Price Formation in the European Emission Trading System:
the Effect of Uncertainty on the Forward Premium
12/06/2019
Abstract:
This paper investigates the price formation in the forward market of the European Emission Trading System (EU ETS). The forward price can be divided into two parts; the expected spot price and a forward premium. By using a time series regression analysis, the expected spot price is linearly predicted. Subtracting this expected spot price from the forward price provides the ex-ante forward premium. As a robustness check, also a ‘naïve’ forward premium is calculated by subtracting the current spot price from the forward price. This paper finds evidence of positive forward premiums in the EU ETS market. This forward premium is increasing when the spot price volatility increases (0.356 and 0.923 euro per unit volatility increase for the two- and three-year forward premiums respectively). It can be concluded that companies that expect a permit deficit are willing to pay a premium in order to insure themselves against undesirable price fluctuations. Besides, this study finds that the price stabilizing measure by the European Commission led to increasing spot price volatility by 0.510 on average after 2018.
JEL Classification: Q4, G13, C1, C22
Keywords: Emissions trading, Derivative instruments, Price volatility, Forward premium
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1. Introduction
In 2005, the European Union (EU) started the largest greenhouse emission trading scheme of the world, known as the European Union Emission Trading System (EU ETS) (Ellerman and Buchner, 2007). The EU ETS is a cap-and-trade system, in which the government allocates greenhouse gas permits by auctioning or providing them for free. This is known as the primary market. In the secondary market, these greenhouse gas permits can be traded. The subsequent supply and demand of these permits determine the price for the allowances. When companies fail to submit enough permits at the end of the year, they will receive a fine. As these permits can be traded freely on the secondary market, theory predicts that reduction of greenhouse gases happens at the most cost-efficient sector. 1
By establishing a market for permits, also derivative instruments for trading of greenhouse gas emissions have emerged (Madaleno and Pinho, 2011). As some companies need to buy price volatile permits in the market, they face price risk. Because this uncertainty exists in the market, companies can hedge this risk by using derivative instruments. One of these instruments is a forward contract. A forward price locks in the price for buying a contract at a specified predetermined period. Standard finance theory assumes that the forward price can be both higher and lower compared to the spot price, depending on whether the buyer or seller of the contract has the higher preference to hedge price risk. The difference between the expected spot and forward price is called the forward premium (discount).
As the expected spot price is argued to be non-observable, the ex-post spot price is used in previous literature. Many studies found positive (ex-post) forward premia when investigating the emissions trading market. As this research method is rather simplistic and non-realistic, this paper will try to investigate to estimate the expected spot price and use this as a proxy in order to examine the ex-ante forward premium. Because the rationale of investors can be seen as expectations about the future spot price, and one cannot look into the investors’ minds, the expected spot price will be predicted by linear regression. Therefore, the first part of this paper will investigate the main drivers of the EU ETS spot price.
After estimating and predicting the expected spot price, the results will be used in order to calculate the forward price as a function of the expected spot price and uncertainty. Volatility can be seen as a proxy for uncertainty, and it is predicted that higher price uncertainty leads to
1 The term ‘greenhouse gases’ is a collective name for carbon dioxide (CO
2), nitrous oxide (N2O), and
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higher willingness to hedge. This means that spot price volatility is one of the drivers of the forward prices (Kettner et al., 2011).
Since the introduction of the EU ETS, many changes occurred in both the price levels and volatility of the emission spot and forward prices. The European commission took some measures in order to ensure price stability in the market. The most important changes of, and impacts on the EU ETS will be examined to determine the volatility and its influence on the forward premium. This could prove whether the price stabilizing measurements have been successful. This leads to the following two research questions;
The first research question to be investigated will be: “What are the main drivers of the EU ETS Spot price?‘’ The results of this first analysis will be used to predict the expected spot price in one year, is used in the second research question: ‘’What is the effect of spot price uncertainty on the forward premium in the EU ETS?’’ Both questions will be answered using daily data analysis over the period 2013 to 2019. To our knowledge, this paper will be the first one to investigate the ex-ante forward premium. Besides, to our knowledge, this time period has not been analyzed in the literature before.
The most important results from this paper are the availability to predict approximately 54% of the EU ETS spot price with 4 fundamental drivers being conventional energy sources and the European production and equity index. Besides, the increase of uncertainty in the EU ETS spot market leads to higher forward premiums for the two- and three-year contracts (0.356 and 0.923 euro per unit increase in the average spot price volatility of the last 10 trading days). Moreover, the spot price stabilizing of the European commission have not proven to stabilize the prices yet. The spot price volatility has proven to be approximately 0.510 higher after the policy reform.
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2. Emissions trading
This section explains the most important concepts of emissions trading. First of all, some general information will be provided about the European emission trading scheme. Besides this, some general information about the spot and forward market for emissions permits is provided.
2.1 The European emission trading system
A cap-and-trade system is a climate policy invented in order to reduce greenhouse gas pollution together environmentally and economically. Within a cap-and-trade system, companies can receive or buy permits to obtain the legal right to pollute greenhouse gases. A ‘cap’ is set by a government by issuing a fixed number of permits per year, which implies a maximum amount of greenhouse gases to be polluted into the atmosphere. The issuance of permits can be seen as the ‘primary market’. One part of the permits are allocated for free; the others are sold via auctioning. The number of permits issued, decreases each year. ‘Trade’ occurs because within the set cap, companies can freely sell their emission permits on the secondary market. Companies that pollute more greenhouse gases than their permits allow will be penalized. The EU ETS is a cap-and-trade system.2 The European Commission sets a boundary level on the maximum amount of greenhouse gases emitted. The tradable contract permits companies to pollute 1 ton of CO2 into the atmosphere during specified period and is called a European Union
Allowance (EUA). When a company does not utilize all its permits (by reducing emissions) it can keep the permits for a future period to utilize, or sell it to another company which faces a shortage of permits. Every year, companies need to send a report stating the number of emissions they have polluted. This report will be verified by an accreditor. A company that fails to submit enough permits at the end of the year will be fined substantially (€100 per ton CO2).
In theory, reductions of greenhouse gases arise at the most cost-efficient sector to do so. This is because the allowances can be traded freely on the market, due to high flexibility of trading, low transaction costs and sufficient competition.
Currently, the system runs in thirty-one countries, being all EU countries, Norway, Lichtenstein, and Iceland. For some specific sectors like the power and heat industry, the EU ETS participation is obligated. For some other sectors, only the largest polluters have
2 The following paragraph is mainly based on the information given in the handbook from the
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compulsory participation in the system. Specific details of the EU ETS can be found at the handbook of the European Commission (European Commission, 2015).
The transitionary process of the EU ETS knows multiple phases. The first phase, running from 2005-2007 was the startup period where the pricing and actual monitoring of greenhouse gases are investigated carefully. Companies were allowed to use their allowances in subsequent years, but after this period the allowances expired. The second phase 2008-2012 is almost equal to the first one, however it had some slight improvements. Besides this, allowances received in the second phase could be carried over to the third phase, this is called ‘banking’. The third period, in which we are recently in, runs for the period 2013-2020 and had again some slight improvements (Bredin and Parsons 2016). Moreover, the European Commission took some measures in order to be able to control prices (section 3 will elaborate on this). The Fourth phase will start in 2021 and will last until 2030. It might be possible that these phases are not bound to a future time bound and will last open-endedly (European Commission, 2015).
2.2 The spot market
In the secondary market, companies can trade EUAs. When the transaction and settlement of cash for a contract happens real time, one refers to as ‘spot trading’. Three of the exchanges where EUAs can be bought directly are the European Energy Exchange (EEX), Intercontinental Exchange (ICE), and BlueNext (European Commission, 2015; Madaleno and Pinho, 2011). The latter is the largest exchange market for emissions allowances. On trading days (Monday to Friday) companies or investors can trade contracts with a minimum of 1000 ton of CO2
equivalents. The price at which the contract can be bought immediately is therefore called the EUA spot price.
2.3 Forward and futures trading
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insure against price movements, or to speculate and earn money from price volatility. Futures can be traded at a futures exchange while forwards are sold over-the-counter (Hull 2003). Like at other commodity markets, a futures contract for emission rights is also a standardized contract. EUA forwards are non-standardized and are traded bilaterally (for example between a company and a bank). Subsequently, the bank secures its price risk with a futures contract bought at the exchange market. One trades EUA futures at the exact same market places as the spot contracts. One futures or forward contract includes 1000 EUA emission allowances, and again one emission allowance contract corresponds to 1 ton of CO2 emission equivalents.
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3. Literature
This section explains the most important economic and finance theory of the emissions trading market. First, the price formation of the EU ETS is explained. Secondly, the financing theory of the relationship between spot and futures prices and the phenomenon of risk premia is elaborated on. The last part of the literature will investigate the most important literature of risk premia in energy commodity trading, and more specifically in the emission markets.
3.1 Price formation EU ETS
As explained in public finance theory, greenhouse gases can be regarded as a public good (because it is a negative phenomenon, it can be regarded as a public bad). Without regulation, one could emit CO2 and affect others without extra costs for doing so. This is known as the term
‘negative externality’. Public goods have the characteristic to be over-utilized when it is not coordinated by a regulator (Seo, 2013). This is why several types of greenhouse gas reduction policies have been seen in the past. One type of policy reduce greenhouse gases is a so-called carbon tax. This is an additional payment on every carbon containing fuel used (Hoeller and Wallin, 1991). The European Union has chosen for a cap-and-trade policy as regulating mechanism to control greenhouse gas emissions. Without regulation, no one would have an economic incentive to reduce greenhouse gases themselves (Hammond, 2009). Both taxations and the cap-and-trade emission system are introduced to reach the socially desirable amount of emission reduction. This amount can be found at the intersection between marginal costs and marginal benefits to additional reduction of greenhouse gases. The intersection between supply and demand give the optimal price and quantity levels. When using a tax policy, a fixed price is set, while the quantity is flexible. Under the EU ETS the quantity is fixed while the price is allowed to fluctuate (Mason, 2009). A fixed boundary level is set for the maximum amount of greenhouse gases emitted participants of the system. As explained in the introduction, participation in the EU ETS is mandatory for a specified spectrum of installations.3 The maximum amount of greenhouse gas permits can be seen as the (vertical) supply curve in the market. Within the boundary of this cap, the European Commission allocates allowances freely towards companies, or companies can buy these allowances in the primary market from the European commission via auctioning. This willingness to pay determines the (downward sloping) demand curve of the cap-and-trade system. The intersection of supply and demand
3 Specific details about sectors and emission types of greenhouse gases can be found in the handbook
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provides the equilibrium price. Figure 1 provides a visual representation of the supply and demand curve in a cap-and-trade system in the primary market.
Afterwards, these allowances can be traded freely on the secondary market. A company with a surplus of allowances may choose to sell permits when the marginal abatement costs are lower than the price received when selling a contract. Other companies are willing to pay for these contracts when their marginal abatement costs are higher than the cost of buying a contract. Besides this, companies with a permit deficit will have to buy allowances on the secondary market in order to avoid a fine. For example, if a company has marginal abatement costs of reducing one ton of CO2 by itself for 50 euro, the company would be indifferent between paying
50 euro for a contract or reducing the emissions themselves. Since different companies have different marginal costs to reduce emissions, the demand curve is downward sloping, starting with the company with the highest costs of reducing emissions themselves (highest willingness to pay), to the lowest. The reasoning for the supply curve is the exact opposite. If a company
Figure 1: Cap-and-trade price formation EU ETS (primary market)
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has marginal benefits of 50 euro by emitting one ton of CO2 more, this company would be
indifferent between selling one contract for 50 euro or emitting one ton of CO2 themselves.
Again, because of a difference in marginal benefits of emitting carbon between companies, this leads to an upward sloping supply curve, starting with a company with the lowest marginal benefits of producing themselves (highest willingness to sell), to the highest. This means that the supply and demand curves are exact opposites, because the same companies are ought to be in the same market, and the marginal costs of reducing carbon are assumed to be equal to the marginal benefits of emitting one extra unit of carbon (Bockel et al., 2012). The price in the secondary market is obviously the equilibrium between supply and demand. A graphical representation can be seen in figure 2.
3.1.1 Factors influencing the EUA price
As the law of one price assumes, the price for emission permits is assumed to be equal in both the primary and secondary market. Many studies have investigated the price formation in the EU ETS. A thorough investigation on the literature of EUA price and market behavior can be found in Hintermann et al. (2016). Several factors have proven to influence the price of the emission allowances. The factors influencing the price can be categorized in two different
Figure 2: Secondary market EU ETS
P
ri
ce
Supply curve
Demand curve Marginal benefits and costs of the 'higher' cost company
Emissions
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groups. One regards the production factors of emissions directly or indirectly influencing the supply and demand of CO2 permits. The other one regards regulatory/political driven
uncertainty (Benz and Trück, 2009; Burtraw, 1996). The factors affecting emission directly are explained thoroughly in Feng et al. (2011). They investigated EU ETS market in the period 2005-2008. They find evidence of four different influences on the spot price of carbon. These four factors are temperature, allowances, energy prices and special events. Since a large amount of permit holders are in the heat and electricity sector, the direct demand for emissions is driven by seasonality. They use the example that when temperature is low, the demand for energy is higher, leading to more coal fired power plants to run. This in turn leads to a higher demand for emission permits. The allowances factor is closely related to the stringency of the cap. Simply because of a larger supply of emission permits, the price drops. The prices of conventional power plant fuels also affect the demand for carbon permits. Because the prices of coal and gas fluctuate, energy producers face a tradeoff when to supply to the market. When the prices of conventional fuels are low, one would expect lower marginal costs of conventional production, hence a higher demand for emission permits. The last impact on the price of carbon emissions is the special events factor. In the paper of Feng (2011), the financial crisis is used as an example. In 2008, one can see a significant drop in the price for emissions. This can be explained by an overall lower production level in the economy. A lot of surplus allowances were sold in the market, leading to a substantial drop in prices. These factors influencing prices are also found in Kettner et al. (2011). Both the direct and indirect factors influencing the EUA spot price lead to expectations of a future spot price level and its consequential uncertainty. 3.1.2 Factors influencing the EUA price volatility
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the quantity of greenhouse gases, they lose the opportunity to control prices leading to price volatility (Murray, 2009).
3.1.3 EUA Spot price stabilizing measurements
The European Commission took several measures in order to be able to control the prices. These were short- and long-term measures.4 The short-term measurement is known as ‘back-loading’. The European Commission postponed the auctioning of 900 EUAs in the period 2014 to 2016. As these contracts were postponed, they were planned to be auctioned again in the 2019-2020 period. It is assumed to rebalance supply and demand in the short-run, and to decrease price volatility. The long-term measurement is known as the market stability reserve and started at the beginning of 2019. The 900 unauctioned, plus the unallocated EUA contracts are added to a reserve. This strategic reserve restricts the total number of allowances in circulation (TNAC) to stay within certain boundaries. In short, when the TNAC drop below 400 million, the European Commission releases contracts from the reserve. When the TNAC is above the 833 million threshold boundary, the European Commission adds permits to the strategic reserve. When the TNAC is in-between these numbers, the European Commission does not intervene. By having this intervention mechanism, the European Commission can react to undesirable shocks in either supply or demand. This may consecutively lead to higher price stability and hence lower price volatility.
3.2 Relationship spot and futures prices
The previous paragraphs investigate the price formation and factors influencing this process in the spot market. This paragraph elaborates on the generic finance theory how the spot and futures price are related. The most standard and non-controversial finance theory states that the futures price should be equivalent to the benefits and costs of holding an asset until maturity. When holding an asset, one will face opportunity costs and benefits with respect to holding a futures contract. It should be noted that holding a commodity means one has invested the money in the asset and takes care of the physical storage. By holding the asset, the first opportunity cost is the foregone interest rate of owning money. Besides this, one would have storage costs of physical storage of the commodity. On the other hand, owning the commodity might have some value. This is known as the convenience yield. The futures price can mathematically be
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related to the spot price by discounting.5 At the delivery date, the futures price should converge
to the spot price. The convergence rate (or discount rate) at which this happens is the cost of carry (Hull 2003). This is the combination of the foregone interest rate, costs of storage, and the convenience yield. Ignoring dividends, this means the following relationship between futures prices and the spot price: 6
𝐹𝑡 = 𝑆𝑡𝑒(𝑟+𝑢−𝑦)(𝑇−𝑡) (1)
Where r is the risk-free rate (opportunity cost of money), u denotes storage cost and y is the convenience yield (this is the additional welfare of having a commodity now, rather than in a future period). F and S are the futures and spot price respectively. Capital T and lower-case t denote the delivery date and time respectively. Equation (1) must always hold, otherwise there is an arbitrage opportunity. This would imply that an investor could make excess returns without running additional risk. Theory assumes that when holding a futures contract (commodity) is economically more advantageous, demand for futures (commodities) will increase, implying the futures price (spot price) must increase. It has widely been debated whether the non-arbitrage condition between spot and futures prices holds for any type of commodity. Bessembinder and Lemmon (2002) find statistically significant evidence that the arbitrage opportunity as explained in equation (1) does not hold in the electricity market, because it is a non-storable good. Uhrig-Homburg and Wagner (2008) conclude that the cost-of-carry relationship does not hold between the first two phases of the EU ETS. This is mainly explained because no banking was possible between these periods. Also, Chevallier et al. (2009) argue that equation (1) does not hold, because changes in expectations led to different price patterns between spot and future prices. Because the non-arbitrage condition is violated, the cost-of-carry relationship may not be the best approach to investigate the relationship between spot and futures prices in the market for greenhouse gas permits. This gives rise to another relationship between spot and the forward market, where the futures price is a combination of the expected spot price plus an additional payment or discount. This additional term is known as the forward premium or discount. The following section elaborates on this theory.
5 Discounting corrects for the time value of money, under normal circumstances one dollar today
worth more than one dollar in the future.
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Keynes (1930), argues that the relationship between the spot and forward market is explained by expectations about the future spot price and its corresponding uncertainty. The futures price is assumed to be a combination of the expected spot price plus an additional premium or discount. This gives the following relationship:
𝐹𝑇,𝑡= 𝐸𝑡(𝑆𝑇 | 𝛿𝑡) + 𝜇𝑡 (2)
At time t, the expected spot price for time T is conditional on all available information (𝛿𝑡) in the market. The forward price is set ex-ante. The risk premium or discount is denoted by the parameter μt and can be both positive and negative.
It is extensively debated whether this risk premium should be positive or negative. According to Keynes (1930), commodity markets follow a pattern of normal backwardation. This means that the futures prices should be lower than the expected spot price in the future. He argues that any commodity producer wants to insure itself against undesirable price drops. By protecting against the downside potential of losing money, the producer of a commodity is called a hedger. The buyer of the futures contract is referred to the term speculator. By shifting the price risk from hedger to speculator, the latter demands a reward for the additional risk taken. The speculator’s profit for bearing the additional risk is the risk premium. At the quotation date, the risk premium can be found by equation (2). It is assumed that the price risk decreases when time gets closer to the maturity date, hence the risk premium (forward discount) reduces as well. This means that the futures price will increase over time, in order to converge to the spot rate at time T (Hull, 2003).
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Cootner (1960) extends the findings of Keynes and finds both evidence for contango and backwardation. He explains the phenomenon of contango from a commodity buyer’s perspective. Instead of an undesirable price drop, a buyer might want to insure itself against an undesirable price increase. By protecting against the downside risk of increasing prices (this is downside risk because the buyer needs to pay this price), the buyer of a product becomes the hedger. Again, by shifting risk between parties an additional risk reward is expected for the one bearing the risk, this is the forward premium.
It can be concluded that the sign of the risk premium is ambiguous because the price risk is different in diverse commodity markets. Also, the risk preferences may differ between buyer and seller in different commodity markets. A seller (buyer) of a commodity loses from price declines (increases). The upward potential and downside risk of price volatility are for both parties the same. It can be argued however that the ‘most risk-averse’ party will become the hedger. Since the hedger insures against the potential losses, he is the one paying the premium. This leads to either futures trading in backwardation, contango or a varying sign of the risk premium (meaning the market can change from backwardation to contango and vice versa). 3.4 Literature on energy commodity markets
Many studies have examined the relationship between spot and future prices in financial markets. However, according to Madaleno and Pinho (2011), the market for greenhouse gas
Figure 3: Relationship spot and futures prices w.r.t. time-to-maturity
Time
P
ri
ce
Today Maturity
Expected future spot price Futures price in contango
Futures price in backwardation
Forward premium (risk discount)
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allowances differ at some aspects. Theory assumes that CO2 emissions reduction happen at the
most cost-efficient sector, as explained in section 2. This means that some companies will innovate, while others have to buy licenses. Once a company has a surplus of contracts, they can be sold to other producers who have an emission permit deficit. In standard financial markets, derivative instruments are either used to hedge against risk or to speculate. Emission allowances can be held to reduce future cost levels due to possible production changes and/or scarcity of permits in future periods. As explained in the previous paragraph, the welfare of having a commodity in stock is known as the convenience yield and is applicable for commodities like oil and gas (Hull, 2003). Because equation (1) has to hold, a higher convenience yield would lead to a lower futures price, as one would rather have the product now than in a future period. Ceteris paribus, one expects a lower forward premium when the convenience yield increases, when looking at equation (2). This means that when the cost-of-carry relationship holds, it is strongly related to the forward premium.
The relationship between spot and forward prices in the energy commodities markets like electricity, gas and oil is examined thoroughly in previous studies. Using empirical analysis, Bunn and Chen (2013) examined the realized spot and futures prices and found the ex-post forward premium. This was simply done by subtracting Ft,T with ST, where Ft,T and ST are
respectively the forward price and spot price realized at time T, and t denotes the quotation date. Evidence was found for fluctuating risk premia in the monthly British futures market of electricity. They discovered evidence of mean reversals, most probably to seasonal changes of demand for electricity. In a study by Pindyck (2001), futures prices in the oil market are examined. In this market, evidence of backwardation is found. According to economic theory, the main driver of backwardation is expected scarcity of a commodity in the spot market. This is evidence of a negative forward premium; hence it is a forward discount. Wei and Zhu (2006) investigate the convenience yield and the relationship with a risk premium in the natural gas market. They find significant evidence of a positive convenience yield, and that this yield is positively correlated with volatility of gas prices. Also, they find that the risk premium is related to the level and volatility of the spot prices in the US futures gas market.
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volatility of the stock price. Another study from Madaleno and Pinho (2011) finds similar results. Again, normal cantango is found. Besides this, they found results providing evidence of a positive relationship between the convenience yield and spot prices levels. A negative relationship is found with respect to the spot price volatility, however. More importantly, they find a positive relationship between the forward premium and the price volatility. This positive relationship between the spot price volatility and the forward premium is also found in Chevallier (2010). More uncertainty makes it relatively more attractive to hedge against price risk, hence the futures prices should increase. Interestingly, Madaleno and Pinho (2011) conclude that spot price levels, uncertainty and the convenience yield are not the only variables that influence the forward premium. They argue that the role of conventional fuels and seasonality may influence the risk premium in the market for emission permits. A study which investigated the convenience yield in the emissions trading markets is from Bredin and Parsons (2016). They find contradicting evidence regarding the relationship between the spot and futures price. In the first phase, a positive convenience yield is found, while in the second phase there was evidence of a negative implied convenience yield. This made futures contracts relatively cheap in the first period, while this was the opposite in the second period. One of the explanations regards the permit banking. When the contracts were expected to expire in 2007, afterwards these contracts’ value becomes zero. One would expect that companies rather held the permit now than in a future period. This can be in line with expected scarcity of emission permit in the first period found in the study of Borak et al. (2006). Like in the oil market example from Pindyck (2001), a positive convenience yield is found because of higher wealth when holding the asset immediately. This should lead to higher spot prices compared to futures prices. In line with Bredin and Parsons (2016), Trück, and Weron (2016) find a negative convenience yield for the second phase as well. Besides this, they also find a positive forward premium for the futures market. Seemingly, buyers are willing to pay a positive premium to insure themselves against the rise in prices.
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the contract in a following period, given that the storage costs are zero. A company with a permit deficit (buyer) does have this price risk, because this company will be fined substantially when it fails to submit enough permits. This means the buyer of a contract wants to hedge against these undesirable price fluctuations, hence it is logical there exists a forward premium. This reasoning also explains the negative sign for the first period of the EU ETS period from Bredin and Parsons (2016), because banking was impossible.
Study Market Forward premium (+) / discount (-)
Bunn and Chen (2013) Electricity + / -
Pindyck (2001) Oil -
Wei & Zhu (2006) Gas -
Borak et al. (2006) Emissions +
Madaleno & Pinho (2011) Emissions +
Bredin & Parsons (2016) Emissions + / -
Trück & Weron (2016) Emissions +
Chevallier (2010) Emissions +
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4. Theory
This section elaborates on the theoretical framework in order to formulate hypotheses and the expected relationships between several factors and the price formation in the spot and forward prices in the EU ETS. As the main research question tries to explain the drivers of the forward premium, the first part of this section will provide economic theory about the price formation in the forward market. Previous researchers have studied the ex-post forward premium, as it is argued that the expected spot price is unobservable. As this paper also investigates the price formation in the EU ETS, the second part of this section will explain the economic model in order to estimate the expected EUA spot price. This expected spot price will be used to determine the ex-ante forward premium.
4.1 Economic model explaining the forward price
As explained in section 3, the forward price can be seen as a relationship between the expected spot price and the forward premium. As the forward premium can be seen as a price for insuring against undesirable price changes, one can see the forward price as a function of the expected future spot price and uncertainty: 𝐹𝑇,𝑡 = 𝑓((𝐸𝑡(𝑆𝑇), 𝜔𝑡), where 𝜔𝑡 denotes uncertainty. The most important factor in explaining uncertainty will be the spot price volatility. Besides this, the stabilizing measurement of the European commission should affect the uncertainty in the market.
4.1.1 Spot price volatility
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Hypothesis 1: Spot price volatility has a positive impact on the (ex-ante) forward premium.
4.1.2 Spot price stabilizing measurements
By having a strategic reserve, the European Commission can immediately react to the balance of supply and demand. Basically, it can be seen as a market mechanism in order to determine the price for emission contracts. The European Commission is however restricted to use the reserves according to pre-determined rules. By having this strategic reserve however, there can be reacted to unexpected shocks in demand. Because theoretically the price can be controlled, this should lead to more certainty in the market for EUAs, and subsequently less price volatility can be expected. This leads to the following hypothesis;
Hypothesis 2: Price stabilizing measurements decrease the spot price volatility (in absolute terms).
4.1.3 Expected EUA spot price
As the forward price is the price paid for a permit at some specified point in the future, one would want to know what the actual spot price is at that time in the future. As no one is able to predict the future, the actual spot price T in the future is unknown at time t. Therefore, investors make expectations about the future EUA spot price. Based on these expected spot prices, the forward prices are established through supply and demand. Companies are willing to pay the expected spot price plus an additional premium, in order to hedge against price fluctuations. It is argued however that the expected spot price is also an unobserved phenomenon, as people cannot read minds of the investors. This paper however tries to estimate the drivers of the EUA spot price and subsequently forecast the future spot price. The forecast of the future spot price can be seen as a proxy for the expected spot price. The economic model explaining the EUA spot price will be provided in the next paragraph.
4.2 Economic model of the (expected) EUA spot price
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In the secondary market, a price establishes through equalizing supply and demand. Both the (quantity) supply and (quantity) demand curve are a function of the price in the market and (un)observed factors influencing the supply and demand. Given that the quantity is in equilibrium, the price can be seen as a function of observed (𝜗𝑑, 𝜗𝑠) and unobserved (𝜃𝑑, 𝜃𝑠)
factors influencing the supply and demand (Davis and Garcés, 2009) 𝐸𝑈𝐴 𝑃𝑟𝑖𝑐𝑒 = 𝑓(𝜗𝑑, 𝜗𝑠, 𝜃𝑑, 𝜃𝑠)
Where standard economic theory assumes that an increase (decrease) in the supply will decrease (increase) in the price, and an increase (decrease) in demand will lead to an increase (decrease) of price. The following section will elaborate on the drivers influencing the EUA spot price.
As multiple studies have investigated factors influencing emission permit prices, it can be argued that these emission price can be seen as a feedback mechanism in which all factors are linked and influence each other. Therefore, it can be argued that most of these factors are non-linear, as this makes it very complex to study the relationship with the EUA price. As in Creti et al. (2012) the choice for fundamental drivers will be factors influencing the production level of the energy sector. These factors will be the energy commodity prices; oil, coal and gas prices and the economic growth; the European production level, and a European stock market index. Temperature and seasonality are ignored as these variables are assumed to affect the EUA price indirectly hence the effect is already incorporated in the other variables.
4.2.1 Energy (input) prices
Many studies have found a relationship between the energy commodity prices and the price for emission permits. This paper includes three different input sources to affect the permit price market. These inputs are the oil, gas and coal price respectively. The oil price is used as a proxy for the energy prices and is assumed to have a positive relationship between the electricity price and subsequently the carbon emissions market.
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expects lower (higher) demand for emission permits, and vice versa for coal. The ratio gas/coal can be seen as the switching cost and is assumed to have a positive relationship with the demand for emission permits, and subsequently the EUA spot price. This leads to the following hypotheses:
Hypothesis 3: The oil price has a positive relationship with the EU ETS spot price. Hypothesis 4: The switching price has a positive relationship with the EU ETS spot price.
4.2.2 European growth level
Various authors have used different proxies for the European growth level to investigate the price for EU ETS contracts. Both the total production level and the stock price equity index measure economic activity in the European sector. The European growth level affects the production level of the energy sector immediately. As higher overall demand due to a flourishing economy leads to more production in the European sector, also the demand for emission permits increases. As this factor has a positive relationship with emission permit demand, we expect a positive relationship between economic growth and the EUA spot price. Whereas the current production level immediately affects the EU ETS spot price, the European equity index affects the EU ETS spot prices by making expectations of the future economic growth. This prediction is incorporated in the European equity index and can therefore explain the EU ETS spot price indirectly. This leads to the following hypotheses:
Hypothesis 5: The European production index level has a positive relationship with the EU ETS spot price level.
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5. Data & methodology
The data used for econometrical analysis is outlined in this section and is subdivided into two parts. The first part gives explanation about the data used for the determination of the expected EU ETS spot price. The second part focuses on the risk premiums and the spot price volatility.
5.1 EU ETS spot price dataset
The dataset for determining the EU ETS spot price contains daily observations from the period January 2013 till April 2019. At some points in time, there was some lack of data availability. Besides this, it is corrected for outliers. This means that the dataset contains some gaps. The dataset is conveniently large enough so this should not lead to problems. An informative summary of the variables and the descriptive statistics are provided in table 2 and 3 respectively.
Variable Specification Source
EUA spot price (€/CO2) EU ETS spot contracts Bloomberg
Gas price (€/MWh) German day-ahead forward contracts Bloomberg Coal price (€/MWh) API 2 Argus/McCloskey index 1-month forward contracts Bloomberg Oil price ($/Barrel) Brent crude oil 1-month futures price Bloomberg Production level (%) Monthly index of European production level 01/2013=100 Eurostat
Euro Stoxx 50 index Daily Euro Stoxx 50 index Bloomberg
Variable Mean Min Max SD N
EUA spot price (€/CO2) 8.23 2.72 27.24 5.32 1637
Gas price (€/MWh) 20.40 11.00 44.60 4.70 1595
Coal price (€/MWh) 7.66 4.63 10.90 1.46 1344
Oil price ($/Barrel) 59.03 25.52 89.03 15.79 1620
Production level (%) 107.27 100 115.07 4.49 1589
Euro Stoxx 50 index 3212.66 2511.83 3828.78 283.91 1614
Table 2: Summary specification of the variables and its corresponding source
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The data of the EUA spot price is taken from Bloomberg. By looking at historical data, one can immediately observe sizable differences in both spot price levels and volatility (figure 4). While in 2013 the initial price started at approximately 6.50 euro, the price fluctuated and increased slowly towards approximately 8.50 euro. In 2016, the price dropped again towards 4 euro per contract, while in 2018, the price rose sharply to more than 25 euro.
The spot price will be tried to be explained by a mix of conventional fuel prices and the European production and stocks level index. All three conventional energy sources data come from Bloomberg. The oil price is denoted by the Brent one-month futures contract. This contract is more liquid than the spot market for oil. The price is given in US dollars per barrel. Although this data could be transformed to euros per megawatt hour, at a later stage when predicting the EUA spot price, also the price in US Dollar per barrel is used. A graphical representation can be seen in figure 5.
Figure 4:EU ETS spot contracts, 01-01-2013 – 16-04-2019, source: Bloomberg 0 5 10 15 20 25 30 1-1-2013 1-1-2014 1-1-2015 1-1-2016 1-1-2017 1-1-2018 1-1-2019 P rice (€ / CO 2 ) Date 0 20 40 60 80 100 1-1-2013 1-1-2014 1-1-2015 1-1-2016 1-1-2017 1-1-2018 1-1-2019 P rice ($ /B ar rel) Date
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The gas price is denoted by German the day-ahead forward price and is denoted in euros per megawatt hour. The German market is chosen because the gas prices in Europe follow the same pattern, and Germany has most probably the most mature market, hence it is a reliable source to proxy the gas price. The coal price is taken from the API2 Argus/McCloskey index and the one-month forward contract is used. The one-month market is more liquid than the spot market for coal. Also, this market can be seen as the primary coal price for the European Union. The price is converted from euro per metric ton to euro per megawatt hour. A graphical representation can be seen in figure 6.
The gas and coal price are used to calculate the switching costs such that the marginal abatement costs between high emitting (coal) and low emitting energy (gas) producers are equal (Creti et al. 2012). The switching price will be calculated by dividing the gas price by the coal price: 𝑆𝑤𝑖𝑡𝑐ℎ =𝐶𝑜𝑎𝑙𝑝𝑟𝑖𝑐𝑒𝐺𝑎𝑠𝑝𝑟𝑖𝑐𝑒.
The production level is denoted by monthly index of production in the European Union and comes from the Eurostat database. This time series is seasonal and calendar adjusted. The production consists of mining and quarrying; manufacturing; electricity, gas, steam and air conditioning supply (except food, beverages and tobacco). The base point (100) is set at January 2013, because this is the starting point of the time series. Coincidentally, this is the lowest production level of the whole times series. Over time, the production of the European Union has gradually increased over time. Since this variable is only available at a monthly basis, the data is transferred to daily data by cubic spline interpolation between these months like in Bredin and Muckley (2011). A visual representation can be seen in figure 7.
0 10 20 30 40 50 1-1-2013 1-1-2014 1-1-2015 1-1-2016 1-1-2017 1-1-2018 1-1-2019 P rice (€ / M W h) Date Gasprice Coalprice
Figure 6: German day-ahead forward gas & Argus/McCloskey 1-month forward coal contracts,
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As a proxy for the economic conditions in the European market the European Stoxx 50 index will be used. This index contains an index of the 50 most important equity stocks in the European Union. The data is collected via Bloomberg and a graphical representation can be found in figure 8.
5.2 EU ETS expected spot price methodology
Instead of using the realized spot prices as a proxy for the expected spot price 𝐸𝑡(𝑆𝑇 | 𝛿𝑡), the expected EU ETS spot price will be estimated using fully modified ordinary least squares (FM-OLS) regression as done before in Creti et al. (2012). The following regression will be estimated, where all variables are log-transformed:
𝑆𝑝𝑜𝑡 𝑝𝑟𝑖𝑐𝑒 𝐸𝑈 𝐸𝑇𝑆𝑡 = 𝛽0 + 𝛽1 𝐸𝑢𝑟𝑜𝑝𝑒𝑎𝑛 𝑀𝑎𝑟𝑘𝑒𝑡 𝐼𝑛𝑑𝑒𝑥𝑡+
𝛽2 𝐸𝑢𝑟𝑜𝑝𝑒𝑎𝑛 𝑆𝑡𝑜𝑐𝑘 𝑖𝑛𝑑𝑒𝑥𝑡 + 𝛽3 𝑆𝑤𝑖𝑡𝑐ℎ𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒𝑡+ 𝛽4 𝑂𝑖𝑙 𝑝𝑟𝑖𝑐𝑒𝑡+ ε𝑡 (4)
Figure 7: European Union production index, 01-01-2013 – 01-02-2019, source: Eurostat
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In order to quantify the determinants of the EU ETS spot price, an econometric model is specified in which the variables are seeming to have a cointegrating relationship. The correlation matrix of the variables can be found in table A.1 in the appendix. As the previous paragraph suggests, the time series used in the regression analysis are likely to be non-stationary. Although the graphical representations of these series seem to have a unit root, this needs to be tested. This will be done by the Augmented-Dickey-Fuller (ADF) test. The null hypothesis states that the data contains a unit root (non-stationarity) while the alternative hypothesis rejects a unit root in the time series (Dickey and Fuller, 1979). The results can be found in table A.2 in the appendix.
The statistical test for a unit root confirms integration of order one for every variable except the European equity stock index. To test for cointegration between the variables, we conduct an Engle-Granger (1979) test with a null hypothesis of no cointegration. The alternative hypothesis states that there is long-term cointegration between the variables. The results can be found in appendix table A.3. This test rejects the null hypothesis at the 1% significant level. As the independent variables are assumed to be cointegrating, a long-term equilibrium between the EUA spot price and the independent variables is possible.
As non-stationary variables lead to spurious regression and unreliable results, some transformation to the model should be done. One solution to overcome the non-stationary problem is to take first differences. Although regressing first differences may investigate the drivers of the EUA spot price, predicting the expected spot price will be impossible. As this study wants to predict the expected spot price, another technique known as fully modified ordinary least squares (FM-OLS) will be used (Philips and Hansen, 1990). The FM-OLS is a semi-parametric modification in order to correct for the cointegration relationship between the (independent) variables. Therefore, the possible violation of endogeneity is already corrected for, hence this is not a problem in the model. As all unit-root variables exhibit serial correlation, the standard errors are calculated using the Newey-West (1987) covariance estimator to correct for serial correlation and heteroskedasticity as well. This will give consistent and non-biased estimators and standard errors. As a robustness check, another technique known as the dynamic ordinary least squares (DOLS) is done. The results of this regression are similar to the FM-OLS test. The results can be found in table A.4 of the appendix.
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price. The results can be found in table 4 below. The adjusted R-squared presents a value of 0.090, however the model is able to predict 60.5% of the spot price when linearly predicting the natural logarithm of the spot price on the actual spot price in logarithms. When transferring the natural logarithms back to levels, the model is able to explain approximately 54% of the variance. The graphical representation can be found in figure 9 below. One can see a high peak at the beginning of 2018. This can be explained by the high value of the switching price at the same date. Also, the model seems to predict the EU ETS spot price fairly well up to September 2017. Afterwards, the lines diverge quite a lot. This could be the consequence of the regulatory intervention by the European commission, which is not incorporated in the model.
Variable Estimate S.E. P-value
Constant -73.99*** 10.870 0.000
European Production Index 15.12*** 2.423 0.000
European Stock index -0.10 0.725 0.890
Oil price 0.76*** 0.218 0.001
Switching price 1.99*** 0.538 0.000
Observations 1276
Adjusted-R2 0.090
***, **, and * denote significance at the 1%, 5% and 10% level respectively.
Table 4: Results of the EU ETS FM-OLS Regression (S.E. Newey-West corrected), daily data 01-01-2013 – 16-04-2019 (Dependent variable: EU ETS Spot price)
0 5 10 15 20 25 30 35 1-1-2013 1-1-2014 1-1-2015 1-1-2016 1-1-2017 1-1-2018 1-1-2019 P rice (€ /C O2 ) Date
Realized EU ETS Spot price (levels) Predicted EU ETS spot price (levels)
Figure 9: Realized and predicted current EU ETS Spot prices by the FM-OLS regression, 01-01-2013 -
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Using the FM-OLS, this will give the following equilibrium relation between the input variables and the EU ETS spot price as provided in equation (5) below7:
𝐸𝑈 𝐸𝑇𝑆 𝑆𝑃𝑂𝑇̂ 𝑡= −73.99 + 15.12 ∗ 𝐸𝑢𝑟𝑜𝑝𝑒𝑎𝑛 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝐼𝑛𝑑𝑒𝑥𝑡− 0.10 ∗
𝐸𝑢𝑟𝑜𝑝𝑒𝑎𝑛 𝑆𝑡𝑜𝑐𝑘 𝑖𝑛𝑑𝑒𝑥𝑡 + 1.99 ∗ 𝑆𝑤𝑖𝑡𝑐ℎ𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒𝑡+ 0.76 ∗ 𝑂𝑖𝑙 𝑝𝑟𝑖𝑐𝑒𝑡+ ε𝑡 (5)
5.2.1 Prediction of the expected EU ETS spot price
As we cannot look into the head of the investors, we would like to simulate their predictions by this model. With the estimated regression as provided in equation (5), the expected spot price can be linearly predicted. This will give the forecasted (expected) spot price 𝑆̂𝑇,𝑡. As this model is able to explain approximately 54% of the current spot price in levels (appendix A.4), one should be able to predict the same percentage of the expected spot price by filling in the future price level. As one does not know the future price level, one could use predictions for the future price and index levels as a proxy. For the conventional energy sources, the one-year future or forward contract is used to form an expectation for the future price level. The underlying derivative is the same as previously. The only thing changing is the maturity to one year ahead. For the gas price and coal prices, the one-year forward contracts are used. Due to a lack of data availability, the December future contract is used as a proxy for the one-year ahead price for predicting the oil price. All data of the conventional energy sources is found on Bloomberg. For the Euro Stoxx 50 index level, the June forward contract is used. This data is found at investing.com. For the European production level, no such forward or future derivative instrument exists. Therefore, the expected production index level in one year should be predicted differently. Since the European Central Bank (ECB) makes quarterly predictions about the future growth level of the economy in one year, the best approximation of the future European production level in one year is the actual production level times the expected growth in one year. The expected growth levels are found at the website of the ECB. As these predicted growth levels are given every quarter, this data is transferred to daily data by cubic spline interpolation. The detailed information about the data is available upon request. By having predictions about the future price levels in one year, one can fill in these values in equation (5), to simulate the expected spot price in one year. The linear predictions of the expected EUA spot
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price is transferred back to levels by taking the exponent of the natural logarithm. The results can be found in figure 10 and 11 below (natural logarithms and levels respectively). Because there are some missing values in the predicting variables, the number of observations of the expected spot price is 836.
One can see that the expected spot price in one year follows the same pattern as the realized
spot price up and until 2015. From then, the expected spot price is predicted noticeably above the realized spot price. From June 2018, the expected spot price in one year drops drastically below the realized spot price.
0 0,5 1 1,5 2 2,5 3 3,5 1-1-2013 1-1-2014 1-1-2015 1-1-2016 1-1-2017 1-1-2018 1-1-2019 L N( P rice) ( €/C O2 ) Date
Current EUA spot price (Natural logarithms) Expected Spot price in one year (Natural logarithms)
Figure 10: Current EUA and expected EU ETS Spot prices in one year (natural logarithms), 01-01-2013 -
31-01-2019 (with gaps) 0 5 10 15 20 25 30 1-1-2013 1-1-2014 1-1-2015 1-1-2016 1-1-2017 1-1-2018 1-1-2019 P rice (€ /C O2 ) Date
Current EU ETS Spot price (levels) Expected EUA spot price in one year (levels)
Figure 11: Current EUA spot and expected EU ETS Spot prices in one year (levels), 01-01-2013 -
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5.3 EU ETS ex-ante forward premium and spot price volatility dataset
When subtracting the expected spot price at time t from the futures price at time t for the same maturity T, one can find the estimated ex-ante forward premium in equation (6).
𝐹𝑇,𝑡− 𝑆̂𝑇,𝑡= 𝜇̂ 𝑡 (6)
The results can be found in figure 12, 13 and 14 respectively.
The summary statistics of the ante forward premium can be found in table 5. The ex-ante forward premiums have a negative mean, which is not in line with our expectations. One
-15 -10 -5 0 5 10 15 1-1-2013 1-1-2014 1-1-2015 1-1-2016 1-1-2017 1-1-2018 1-1-2019 Fo rw ar d pr em iu m in € Date -15 -10 -5 0 5 10 15 1-1-2013 1-1-2014 1-1-2015 1-1-2016 1-1-2017 1-1-2018 1-1-2019 Fo rw ar d pr em iu m in € Date -15 -10 -5 0 5 10 15 1-1-2013 1-1-2014 1-1-2015 1-1-2016 1-1-2017 1-1-2018 1-1-2019 Fo rw ar d pr em iu m in € Date
Figure 12: Ex-ante forward premium one-year forward, 01-01-2013 - 31-01-2019
Figure 13: Ex-ante forward premium two-year forward, 01-01-2013 - 31-01-2019
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can see that the forward premium is mainly negative until June 2018. Afterwards the forward premium becomes mainly positive.
The spot price volatility is calculated by equation (7). First, the first difference of the log returns is squared to obtain the variance. By taking the square root, the standard deviation (volatility) is obtained. This provide us the daily percentage change of the EU ETS spot price and can be seen as a proxy for daily volatility.
𝜎𝑡= √(𝐿𝑁(𝐸𝑈 𝐸𝑇𝑆 𝑆𝑝𝑜𝑡 𝑝𝑟𝑖𝑐𝑒)𝑡− 𝐿𝑁(𝐸𝑈 𝐸𝑇𝑆 𝑆𝑝𝑜𝑡 𝑝𝑟𝑖𝑐𝑒)𝑡−1)2 (7)
One outlier with a standard deviation of 16 has been deleted from the dataset. As investors do not base their expectations on just one trading day, also the moving average of the last 10 trading days is calculated. The graphical representation can be seen in figure 15 and 15a respectively.
Obviously, the standard deviation is always positive. Noteworthy is the fact that the spot price volatility is fairly stable, however it has some peaks. Besides, the spot price volatility increases from June 2018 onwards. Also, the summary statistics can be found in table 5. The variable to be used in the regression analysis will be the moving average of the standard deviation, denoted by 𝜎̅ . 𝑡 0,00 0,50 1,00 1,50 2,00 2,50 2-1-2013 2-1-2014 2-1-2015 2-1-2016 2-1-2017 2-1-2018 2-1-2019 Stan d ar d d ev iatio n Date
Figure 15: Spot price volatility EU ETS, 01-01-2013 - 15-04-2019
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1-1-2013 1-1-2014 1-1-2015 1-1-2016 1-1-2017 1-1-2018 1-1-2019 Stan d ar d d ev iatio n ) Date
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5.3.1 EU ETS ‘naïve’ forward premium and spot price volatility dataset
Besides calculating the ex-ante forward premium, one could also use the current spot price at time t as proxy for the expected spot price. As the EU ETS spot price seems to be a random walk, the best prediction of the future value is its current value. This will provide us a rather ‘naïve’ forward premium. This is simply done by using the current EUA spot price and the forward contracts. The calculations are basically the same as calculating the ex-post forward premium, however one would use the realized spot price at time T and the ex-post futures price FT,T.. I prefer to call it ‘naïve’ forward premium, as the term ‘ex-post’ is not entirely correct and
could lead to confusion. One can see a graphical representation of the spot price and the one, two and three-year forward contracts in figure 16 respectively.
Variable Mean Min Max S.D. N
Ex-ante forward premium One-year forward -3.092 -11.127 10.866 3.937 670 Ex-ante forward premium Two-year forward -2.036 -10.934 11.536 4.460 190 Ex-ante forward premium Three-year forward -0.965 -10.934 11.822 4.972 132 Spot price volatility (𝜎𝑡) 0.174 0.000 2.020 0.237 1633 Spot price volatility 10-day moving average (𝜎̅ ) 0.173 𝑡 0.025 1.173 0.157 1623
0 5 10 15 20 25 30 1-1-2013 1-1-2014 1-1-2015 1-1-2016 1-1-2017 1-1-2018 1-1-2019 P rice (€ /C O2 ) Date
Spot price One-year forward Two-year forward Three-year forward
Figure 16: EUA spot price, one, two- and three-year forward contracts, 01-01-2013 -
17-04-2019, source: Bloomberg
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Although one cannot easily see the forward premia in figure 16, there is some difference between the spot price and the derivative instruments. The ‘naïve’ forward premium will be calculated by subtracting the current spot price from the forward price at time t (equation (8)).
𝐹𝑇,𝑡− (𝑆𝑡) = 𝜇𝑡 (8)
A graphical representation can be found in figure 17, 18 and 19 respectively.
Noteworthy is the fact that the forward premiums are fairly stable, however they increase at the beginning of 2018, continuing in 2019. The summary statistics can be found in table 6. Like expected, the average risk premium of the contracts is positive for all the three maturities (0.030, 0.176 and 0.320 euro) respectively. Besides this, one can see higher risk premiums for the two- and three-year forward contracts. This is logical because more uncertainty exists about future
-2,00 -1,00 0,00 1,00 2,00 1-1-2013 1-1-2014 1-1-2015 1-1-2016 1-1-2017 1-1-2018 1-1-2019 Fo rw ar d pr em iu m ( €) Date
Figure 17: ‘Naïve’ forward premium one-year forward, 01-01-2013 - 15-04-2019
-2,00 -1,00 0,00 1,00 2,00 1-1-2013 1-1-2014 1-1-2015 1-1-2016 1-1-2017 1-1-2018 1-1-2019 Fo rw ar d p rem iu m (€ ) Date
Figure 18: ‘Naïve’ forward premium two-year forward, 01-01-2013 - 15-04-2019 -1,00 0,00 1,00 2,00 1-1-2013 1-1-2014 1-1-2015 1-1-2016 1-1-2017 1-1-2018 1-1-2019 Fo rw ar d p rem iu m (€ ) Date
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price levels when the maturity is longer. A lack of data availability leads to less observations of the two- and three-year contract forward premiums.
5.4 Ex-ante forward premium and spot price volatility methodology
In order to investigate the effect of price uncertainty on the behavior of the ex-ante forward premium, standard OLS will be used. In the regression analysis, the dependent variable will be the ex-ante risk premium 𝜇̂, where i stands for the time to maturity of the forward contract (in 𝑡𝑖 years). The most important independent variable is the spot price volatility 𝜎̅ , and there will be 𝑡
controlled for the expected spot price level 𝑆̂𝑡. The variables are tested on a unit root. The results
of the ADF-test can be found in appendix table A.6. As the ADF test is not able to reject non-stationarity, the first differences will be taken of both the forward premium and the expected spot price. This will lead to the following time series OLS regression (equation (9)):
∆𝜇̂𝑡𝑖 = 𝛽0+ 𝛽1𝜎̅ + 𝛽𝑡 2∆𝑆̂𝑡+ 𝜀𝑡 (9)
Some additional econometrical tests on the distribution of the error term needs to be done to ensure consistency of the regression analysis parameters and corresponding standard errors. The model most probably does not violate the endogeneity problem, since any source of endogeneity is not likely to be present. There is tested for both serial correlation and heteroskedasticity. Both the Durbin-Watson and Breusch-Godfrey test fail to reject the null-hypothesis of first order serial correlation for the one- and two-year forward premiums. For the three-year premium, evidence of serial correlation is found (Breusch (1976); Durbin and Watson (1950). When conducting the White-test (White 1980), it rejects the null-hypothesis of
Variable Mean Min Max S.D. N
‘Naïve’ forward premium One-year forward 0.030 -1.370 1.510 0.188 1228 ‘Naïve’ forward premium Two-year forward 0.176 -0.670 1.380 0.257 362 ‘Naïve’ forward premium Three-year forward 0.320 0.960 1.720 0.352 237 Spot price volatility (𝜎𝑡) 0.174 0.000 2.020 0.237 1633 Spot price volatility 10-day moving average (𝜎̅ ) 𝑡 0.173 0.025 1.173 0.157 1623
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homoskedasticity at the one-percent significant level. Before inferencing the regression results, this problem(s) of unrestricted heteroskedasticity (and first-order serial correlation for the three-year premium) should be corrected for. The statistical tests can be found in appendix table A.7 and A.8.
5.4.1 ‘Naïve’ forward premium and spot price volatility model
Because the ex-ante forward premium has not been investigated in previous literature, as a robustness check, the effect of price uncertainty on the ‘naïve’ forward premium 𝜇𝑡 is investigated. The same OLS procedure will be used like in the previous paragraph. Again, there is tested for non-stationarity in the variables. The results can be found in table A.9 of the appendix. This will provide the following time series regression analysis (equation (10)):
𝜇𝑡𝑖 = 𝛽0+ 𝛽1𝜎̅𝑡+ 𝛽2∆𝑆𝑡+ 𝜀𝑡 (10) Again, there will be tested for violations of econometrical assumptions. In this case, both the null hypothesis of no first order autocorrelation and the null hypothesis of homoskedastic variance of the error terms are rejected at the one-percent significant level. The results of the statistical tests can be found in table A10 and A.11 of the appendix respectively. There will be corrected for both violations of econometrical assumptions when doing the regression analysis.
5.5 Spot price volatility and government interventions
As the European Commission took some measures in order to stabilize spot prices in the EU ETS market, it is interesting to know whether this has been successful. Although the short-term measures started in 2014, the long-term market stability reserve started in 2019. By having a dummy variable 𝐷𝑡 taking a value of 0 before the first of January 2019 and 1 afterwards, one can verify if the spot price volatility 𝜎𝑡 decreases because of the long-term market stability reserve by the European Commission. The control variables will be the daily changes of the fundamental drivers of the EU ETS spot price. All spot price driving variables are log transformed. This will lead to the following regression analysis:
𝜎𝑡= 𝛽0+ 𝛽1∆ 𝐸𝑢𝑟𝑜𝑝𝑒𝑎𝑛 𝑀𝑎𝑟𝑘𝑒𝑡 𝐼𝑛𝑑𝑒𝑥𝑡+ 𝛽2 ∆ 𝐸𝑢𝑟𝑜𝑝𝑒𝑎𝑛 𝑆𝑡𝑜𝑐𝑘 𝑖𝑛𝑑𝑒𝑥𝑡 +
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6. Results
The results of the regression analyses are presented in this section. The results will be used to answer the main research questions and provide evidence of whether to reject the previously stated hypotheses or not.
6.1 Ex-ante forward premium model results
To overcome the heteroskedasticity problem, OLS with robust standard errors is used for the one, two and three-year ex-ante forward premium regressions (White 1980). The results can be found in table 7 below.
Due to a lack of data availability, the number of observations is 38 and 36 for the two- and three-year premium models. Although the model is able to explain 21.0 – 38.2 percent of the variance in the ex-ante forward premium, the spot price volatility is not statistically significant for both the one- and three-year ex-ante forward premium. We conclude that the spot price volatility has no statistically significant effect on the ex-ante forward premium. In the two-year forward premium model, the parameter is significantly different from zero at the 10% level. As the model is denoted in first differences in levels, interpretation of the coefficients can be seen as the change at one point in time with respect to the next period. (i.e. if the volatility increases with 1 (in levels), it is expected that the risk premium decreases by 1.610 (in levels), ceteris paribus. This is the exact opposite from what we expected. In the ex-ante premium model, the change in the expected spot price can be seen as the main driver of the ex-ante forward premium. This parameter is significant in the one- two-and three-year forward premium model. Ceteris paribus, an increase of the expected spot price by 1 euro in levels leads to a decrease of the ex-ante one- two- and three- year forward premiums of 0.826, 0.877 and 1.230 euro in the next period respectively.
Variable 𝛽0 (constant) 𝛽1 (volatility) 𝛽2 (price change) R2 N
∆𝜇̂𝑡1 0.059 (0.045) -0.423 (0.325) -0.826***(0.109) 0.315 368 ∆𝜇̂𝑡2 0.323 (0.094) -1.610* (1.080) -0.877** (0.354) 0.210 38 ∆𝜇̂𝑡3 0.162** (0.073) -0.637 (0.454) -1.230*** (0.284) 0.382 36
37 6.2 ‘Naïve’ forward premium model results
For completeness, also regression analysis on the ‘naïve’ forward premium is done. To overcome the heteroskedasticity and first-order autocorrelation problem, The Prais-Winsten, (FGLS) regression analysis is done for the one-, two- and three-year ‘naïve’ forward premiums (Prais and Winsten 1954). The results can be found in table 8 below.
The model is able to explain approximately 22 to 31 percent of the variance in the ‘naïve’ forward premiums. More importantly, almost all variables are significant different from zero at either the five or one percent significance level. When no volatility exists or price change occurs, we can conclude that the forward premium is 0.042, 0.104 and 0.132 euro for the one-, two-, and three-year ‘naïve’ forward premiums respectively. This is in line with our expectations, because we expected the forward premium to be a positive number. Also, the constant is higher for the two-, and three- year premiums. The spot price volatility affects the forward premiums statistically significant for the two- and three-year premiums. For an increase of volatility by 1 (in levels), the forward premiums are expected to increase with 0.356 and 0.923-euro respectively, ceteris paribus. The effect on the one-year premium is not significantly different from zero. One can conclude that higher price uncertainty in the EU ETS spot market leads to higher risk premia. This result is in line with the expectation in hypothesis 1.
6.3 Spot price volatility and market stability reserve model results
To investigate the effect of the market stability reserve on the price stability of the EU ETS spot price, the Prais-Winsten FGLS regression analysis is used. The results can be found in table 9 below.
Variable 𝛽0 (constant) 𝛽1 (volatility) 𝛽2 (price change) R2 N
𝜇𝑡1 0.042*** (0.009) -0.073 (0.070) -0.269 ***(0.044) 0.228 1218 𝜇𝑡2 0.104*** (0.018) 0.356*** (0.124) -0.286 ***(0.092) 0.265 362 𝜇𝑡3 0.132*** (0.029) 0.923*** (0.180) -0.169** (0.090) 0.310 237
