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ISSN 1836-8123 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 4 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 5 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 6 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. 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