms of hedging; therefore, further research is encouraged.
Ultimately, from the portfolio manager’s perspective, the asset allocation
problem and portfolio optimization can be revised after incorporating carbon
instruments. Thus, management of risk and return on such revised portfolio
becomes essential for possible future research.
39
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