Determinants of the Premium in Futures on
the Spatial Price Spread in the Nordic
Determinanter av Premien i Terminskontrakt
på Områdesprisskillnader i den Nordiska
Author: Marcus Ingelgård (930503)
Master’s Thesis in Finance, Second Cycle, 30 credits Subject: Economics
School of Business, Örebro University Supervisor: Niclas Krüger
Electricity markets are subject to spatial price differences because of congestion in the transmission grid. In the Nordic market this price risk is handled with EPAD contracts, a future on the spread between an area price and the (uncongested) system price. Electricity is non-storable so the price for an electricity forward is derived from the expected future spot price and a premium for risk. This thesis examines the forward premium in EPAD contracts during the period 2011-2016. The forward premium is the difference between the futures price and the realized spot price during the futures delivery period. The results show that there is a non-zero forward premium that varies over time and space as well as showing signs of a seasonal effect. There is weak support for the Bessembinder and Lemmon (2002) model where the forward premium is explained by the variance and skewness of the underlying spot price. Using a multivariate VAR model to explain dynamic relationships between the forward premium and fundamental factors it is shown that a shock to consumption of electricity affects the forward premium in EPAD contracts. This thesis both supports and rejects the findings of previous studies and brings light to new determinates of the forward premium in EPAD contracts.
The Nordic electricity market has drastically changed since Norway, in 1991, decided to deregulate their market for trading electricity.1 Sweden quickly followed and in 1996 together
they established Nord Pool, the exchange for trading electricity. Finland and Denmark joined the exchange and by 2000 a common Nordic electricity market was created (Nord Pool, 2017). Electricity is a unique commodity with two important features that effect the exchange of it, first one cannot physically store electricity and secondly, electricity must be transferred through the existing electrical grid. This means if demand is large enough there can be congestion in the transmission grid. To handle this Nord Pool has divided the Nordic market into twelve different areas. When congestion occurs between two areas the spot price between them will decouple. The area spot prices are the prices that all market participant will either pay or receive. Nord Pool also calculates what the market price would be if the transmission grid was not congested, this theoretical price is the system price. The system price is used as the underlying price for Nordic power derivatives, but this doesn’t provide any opportunity to hedge against the area spot price. Therefore EPAD (Electricity price area differentials) contracts, futures on the difference between an area spot price and system price, were introduced in 2000 as a complement to power futures. Combining the two futures, one on the system price and one on the spot price difference, allows one to hedge the area price.
The common approach to commodity futures pricing is with the theory of storage, but as mentioned it is not possible to physically hold electricity. The risk premium theory is therefore used instead. There the futures price is equal to the expected future spot price and a premium for holding systematic risk. This thesis denotes the premium as the forward premium and defines it as the difference between the price of the future today and the realised difference between the area spot price and the system price (Bessembinder & Lemmon 2002; Fama & French 1987; Marckhoff & Wimschulte 2009; Weron & Zator 2014). The forward premium in EPAD contracts for nine Nord Pool price areas are examined. The size and direction of the forward premium is tested. How it has changed over time and the seasonal effects in the forward premium are also tested. Models from the seminal papers by Bessembinder and Lemmon (2002)
and Fama and French (1987) are replicated with the forward premium in EPAD contracts, testing if the forward premium is explained by different risk factors and if EPAD contracts contain a forward premium or power to forecast the underlying price difference. Lastly a VAR model is specified to test for Granger causality between the forward premium and different factors. Among these factors are energy commodities, different generation and consumption variables.
The results show that in EPAD contracts for most of the Nordic areas there is a significant forward premium that is time varying and exhibits a seasonal pattern of being larger in the winter and smaller during the summer. The Fama and French (1987) regressions show evidence of EPADs containing both strong forecast powers and time varying forward premiums. The Bessembinder and Lemmon (2002) model is supported only in EPADs for the Stockholm and Oslo area. The multivariate VAR model shows support of electricity consumption Granger causing the forward premium. It also shows signs of hydro reservoirs levels and the coal price to Granger cause the forward premium, but the evidence is weak, and no firm conclusions can be drawn regarding hydro or coal influencing the forward premium in EPAD contracts. This thesis continues research of EPAD contracts by using a new data set from the point when Sweden was split into four area prices making it possible to investigate nine different EPADs for nine unique but interconnected areas. It also investigates new dynamic relationships between EPAD contracts and fundamental factors. The outline of this thesis is as follows. Section 2 presents institutional background regarding the Nordic electricity market. In section 3 the different theories of futures pricing are presented. In section 4 previous studies in the field of electricity derivatives are discussed. Section 5 describes the data used in this thesis. Section 6 presents the empirical methods and models used in the thesis. Section 7 presents the results from the empirical models. Section 8 is a discussion regarding the results and lastly in section 9 the thesis is concluded.
2. Institutional background
2.1 The Nordic electricity market.
The Nordic electricity markets were one by one liberalized during the 1990s and Nord Pool was established as the common market exchange for electricity in the Nordic region. The Nord Pool exchange has grown from a yearly turnover of 18.4 Terawatt hours (TWh) in 1993 to a turnover of 394 TWh in 2017 (Nord Pool, 2017). Sweden, Denmark, Finland and Norway are the largest markets connected to Nord Pool exchange making the market unique in several aspects. Firstly, because consumption in the Nordics is driven by both climate and industry. Secondly, because each area has their own unique combination of electricity generation sources.
Demand of electricity in the Nordic countries are based on mainly two factors, climate and overall economy (Nordic Energy Regulators (NordREG), 2014). Climate effects the demand for electricity in a way that, during winter months temperatures drop well below freezing in the Nordic area, more electricity is then consumed for heating commercial and residential areas. As Table 1 shows, households stand for about 30 percent of the total electricity consumption in the Nordics and commercial and public services for 20 to 30 percent, indicating that climate has a large effect on the demand of electricity in the Nordics. The other factor driving electricity consumption is the overall economy. Nordic countries have a large amounts of manufacturing industry (Nordic Council of Ministers, 2013). The industry sector accounts for 26 to 47 percent of total electricity consumption in the Nordic countries. An increase in the overall economy leading to an increase in manufacturing will all else equal lead to a larger amount of electricity consumed by the industrial sector.
Table 1. Electricity consumption by sector in percent of total electricity consumption 2016.
Sector Sweden Denmark Finland Norway
Industry 38.50% 26.28% 46.94% 37.74%
Households 34.08% 32.13% 27.44% 31.97%
Commercial and public services 22.00% 31.92% 21.34% 21.51%
Other Sectors 5.42% 9.67% 4.28% 8.77%
The supply side is more diverse between countries than the demand side is. Overall electricity generation in the Nordics is distinguished by large amounts of hydro and nuclear power but differs vastly between countries. Denmark being a flat country and with few rivers is not suited for hydropower production but instead has large amounts of wind power. One important aspect of wind power is that it is a volatile production type, since wind is unpredictable. To balance winds unpredictability, Denmark has large amounts of production from fuel combustion such as fossil and biofuels that is very flexible and can compensate production to match demand. Norway on the other hand is perfectly suited for hydropower, with large mountains and many rivers. In 2017, 96 percent of Norway’s production was from hydropower. Sweden and Finland are similar in their sources of electricity generation. They both have a large amount of stable but inflexible nuclear production and large amounts of hydropower production combined with smaller amounts of wind and fuel combustion. In 2017 Norway and Sweden were net exporters, while Denmark and Finland were net importers.
Table 2. Total electricity production 2017 per production type and country. Values are in (TWH) and percent share of total net generation (%).
Production type Sweden Denmark Finland Norway
TWh % TWh % TWh % TWh %
Nuclear 63.0 39.6% - - 21.6 33.2% - -
Fossil fuels 2.7 1.7% 8.8 29.8% 12.2 18.8% 3.1 2.1%
Of which Fossil Gas 0.4 0.3% - - 3.2 4.9% 3.1 2.1%
Of which Fossil Hard coal 0.5 0.3% 2.2 7.5% 6.1 9.4% - -
Of which Fossil Oil 0.2 0.1% 6.5 22.0% 0.2 0.3% - -
Of which Fossil Oil shale - - 0.1 0.3% - - - -
Of which Other Fuels 1.6 1.0% - - 2.7 4.2% - -
Wind power 17.3 10.9% 14.8 50.2% 4.8 7.4% 2.7 1.8% Solar PV - - 0.8 2.7% - - - - Biofuel 10.1 6.3% 3.7 12.5% 10.9 16.8% - - Hydro 63.9 40.1% - - 14.6 22.5% 142.1 95.6% Other 2.2 1.4% 1.4 4.7% 0.9 1.4% 0.7 0.5% Import (-) /Export (+) 19.3 12.1% -4.6 -15.6% -20.5 -31.5% 14.9 10.0% Total net generation 159.2 100.0% 29.5 100.0% 65.0 100.0% 148.6 100.0% Consumption 139.9 87.9% 34.1 115.6% 85.5 131.5% 133.7 90.0%
Note: Import and export includes transmissions between the countries included above and also with other countries not included.
2.1 Price setting on the Nordic electricity market.
Nord Pool operates two different physical exchanges, the day-ahead market and the intraday market. The day-ahead market is the primary exchange for electricity trading and the intraday market is the balancing market, acting to compliment the day-ahead market. Since electricity must be produced and consumed instantaneously both producers and consumers need to plan how much they need sell or buy in advance. The Nord Pool day-ahead market makes the price and quantities known for a short period in advance because of its price formation mechanism.
The price formation mechanism used in Nord Pool’s day-ahead market and many other physical power markets is often called marginal price setting and is different from the typical financial exchange where trading is continuous when the exchange is open. At Nord Pool´s day-ahead market both producers and consumers submit bids for how much they are willing to sell or buy at a certain price for each hour of the next day. The sell bids are then for each hour ordered from the lowest to the highest price to form a supply curve and the buy bids are ordered from the highest to the lowest price to form a demand curve. The intersection between these two curves is the price for that hour during the next day, this is then done once a day for the next 24 individual hours. All producers and consumers are then paid or pay the same equilibrium price.
In a competitive market the market clearing price is equal to the short-run marginal cost of production, this is the case for day-ahead electricity markets as well. Producers placing bids lower than their marginal cost will not cover costs and placing higher bids than their marginal production cost may result in them losing the auction. Therefore, placing bids equal to their short-run marginal cost is optimal (Huisman, Michels & Westgaard, 2014). This is illustrated in Figure 1 below, the supply curve is the marginal cost bids of all producer’s ordered from lowest to highest and the demand curve, the dashed line, is the buy bids ordered from highest to lowest price. Demand is assumed to be inelastic because electricity is a necessity and therefore illustrated as almost vertical.
Figure 1. Marginal price setting in Nord Pool’s day-ahead market.
Wind, hydro and other renewable energy sources have very low marginal production cost, as an example once a wind turbine is installed the marginal production cost is close to zero since wind is free, hence wind production and other renewable generation sources are the far to the left in the supply curve of Figure 1. Nuclear has higher production costs and fossil fuel combustion has the highest production costs since these require coal, oil or gas as input fuels and are subject to EU emission allowance rights (EUA) (The Swedish Energy Markets Inspectorate (EI), 2006). An increase in fuel or EUA prices is expected to transfer to the electricity price since the marginal production cost for fuel combustion generation is higher shifting parts of the supply curve upwards creating a new higher equilibrium. This is assuming that the equilibrium price intersects at generation source that relies on fuel combustion. As mentioned, Denmark and Finland all use large amounts of fossil fuel combustion as a generation source. Therefore, when consumption is high the equilibrium price is expected to intersect at the marginal price of fuel combustion sources in these countries leading to higher prices, all else equal. Another aspect with marginal price setting is that if low marginal cost generation sources increase production then the entire supply curve will shift to the right and all else equal the price will be lower. The effect of low-cost renewable fuels lowering electricity prices is called the merit order effect (Sensfuß, Ragwitz & Genoese, 2008). An increase in wind power production will all else equal lower the equilibrium electricity price.
Wind Hydro Nuclear
The Nord Pool operating area is divided into 15 bidding areas. Sweden is divided into four areas, Denmark into two areas and Norway into five areas. Finland, Estonia, Latvia and Lithuania are all their own area. Aggregated demand and supply curves are constructed for each bidding zone and hour of the day. Each area can import and export electricity to a certain degree, but since electricity is not storable and physical connections between areas are limited there is the possibility of there being a surplus or deficit of supply. When the transmission grids capacity is not sufficient enough to handle all transmissions between areas, there will not be one single price in all areas. Congestion in the transmission grid leads to the prices decoupling between areas. Prices will be higher where there is a supply deficit, and lower where there is a supply surplus. Electricity will flow from the area with a surplus to the area with a deficit. The area price is the price producers and consumers in each respective area pay or receive when trading electricity on the physical market at Nord Pool. The theoretical price that would occur if there is no congestion is the system price, this is the equilibrium price when aggregating all supply and demand curves for every area in the system. The system price is used as a reference price for derivatives on Nordic electricity. Table 3 presents the different electricity price areas in the Nordic countries. It also shows percent of days were the area price is different from the system price and the percentage difference between the area price and the system price.
Table 3. Summary of electricity price areas, percentage deviation of area prices from system price and frequency of area prices deviations from the system price during 2011-2018.
Country Area Abbreviations Price deviation Frequency of prices deviating
Luleå LUL SE1 3.40% 99.18%
Sundsvall SUN SE2 3.44% 99.18%
Stockholm STO SE3 4.63% 99.18%
Malmö MAL SE4 7.59% 99.18%
Denmark Copenhagen CPH DK2 11.47% 99.65%
Aarhus ARH DK1 8.80% 99.70%
Finland Helsinki HEL FI 10.91% 99.67%
Oslo OSL NO1 -3.27% 99.67%
Kristiansand - NO2 -5.06% 99.49%
Trondheim - NO3 3.36% 99.61%
Tromsø TRO NO4 1.41% 99.61%
Bergen - NO5 -4.12% 99.61%
Note: Price deviation is the average difference between the average daily area price and the average daily system price in percent. Frequency of price deviation is how many days the daily area price is different from the daily system price during the years 2011-2018.
2.2 Power futures
A future or a forward is an agreement between two parties to either buy or sell an asset at a specific time at a certain price (Hull, 2018). Futures are available on a range of different assets. The main interest of this thesis is futures on the Nord Pool electricity price. Futures on Nordic electricity are traded on the Nasdaq exchange since 2013 (Nasdaq Commodities, 2019a) and before that they were traded on the Nord Pool market. Nasdaq offer a range of different futures with the underlying asset as either the system price, called power futures, or the difference between an area price and the system price futures, called EPAD. Power futures and EPAD contracts are available with monthly, quarterly or yearly delivery (Nasdaq, 2018). Futures where the Nordic system price is the underlying asset allows market participants to hedge against changes in the system price and combining a future with an EPAD lets markets participants hedge against the price risk that occurs when there is congestion in the transmission grid (Nasdaq Commodities, 2019b). EPAD contracts are not available in all of the Nordic areas. Regarding the Nordic bidding areas, they are available for the Finnish area, the two Danish areas, the four Swedish areas and two of the five Norwegian areas; Oslo and Tromsø. Contracts are therefore not available for the Kristiansand, Trondheim and Bergen areas.
The underlying asset in EPAD contracts is the difference between an area price and the system price, were the difference is measured as an area price minus the system price. EPAD contracts are settled at maturity against the average difference between an area price and the system price during the delivery period. These futures have cash settlement, so buyers and sellers of these contracts do not have to worry about having to deliver or receive physical electricity. Instead the parties involved settle the contract by exchanging the associated cash positions. The price that EPAD contracts are settled each day against is called the daily fix. This price is set by the exchange, Nasdaq Oslo ASA, following certain criteria. Specified by Nasdaq (2018) the daily fix will be the price of last transaction registered. If no transactions were registered on the relevant bank day then the daily fix will be the average of the spread. If the spread is also not available, then a theoretical daily fix will be set based on historical price sources. The clearing house, Nasdaq Clearing AB, can set a different daily fix if it determines that the daily fix set by the exchange is not reflective of the market value.
3. Theoretical background
3.1 Futures pricing
There are two theories on futures pricing, the most common is the theory of storage by Working (1933, 1949), Brennan (1958) and Kaldor (1939) among others. The theory of storage involves the time value of money, the assets storage costs and the convenience yield. The second less common theory is the risk premium theory were the futures price is the expected spot price and a premium for holding systematic risk. There is a difference in the theoretical approach when pricing futures and forwards but as argued by Hull (2018) the differences are in most cases small enough to be neglected. This thesis makes no difference between futures and forwards.
3.1.1 Theory of storage
The approach to pricing most financial derivatives starts with a no-arbitrage or law of one price argument. Participants on the market cannot make a risk-free profit by creating a portfolio with different combinations of the future, the asset and the risk-free rate. This is assuming that market participants are not subject to transaction costs or taxes when trading, that they can borrow at the risk-free rate and that they take advantage of arbitrage opportunities (Hull 2018). The futures price at time t and with delivery at time T is denoted as Ft,T. Following Hull (2018) the futures price on an investment asset without income or storage costs will be,
Ft,T = Ster(T"t), (3.1)
were St is the underlying spot price at time t, the risk-free rate is r, and T-t denotes time until
delivery. Market participants can either buy the underlying asset for the spot price today and forego any potentially earned interest or they could enter into a futures contract, invest the same amount and earn the risk-free interest rate and receive the underlying asset for the same amount.
It is important to differentiate between consumption assets and investment assets. Consumption assets are commodities held primarily for consumption and investment assets are commodities that are held by at least some investors for investment purposes (Hull, 2018). Futures with physical delivery on these two types of assets have at least one thing in common, they are subject to storage cost. There is a cost associated with storing the asset. The futures price were
Ft,T = Ste(r+u)(T"t), (3.2)
where u is the yearly storage cost as a proportion to the spot price. Further one can take into account the convenience yield with the following equation.
Ft,T = Ste(r+u"y)(T"t) (3.3)
The convenience yield, y, is the benefit of physically holding the consumption asset. The benefit of storing the physical asset is often to secure production. Explained by Hull (2018) the convenience yield can be seen as the market’s expectations of the availability of the commodity in the future. The relationship between the futures price and the price of the underlying asset is often summarized as the cost of carry. For a commodity with storage costs the cost of carry is r+u.
3.1.2 Risk premium theory
The second theory on futures pricing is the risk premium theory. The theory originates from Keynes (1930) and Hicks (1939). They argue that the futures price of an asset can deviate from the expected spot price because of hedging pressures from speculators holding short positions and hedgers that hold long positions (Hull, 2018).2 Cootner (1960) expands this theory to where
hedgers can be both long and short futures contracts. Dusak (1973), Breeden (1980) and Hazuka (1984) and others then expand the theory in the framework of the Sharpe, Lintner and Mossin Capital asset pricing model (CAPM) where non-systematic risk can be diversified away but systematic risk cannot. Investors can thus require higher returns for bearing systematic risk but not when bearing non-systematic risk.
Following the notation of Hull (2018) the futures price can be shown with the following example. Assuming that investors enters a futures contract and at the same time invests the present value of the futures price in the risk-free asset. The asset is then, with the future, bought on the delivery day using the earnings of the investment in the risk-free asset and then
immediately sold at the market price. The present value of the cash flow from this investment is,
-Ft,Te-r(T-t) + E
where Et denotes the expectations at time t, ST is the spot price at delivery and k is the
appropriate risk-adjusted discount rate for the investor. If it is assumed that all securities are priced so they have a net present value of zero, i.e. equation 3.4 equals zero, then the futures price can be written as,
Ft,T = Et(ST)e(r"k)(%"&). (3.5)
Seen from an equilibrium asset pricing view; the discount rate k is the investors required return for holding systematic risk. If the asset is uncorrelated with the systematic risk then the appropriate discount rate, k, will be the risk-free rate, r. If k = r, then the futures price is an unbiased estimate of the spot price and,
Ft,T = Et(ST). (3.6)
The futures price is equal to the expected spot price at delivery. Pindyck (2001) and Hull (2018) state if the underlying asset has a positive correlation with the overall economy then the expected return of the underlying asset is generally more than the risk-free return, k > r. In context of the CAPM, the commodity has a positive beta and the investor holding the underlying asset expects to, on average, earn a premium as a reward for holding positive systematic risk. The expected spot price is then larger than the futures price. If the asset is negatively correlated with the economy, then investors holding the underlying asset will expect to pay a premium for holding negative systematic risk.
Ft,T + πt,T = Et(ST) (3.7)
The equation above follows Chance and Brooks (2015) where the premium, πt,T, is the premium for holding (or selling) systematic risk on the spot market transferred to the futures market in time t for the contract with maturity in time T. Investors that hold long positions of the underlying asset are expected to earn the risk premium, but if they are unwilling to accept the systematic risk they can hedge their portfolio by selling futures contracts and in effect transfer the systematic risk from the spot market to the futures market. Futures prices will then be a
biased estimate of the spot price since speculators will be rewarded for bearing risk (Chance and Brooks, 2015).
3.2 Forward premium in electricity futures
When pricing futures on electricity one important characteristic of electricity come heavily into play; electricity is a flow rather than a stock. Being a flow means that electricity is consumed instantaneously after it is produced since storing electricity is not economically feasible. As mentioned by Aïd (2015) the only large-scale storage that is economically feasible is indirect storage in hydro reservoirs. The arbitrage (buy-and-hold) argument is not applicable for pricing electricity futures since it is not possible to hold the underlying asset and therefore, replicate the derivate with a portfolio of the underlying asset and the risk-free rate is not possible. Hence the theory of a premium, described in section 3.1.2, is used for pricing electricity futures.
Noted by Weron (2008) the definition for this premium is not consistent in previous literature. There is no consensus in both on how to calculate the premium and what term to use for this premium. From the previous sections the premium, πt,T, can be rewritten as,
πt,T = Et(ST) − Ft,T, (3.8)
where the premium is the difference between the expected spot price and the futures price. Others have defined it as the negative of the premium, here denoted as FP for forward premium, FPt,T = − πt,T = Ft,T− Et(ST). (3.9)
For this thesis the definition of the forward premium in equation 3.9 will be used. The forward premium is the difference between the futures price and the spot price, or it is the negative of the premium from equation 3.7. The most common approach in recent electricity forward premium research has been to use this definition (Bessembinder & Lemmon 2002; Fama & French 1987; Marckhoff & Wimschulte 2009; Weron & Zator 2014). Therefore, it will be used for the rest of this thesis to be able to compare results. Pindyck (2001) explains that the forward premium is positive if the assets beta is positive entailing a compensation for bearing positive systematic risk.
There are two common approaches to calculating the forward premium, the ex-post approach and the ex-ante approach. Explained by Cartea and Villaplana (2014) the ex-ante forward premium is the difference between the observed futures price today and the expected spot price at maturity of the contract and can be calculated at time t. The ex-ante premium is not observable since the expected spot price requires one to model and forecast the spot price. Cartea and Villaplana (2014) note that the main problem with this approach is that different models will result in different forward premiums for each model and the ex-ante forward premium may not be consistent across different models. The ex-post forward premium is instead the difference between the futures price today and the realised spot price at maturity of the futures contract, this is calculated at time T.
Ex-ante forward premium FPt,Tex-ante = Ft,T − Et(ST) (3.10)
Ex-post forward premium FPt,Tex-post = Ft,T − ST (3.11) In equation 3.10, Et(ST) is the expectations at time t of what the spot price will be at maturity,
time T. In equation 3.11 the spot price, S% is the observed spot price at maturity, T. Shown by Redl and Bunn (2013) the ex-post forward premium can be written as,
FPt,Tex-post = Ft,T− ST = Ft,T− Et(ST) + [Et(ST)−ST] = FPt,Tex-ante + εt,T (3.12)
where the ex-post forward premium is the ex-ante forward premium plus a random error term that is a forecast error from the expected spot price. The ex-post approach of defining the forward premium will be used in this thesis, henceforth the ex-post forward premium and the forward premium will be used interchangeably. The ex-post approach is used since the aim of this thesis is not to construct a forecasting model for electricity spot price but to test the determinants of the forward premium. The disadvantage of this approach is that it can be hard to know is the forward premium is a premium for holding systematic risk or if it is a forecast error.
Pricing EPAD contracts using the ex-post forward premium approach is fairly straight forward. EPAD contracts are settled against the average price difference between the area spot price and the system spot price during the delivery period. As shown by Marckhoff and Wimschulte (2009) the payoff for an EPAD on area A is,
EPADT1,T2 = 1 T2 − T1-.St A− S t S/ T2 t=T1 (3.13)
where EPADT1,T2 is the futures price for a contract on area A with delivery that starts at T1 and
ends at T2. The area price at time t is denoted StA and the system price is StS. The payoff for
holding an EPAD contract until maturity is the average price difference between an area spot price and the system price for the delivery period. The payoff for an electricity future is similarly the average system price during the delivery period, the EPAD future can therefore be written as,
EPADt,T1,T2 = Ft,T1,T2 A -F
S . (3.14)
Where the EPAD can be written as a portfolio of a long position in a power future for the area price, Ft,T1,T2
A , and a short position in a future for the system price, F t,T1,T2
S , at time t and with
delivery starting at T1 and ends at T2. Equation 3.14 can also be rewritten as,
EPADt,T1,T2+ FSt,T1,T2 = Ft,TA 1,T2. (3.15)
Hedgers wanting to hedge the area price can replicate an area future by combining a system future with the appropriate EPAD contract in a portfolio. Combining the ex-post forward premium and the EPAD contracts payoff, equation 3.11 and 3.13 respectively, results in the following equation, FPt,TEPAD1,T2 = EPADt,T1,T2− 0 1 T2− T1 -.ShA−ShS/ T2 h=T1 1 . (3.16)
The ex-post forward premium for an EPAD contract, FPt,TEPAD1,T2, is the difference between the
EPAD contract price at time t with delivery starting at T1 and ending at T2 and the average price
difference between the relevant area price and the system price during the delivery period. This is how the forward premium in EPAD contracts will be defined in this thesis.
4. Previous studies
The literature regarding pricing commodity futures with the risk premium theory is large. As mentioned, the theory was first introduced by Keynes (1930) and Hicks (1939), where the premium is determined by hedging pressures. The theory has been expanded and tested by many, previously mentioned are Cootner (1960), Duska (1973), Breeden (1979) and Hazuka (1984) but papers such as Fama and French (1987) and Kolb (1992) should also be mentioned. Fama and French (1987) devise a pair of regressions models to test if futures price can predict the spot price and if there is a time-varying forwards premium present. There is no conclusive evidence across these papers that there is a general non-zero premium in commodity futures nor if futures prices are predictors of the future spot price.
Studies examining electricity futures is considerably smaller since most electricity markets have only been deregulated since the mid 1990s. Although the time period possible to study electricity price futures is short there are a couple very influential papers regarding the premium in futures prices. The following papers study futures on the traded spot prices or system prices. A seminal paper is Bessembinder and Lemmon (2002), they derive an equilibrium pricing model using a second-order Taylor series expansion where buyers and sellers have risk preferences implying that futures prices are bias predictors of the future spot prices. The model suggests that the forward premium is negatively correlated with the spot price variance and positively correlated with the skewness of spot price. Their results indicate a forward premium in the PJM and CALPX markets that varies in size over season.3 Longstaff and Wang (2004)
replicate the Bessembinder and Lemmon (2002) model using hourly data from the PJM market and show that the forward premium is correlated with the risk measures variance and skewness of the spot price. They also show that the forward premium varies throughout the day and over the season. Huisman and Kilic (2012) test the Fama and French (1987) method as well as the effects of different electricity production types on the forward premium in the Nordic and Dutch market using a multivariate model. They find that futures in the Nord Pool market contains no time-varying forward premium but does contain the power to forecast spot price changes. Redl and Bunn (2013) use EEX futures contracts to show that the forward premium in electricity is
explained by the forward premium in gas future and the variance in oil prices.4 They also show
that spot price variance and skewness explain the forward premium, results that are consistent with the Bessembinder and Lemmon (2002) model. Bunn and Chen (2013) using a dataset on British futures specify and test a multivariate model and also find that the forward premium is explained by fuel prices as well as spot price variance and skewness. A paper that tests if the forward premium is a premium or a bias is Gjolberg and Brattested (2011). They use Nord Pool data to conclude that the size of the premium is large but does not differ in size across seasons. They find no support for the Bessembinder and Lemmon (2002) model and attribute the forward premium to a market inefficiency since it is so large and shows no seasonal pattern. Weron and Zator (2014) find that the forward premium in Nord Pool futures is explained by hydro reservoir levels but find no support for the Bessembinder and Lemmon (2002) model.
A handful of studies have examined the forward premium in Nordic EPAD contracts. Marckhoff and Wimschulte (2009) investigate EPAD contracts over the period 2001 to 2006 and find that the forward premium varies substantially between areas and delivery periods and they find support for the Bessembinder and Lemmon (2002) model in the forward premiums of EPAD contracts. They also show that hydropower generation has a large impact on area price spreads. Spodniak, Chernenko and Nilsson (2014) using a data set from 2000-2013 find support of a forward premium in EPAD contracts and that the forward premium is explained by the hydro reservoir levels deviation from its long-term mean. They also find during this longer period that hydropower generation has had a significant impact on area price spreads supporting the results of Marckhoff and Wimschulte (2009). Junttila, Myllymäki, and Raatikainen (2018) use a data set on monthly Finnish EPAD contracts find no support for either the Bessembinder and Lemmon (2002) model nor that hydro reservoir levels explain the forward premium, they attribute this to the market being inefficient.
The previous studies presented show that while there is no disputing that there is the presence of a forward premium in electricity futures there is less support for the notion of the forward premium being a premium for bearing systematic risk. This thesis will, similar to Marckhoff and Wimschulte (2009), Spodniak, Chernenko and Nilsson (2014) and Junttila, Myllymäki, and
Raatikainen (2018), test different models that explain the forward premium in EPAD contracts. How this thesis differs from them is foremost that this thesis studies all nine areas where EPAD contracts are available. This has not been done before since Sweden has only been divided into four areas since 2011. The period examined is also more recent than the cited papers. As done by many others the Bessembinder and Lemmon (2002) model, testing spot price variance and skewness, will be replicated to estimate the effects of the risk factors. The Fama and French (1987) regressions will be replicated using EPAD contracts, testing if they have forecasting power or if there is a time varying risk premium. A multivariate model will be specified and tested. The model will test the relationships between the forward premium and several different factors such as fuel prices, hydro reservoirs, consumption and the merit-order effect with the support of the aforementioned studies.
To test if there is a significant forward premium in EPAD contracts and what risk factors determine the forward premium a comprehensive dataset of several variables is constructed. The dataset consists primarily of Nord pool spot prices and EPAD contracts but also includes several different explanatory variables. Data on EPAD contracts has been provided by Nasdaq and includes the daily fix and the contract specifications for EPAD contracts in the following areas; Luleå, Sundsvall, Stockholm, Malmö, Copenhagen, Aarhus, Helsinki, Oslo and Tromsø. Spot prices are provided by Nord Pool through access to their FTP- server and consists of the daily average system and area price for the nine areas. The sample consists of daily observations from 2011-01-03 to 2018-12-31, excluding weekends and Norwegian bank holidays since futures on Nasdaq only are traded on non-bank weekdays. The final sample for testing each area individually varies between areas, this is due to EPAD contracts for some areas not being available in either the start or the end of the sample. The years chosen to study are because in 2011 Sweden was divided into the four areas that it still is today. Following that EPAD contracts for each Swedish region were also introduced and the years 2011-2018 is the longest period possible to study without any further changes to electricity price areas.
To limit the study, only contracts with monthly maturities have been included in the dataset. This is to maximize the length of the series tested and as mentioned by Redl and Bunn (2013) monthly contracts have the shortest time to maturity so the forecasting error is assumed to be the smallest. A further restriction to this thesis is to only include nine of the eleven available EPAD contracts at Nasdaq. Contracts that are not included in the dataset are for areas Riga and Tallinn, this has been done for two reasons. First because spot prices at Nord Pool for Riga and Tallinn were first introduced 2010 and 2013 respectively (Nord Pool, 2015). Secondly because the market dynamics in the Baltics are different from the Nordic region.
At Nord Pool electricity is traded every hour of the day and every day of the week while futures contracts at Nasdaq are only traded on weekdays that are not Norwegian bank holidays. This means that there are days were electricity spot is traded but not futures contracts, these days have been excluded from the sample so that the sample only consists of days were the relevant EPAD contracts are available for trading. To estimate time series models the variables must be a single continues series. A front-month series is therefore constructed of the monthly EPAD
contracts. The front-month series will always consist of the contract closest to maturity, i.e. once the current contract is closed out the series is rolled over to the next contract that is at that time closest to maturity. Table 4 presents descriptive statistics of the Nord Pool system price and spot prices for the relevant nine areas as well as the front contract series of EPAD contracts for each area. The different series are graphically presented in the appendix, Figure 1 and A-2.
Table 4. Descriptive statistics of the system and area spot prices areas and for the constructed front month series of EPAD contracts.
Variable Area Unit Mean S.D. Skewness Kurtosis Min Max N System price System EUR/MWh 34.39 12.05 0.84 4.50 6.23 96.15 2,050
Spot Price Luleå EUR/MWh 35.63 12.31 0.72 4.66 5.42 99.61 2,050 Sundsvall EUR/MWh 35.64 12.31 0.72 4.67 5.42 99.61 2,050 Stockholm EUR/MWh 36.17 12.49 0.74 4.62 5.42 101.26 2,050 Malmö EUR/MWh 37.36 12.80 0.66 4.29 5.42 101.26 2,050 Copenhagen EUR/MWh 36.60 12.11 0.32 3.31 -6.28 96.18 2,050 Aarhus EUR/MWh 38.53 12.49 0.50 3.96 -6.28 101.26 2,050 Helsinki EUR/MWh 40.48 11.07 1.05 6.14 7.38 101.26 2,050 Oslo EUR/MWh 33.10 12.88 0.85 4.45 2.96 95.76 2,050 Tromsø EUR/MWh 33.75 12.44 0.90 4.82 5.51 99.61 2,050 Front Contract Luleå EUR/MWh 1.21 1.65 1.95 9.37 -1.98 13.00 1,883 Sundsvall EUR/MWh 1.26 1.65 2.04 10.45 -1.95 13.98 1,883 Stockholm EUR/MWh 2.38 1.97 1.72 7.77 -0.60 16.00 2,050 Malmö EUR/MWh 3.82 2.79 2.09 8.59 -0.10 17.50 1,883 Copenhagen EUR/MWh 4.68 4.36 0.10 5.67 -12.83 22.65 2,005 Aarhus EUR/MWh 2.31 4.56 0.04 4.97 -18.70 19.00 2,005 Helsinki EUR/MWh 6.12 3.40 0.69 3.69 -2.23 18.70 2,050 Oslo EUR/MWh -0.90 1.48 0.35 8.02 -9.00 6.00 2,050 Tromsö EUR/MWh -0.72 2.00 -0.55 4.11 -6.75 6.00 1,883
Note: S.D. refers to standard deviation and N refers to the sample size. EUR/MWh refers to euros per megawatt hours.
The explanatory variables included in the data set are variables that are expected to explain the forward premium in EPAD contracts and are motivated by previous studies. These Variables include; hydro reservoir level, wind power production, electricity consumption, fossil fuel and
EUA prices. Hydro reservoir level is compiled by Nord Pool and provided through access to
for reservoirs in Sweden, Norway and Finland.5 The weekly average level from 1995-2018 is
then calculate and the reservoir levels deviation from this long-term mean is then calculated. It is the hydro reservoirs long-term mean that is used in the final analysis, the absolute reservoir level is not included since it was determined to be non-stationary. Hydro reservoir level is only provided on a weekly frequency, resulting in a mismatched between the rest of the datasets frequency, the variable has been interpolated to a daily frequency to match the rest of the dataset. Total daily electricity consumption in the four Nordic countries is provided by Nord Pool through access to their FTP- server. Consumption deviation from long term average level is calculated in a two-step process, first is adjusted for the monthly average level and then it is adjusted for average level for the day of the week, the long-term mean is from the period 2000-2018. Examining the consumption level in Figure A-3 shows no signs of any trend in level or deviation even though population has grown over time.
Wind power pertains to total wind power production in Sweden and Denmark and is collected from Svenska Kraftnät and Energinet respectively. Brent oil, API 2 coal and EUA precis are collected from Bloomberg. EPAD contracts are quoted in euro while both oil and coal are in US dollars, this could possibly lead to the results incorporating an exchange rate effect. To handle the fact that the commodity price series are non-stationary, the daily returns of the commodities will be used. Explanatory variables also are adjusted so they match the EPAD contracts series frequency. Explanatory variables are presented graphically in the appendix, Figure A-3.
Table 5. Descriptive statistics of explanatory variables.
Variable Area Unit N Mean S.D. Skewness Kurtosis Min Max Hydro Reservoir Deviation System % 2,050 0.53 6.79 -0.70 3.80 -21.49 14.23 Wind Power Production System TWh 2,050 69.13 43.11 0.87 3.29 1.99 229.86 Consumption System TWh 2,050 1,077.04 182.48 0.38 2.06 765.01 1,558.37 Consumption Deviation System TWh 2,050 -4.30 63.13 0.38 4.76 -277.93 280.60 Oil return Brent % 2,049 -0.27 1.21 -0.52 8.02 -7.942 7.272 Coal return API2 % 2,049 -0.15 1.04 2.02 51.34 -8.933 17.139 Emissions rights return EU % 2,049 0.01 3.01 -1.19 19.23 -38.331 17.287
Note: S.D. refers to standard deviation and N refers to the sample size.
6. Method/empirical model
There are two main items this thesis aims to investigate first the characteristics of the forward premium in EPAD contracts and secondly what factors affect the forward premium. These questions are answered using several different models and two different statistical estimation techniques. The methods used are ordinary least squares (OLS) and VAR estimations. The estimations using OLS are presented with Newey and West (1987) heteroskedastic and autoregressive consistent (HAC) standard errors.
6.1 Characteristics of the Forward Premium
The first step of determining the forward premium is to construct the front-month series of the ex-post forward premium and test if it is significantly different from zero during the full sample period, then if the forward premium has changed over time. Similar to Marckhoff and Wimschulte (2009), this is done using t-tests and HAC standard errors. Since the Nordic spot price and the forward premium of power futures are shown to exhibits seasonal patterns (Bessembinder & Lemmon 2002; Longstaff & Wang 2004; Weron & Zator 2014) it will be tested if this is present in the forward premium of EPAD contracts as well. This is done by estimating a model that explains the forward premium with monthly indicator variables using OLS with Newey and West (1987) HAC standard errors.
6.1.1 Fama and French regressions
To test if futures prices contain a time varying forward premium and if they contain the information about the expected spot price the Fama and French (1987) regressions are used. In the risk premium theory, the futures price is comprised of the expected spot price and a premium for holding systematic risk that occurs because of uncertainty. As shown by Fama and French (1987), taking equation 3.8 and subtracting the current spot price results in,
Ft,T − St = Et(ST) − St + FPt,T. (6.1)
The basis, Ft,T− St, is comprised of the expected spot price change, Et(ST) − St, and the forward premium, FPt,T. Under the assumption that investors make rational forecasts, forecast
premium. This approach is also used by Huisman and Kilic (2012) to test the forward premium in the Nordic power futures. The two equations are,
ST− St = c1 + β1.Ft,T− St/ + ε1,t, (6.2)
FPt,T = c2 + β2.Ft,T− St/ + ε2,t. (6.3) Equation 6.2 shows if the basis, Ft,T− St, contains information about the expected spot price
change, ST− St, i.e. if the futures prices have power to forecast the future spot price. Equation 6.3 shows if the basis has information about the ex-post forward premium. As explained by Fama and French (1987) the regressions are additive since the expected change in spot price, ST− St, and the forward premium, FPt,T, sum to the basis as seen in equation 6.1. This
restriction means that the intercept coefficients, c1 and c2, should sum zero and that the basis coefficients, β1 and β2, should sum to one. To apply these two regressions to EPAD contracts the difference between the area spot price and the system price will be used. The models are,
2S%3A ,%4 − S %3,%4 S 5555555555555555556 − .SAt − StS/ = c1 + β12FEPADt,%3,%4− .StA− StS/6 + ε1,t, (6.4) FP&,%3,%4 EPAD = c 2 + β22F%3,%4 :;<=− .S t A− S t S/6 + ε 2,t. (6.5)
Where the average price difference during the delivery period of T1 to T2 is 2S%3,%4 A − S
5555555555555555556, the difference between the area and system price at time t is .StA− S
S/, the EPAD futures price
is Ft,%3EPAD,%4 and the forward premium in the EPAD contract is FP&,%3EPAD,%4. The two equations show the allocation of the forward premium and the forecast ability in the basis. A β1 that is significantly different from zero indicate that the basis contains information about the future spot price difference and a β2 significantly nonzero indicates the presence of a time-varying forward premium in the contract series.
6.2 Determinants of the Forward Premium
6.2.1 The Bessembinder and Lemmon model
One of the most influential papers in electricity futures research is Bessembinder and Lemmon (2002). They specify a model where the forward premium in electricity futures can be explained
by the underlying spot price variance and skewness. Their equilibrium model assumes that market participants are subject to uncertainty in power demand and have risk preferences. The model shows that the electricity futures price is dependent on the expected spot price, the variance of the spot price and the skewness of the spot price. Rearranging the model, solving for the forward premium and applying it to EPAD contracts gives,
FP&,%3,%4A = C + β1Vart.SA−SS/ + γ
A− SS/ + ε
The underlying asset for EPAD contracts is the spot price difference therefore the explanatory variables are variance, Vart, and skewness, Skewt, of the difference between an area price and the system price. Marckhoff and Wimschulte (2009) apply the model on Nordic EPAD contracts and expand the model so that it includes the variance and skewness for the area price and the system price separately. The Marckhoff and Wimschulte (2009) version of the Bessembinder and Lemmon (2002) model is used in this thesis and is specified as,
FP&,%3,%4 A = C + β 1Vart.S A/ + β 2Vart.S S/ + γ 1Skewt.S A/ + γ 2Skewt.S S/ + ε t. (6.7)
Bessembinder and Lemmon (2002) use monthly data and define variance and skewness as the variance and skewness of the daily spot price during the current month. Longstaff and Wang (2004) use a similar approach but use daily data and define the spot price variance and skewness using the hourly spot price during the current day. Marckhoff and Wimschulte (2009) use a different approach and estimate the average forward premium of each contract against the average system and spot price variance and skewness during the delivery period of each contract. The approach for calculating variance and skewness in this thesis is to estimate the sample variance and skewness on the previous 30 days system and spot price and rolling the 30-day window forward one step each day. As mentioned in equation 3.13, an EPAD contract implies a long position in the area future and a short position in the system future, this means that the expected signs of the coefficients for the area variables and the system variables are different from each other. As stated by Marckhoff and Wimschulte (2009), the expectations are that; β1 is negative, γ1 is positive, β2 is positive and γ2 is negative.
Equations 6.4, 6.5 and 6.7 will be estimated using OLS. Two of the assumptions when using this estimation method on time series data is that the error term is homoscedastic and that there is no serial autocorrelation. Since the data used in this thesis is time series data and possibly
autocorrelated as well as regression errors being heteroskedastic the assumptions are violated, and normal standards errors are biased. To correct for this bias the coefficient variance matrix is estimated with the Newey and West (1987) HAC estimator. This estimator corrects the variance-covariance matrix for possible autocorrelation and heteroskedasticity producing consistent standards errors (Newey & West, 1987). The lag length that the Newey West estimator handles autocorrelation up to is determined by the Schwartz information criteria (SIC). This is since the SIC criterion is consistent in large sample sizes as mentioned by Lütkepohl (2005). Other criterions will be considered if they deviate far from the SIC, but the main criterion will be the SIC.
6.2.1 VAR and Granger Causality
184.108.40.206 VAR and Granger Causality Method
VAR models are a convenient way to model several multiple time series and to analyse the dynamic relationships between a set of variables. The VAR model is an extension of the univariate autoregressive model so that the model is not only dependent on the past values of one time series but also the lagged variables of the entire set of time series. Following the notations of Lütkepohl (2005) the VAR model with p lagged values can be specified as,
Yt = C + Φ1Yt"1 +…+ ΦpYt"p + εt. (6.8)
In the equation above, Yt is a (K × 1) vector of endogenous variables, C is a (K × 1) vector of
constants, the Φp are (K × K) vectors of coefficients and εt is a (K × 1) vector of white noise error terms with time invariant covariance vectors, E(εtε'
t) = ∑ε, and a zero mean, E(εt) = 0.
Granger (1969) presents a simple test that says if one variable helps predict another variable. The concept is based on that cause comes before effect. X is said to Granger cause Y if the lagged values of X contain information that helps improve predictions of Y beyond predictions that only contain lagged values of Y. This concept of Granger causality is simple to apply in the VAR framework (Lütkepohl, 2005). Consider a VAR(1) model of the variables X& and Y&,
@Xt YtA = B c1 c2C + @ Φ11 Φ12 Φ21 Φ22A @ Xt"1 Yt"1A + B ε1t. ε2t.C. (6.9)
The null hypothesis for testing if Xt Granger causes Yt is H0: Φ12 = 0. If one can reject the null
hypothesis then it can be said that Xt Granger causes Yt (Becketti, 2013). A Granger causality
test provides a framework to test the influence variables have on each other.
A commonly used tool to further examine the dynamic relationships and Granger causality in the VAR system is impulse response functions (IRF). Often when analysing the relationships in VAR systems one particular variable is of interest, to isolate such affects the IRF is a good tool. Suppose that the effect of a shock to one variable in a system is of interest, the IRF traces out what effect a shock to one variable has to the system. If the impulse response of one variable is zero, then the impulse variable does not Granger cause the response variable. In ordinary IRFs shocks occur in one variable at a time, this can be problematic if the shocks, error terms, are correlated across equations. It is likely a shock to one variable is followed by a shock to another. The common approach to this problem is to decompose the covariance matrix of white noise errors using the Cholesky decomposition (Lütkepohl, 2005). These orthogonalized IRFs have the attribute that the order of variables in the system matters, the first variable affects the second variable and all the variables following but the second variable does not affect the first variable and so on. As stated by Lütkepohl (2005) the ordering of variables cannot be determined by statistical methods but follows from economical intuition.
220.127.116.11 VAR Model
To examine what affects the ex-post forward premium of EPAD contracts a VAR model containing several fundamental factors is constructed. The dynamic relationships are evaluated using a Granger causality test and through interpreting the orthogonal IRFs. As mentioned, the variable of interest is the forward premium in EPAD contracts, the variables that are expected to affect this and are subsequentially included in the model are the following; ex-post forward
premium for respective area, the hydro reservoirs levels deviation from its long term mean, wind power production, consumption level, consumption levels deviation from its long term mean, oil price returns, coal price returns, and emission rights returns. Nine different models
are estimated one for each area and all variables are determined to fulfil the covariance-stationary condition using the appropriate augmented dickey fuller test, the results of this test are presented in Table A-1 in the appendix. The Optimal lag length is chosen using the SIC and
was determined to be one in all VAR models. A general specification of the VAR(1) model for the forward premium is,
Yt = C + Φ1Yt"1 + εt. (6.10) Where Yt is a (8 × 1) vector of the specified fundamental variables for the respective area, C is
a (8 × 1) vector of constants, Φ1 is an (8 × 8) vector of coefficients and lastly εt is a (8 × 1)
vector of white noise error term with time invariant covariance vectors, E(εtε't) = ∑ε, and a
zero mean, E(εt) = 0. Determining the order of the variables in the system for the orthogonal IRFs is not a straight forward approach, there is no clear economic intuition of what variables are faster or slower. Therefore, variables that show significant results postestimation are placed last in the order. The ordering is as follows; emission rights returns, oil price returns, wind
power production, coal price returns, consumption level, consumption levels deviation from its long-term mean, the hydro reservoirs levels deviation from its long term mean and lastly the ex-post forward premium for respective are.
7.1 Forward Premium characteristics
In this section the mean front month series of the ex-post forward premium for Nordic EPAD contracts is presented, how it has changed over years and if there is a seasonal effect in the series. Using the Fama and French (1987) models it is examined how much of the futures basis in EPAD contracts is explained by a premium term and how much forecasting power is has.
Table 6 presents the front month series of the ex-post forward premium for EPAD contracts in the nine areas. Mean of each area shows that for all areas expect the Norwegian areas Oslo and Tromsø the forward premium is significantly different from zero on the 5 percent level. Further the premium varies both in sign and magnitude, all the Swedish areas and the Finnish area are positive and vary between 0.15 and 1.26 EUR/MWh. The Danish areas are very interesting, Copenhagen has the largest mean of 3.13 EUR/MWh while Aarhus has a large negative mean of -1.0 EUR/MWh. The standard deviations of the forward premium in EPAD contracts is the largest in the Danish areas as well.
Table 6. Descriptive statistics of the front contract forward premium series for the period 2011-2018 and for respective area.
Area Mean S.D. Skewness Kurtosis Min Max N
Luleå 0.155b 1.95 -0.78 5.06 -7.51 9.64 1,863 Sundsvall 0.188 b 2.13 -0.06 4.45 -5.51 11.13 2,030 Stockholm 0.932 a 1.96 -0.71 5.26 -7.46 10.62 1,863 Malmö 1.231 a 2.84 0.54 4.37 -5.92 12.39 1,863 Copenhagen 3.127 a 3.48 -0.50 6.04 -12.60 17.82 2,005 Aarhus -1.016 a 3.16 -0.17 5.04 -14.61 10.28 2,005 Helsinki 1.263a 2.81 0.01 3.37 -7.07 10.75 2,030 Oslo 0.104 1.69 0.51 4.52 -7.04 6.32 2,030 Tromsø -0.081 1.78 -0.37 3.67 -7.51 6.08 1,863
Note: a denotes p-value < 0.01, b denotes p-value < 0.05 and c denotes p-value < 0.1. Significance level is based on two-sided
Table 7. Mean of the front contract forward premium series for each area and for each year individually. Area 2011 2012 2013 2014 2015 2016 2017 2018 Luleå 0.278b -0.604 a -0.525 b 0.371 b 1.199 a -0.680 a 0.517 a 0.771 a Sundsvall 0.816a -0.655 a -0.451 0.372 1.185 a -0.641 a 0.540 b 0.762 a Stockholm 2.513 a 1.384 a 0.254 0.686 a 0.846 a -0.15 0.678 b 1.305 a Malmö 7.654 a 2.651 a 0.263 0.954 a 1.005 a 0.094 0.928 a 0.554 Copenhagen 2.047 a 4.039 a 2.836 a 3.174 a 3.278 a 2.626 a 3.407 a 3.709 a Aarhus -1.531 a 1.140 a -1.205 a -0.459 b -0.848 a -2.978 a -1.049 a -1.175 a Helsinki 0.959 b 2.036 a 0.464 c 1.236 a 0.401 1.621 a 1.406 a 2.033 a Oslo 0.970 a -0.364 c 0.325 b 1.005 a -0.918 a -0.193 c 0.060 -0.050 Tromsø 0.972 a -0.406 a -0.051 -0.292 1.435 a -0.179 -0.534 b -0.970 a
Note: a denotes p-value < 0.01, b denotes p-value < 0.05 and c denotes p-value < 0.1. Significance level is based on two-sided
T-test with HAC standard errors (Newey and West, 1987) testing a null hypothesis of zero. Values are in EUR/MWh.
The forward premium series is presented for each year and area individually in Table 7. There is no apparent pattern for any particular year or area. In most contracts the forward premium varies in size, but no forward premium series show signs of a trend or to follow a cycle. All forward premiums except those regarding contracts for Luleå, Copenhagen and Aarhus are non-significant for at least one of the eight years in the sample period. The statistically non-significant forward premiums in Stockholm, Malmö, Copenhagen, Aarhus and Helsinki contracts are all either positive or negative for all years. Contracts for Luleå, Sundsvall, Oslo and Tromsø display forward premiums that vary in sign from year to year, these four areas are all in the northern part of the Nordics where temperatures are relatively much lower than the southern parts of the Nordic area as well as being dependent on hydro generation.
The results from testing if there is any seasonality in the ex-post forward premium series are presented in Table 8. Estimating the ex-post forward premium against twelve monthly indicator variables without a constant shows the average forward premium in each month. January is represented by M1, February by M2 and so on. Copenhagen is the only area where the forward premium is statistically different from zero on at least the 5 percent level for all months, the other areas display months where the forward premium is not different from zero. All areas expect the Norwegian areas show indications of a seasonal effect in the forward premium series; the premium is more positive in winter months than in summer months. The contract for
Tromsø shows no signs of a seasonal effect in the forward premium and the Oslo forward premium is increasing from January to August and then very negative from September to December. The adjusted R-squared values are relatively large for all areas, varying between 0.15 and 0.56. The Copenhagen forward premium is explained best by only a seasonal effect and the Tromsø area is explained the least by a seasonal effect.
Table 8. Regression testing seasonality in the forward premium. Dependent variable is the front month forward premium series for respective areas and explanatory variables are monthly indicator variables, M1 represents January, M2 February etc. No intercept was included in the model.
Area Luleå Sundsvall Stockholm Malmö Copenhagen Aarhus Helsinki Oslo Tromsø M1 1.050a 1.066a 2.301a 2.444a 4.814a -0.562 3.300a 0.368a 0.508a (0.124) (0.0850) (0.140) (0.163) (0.259) (0.347) (0.247) (0.129) (0.117) M2 0.0716 -0.0359 0.800a 1.596a 3.027a -0.285 1.490a -0.158 -0.320 (0.139) (0.0970) (0.154) (0.224) (0.307) (0.338) (0.301) (0.127) (0.242) M3 0.218 0.231b 0.817a 1.507a 2.255a 0.330 0.469a 0.220 -0.0634 (0.147) (0.0940) (0.113) (0.105) (0.468) (0.531) (0.141) (0.170) (0.153) M4 -0.552 -0.571c 0.131 0.254 1.749a -0.653 1.024a 0.679a -1.460a (0.473) (0.310) (0.308) (0.340) (0.300) (0.439) (0.296) (0.227) (0.302) M5 -1.487a -1.488a -0.813b -2.335a 0.673b -2.203a -0.788b 0.782a -0.657b (0.487) (0.316) (0.318) (0.232) (0.267) (0.256) (0.335) (0.158) (0.260) M6 -0.481c -0.467a -0.0009 0.430 2.936a 1.211b 0.278 -0.500a 0.189 (0.268) (0.173) (0.231) (0.304) (0.299) (0.476) (0.421) (0.152) (0.187) M7 -1.134a -1.090a -0.581a -0.105 1.066a -2.337a -0.581 1.026a 0.383c (0.317) (0.199) (0.193) (0.244) (0.236) (0.341) (0.425) (0.158) (0.208) M8 0.155 0.179 1.382a 1.476a 2.140a -3.049a 1.516a 1.639a -1.244a (0.600) (0.397) (0.429) (0.489) (0.783) (0.750) (0.444) (0.189) (0.178) M9 0.193 0.254b 1.214a 1.460a 4.500a -1.599b 1.342a -0.866a 0.248 (0.160) (0.100) (0.241) (0.491) (0.420) (0.711) (0.355) (0.211) (0.306) M10 0.977a 1.152a 1.597a 1.406a 3.805a -1.886a 2.754a -0.810a 0.692a (0.124) (0.0642) (0.173) (0.291) (0.359) (0.387) (0.247) (0.136) (0.253) M11 1.056a 1.140a 1.872a 2.695a 5.040a -1.245c 1.590a -0.740a -0.268 (0.137) (0.0960) (0.209) (0.395) (0.367) (0.690) (0.230) (0.0749) (0.205) M12 1.517a 1.569a 2.610a 3.717a 6.194a 0.507 2.938a -0.539a 0.819a (0.130) (0.0853) (0.189) (0.362) (0.368) (0.682) (0.319) (0.117) (0.135) Adj. R2 0.205 0.218 0.356 0.376 0.564 0.230 0.329 0.220 0.147 N 1,863 1,863 2,030 1,863 2,005 2,005 2,030 2,030 1,863
Note: HAC standard errors (Newey & West, 1987) in parentheses. a denotes p-value < 0.01, b denotes p-value < 0.05 and c
denotes p-value < 0.1. Values are in EUR/MWh.