Future price dynamics of CO2 emission certificates

Futures Price Dynamics of CO2 Emission Certificates – An Empirical Analysis Marliese Uhrig-Homburg * Michael Wagner * Chair of Financial Engineering and Derivatives Universität Karlsruhe (TH) First version: August 29th, 2006 Current version: August 26th, 2007 * Chair of Financial Engineering and Derivatives, Universität Karlsruhe (TH), 76128 Karlsruhe, Germany Corresponding Author: Michael Wagner, Email The authors would like to thank Wolfgang Härdle, Olaf Korn, Jan Seifert, Stefan Trück, and two anonymous referees as well as participants at the Quantitative Finance Seminar, Collaborative Research Center 649: Economic Risk, Berlin, for their helpful comments and suggestions Futures Price Dynamics of CO2 Emission Certificates – An Empirical Analysis Abstract CO2 emission certificates are traded with increasing liquidity within the EU emissions trading scheme Besides spot certificates, forwards and futures are also currently available OTC and on exchanges across Europe The focus of this study is on the relationship between spot and futures markets in the EU ETS A thorough empirical examination reveals evidence that spot and futures prices are linked by the cost-of-carry approach After an initial period of market inefficiency, spot prices now seem to equal discounted futures prices within a trading period, which has implications for the pricing of derivative instruments on emission certificates Moreover, we find that futures markets lead the price discovery process of CO2 emission certificates JEL Classification: Q28, Q50, G13 Keywords: CO2 emission certificates, price dynamics, CO2 futures Introduction Since the introduction of the EU emissions trading scheme (EU ETS) in 2005, CO2 emission certificates have been traded with increasing liquidity These emission certificates allow for the emission of one ton of CO2 each and are called EU allowances (EUAs) Besides spot certificates, forwards and futures on EUAs are also already being traded actively OTC and on exchanges across Europe Currently, the EU ETS comprises two trading periods, the trial period from 2005 - 2007 and the so-called Kyoto commitment period from 2008 - 2012 Within these trading periods, not only regulated CO2 emitters but any person or company may trade EUAs without restriction As storage of EUAs is possible and virtually costless within the trading periods, a long forward position can easily be replicated by buying EUAs on credit If, on the other hand, there is no direct benefit of possessing EUAs until needed for compliance, regulated CO2 emitters could sell some of their EUAs and use a money market account to replicate a short forward position In this case, the relationship between spot and forward prices should be described entirely by the cost-of-carry approach The question of correctly pricing EUA forward contracts is important for all market participants in the EU ETS seeking to embed CO2 trading in their risk management strategy Moreover, the question of pricing forwards and futures on EUAs will also have implications for the pricing of more complex derivatives on EUAs For example, in the case of EUA options with maturities extending into the second trading period beginning in 2008, the underlying spot EUAs are not yet being traded However, forwards and futures with end dates in 2008 are already being traded The relationship between spot and forward EUA prices will therefore give an indication on how to price these options The literature analyzing CO2 emission certificates in the EU ETS is still rather sparse We contribute to the growing field by thoroughly analyzing the relationship between spot and futures markets Within the first trading period, we expect the cost-of-carry approach to be valid, whereas no clear relationship is expected to exist between spot prices and prices for futures maturing in the second trading period To test this formally and to deepen our understanding of these young markets, we perform an empirical study based on the cointegration methodology First, we test whether spot and futures prices follow the costof-carry approach in the long-term We begin with a visual inspection of the data and find that there exists a structural break in the data at the end of 2005 Before this break, there existed obvious arbitrage possibilities in the immature market Our findings suggest that after these arbitrage opportunities vanished at the end of 2005, a fairly stable cointegrating relationship emerged between spot and futures prices in accordance with the cost-of-carry approach We thus also continue to analyze the short-term dynamics and find that due to the immaturity of the EU ETS, deviations from the equilibrium relationship may have existed for some time However, our cointegration analysis indicates that for spot and futures prices, the equilibrium is restored quickly (i.e within only a few days) In order to also study whether the futures market serves as a price discovery vehicle for the spot prices, we then estimate a suitable vector error correction model using the most liquid spot and futures contract This gives an indication of which market processes information more efficiently Some research examining the spot price dynamics of EUAs is already underway: see Benz/Trück (2006), Fehr/Hinz (2006), Paolella/Taschini (2006), or Seifert/UhrigHomburg/Wagner (2006) As opposed to these papers, our focus is not on spot price dynamics but rather on the relationship between spot and futures markets for EUAs To our knowledge, the first work to analyze both spot and futures prices of EUAs together was by Daskalakis/Psychoyios/Markellos (2006) However, they not test the cost-ofcarry relationship of spot and futures prices within the current trading period (2005 2007) but rather adopt an equilibrium pricing model for futures prices in the trading period 2008 - 2012 based on current spot prices In a recent working paper, Borak et al (2006) analyze convenience yields for futures prices with maturities up to 2012 Our analysis differs from theirs in that we argue that futures for the second trading period are written on an underlying that is not actually being traded yet EUAs for the first trading period cannot be used for compliance in the second trading period, and thus there is no direct relationship between EUA prices and prices for futures maturing in the second trading period We will show, however, that our results are consistent with their findings In the following, we provide a short overview on the EU ETS and introduce the institutional details that are relevant for our analysis Section discusses the relation of our analysis to the cointegration methodology in the literature and then focuses on the dynamics of the relationship between spot and futures prices Section analyzes whether spot or futures prices lead the price discovery process, and Section concludes 2 The EU Emissions Trading Scheme The EU-wide emissions trading scheme (EU ETS) started in 2005 It was introduced on the basis of the Kyoto Protocol, an international agreement adopted in 1997 with the aim of reducing global greenhouse gas emissions caused by humankind.1 The Kyoto Protocol therefore defines emission caps for industrialized and transition countries These caps are valid for the first Kyoto commitment period from 2008 - 2012 To facilitate the reduction of greenhouse gases, the Kyoto Protocol includes three flexible mechanisms, which are the clean development mechanism (CDM), joint implementation (JI), and international emissions trading (IET) While JI allows industrialized or transition countries to jointly invest in emission reduction projects in other industrialized or transition countries, the CDM allows industrialized or transition countries to invest in emission reduction projects in developing countries For emission reductions resulting from JI and CDM projects, countries are granted Emission Reduction Units (ERU) and Certified Emission Reductions (CER), respectively Countries may use ERUs and CERs to comply with their emission caps IET allows for emissions trading between governments The EU member states implemented the emissions trading scheme in order to jointly reach their Kyoto goals in a cost-efficient way.2 While IET allows for emissions trading between governments on the basis of the Kyoto Protocol, the EU ETS breaks down the emissions trading to the company level The EU ETS comprises combustion installations exceeding 20 MW, refineries, and coke ovens as well as the metal, pulp and paper, glass, and ceramic industries Each year at the end of February, companies with any of these installations are allocated a certain number of EU Allowances (EUAs) One EUA allows for the emission of one ton of CO2 in the current calendar year On April 30th of the following year, companies have to submit EUAs to the national surveillance authorities according to their actual emission volumes If projected emissions exceed their allocated EUAs, companies have two possibilities to solve the problem They may either abate some of their emissions or buy the EUAs they lack on the market The intended effect is that companies with cheap abatement opportunities will abate more CO2 and sell the EUAs in the market to companies for which abatement is more costly If companies fail See United Nations (1998) See European Union (2003) to comply, they have to pay a penalty and must also deliver the missing EUAs in the following year EUAs are freely tradable across all EU member states, meaning that companies may also buy EUAs from companies in other countries However, there is a major restriction, commonly referred to as the trading period break EUAs that are issued in the first trading period (2005 - 2007) are only valid during this trading period in most countries This means that an EUA issued in 2005 may be used at the latest for emissions stemming from 2007 They may not be used for the second trading period, the Kyoto commitment period (2008 - 2012) The act of storing an EUA for later usage is commonly called banking Only France and Poland allow limited banking between 2007 and 2008; none of the other countries allows banking at all However, even in France and Poland, operators may at a maximum bank the difference between the initially allocated allowances and the effective emissions of the installation In particular, as Dufour (2006) points out, operators may not bank EUAs purchased on the market Companies may also use CERs and ERUs generated from CDM and JI projects for compliance instead of EUAs CERs are bankable from the first to the second trading periods, but there is a percentage limit for their usage in the EU ETS The opposite approach – borrowing an EUA from a future year – is also possible within a trading period As companies obtain their EUAs for the current year at the end of February, they may already use these EUAs to comply with the preceding year, as the compliance date can be as late as April 30th However, this is not possible between 2007 and 2008 As a result, there are essentially two markets, one for the first trading period (2005 - 2007) and one for the second trading period (2008 - 2012) While forwards and futures are traded both OTC and on exchanges across Europe for both trading periods, spot certificates are traded only for the first trading period, as the first EUAs valid for the second trading period will be handed out to companies in February 2008 Spot versus Futures Prices 3.1 NO-ARBITRAGE RELATIONSHIP SPOT VERSUS FUTURES PRICES The relationship between spot and futures prices depends on the underlying market characteristics As Ross (1997) points out, there exists a whole spectrum of markets At the one end there are commodities such as gold, which behave like investment assets and can easily be stored The futures price is then determined by no-arbitrage conditions If we assume for the moment a constant interest rate r and no storage costs or dividends, then the only cost of holding the underlying is the foregone interest It therefore follows that (3.1) Ft (T ) = e r (T −t ) S t St denotes the spot price at time t while Ft(T) stands for the futures price of a contract with delivery in T This relation is also known as the cost-of-carry approach If the spot price is below the discounted futures price, buying the underlying while simultaneously entering into a short futures contract results in a riskless profit (cash-and-carry arbitrage) The same is true for the opposite However, in many commodity markets, a significant part of the demand is driven by real needs As a consequence, holding the physical commodity not only imposes costs but may also result in an additional benefit for the holder According to Brennan (1991), this benefit, which accrues to the owner of the spot commodity as opposed to the owner of a futures contract, is defined as a convenience yield Such benefits may arise through the opportunity to circumvent shortages in the spot commodity when needed for a production process Typical examples are fuels like gas, coal, and oil If we assume a constant flow of benefits, according to Geman (2005), the convenience yield approach is thus given by (3.2) Ft (T ) = e ( r −c )(T −t ) S t Here c describes the constant convenience yield net of physical storage costs It is sometimes argued that the convenience yield shows a correlation to some exogenously given variables An example for such a correlated variable is the total stock of inventory for the corresponding commodity In this case, the convenience yield itself may be stochastic and will weaken the link between spot and futures prices Finally, at the other end of the market spectrum, there exist pure consumption goods, which are either virtually unstorable or are storable only at prohibitive costs, such as power or wheat In this situation, there is no longer a clear connection between spot prices and futures prices A definition of a convenience yield in a backwards manner, such that the usual no-arbitrage pricing relationship holds, might be useful from a modeling perspective However, the economic meaning would then no longer correspond to Brennan's definition of the flow of services that accrues to the investor from holding an inventory We are not able to learn much about an appropriate equivalent martingale measure from the current spot market; it is thus necessary to build expectations vis-à-vis the future spot prices in order to price futures contracts As explained above, EUAs are tradable without restrictions within a specific trading period, and the only significant storage cost is the foregone interest rate The only plausible reason for discounted futures prices to differ from spot prices in the absence of stochastic interest rates is thus a potential convenience yield of the spot EUA Is there a positive effect of possessing EUAs as opposed to holding a futures position capable of creating a positive convenience yield? Spot EUAs are only needed once a year to fulfill compliance requirements Thus, if futures mature before the end of the next compliance date, there is no benefit of holding spot EUAs as opposed to holding the corresponding long futures position If, on the other hand, futures mature after the next compliance date, the futures position has the disadvantage of not being usable for compliance purposes before delivery However, companies may borrow EUAs from the future year if they run short of EUAs This is a real constraint only if a company's position in futures maturing after the next compliance date is larger than its ability to borrow EUAs from the future year This scenario is best described as a short-selling constraint in the magnitude of the yearly EUA allocation A second reason for a positive convenience yield may be that companies not trust in the reliable delivery of maturing futures contracts However, we believe that from an economic point of view, the convenience yield of EUAs should be negligible in a rational and efficient market In general, forward and futures prices differ due to marking-to-market and implied options Since the futures on EUAs generally not include valuable options, such as those regarding the quality of the underlying to be delivered, only the valuation differences due to marking-to-market effects stemming from correlations between the EUA spot price and the risk-free interest rates remain However, the evidence for such a correlation is weak We perform a short correlation analysis of changes in EUA spot prices from the Powernext exchange and changes in the interest rates relevant for the futures contract maturing in December 2006 The time period coincides with our sample period from June 2005 to November 2006 Although statistically significant, the correlation coefficient is as low as -0.16 Thus, for the purpose of this study, we neglect the difference and treat forwards and futures equivalently The relationship between spot and futures prices within a trading period should thus be explained entirely by the cost-ofcarry approach as described in equation (3.1) The second trading period, however, constitutes a different situation The current spot certificate may not be transferred to the second trading period For a future 2008, for example, the situation is thus comparable to the situation described above for power and wheat The cash-and-carry arbitrage is not possible and the current spot certificate is of no use for the second trading period Moreover, the expected spot price for the year 2008 is influenced by factors that not have any impact on today's spot price, such as the final decision of the EU vis-à-vis EUA allocations for the second trading period As a consequence, we not expect the cost-of-carry or constant convenience yield approach to hold in this situation Equation (3.1) allows us to calculate theoretical futures prices from spot prices and interest rates and compare them to observed futures prices The analysis of these theoretical and observed futures prices tells us whether our pricing assumption for futures contracts is valid However, it does not explicitly test whether a convenience yield exists For this, we calculate implied yields by (3.3) yt (T ) =  F (T )  ln  t , T − t  St  where yt(T) describes the yield between times t and T implied from spot and observed futures prices According to equation (3.1), this implied yield should equal the risk-free interest rate for the relevant time period Any difference of yt(T) and r can be attributed to a possible convenience yield Our analysis of equation (3.3) is thus directly comparable with the results of the convenience yield analysis in Borak et al (2006) Before we actually explain our methodological approach to testing equations (3.1) and (3.3), we first continue by visually analyzing and discussing the observed pricing relationships in order to detect potential problems, such as structural breaks in the data 3.2 DATA DESCRIPTION AND VISUAL INSPECTION Both spot EUAs and futures contracts are traded on several exchanges across Europe Due to no-arbitrage arguments, there should not be significant price differences for spot EUA prices among the different exchanges The same is true for futures prices for contracts with the same maturity Daskalakis/Psychoyios/Markellos (2006) show convergence for EEX and Nordpool spot EUA prices We choose to work with spot prices from the Powernext exchange and futures prices from the ICE/ECX for two reasons First, volume data from Bloomberg show that the Powernext is the most liquid EUA spot exchange, while the ICE/ECX is the most liquid futures exchange for EUAs Second, the Powernext and the ICE/ECX have already announced plans to merge their operations in order to offer both spot and futures trading for EUAs from the same screen.3 Traders will thus concentrate on these two exchanges for reasons of both liquidity and transaction costs Our analysis would ideally use time-stamped intraday data in order to match spot and futures prices However, the EU ETS is a rather immature market Even for the most liquid exchanges, the Powernext for spot emission certificates and the ICE/ECX for EUA futures, transaction data reveal that many days exhibit virtually zero trading volume For the Powernext spot emission certificate and the ICE/ECX 2006 future contract, the fraction of days that does not show trading volume for at least one of the two is about 15% from June 2005 to November 2006 (source: Bloomberg volume data) In such circumstances, it is not reasonable to match spot and futures prices on an intraday basis Instead, we use daily settlement prices Our data sample comprises data from 24/06/2005 - 15/11/2006 In the following, we compare spot prices with futures prices maturing in December 2006 and December 2007 In addition, we also compare the future 2006 directly with the future 2007 In order to show the effects of the trading period break at the end of 2007, we include future 2008 prices to our analysis Regarding interest rates, we use EURIBOR mid-quotes for maturities up to one year and EuroSwap mid-quotes for maturities above one year Table explains the abbreviations for all the time series used to analyze the pricing relationships and shows some descriptive statistics [Insert Table about here] Figure provides a first impression by showing theoretical future 2006 prices calculated with equation (3.1) from spot prices and interest rates along with observed future 2006 prices (F06/TF06) While a small difference between the two lines is noticeable at the See press release "Joint emissions platform planned" from FT.com (Financial Times), June 24, 2005 long-term equilibrium relationship between spot and futures prices if interest rates are taken into account As expected, the results clearly argue against the hypothesis of stationarity for the combination of future 2008 prices and theoretical futures prices constructed from current spot prices In 2008, a new trading period will start and the corresponding spot certificates are not yet being traded If one needs to price the future 2008, it is first necessary to build an expectation about future spot prices in the second trading period and to add a suitable risk premium This expectation may be influenced by the current spot price; however, additional information sources must be used in order to quantify the factors only affecting the second trading period, such as EUA allocations for the years 2008 - 2012 Short-term dynamics of equilibrium error The above-discussed analysis indicates that the equilibrium relationship between spot and futures prices in the current trading period generally holds and never drifts too far from its supposed level, at least after December 2005 However, in a mature market, one would expect the equilibrium relationship to hold on a daily basis and not to drift apart for several days One might therefore be tempted to regress the first differences of observed and theoretical futures prices as well as of implied yields and interest rates to test for the short-term dynamics of the equilibrium relationship But the analysis of the long-term dynamics suggests that the equilibrium errors are stationary This indicates that the variables used to calculate the equilibrium errors are driven by cointegrated processes As we did not explicitly estimate but rather pre-specified the cointegration vector, the unit root tests performed above can be interpreted as restricted cointegration tests whereby the cointegration vector is derived from theoretical considerations In that case, the same critical values apply for the test statistics as well as for the unit root tests; see Hamilton (1994, p 582f) From an econometric point of view, we run the risk of obtaining a spurious regression Instead of regressing the first differences, we refer to Engle/Granger (1987, p 255f), who assert that a valid representation for two cointegrated variables TFt and Ft is a vector error correction model of the form (3.6) TFt − TFt −1 = δ ( Ft −1 + θ 2TFt −1 ) + ε t Ft − Ft −1 = δ ( Ft −1 + θ 2TFt −1 ) + ε t 15 In our case, the cointegration coefficient θ2 should equal -1 It is easy to see that the coefficients δ1 and δ2 determine the speed of adjustment of the respective variable towards the equilibrium We estimate equations (3.6) for the same combinations of prices and yields as in the above-presented stationarity analysis All time series tested are assumed to be integrated of order one, i.e I(1), meaning that their first differences are stationary This is a prerequisite for variables cointegrated of order one Analyses showing that the time series tested are indeed I(1) are available on request from the authors Table reports estimated parameters and t-statistics for the cointegration coefficients To further support our assumption of cointegrated time series, we also report the results of Johansen's cointegration test.5 The null hypothesis of this test is the number of cointegrating relations Table reports the trace statistics for the null hypotheses of zero and at most one cointegrating relation Our interest is whether the disequilibrium is restored quickly or if the disequilibrium persists over several days Looking at equation (3.6), we notice that in order to have the equilibrium relation Ft −1 + θ 2TFt −1 = restored in only one time step, the estimated coefficients must satisfy = −(δ1 + θ 2δ ) We call the right-hand side of this equation the "speed of adjustment" and also report the values in Table A value of means that the equilibrium relation is restored in one day, lower values mean that it takes longer, and a value of means that the equilibrium is not restored at all As our analysis of the longterm dynamics showed, we can only accept the cost-of-carry hypothesis after December 2005 We thus report the short-term dynamics only for the shortened sample period [Insert Table about here] Several interesting results become obvious in Table The cointegrating coefficients θ2 of prices are all very close to their supposed level of -1 for the first trading period (F06/TF06, F07/TF07, and F07/TF0607) Also, the trace statistics clearly indicate that there exists one cointegrating relationship The speed of adjustment measures of 0.88 and 0.80 show that in the first trading period, spot and futures prices actually revert back to their equilibrium relationship rather quickly A value of 0.16 for the combination See Johansen (1991) and Osterwald-Lenum (1992) 16 F07/TF0607 shows that among futures, the disequilibrium may persist longer This may be partly explained by the fact that the equilibrium error between the two futures 2006 and 2007 is much less volatile compared to the others The future 2008 is not cointegrated with the spot price; the coefficients should therefore not be interpreted, because the error correction model is misspecified in this case The picture looks somewhat similar for the yields, although the cointegrating coefficients are not as close to their supposed levels compared to the prices However, for the yield combination Y0607/I0607, a cointegration rank of is accepted in combination with a cointegration coefficient of -0.9133, which is statistically not significantly different from -1 Knowing that the market is in its infancy and that transaction costs may still prohibit the instantaneous adaptation of spot and futures prices, this is a surprisingly good result Overall, the evidence suggests that the futures market is already functioning well and that the no-arbitrage relationship seems to hold, although market inefficiencies still exist temporarily The cost-of-carry approach does not work across the trading period break, which can be gathered from looking at the results for the forward 2008 Price discovery in the EU ETS The above analysis established that the spot and futures price dynamics for CO2 emission certificates can be described sufficiently well with the cost-of-carry approach after December 2005 However, in order to better understand the market for EUAs, one might also ask how pricing-relevant information is processed in the market Will new information show up in spot or futures markets first? In other words, which kind of prices (spot or futures) leads the price discovery process on exchanges? To answer this question, we compare the most liquid CO2 spot contract, which is traded at Powernext, with the most liquid futures contract, which is the future 2006 from ICE/ECX Volume data from Bloomberg show that CO2 futures trading is now far more liquid than CO2 spot trading This is common in many commodity markets A first guess would thus be in favor of the futures contract In order to assess whether spot or futures prices lead the price discovery process, we follow common practice and estimate a vector error correction model (VECM) with lagged differences to the prices under scrutiny; see De Jong (2002) and Baillie et al (2002) Based on the estimated VECM, a variety of measures can be applied in order to assess the price leadership 17 Spot and futures prices are usually tested in mature markets with very high data frequency For example, Theissen (2005) uses data with a frequency of 15 seconds For the as yet immature EU ETS, only daily data are available to us However, in thinly traded markets, differences in price discovery between spot and futures contracts may also be observed on a daily data basis, as shown, for example, by Kavussanos/Nomikos (2003) for the freight futures market The VECM approach, as opposed to calibration of pure ARIMA models, is necessary due to the cointegration of the tested variables Let p −1 (4.1) ∆S t = α + Π S t −1 + ∑ Φ i ∆S t −i + ε t i =1 describe a VECM model of order p, where S t' = (TFt , Ft ) are theoretical and observed futures prices, whereas ∆S t are first differences Using theoretical futures prices instead of spot prices has the advantage of ensuring that the cointegration relationship remains constant over time An alternative would be to use discounted futures prices or a timevarying cointegration vector The number of lags to be included in the model is denoted by k = p – 1, while α denotes a constant vector Error terms εt are assumed to be normally distributed We know from our analysis of the cost-of-carry relationship that for spot and future 2006 prices, TFt and Ft are cointegrated with cointegrating vector θ' = (1, -1) Thus (4.1) has cointegration rank r = 1, and with δ' = (δTF, δF), we may factor П as П = δθ'  β iTF With Φ i =  F  γi γ iTF   , we may expand (4.1) to β iF  k k i =1 i =1 (4.1a) ∆TFt = α TF + ∑ β iTF ∆TFt −i + ∑ γ iTF ∆Ft −i + δ TF (TFt −1 − Ft −1 ) + ε tTF k k i =1 i =1 (4.1b) ∆Ft = α F + ∑ β iF ∆Ft −i + ∑ γ iF ∆TFt −i + δ F (TFt −1 − Ft −1 ) + ε tF The advantage of the latter formulation is that we obtain consistent and efficient parameter estimates with simple ordinary least squares estimations of each equation.6 While the Schwarz information criterion (SIC) recommends excluding any lags, the Akaike information criterion (AIC) would include more than 10 lags However, the AIC See Kavussanos/Nomikos (2003) Estimated standard errors are corrected for autocorrelation and heteroscedasticity using Newey/West (1987) 18 has a local minimum at lags Table thus presents results for the estimation of (4.1) with k = lags included The upper panels of Table show coefficient estimates and t-statistics for the VECM; the lower panel shows statistics that help to assess the contribution of spot and futures prices to price discovery As before, results are shown for the sample period starting December 2005 [Insert Table about here] The first thing to note is that lagged values of TFt and Ft can much better explain the returns derived from spot prices (theoretical futures prices) than returns of observed futures This can be seen by a coefficient of determination R2 of 0.49 for theoretical futures prices as opposed to 0.16 for observed futures prices We test whether lagged returns derived from the spot market have an impact on returns in the futures market and vice versa with an F-test on the joint significance of coefficients The F-statistic tests the null hypothesis that the coefficients for lagged returns of the other market are jointly zero Both test statistics are significant, indicating bi-directional causality However, the observed futures market coefficients have more explanatory power than the coefficients for the theoretical futures market (11.53 as opposed to 6.80) A third measure is the common factor weight (CFW) The CFW is a direct measure of the contribution to price discovery See Theissen (2002) for a formal justification of this measure It is obtained by (4.2) CFW TF δF − δ TF F = F , CFW = F δ − δ TF δ − δ TF The adjustment coefficients δTF and δF from equation (4.1a/b) determine the permanent effect of a shock of the respective market on the system In the definition given above, a CFW of means that this market contributes exclusively to price discovery A CFW of 0.5 means that both markets contribute equally to price discovery Looking at Table 5, we see that for the futures market ( ∆Ft ), the CFW is actually above 1, while for the spot market ( ∆TFt ), it is below This becomes clear when looking at the size of the speed of adjustment coefficients δTF and δF When the lagged observed futures price is above its theoretical forward price, meaning that (TFt −1 − Ft −1 ) < , one would expect the current observed futures' return to be negative, while the return for the theoretical futures' return is positive in order to restore equilibrium This would translate into a positive δF and a 19 negative δTF But the estimated coefficient δF is negative (-1.34) meaning that δTF must be even more negative in order to compensate (-2.29) In other words, the spot market moves in the wrong direction and the futures market overcompensates for that In addition, we also perform a Granger causality test on the theoretical and observed future 2006 with two lags included.7 While the null hypothesis "Observed future does not Granger-cause the theoretical future" is clearly rejected with an F-statistic of 62.97 at the 1% significance level, the contrary null hypothesis "Theoretical future does not Grangercause the observed future" is only rejected at the 10% significance level with an Fstatistic of 2.65 All four measures indicate that the futures market leads the price discovery process This is consistent with results known from many financial markets One reason may be the higher liquidity in the futures market As opposed to spot certificates, transactions with EUA futures not have to be accounted for in the emissions registers before maturity Moreover, companies without their own EUA allocations can only achieve short positions in the futures and not in the spot market Companies seeking reliable price signals in the EU ETS should therefore always start by looking at the futures market Conclusion The purpose of this study was to examine the relationship between spot and futures markets for CO2 emission certificates in the EU ETS Our hypothesis was that within a trading period, spot and futures prices can be described by the cost-of-carry approach, meaning that spot prices plus accrued interest should be equal to futures prices Although there existed obvious arbitrage possibilities in the market during the year 2005, empirical evidence suggests that after December 2005, the market efficiency increased, and spot and futures prices now actually seem to be linked by the cost-of-carry approach Temporary deviations from this linkage may exist but generally vanish after only a few days Moreover, it is shown that the CO2 futures market leads the price discovery process An important implication from our findings for energy producers and other market participants in the EU ETS is that EUA futures are suitable instruments for hedging CO2- See Granger (1969) 20 related risks This is due to their strong and clear linkage to EUA spot prices For example, power producers selling power futures may at the same time hedge their need for EUAs in the EUA futures market Our findings also have important implications for the valuation of derivatives on EUAs For the first trading period, the underlying EUA is a traded and storable commodity Thus, standard risk-neutral valuation methodology based on the EUA spot price dynamics can be applied No underlying is being traded yet for EUA-derivatives with end dates in the second trading period The valuation of such derivatives should not be based on the current spot price, because it does not reflect all the information necessary for building an expectation about future spot prices in the years 2008 and beyond However, the future 2008 does reflect this information As it can be traded both short and long and matures before the first compliance date in the second trading period, we suggest pricing respective derivatives relative to the future 2008 Again, standard risk-neutral valuation methodology is applicable This is not purely an academic question As announced by the European Climate Exchange (2006), European options on EUAs have been available for both trading periods on a standardized basis at the ICE Futures since October 13th It might be a rewarding task for further research to examine the pricing of such options Finally, policy makers should be aware of the results of this paper as well The empirical analysis clearly shows the effect of the trading period break between 2007 and 2008 The fact that there is no continuous spot trading possible between the two trading periods results in two separate markets This makes planning or risk management a lot more difficult for companies active in the EU ETS Policy makers should thus think about a smoother transition into a potential third trading period 21 EUR Dashed line : Theoretical Forward 2006 HTF06 L Solid line : Observed Forward 2006 HF06 L 30 25 20 15 10 Date 8ê05 10 ê05 12 ê05 2ê06 4ê06 6ê06 8ê06 10 ê06 Figure 1: Observed future 2006 price versus theoretical future 2006 price The solid line represents observed EUA prices for the future maturing December 18th, 2006 at the ICE/ECX The dashed line represents the corresponding theoretical futures prices when the cost-of-carry argument using spot prices from Powernext and riskless interest rates is applied Prices are in EUR EUR 35 Dashed line : Theoretical Forward 2008 HTF08 L Solid line : Observed Forward 2008 HF08 L 30 25 20 15 10 Date 8ê05 10 ê05 12 ê05 2ê06 4ê06 6ê06 8ê06 10 ê06 Figure 2: Observed future 2008 price versus theoretical future 2008 price The solid line represents observed EUA prices for the future maturing December 15th, 2008 at the ICE/ECX The dashed line represents the corresponding theoretical futures prices when the cost-of-carry argument using spot prices from Powernext and riskless interest rates is applied Prices are in EUR 22 Per cent 15 Dashed line : Observed Interest Rate HI06 L Solid line : Implied Yield Spot − Forward 2006 HY06 L 12.5 10 7.5 2.5 Date 8ê05 10 ê05 12 ê05 2ê06 4ê06 6ê06 8ê06 10 ê06 -2.5 -5 Figure 3: Implied yields from spot and future 2006 prices versus observed interest rates The solid line represents the implied yield in per cent calculated with the cost-of-carry relationship using both futures and spot EUA prices (future maturing December 18th, 2006; data from Powernext and ICE/ECX) The dashed line represents the corresponding riskless spot interest rate observed in the market Per cent 15 Dashed line : Observed Interest Rate HI0607 L Solid line : Implied Yield Forward 2006 − Forward 2007 HY0607 L 12.5 10 7.5 2.5 Date 8ê05 10 ê05 12 ê05 2ê06 4ê06 6ê06 8ê06 10 ê06 -2.5 -5 Figure 4: Implied yields from future 2006 and 2007 prices versus observed interest rates The solid line represents the implied yield in per cent calculated with the cost-of-carry relationship using futures EUA prices for 2006 and 2007 (data from ICE/ECX) The dashed line represents the corresponding riskless forward interest rate observed in the market 23 Table 1: Description of time series tested Time series' name Description Mean Observed futures prices St dev EUR F06 ICE/ECX future, maturing Dec 18th, 2006 20.47 5.37 F07 ICE/ECX future, maturing Dec 17th, 2007 20.95 5.46 F08 ICE/ECX future, maturing Dec 15th, 2008 21.04 3.69 Theoretical futures prices1 TF06 Future 2006 calculated from Powernext spot price 20.64 5.46 TF07 Future 2007 calculated from Powernext spot price 21.30 5.59 TF0607 Future 2007 calculated from ICE/ECX future 2006 21.14 5.50 TF08 Future 2008 calculated from Powernext spot price 21.21 6.45 Implied yields2 Per cent Y06 Yield calculated from spot and future 2006 price 2.62 3.30 Y07 Yield calculated from spot and future 2007 price 2.40 1.74 Y0607 Yield calculated from future 2006 and future 2007 2.37 1.40 Y08 Yield calculated from spot and future 2008 price 7.76 17.00 I06 Spot rate corresponding to future 2006 2.88 0.40 I07 Spot rate corresponding to future 2007 3.17 0.50 I0607 Forward rate corresponding to the time period between future 2006 and future 2007 maturity dates 3.29 0.49 I08 Spot rate corresponding to future 2008 3.35 0.52 Observed interest rates3 1) 2) 3) Theoretical futures prices are calculated with the cost-of-carry relationship (3.1) using observed spot/futures prices for EUAs and observed interest rates Implied yields are calculated with the cost-of-carry relationship (3.3) using observed spot and futures prices for EUAs Yields are expressed on an annualized basis Spot and forward interest rates are calculated from the observed riskless interest rate curve according to the maturity dates of the corresponding futures Interest rates are expressed on an annualized basis 24 Table 2: Equilibrium errors of prices and yields 06/05 - 11/06 Time series 12/05 - 11/06 Mean of equilibrium error Standard deviation Mean of equilibrium error Standard deviation F06, TF06 -0.16*** 0.45 0.03 0.36 F07, TF07 -0.36 *** 0.62 -0.03 0.41 F07, TF0607 -0.19*** 0.23 -0.06*** 0.13 3.94 *** 4.29 ** 3.39 * 1.27 *** 0.81 *** 18.99 F08, TF08 Y06, I06 Y07, I07 Y0607, I0607 Y08, I08 -0.17 -0.26 *** -0.76 *** -0.92 *** 4.41 0.77 3.13 0.55 1.46 -0.16 1.07 *** -0.39 16.74 7.63 *, **, and *** stand for rejection of the null hypothesis of a zero mean at the 10, 5, and per cent levels Table 3: Unit root tests of equilibrium errors Period 06/05 - 11/06 ADF Intercept ADF tµ (Lag SIC) F06, TF06 -0.03 -3.45*** F07, TF07 F07, TF0607 F08, TF08 Y06, I06 -0.03 -0.00 0.04 -0.12 -2.37 (4) (4) -1.72 (2) -0.18 -3.21 PP Ztµ (Lag NW) (1) *** (4) -14.47*** -9.88 *** -2.46 -0.42 -17.48 *** -1.48 (10) -14.29 Y0607, I0607 -0.03 -1.89 (2) -2.76* Period 12/05 - 11/06 ADF Intercept ADF tµ (Lag SIC) F06, TF06 0.03 -13.47*** F07, TF07 F07, TF0607 2.77 (0) *** -0.02 -12.49 -0.00 ** -3.30 1.41*** (14) (13) 1.38 *** (15) 1.29 *** (15) 1.41 *** (15) (1) *** -0.07 0.14 (13) (9) Y07, I07 Y08, I08 KPSS (Lag NW) 2.71 (13) -1.33 1.00 (11) -0.90*** (3) 1.11 -13.47*** (2) 0.09 (0) *** (4) 0.22 (2) -4.37 (3) 1.10 (4) *** (12) (1) -0.77 (1) 1.38 Y06, I06 0.51** -13.63*** (0) -14.04*** (7) 0.46* (9) *** -13.54 Y0607, I0607 -0.02 -2.53 (2) -3.58 Y08, I08 0.19 2.11 (0) 2.11 *** (15) (6) -0.45 -1.12 (15) *** 0.07 -0.05 (15) (2) F08, TF08 Y07, I07 *** (13) KPSS (Lag NW) (0) *** *** (14) PP Ztµ (Lag NW) -12.52 *** (7) 0.50 ** (8) (8) 0.59 ** (11) (5) 1.08*** (7) (12) *, **, and *** stand for rejection at the 10, 5, and per cent levels For the ADF and PP tests, the null hypothesis is the existence of a unit root; for the KPSS test, the null hypothesis is a stationary series All unit root and stationarity tests assume an intercept and no linear trend For the ADF test, the estimated intercept is also shown 25 Table 4: Short-term dynamics of equilibrium errors Period 12/05 - 11/06 δ1 δ2 θ2 t-stat (θ2 = -1) Speed of adjustment Trace r=0 Trace r