Why is Spot Carbon so Cheap and Future Carbon so Dear? The Term Structure of Carbon Prices.

AuthorBredin, Don
PositionReport
  1. INTRODUCTION

    In January 2005 the European Union (EU) formally introduced the Emissions Trading Scheme (ETS), a multi-country cap and trade system for emissions of carbon dioxide (C[O.sub.2]). Under the system a fixed quantity of allowances for emissions are issued each year. Companies covered by the system must submit allowances to match their emissions. The allowances are initially distributed either directly to targeted companies, or sold in auctions. Allowances then trade freely in the secondary market. The system's Phase 1 (Pilot Phase) covered the years 2005 to 2007, while Phase 2 (Kyoto Phase) covered the years 2008 to 2012. (1) The system is now in Phase 3 covering the years 2013 to 2020. In Phase 1, companies were allowed to bank allowances from one year to the next, but all Phase 1 allowances expired at the end of the Phase. In Phase 2 companies were allowed to bank allowances for use in later years, and this banking can continue into Phase 3 and, potentially indefinitely. (2)

    It is the banking provision of the ETS that is central to our analysis. The only obvious cost of banking an allowance is the opportunity cost of money. Other commodities have costs of storage, but the cost of holding an allowance is nil; just the overhead involved in managing the electronic account. Other commodities have convenience yield associated with holding the physical good, which reflects the avoided cost of stock-outs or related benefits to the production process. It is hard to imagine a comparable source of convenience yield holding for a carbon allowance. Allowances are submitted annually by the 30th April, after the full inventory of the previous year's emissions is completed and reported by the 31st March. The company has plenty of time to source additional allowances that may be needed. Therefore, a casual analysis of the rules of the EU ETS would suggest that the term structure of carbon prices should be an exact duplicate of the term structure of interest rates, see Parsons et al. (2009). The data, however, contradict this theory.

    Spot carbon allowances were originally expensive relative to futures, but since late 2008 the situation reversed and spot carbon allowances have been persistently cheap relative to futures prices. That is, the return to holding a carbon allowance together with a short futures position was originally less than the interest rate, but since late 2008 has been much greater than the interest rate. This relationship holds all along the futures curve, with shorter maturity futures being cheap relative to longer maturity futures. The magnitudes are quite large. This dramatic shift coincides with the onset of the global financial crisis in late 2008 and the ongoing European banking crisis of 2010-2013. These events constrained leverage and placed a high premium on liquidity, which may explain the implied cost of carry and its volatility. Alternatively, it may reflect overlooked, but important facts about market expectations for the evolution of EU ETS rules related to the banking of allowances across years. Or, it may reflect a combination of these factors.

    There is a large empirical literature on the EU-ETS. Much of it focuses on the determinants of the level of the carbon price and on important events that precipitated major price changes. A number of studies have examined the relationship between spot and futures prices. These include Benz and Truck (2009), Borak et al. (2006), Uhrig-Homburg and Wagner (2009), Joyeux and Milunovich (2010), Chevallier (2010), Madalena and Pinho (2011) and Truck et al. (2012). The studies differ in how they treat the rupture in the relationship between the spot price in 2006-2007 and futures prices for delivery in 2008 and later. This rupture was a consequence of the seam between the two trading periods, where banking of allowances across years was not allowed. In some of these studies this rupture is the focus of the analysis, while in others it is included as part of the time series of the relationship between spot and futures. Our concern is the term structure when banking is allowed i.e., within Period 1 and from Period 2 onward. Consequently, we do not examine the term structure across this seam. Along this line, Uhrig-Homburg and Wagner (2009) document that carbon spot prices were expensive early in the first phase, although for the balance of the period they find long-run relationships consistent with the cost of carry model. Uhrig-Homburg and Wagner (2009), show that these results are even cleaner when looking at futures prices of different maturity.

    Joyeux and Milunovich (2010) take the analysis a step further and formally test whether the coefficient values in the cointegrating equation for spot and futures prices are consistent with the cost of carry model during the first phase. Using a joint hypothesis test the authors reject the null that the coefficient on the EUA spot price and the interest rate in the cost of carry futures price relationship simultaneously equal one. Truck et al. (2012) look at data extending into the beginning of the second phase and document that the relationship switched by mid- 2009, when their data ends, so that spot prices had by then become cheap relative to futures prices. They explore using a two-factor term structure model to capture the dynamics of the convenience yield and its relationship to the spot price. We extend these results out through 2014, including the remainder of Phase 2 and into Phase 3 and show that carbon spot prices remained cheap as do shorter maturity futures relative to longer maturity futures.

    We explore the use of the term structure model proposed by Nelson and Siegel (1987). The model is widely used by central banks to model interest rates, see Bank of International Settlements (2005) and European Central Bank (2008). One of the model's advantages is the reduction in the dimensionality of the data, see Diebold and Li (2006). In our case, there is little reduction in dimensionality. However, the model takes the raw time series data, which are defined by a constantly changing maturity and transforms it into a time series of parameters which are consistent through time. Both our term structure analysis and our individual contract analysis results, consistently point towards towards evidence counter to theory.

  2. SPOT AND FUTURES PRICE RELATIONS

    The theory of storage defines an arbitrage relationship between the current spot price and the current futures price for a commodity (see Brennan, 1958). Assume an investor purchases a commodity at the current spot price, [S.sub.t], planning to hold it over a window of time, [tau], to period T = t + [tau]. The investor pays the current cost of storage for window of time, [tau], [K.sub.t]([tau]) earns the current convenience yield for window of time [tau], [[PSI].sub.t]([tau]), and anticipates receiving the spot price at T, [S.sub.T] (see Pindyck, 2001). The payoff on this investment is:

    [S.sub.T] - [K.sub.t]([tau]) + [[PSI].sub.t]([tau])- [S.sub.t] (1)

    Since this payoff varies with the commodity spot price at T, [S.sub.T], it is risky. Assume now that the investor also sells short one futures contract for the commodity maturing at T, agreeing to pay the difference between the futures price today, [F.sub.t]([tau]) and the price at maturity, [F.sub.T](0) = [S.sub.T]. The payoff on this investment is:

    -([F.sub.T](0)- [F.sub.t]([tau])) = [F.sub.t]([tau])- [S.sub.T] (2)

    This payoff also varies with the commodity spot price at T, with an exposure exactly opposite to the first payoff. The combined payoff is:

    [F.sub.t]([tau])- [S.sub.t]-[K.sub.t]([tau]) + [[PSI].sub.t]([tau]) (3)

    This is a riskless payoff. By arbitrage this riskless payoff should equal the payoff to investing the cost of the commodity in a riskless bond, i.e., the spot interest rate for maturity [tau], [Y.sub.t]([tau]):

    [F.sub.t]([tau])- [S.sub.t]-[K.sub.t]([tau]) + [[PSI].sub.t]([tau]) = [Y.sub.t]([tau]) (4)

    While most physical commodities have substantial costs of storage, the cost of storing EUAs is essentially zero. Therefore, we proceed with [K.sub.t]([tau]) = 0. Expressing the interest rate and the convenience yield as continuously compounded spot rates, [y.sub.t]([tau]) and [[psi].sub.t]([tau]), and rearranging, we can restate this equality as:

    [F.sub.t]([tau]) = [S.sub.t]exp(([y.sub.t]([tau])-[[psi].sub.t]([tau]))[tau]) (5)

    Since EUAs can be banked from one period to the next, an argument can be made that the convenience yield should be zero, [[psi].sub.t]([tau])=0. In that case, the futures price equals the spot price grown at the spot interest rate:

    [F.sub.t]([tau]) = [S.sub.t]exp([y.sub.t]([tau])[tau]) = [Z.sub.t]([tau],[S.sub.t],[y.sub.t]([tau])) (6)

    We call [Z.sub.t] the cost of carry futures price. An alternative way to look at the same relationship is to calculate the implied continuously compounded spot convenience yield:

    [[psi].sub.t]t([tau]) = [y.sub.t]([tau])- [1/T-t]ln([[F.sub.t]([tau])/[S.sub.t]]) (7)

    If the observed futures price is above the cost of carry price, then the implied convenience yield is negative and we say that the futures contract is expensive and the spot is cheap. If the futures price is below the cost of carry price, then the implied convenience yield is positive and we say that the futures contract is cheap and the spot is expensive.

    The arbitrage argument applies to any investor, including those with no natural long position as an emitter of carbon and with no endowment of carbon allowances, but it is predicated on the ability to borrow at a risk-free rate in order to construct the riskless portfolio of a spot purchase and a future delivery obligation. An alternative approach not based on arbitrage is to understand the risk-return tradeoffs facing an industrial or electricity generation company that, because it expects to emit carbon in futures years, is short a future carbon allowance, but also has a surplus of spot carbon allowances. If...

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