Pricing of Electricity Futures Based on Locational Price Differences: The Case of Finland

We find that the pricing of Finnish electricity market futures has been inefficient during the latest 10 years, when the trading volumes of Electricity Price Area Differentials (EPADs) have more than doubled. Even though the calculated futures premium on EPADs is related to some risk measures and the variables capturing the demand and supply conditions in the spot electricity markets, there has been a significant positive excess futures premium in the Finnish market, and financial market participants should have been able to utilize this also in economic terms. This finding is new and relevant for the participants of the Nordic electricity markets also in the future, because both the speculative and hedging-based trading is increasing in the Nordic markets.


Introduction
Electricity markets around the world have undergone a wave of deregulation and liberalization since the 1990s. The Nordic electricity market is a typical example of this development. In the Finnish and Nordic markets, vertically integrated monopolies that used to manage production, transmission and sales of electricity have been restructured. Nowadays production and sales operate under free competition, while nation-wide transmission and communal-level distribution networks remain regulated natural monopolies. A natural extension to the restructured wholesale markets has been the development of derivatives markets, since electricity is a homogenous commodity in a given geographical area with sufficient transmission network, capacity and similar power system. Well-functioning derivatives market is of high importance for market participants, since electricity is practically non-storable, and hence, subject to extreme price volatility.
Similar to retail and wholesale markets, pricing of derivatives written on different reference prices in the electricity markets has gained notable academic interest. The focus of research has unsurprisingly been on the derivatives in the largest and most mature markets, such as the ones in particular states in the US, the Nordic countries, and Germany/Austria (see e.g. Bessembinder & Lemmon 2002, Redl et al. 2009, Gjolberg & Brattested 2011, and Fleten & Hagen 2015. Due to physical transmission congestion, local prices may differ substantially from the reference prices causing market participants to incur locational basis risks. The Nordic market has been divided into 15 bidding areas based on transmission capacities between the areas, and Finland composes one area. Electricity Price Area Differentials (EPADs) are used to hedge price differences between a bidding area and the Nordic system price. Furthermore, Marckhoff & Wimschulte (2009) note that explicit exchange-listed derivatives on the area prices do not exist, since the market was designed on purpose so that overall liquidity would not split among several products. In bidding areas where the area prices differ significantly from the system price, hedging is based on dealing with two separate contracts, which together yield an implied futures contract on the area price, that is, by using 1) a futures contract based on the system price; and 2) futures contract, commercially known as an EPAD, based on the area price difference.
Contrary to the futures on electricity reference prices, such as the Nordic system price, the previous literature on EPADs is very limited. To our knowledge, only three studies (Marckhoff & Wimschulte, 2009;Kristiansen, 2004a and b) on EPADs pricing have been published in academic journals previously. More recently, EPADs have been studied by Spodniak et. al (2014) and Spodniak (2015) in conference papers. The main contribution of our research is to provide new empirical results on EPADs pricing. All the previous studies have focused on the relationship between the EPADs and respective area price difference or the ex-post futures premium, and we follow this approach, too. However, unlike Marckhoff & Wimschulte (2009) Spodniak et. al (2014 or Spodniak (2015), we attempt to link the ex-post futures premium of EPADs also to abnormal supply and demand conditions that might be of high importance specifically in the Finnish electricity market.
Electricity prices (and associated costs) are of particular importance to the competitiveness of Finnish economy due to Finland's cold climate and energy-intensive industry's large share of GDP that cause Finland to have one of the largest energy intensities, that is, the ratio of gross inland energy consumption to GDP in the EU. The electricity market spot price in Finland has differed substantially from the Nordic system price. For example, in 2015 the Finnish monthly area spot price exceeded the Nordic system spot price on average by 54.6%, exposing the Finnish market participants to a significant basis risk. Moreover, between 2006 and 2015 the system price and the area spot prices of Norway, Sweden and Denmark were on average 10.47%, 5.97%, 10.72% and 2.86% lower than the spot price in Finland, respectively. Furthermore, the Finnish area price difference has widened during the last years.
A natural question for the Finnish market participants is whether the area price differences are reflected in the EPAD prices. Self-evidently, this question is of interest for market participants hedging the future electricity consumption and generation. Speculators alike are interested to discover whether there are profitable trading strategies to be exploited. Prices of derivatives have also wider ramifications. In a market economy they provide price signals, which are essential for an efficient allocation of resources. EPADs prices could for example provide signals for investments in transmission capacity, or production planning of energy-intensive industry or electricity generators. Furthermore, a regulatory point of view matters here, too.
The European Union is harmonizing the European electricity market, and EPADs are under review. Regulators are inclined to discover, whether EPADs can efficiently be used to hedge against the area price difference, or should an alternative market structure be established, where the transmission system operators (TSOs) would for example issue financial transmission rights (FTRs) (Spodniak et. al, 2014).
Following all this motivation, we attempt to contribute to the existing literature by analysing first the size of the futures bias for Finnish EPADs, and how biased forecasts do the EPAD futures prices provide for the realized difference between the Finnish area and the Nordic system price. Furthermore, we want to find out which market factors can help to explain the possibly observed bias, or in other words, is the bias a consequence of market inefficiency, a risk premium, or a combination of them.
To answer these research questions we use monthly observations from January 2006 to January 2016 on the Finnish EPADs or the difference between the realized area spot price and futures price for the corresponding delivery period. Futures price data were obtained from a third party that have received it from the Nasdaq OMX Commodities exchange, whereas the spot prices were obtained from the Nord Pool, the physical power exchange in the Nordic market.
Our results imply that on average there has been a positive bias in the pricing of monthly Finnish EPADs. In other words, the futures price before the delivery period has exceeded the spot price difference in the respective delivery period in general. However, the bias is statistically significant only after excluding the extreme observations from the sample. Furthermore, the bias seems to exhibit seasonality being the highest during autumn and winter, and the lowest and even negative during the summer time. Both risk considerations and market efficiency seem to explain the bias and we find only little support for the findings of e.g. Bessembinder & Lemmon (2002), or Marckhoff & Wimschulte (2009), but we do find that the bias has increased after 2012. This could be attributed to the decrease in Russian imports, which may have widened the imbalance between the electricity consumers and generators that naturally hedge the Finnish area price leading to a positive premium in the futures market.
Finally, we also document a feedback mechanism (bi-directional causality) between the Finnish area price difference and the EPADs, which could hint that the futures market may be inefficient to some extent.
The rest of this study is structured as follows. In section two we give a short overview on the specific characteristics of Nordic and especially the Finnish electricity markets to lay some background regarding the market specific factors relevant for our empirical analysis. In section 3 we present the theoretical framework and results from some previous studies to serve as the background for our empirical analysis. Section 4 describes the data and empirical methodology used for our analysis, section 5 reports the empirical results, and finally, section 6 gives conclusions and suggestions for further research.

Characteristics of the Nordic and Finnish electricity markets
The Nordic market is one of the largest and was among the first liberalized electricity markets.
The history of the common Nordic market dates back to 1991, when Norway deregulated its wholesale electricity market. This formed a model for Sweden, Finland, and Denmark, that joined the common exchange titled Nord Pool, in 1996, 1998and 2000, respectively. Estonia, Lithuania and Latvia joined the exchange in 2010, 2012and 2013 coupled with the Western European spot markets. In practice this implies that a single algorithm is used to compute spot prices across the involved exchanges and to allocate the cross-border capacities. Currently the physical exchange is owned by the Nordic and Baltic transmission system operators (TSOs, see Nord Pool, 2015a and b). The first financial contracts on the system price were introduced in 1997, while the trading of EPADs, or CfDs (contracts for differences, as they were called at that time), were launched in 2000. In 2002 the physical and financial exchanges were demerged into separate companies, and in 2008 the financial exchange was acquired by Nasdaq OMX and merged into Nasdaq OMX Commodities (Nasdaq OMX, 2015).
Wholesale markets in the Nordic countries can be divided into short-term physical market and longer-term financial market. Market participants in the physical market include retailers and large industrial consumers, generators and trading houses. They have to be physically connected and to have a balance agreement with the TSO in the bidding area they are residing, as the physical market balances the supply and demand of electricity at every instant. In the day-ahead spot market the participants purchase and sell electricity for each hour for the next day according to their preliminary supply or consumption plans, which yields the spot prices for each hour. In the secondary market the trading is continuous, and participants can manage unanticipated imbalances or optimize their supply or purchase plans up to one hour before the delivery hour. Finally, the ancillary market maintained by the TSOs balances the power system in real-time, maintains system security and quotes the balance prices, which are used in settling the imbalances, i.e. the difference between actual generation (consumption) and electricity sold (purchased). The TSO of Finland is called Fingrid.
Trading in the day-ahead physical market takes place either bilaterally in the OTC list or in the Nord Pool market. The physical spot market is operational 365 days a year and produces spot prices for each hour. Over 300 market participants from the Nordic and Baltic countries submit daily their bids to the Nord Pool before 12:00 CET. Bids are like individual demand and supply curves: they reveal the quantity demanded and supplied at a given price. Nord Pool aggregates the bids to the market-wide supply and demand curves for each hour and the spot price clears the market. The individual orders are fulfilled if price at which the quantity demanded (supplied) is above (below) the spot price. This procedure is repeated for each hour yielding a spot price for every hour, and results for the next day are published normally before 13:00 CET.
Daily, weekly, monthly, quarterly and annual spot prices are computed as simple averages from the hourly prices.
The system price is computed from the aggregated supply and demand curves assuming no transmission constraints, yielding a reference price for the whole Nordic area. In a competitive market the clearing spot price then represents the marginal cost of the last generation unit needed to meet the given, highly inelastic demand. The area spot prices are computed similarly for each hour but there the exchange aggregates the orders only for each bidding area and takes into account the available transmission capacity which is determined by the TSOs. The flow of power is directed from the surplus (lower price) area to the deficit (higher price) area and the transmission capacity between them is utilized to the maximum, so the aggregated supply (demand) curve in the deficit (surplus) area is shifted in parallel right to the extent of maximum transmission capacity, which increases (decreases) the price in the surplus (deficit) area . If the   transmission computed by the Nord Pool exceeds the available capacity set by the TSOs for   example from SE1 bidding area to Finland, a higher spot price clears the Finnish market. Conversely, if the computed flow of power in all areas is within the limits set by TSOs, then the entire market has one common price, called the system price (Nord Pool, 2015b). The formation of area spot prices is depicted in Figure 1 whereas Figure 2 presents the bidding areas as well as the maximum transmission capacities between the areas. The financial market in turn allows the market participants to hedge their generation or consumption volumes in the longer-term and provides the access to the market also for the financial players, such as banks or hedge funds. In the Nordic market longer-term hedging can be either done over-the-counter (OTC) or in the Nasdaq OMX Commodities (NOC) exchange, where standardized futures, forwards (commercial name deferred settlement (DS) futures) and options are listed and traded on weekdays from 08:00 am to 16:00 (CET). NOC also provides clearing services, and in fact, a significant amount of OTC trades are cleared in the NOC.
Futures are contracts with a delivery period from one day to week, whereas forwards' delivery period is one month, quarter or year. Before they expire, the yearly contracts are cascaded into quarterly contracts, and quarterly contracts into monthly contracts. Neither forwards nor futures lead to physical delivery of electricity: they are cash-settled in the delivery (or settlement) period.
EPADs' delivery period ranges from one week to one year. However, in practice the weekly contract is illiquid, and hence, impractical for hedging. Monthly EPADs are listed for four months, quarterly EPADs for four quarters, and yearly EPADs four years prior to the delivery period.
Futures and forward contracts differ by their settlement. Forwards are settled only during the delivery period, whereas futures are settled also on a daily basis during the trading period. In theory, this has some implications for their pricing, as the cash flows occur at different times.
However, in practice, this effect is negligible. If interest rates are a given function of time, i.e. not stochastic, futures and forward prices are equal (Hull, 2009, 110). In this study, we make no distinction between them and from now on refer to both of them as the "futures".
All the contracts in NOC are quoted as €/MWh (with the minimum tick size of 0.01€) and refer to a baseload of one MW during the delivery period, which varies from 24 to 8760 hours. For a system futures contract the underlying price is the arithmetic average of hourly system spot price during the delivery period, whereas for an EPAD, the underlying price is the arithmetic average of the difference between the hourly area and system spot prices during the delivery period.
To understand how different futures can be used in hedging we give a simple example. Assume a Finnish industrial consumer with constant electricity consumption of one MWh per hour participates on the wholesale markets and intends to fix the purchase price for the next year (=delivery period). It purchases one MWh per each hour from the spot market, a one year contract written on system price, and a one year EPAD written on the Finnish area price difference. Now, suppose the futures prices are fixed at 25 €/MWh for the system future, and 7 €/MWh for the Finnish EPAD, and that next year the average system and Finnish spot prices realize at 26 €/MWh and 35 €/MWh, respectively. The realized area price difference is then 9 €/MWh. Hence, the cash flows for the consumer will be the following: Hence, the total cost is 306 600€ -8760€ -17 520€ = 280 320€, and when the annual purchase volume is 8760MWh, the average purchasing price realizes at 280 320 €/8760MWh = 32 €/MWh, which is the sum of the two hedges.
Liquidity among the different products and maturities varies a lot. Figures 3 and 4 describe the development of trading volumes in the past years for the futures on system price and Finnish EPADs on trades conducted or cleared at the Nasdaq OMX Commodities. Comparing annual turnovers, it is evident that the Finnish EPADs are far less liquid than the system futures. In 2015 the turnover of Finnish EPADs constituted barely half of the consumption in Finland, whereas for the system futures and the respective consumption in the Nordic and Baltic region the same ratio was nearly four in 2013. The trading of Finnish EPADs is concentrated on yearly contracts, and usually takes place at the OTC market. Regarding again the physical market, the Finnish electricity market has a number of important different characteristics compared to the whole Nordic market (see Figure 5). First, although nuclear and hydropower productions constitute a considerable share of the generation mix also in Finland, the share of hydropower is much lower than in the Nordic market and relatively larger share of it is based on unregulated, run-on-river hydro assets. Second, Finland also has less renewable and more fossil fuels based generation especially in the form of CHP generation.
The amount of plain condense generation has decreased as it has become less profitable due to the decreasing spot prices. Finally, and most importantly, as can be seen from the continuous difference between consumption and generation values, Finland is a net importer of electricity throughout the year. As seen from Figure 6, until 2011 Finland both exported and imported electricity to Sweden on a monthly basis, and the imports from Russia were relatively stable. However, in late 2011 Russia introduced capacity tariffs on its market, and as a consequence, imports from Russia decreased on weekdays during the peak hours. Reduced imports have primarily been replaced Net import by exports from Sweden and hence, increased the price difference between Sweden and Finland (see Table 1 below). While the price difference between the Finnish area and Nordic system price has not increased notably in absolute terms, in relative terms the difference has widened substantially.  The key interesting time series for our empirical analyses, i.e., the development of the monthly system spot price, Finnish area price and the Finnish area price difference are depicted in Figure   7. In the past years the system price has been historically low as the volume of price independent renewable (mainly wind) production has increased due to subsidies, prices of fossil fuels have decreased, weather has been relatively mild during winters, and the availability of hydropower has not been particularly tight. On the other hand, the sharp increases 06 -Jan 06 -Jul 07 -Jan 07 -Jul 08 -Jan 08 -Jul 09 -Jan 09 -Jul 10 -Jan 10 -Jul 11 -Jan 11 -Jul 12 -Jan 12 -Jul 13 -Jan 13 -Jul 14 -Jan 14 -Jul 15 -Jan 15 -Jul

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have remained largely unclear. This obviously calls for more research on this theme. In the next section we give details of the theoretical background behind our empirical analyses.

Theoretical background and previous studies
We use the expectations theory of futures pricing as the main theoretical background for our empirical analyses. Following Hull (2009), in this case the futures price at time t for delivery at time T, that is, , is based on equation where Et(St+T) is the expected spot price at time t+T, r is the risk-free interest rate, k the riskadjusted discount rate, and T measures the time to maturity. Denoting (k-r)=P, which can be interpreted as the risk premium, and substituting it into equation (3.1), yields and in a linear form for the log of prices, assuming the risk premium P is not time-varying, equation (3.2.) is given as , = ( + ) − . The risk premium in the expectations theory can be explained in two ways. For an investment asset, Hull (2009) explains it as the correlation between the returns of a futures contract in question and a broader, well-diversified stock and bond portfolio. However, for electricity markets and EPAD pricing the approach by Anderson & Danthine (1983), that considers the microstructure of the market seems more appropriate, or as Gjolberg & Brattested (2011, p. 4) note "in a balanced market, i.e., market where short hedging demand is exactly matched by long demand, the futures price should equal the expected spot price" and that "in a wellfunctioning market with unbalanced hedging demand, the futures price deviates from the expected spot price by the risk premium". Vehviläinen (2002) details the basic pricing ideas of electricity derivatives in competitive markets. He notes that "electricity that is delivered at any given future time is a separate asset from the electricity that is delivered now" and that "the non-storability of electricity makes the electricity market different from the financial and other commodity markets" (Vehviläinen, 2002, 49). Due to the non-storability he lists two unique features of the electricity futures pricing compared to other commodities. First, he notes that the electricity spot prices, i.e. the underlying prices for futures, are subject to spikes and volatility, because supply and demand has to be in balance all the time. Hence, they are difficult to model. Second, Vehviläinen (2002, 47) adds that "at no time it is allowed to own spot electricity as an asset" meaning that the market is incomplete, because it is not possible to hedge financial futures by creating a mimicking portfolio with a bank account and physical spot electricity. Based on this, he proposes that in a competitive market the electricity futures prices converge to risk-adjusted expected future spot price, as given in equation 3.2. Moreover, he notes that the final quotation of the futures price is the market's risk-adjusted expectation of the spot price at the delivery period.
In Figure 8 we clarify the notation used throughout our empirical analysis.
denotes the spot price in the delivery month T and −1, the futures price whose settlement occurs in the delivery period T. Note that the futures price is observed at T-1, i.e., before the delivery period T at the end of the previous month. To obtain the respective relative premiums, equations (3.3) and (3.4) are divided by the expected or realized spot prices at time T. Defined this way, the risk premium has similar interpretation as the market price of risk, which is commonly used in the financial literature (Weron & Zator, 2014). Some authors use the definitions above interchangeably, while some use the term bias (not every author uses logarithmic prices). Additionally, some make a distinction between them, but define the signs the opposite way.
In a widely cited paper Bessembinder & Lemmon (2002)  futures prices, while the opposite is not true, which would suggest the markets to be inefficient, and that the trading strategies of market participants could rely on the current spot prices. They also compute an ex-post average future premium for monthly contracts using the average futures prices during the last month of trading and prices from the last trading day, and find positive premiums for both the EEX and Nord Pool contracts on average. Additionally, they find evidence that the premiums are smaller in absolute terms for the last trading day than for the monthly average. They argue that this could indicate that the forecast error is a meaningful component of the premium as the market participants have more information available at the last trading day, and this is reflected in the futures prices. They also note that the sign of the premium varies over time, which they argue to provide further support for the presence of forecast errors.
Finally, Redl et al. (2009) test the above mentioned Bessembinder & Lemmon (2002) model and expand it to include factors that proxy for the supply and demand shocks in the delivery period. Their demand shock variable is the ratio between actual consumption and its long-term average in the relevant area. In the same manner, they construct the supply shock variable incorporating generation data for hydro and nuclear power. Their results from this part are somewhat mixed. In the EEX market they find partial support for the basic Bessembinder and Lemmon model, i.e., skewness of the spot prices explains the premium, but variance does not.
From the Nordpool data they find no support for the model, and attribute this finding to the fundamentals of the Nordic market, like the high amount of flexible hydropower, which yields less skewed spot prices. They conclude that the positive future premiums arise from the risk assessments of market participants and unforeseen shocks may help to explain the forecast error, but still, market inefficiency cannot be ruled out.
The Nordic market is also studied in Lucia & Torro (2011) Gjolberg & Brattested (2011) examine the "forecasting performance" of weekly Nordic system futures, and, unlike most authors, abstain from using the terms risk or futures premium. They document that the future prices exceed spot prices by (or the ex-post futures premium equals) 7.4 % -9.3 % on average on a monthly basis. They argue that for a number of reasons this cannot be explained solely based on risk considerations but also hints towards market inefficiency. They also note that the magnitude of error is suspiciously large and that the correlation of ex-post forecast error with different ex-post risk measures is zero. Moreover, they argue that the seasonality in forecast errors would indicate the presence of risk premium, as the demand risk varies seasonally. However, unlike Lucia & Torro (2012) they find that the forecast error does not exhibit clear seasonality. Finally, they interestingly discover that the forecast error has actually increased as the market has matured.
Weron & Zator (2014) study weekly futures in the Nordic market, and document negative futures premium for the front contract, and positive premiums for the contracts of three and six weeks from maturity. They extend some results of Lucia & Torro (2011) finding that the effect of unexpected availability of hydro power futures is not restricted only to low water reservoir levels. They document that the relationship between the risk (futures) premium and deviations in water reservoir from mean levels is positive (negative). Moreover, their regression results imply a weak positive relationship between the risk premium and unexpectedly high consumption. For the Bessembinder and Lemmon model they find no evidence that would support nor contradict it. Finally, they conclude that since fundamental factors can explain the premium to some extent, it more likely represents the price of risk than market inefficiency.
All the previously discussed studies define the risk or futures premium based on the realized (or expected) spot price during the delivery period, and the futures price based on the trading before the delivery period. Fleten & Hagen (2015) utilize a different approach. They view that the ex-post risk premium is hard to interpret. Furthermore, they argue that it measures the risk that does not need to be held. According to them the risk premium is determined by the hedging needs of retailers and producers as well as actions of traders, who have no incentive to hold futures over the delivery period. Even if they had, Fleten and Hagen argue that traders could offset the position with shorter maturity. Moreover, they highlight the same issue, as Fama & French (1987), namely the possible forecast error component of the ex-post risk premium.
Therefore, they conclude that the methods based on the delivery price are inappropriate. Fleten & Hagen (2015) study the risk premium and its determinants overnight during the trading period using data from January 2002 to September 2012 from the German and Nordic markets.
Similar to Gjolberg & Brattested (2011) they hypothesize that the producers hedge in longerterm, while retailers in short-term, as their volume forecasts become more accurate. They also find empirical support for this, because on average the risk premium for a contract is positive before it becomes a front contract (that nearest to maturity), and negative when it is a front contract.
The overnight approach by Fleten and Hagen would indeed seem more reasonable than the one based on ex-post delivery price given their focus is on risk premium of speculators, who close their positions before the delivery period. Their research provides also further support for the relevance of the time-to-maturity in the pricing of electricity futures. However, in this study the emphasis is on the delivery period risk premium for the reasons mentioned in the introduction. Therefore, in the empirical section we will stick to the ex-post approach.
Kristiansen (2004a) Kristiansen (2004a) notes that the sample size is limited. Therefore, the inference should be treated cautiously.
Marckhoff & Wimschulte (2009)  i.e., that the producers hedge for longer-term, while the retailers for short-term. For the Helsinki EPADs they compute the average futures premium for different contracts (yearly, quarterly, seasonal, and monthly) and find that they range from -1.34 €/MWh to 2.79 €/MWh and that positive premium occurs significantly more often than negative. They document also that the futures premium for the Finnish EPADs is higher for the winter contracts compared to the summer contracts, which could indicate asymmetric hedging demand between the seasons.
As mentioned earlier, the Bessembinder & Lemmon (2002)  In our analysis the set of additional variables includes water reservoir level at time t-1, i.e., from the period before the delivery period to examine whether the abnormal demand and supply conditions affect the ex-ante premium (assuming rational expectations and a zero forecast error). However, we replace the consumption variable by the temperature as the electricity demand may have changed structurally over the years due to changes in industrial demand. Hence, the temperature variable provides a proxy for purely exogenous demand shocks as the electricity demand depends on the temperature during the heating season.
Following Weron & Zetor (2014), in our empirical analyses we decompose the observed water reservoir level variable to the seasonal (historical) and stochastic (deviation from mean) components, and a similar decomposition is applied to the temperature variable. The decomposition mitigates the problem that the water reservoir level (or temperature) exhibits strong seasonality, and hence, captures the effects of all omitted, seasonal variables, whereas the stochastic component reflects the real effect of the varying water reservoir level or temperature (Weron & Zetor, 2014). In this case the regression model reads as where −1 is the historical water reservoir level in Norway, −1 the water reservoir level deviation from the average in Norway and −1 the temperature deviation from the historical average in Helsinki one month prior to the delivery period.
Only the water reservoir level variables from Norway were included since Norway has the largest hydro-reserves, and the water reservoir levels in Finland and Sweden are correlated with the Norwegian levels which would potentially lead to multicollinearity. Similarly, only the temperature in Helsinki is included as it has the highest impact on the Finnish area price difference, and temperatures in Oslo are correlated with temperatures in Helsinki. Finally, the historical temperature in Helsinki is omitted as it exhibits strong seasonality, which is already captured by the historical water reservoir level. Weron & Zetor (2014) document that the below (above) -average water reservoir level increases (decreases) the futures premium on system futures. For the Finnish EPADs the impact should be the opposite, i.e., below-average water reservoir levels in Norway decrease the possibility of widening area price difference and hence decrease the futures premium. The temperature coefficient should in turn have a negative sign, i.e., below-average temperature in Helsinki increases the electricity demand in Finland and the risk of widening area price difference, which should increase the futures premium. Finally, in order to shed light on the dynamics of the Finnish EPADs vs. Finnish area price difference, we estimate a VAR system (similar to Redl et al. 2009). We also argue why their model may be incomplete and lead to misleading interpretation of the market inefficiency. Next we describe the details of the data and methods used in the empirical part of this study.

Data and empirical methodology
Monthly system and Finnish spot price (computed from hourly averages) data were retrieved   The spikes have been explained by below-average temperatures, low availability of Swedish nuclear power plants as well as outages from the transmission lines from Norway to Sweden, which increased the area prices in Sweden, Eastern Denmark and Finland (NordReg, 2011, 11-17). Moreover, hydropower availability has also been below-average (see Figure 10 below).
The  As discussed earlier, asymmetric hedging needs and the fact that Finland is a net importer of electricity might well reflect the observed positive realized futures premium. However, the premium seems to vary between seasons. Table A1 in the Appendix exhibits descriptive statistics within seasons. Futures premium seems to be the highest in autumn and the lowest, even negative in summer. Furthermore, excluding again the spikes during the winter of 2009 -2010, the premium becomes statistically significant also in winter exceeding that of autumn.
A possible reason for the seasonality in the premium is that electricity consumption varies seasonally which could cause the mismatch of hedging demand between natural sellers and buyers of Finnish EPADs to vary, too. Alternatively, the market participants' perceived risk is greater in autumn and winter than in summer leading to a positive premium during winter and autumn and negative in summer. Lucia & Torro (2011) document that the weekly Nordic futures have smaller futures premium in summer than in winter and attribute this to the seasonally varying electricity demand and the risk of price spikes.
As the final part of our descriptive data analysis we performed the Dickey-Fuller and Phillips-Pearson unit root tests, that both gave the same conclusion that the two key interesting price series for our analysis are both stationary processes3. This is in line with the previous findings of e.g. Redl et al. (2009) who document that the monthly Nordic system futures and spot time series are stationary. Hence, we will continue our further analyses assuming that the data generating processes for the electricity market price series in our data set are stationary.
In addition to the actual price data, in the regression analysis we will also utilize some exogenous variables that have previously been found important in empirical electricity market research. As discussed earlier, the demand and supply conditions in the Nordic market are significantly affected by the climate and weather. For our study the time series of water reservoir level data (as a fraction of the total capacity) for Finland and Sweden were retrieved Since the water reservoir levels vary seasonally, the market participants focus on the deviations from the historical average levels (Lucia and Torro, 2011). Therefore, following Lucia & Torro  Table A2 in the Appendix.
The historical and observed values are plotted in Figure 10, where the seasonal pattern is evident. As Weron & Zator (2014) note, water inflows lead the reservoir levels; the largest inflows to the reservoirs occur in the spring and early summer as snow begins to melt. Vice versa, the inflows decrease in the autumn as temperature decreases below zero. As a result, the water reservoir levels are the highest in autumn and lowest in the early spring. To our knowledge, previous research has not examined the effect of temperature to the futures bias directly. Redl et al. (2009) and Weron & Zator (2014) included electricity consumption indices to their models (as deviations from the long-term averages). As discussed above, electricity demand varies considerably within seasons in the Nordic countries, and Finland, too. Hence, temperature (being more stable than consumption over longer periods) deviations from the long-term average seem as a viable proxy for the demand shocks.  In addition to the standard OLS regression analysis we will use the Vector Autoregressive (VAR) approach utilized also in some previous studies regarding the Nordic electricity market.
For example Redl at al. (2009) have used an unrestricted VAR model to examine the relationship between the EEX peak load and Nord Pool base load contracts. We will use the same methodology for the Finnish area price difference and EPADs prices. We will also use Granger (1969)  Here it is worth to mention that according to Redl et al. (2009) where ai, bj and cj are the parameters to be estimated, m is the optimal lag length from the VAR model for variables X and Y, and , , , are the error terms in the estimated equations.
Variable Xt Granger causes Yt, if some of the coefficients bj differ from zero. Similarly, Yt Granger causes Xt, if some of the coefficients dj are not zero. If both occur, there is a feedback relationship or bi-directional Granger causality between Xt and Yt. The model can also be extended to include a contemporaneous cross-term: values. In addition, they find that the spot prices Granger cause the futures prices (d1 is significantly different from zero) but the futures prices do not Granger cause the spot prices (b1 is not significantly different from zero). Hence, they conclude that "spot prices in the trading period of the forward contracts are relevant for the price formation of the forwards whereas the opposite is not true" and therefore argue that "there is strong evidence that the predictive power of the forward price is weak" (Redl et al. 2009, 361).
Because these findings actually speak for the possibility of inefficiencies in the relevant markets, it is worth to take a closer look at their results. In fact, their conclusions can be criticized at least from two points of view. First, notice the time notation for the futures term in equation 4.5b. The term −1 −2, −1 refers to the price of futures contract, whose delivery period is T-1. Hence, it should be of no surprise that it does not explain well the spot price at T. A more fruitful approach will be to replace −1 −2, −1 with an "instantaneous" term −1, so that for this stage the set of equations will be: −1, = 2 + 1 −1 − , −1 + 1 −1 −2, −1 + , (4.6a) − , = 1 + 1 −1, + 1 −1 − , −1 + , (4.6b) Second, Redl et al. (2009) argue that their results imply that the futures market might not be efficient, since spot prices in the trading period affect futures (whose delivery period is the next month) prices. This would certainly be a valid conclusion if the spot prices of the consequent months would not be strongly correlated. However, spot prices are auto-correlated as is evident from the significance of the parameter 1 in their results. Therefore, it is not completely surprising that the market participants' expectations (futures price) of the next month's spot price are affected by the spot price in the preceding month. Nevertheless, in an efficient market one should a priori expect the coefficient 1 to be less significant and further away from unity than the coefficient 1 * .
All the previous studies give us the basis to discuss own results based on the most recent data.
Next we will report the results from our empirical analyses utilizing the Nordic and Finnish electricity market data from the period of January 2006 -January 2016.

Empirical results
In Table 3 we report the empirical results based on the regression models (3.6.) and (3.7), that are comparable to the much cited Bessembinder and Lemmon (2002) Table 3. Results from the OLS regressions of equations (3.6) and (3.7). We used the Newey-West correction to obtain the autocorrelation and heteroscedasticity consistent standard errors in our estimations, and t-statistics for the null of zero coefficients on the variables are reported in parenthesis. The full sample is from January 2006 to January 2016, n denotes the number of observations, R 2 the coefficient of determination from the regression, and *, ** and *** the significance of parameter estimates at 10, 5 and 1 % risk levels, respectively. When regressing the premium to the fundamental variables affecting the demand and supply of electricity, we find that the average excess premium (i.e., the constant term in the regressions) is not statistically significantly different form zero anymore, so the arbitrage possibilities would seem to vanish from this market. In addition, according to our results reported in Table 4, contrary to e.g. the findings of Weron & Zetor (2014) only the seasonal component of the water reservoir variable −1 seems to be statistically significant in our data, and especially after controlling for the hard winter of 2009 -2010, it is significant even at the 1 % risk level, and increases the premium. It captures all the seasonal effects so that the higher is the absolute water reservoir level, the higher is the futures premium. This is consistent with the fact that the premium has been highest during autumns and lowest during summers as presented in section 4. Table 4. Results from the OLS regressions of equations (3.9) and (3.10). We used the Newey-West correction to obtain the autocorrelation and heteroscedasticity consistent standard errors in our estimations, and t-statistics for the null of zero coefficients on the variables are reported in parenthesis. The full sample is from January 2006 to January 2016, n denotes the number of observations, R 2 the coefficient of determination from the regression, and *, ** and *** the significance of parameter estimates at 10, 5 and 1 % risk levels, respectively. Equation (3.10) is , 2012 and equation (3.9) is the same without the Russian import dummy Y2012.

Parameters
Equation ( The results from the regression taking into account the period after 2012 are shown in the righthand side (the second and fourth) columns of Table 4. There we see that the decrease of Russian imports from the autumn of 2011 onwards has a statistically significant (at 10% level) effect, and the coefficient on the dummy variable implies that the premium has been 0.95 €/MWh higher after 2012 due to this effect. The result is intuitive as the Russian importers might have been natural sellers of Finnish EPADs and as imports from Sweden have increased, the "deficit" between natural buyers and sellers of Finnish EPADs has widened further. Based on the observed very low R 2 values it is obvious that also the regression analysis based on equations (3.9) and (3.10) may still suffer from an omitted variable bias. Important variables that may affect market participants' perception of risk are for example the expected availability of transmission lines from Sweden to Finland, and the availability of nuclear power in Finland.
Both of them affect the area price risk in Finland. Unfortunately, data on them were not available, and hence, they could not be included in the regression. It seems obvious that we are not able to find very strong empirical support for many of the previous studies from our data set based on the standard regression model approach. However, it is also obvious that there are arbitrage opportunities in the financial market segment of the Finnish electricity markets, because the excess futures premium is positive and statistically significant in every specification considered so far. This speaks for the possibility that the Finnish EPADs market might not be efficient. Hence, as the final stage of our study we report the results from the VAR analysis that should give us more specific information about the possible inefficiencies, i.e., dynamic connections between the relevant variables in the pricing of Finnish EPADs. Optimal lag lengths for our VAR analyses were chosen based on using the minimum values for the Akaike and Schwarz information criteria, and they suggested that the proper lag length is two in our data set. However, for comparison we also ran the regressions with a lag length of one to compare the results to those of Redl et al. (2009).The results for the basic VAR model are presented in Table 5, where we report the actual regression coefficients from the VAR analysis enabling to reveal the actual dynamic dependencies between the examined price series.  (2) and VAR(1) models especially the first lag of spot prices is significant in explaining the current futures prices. This is also confirmed by the F-tests, which indicate that the spot prices Granger-cause the futures prices, but the futures prices do not Granger-cause the spot prices (even though this is not the case at 10% risk level in the case of VAR(2) model). This implies that the previous spot price affects the market's expectation of the next month's spot price, that is, the futures price for the next month's delivery period, and provides evidence that the futures pricing may be inefficient at least to some extent. However, it is not possible to state that the market is completely inefficient although the past spot prices help explain the futures prices. As the consecutive area spot differences are serially correlated, the market is not totally irrational when it resorts to the previous realized spot price difference in estimating the next month's area price difference Because in our previous results the extreme winter conditions in 2009 -2010 and also the reduction of Russian imports from 2012 onwards proved to have role to play in the analysis of pricing behavior in the Finnish markets, for the sake of robustness of our results, we next estimated the VAR models with time dummies to control for these effects. The results are presented in Table 6 and do not change much from the results given above, although they indicate the clear significance of the respective periods, too. However, here we find that the hard winter of 2009 -2010 has had an increasing effect specifically on the spot prices but not on the futures prices at all, whereas the reduction of Russian imports has had a statistically significant and positive, i.e. increasing effect both on the spot and futures prices, and the effect has been almost of same magnitude in both markets. where in addition to the notations given in Table 5, Y12 refers to the dummy variable describing the reduction of Russian imports from 2012 onwards (Y12 =1 after January 2012, and zero before that), and W0910 is the dummy variable for the winter 2009 -2010 (W0910 = 1 from 12/2009 to 3/2010 and zero otherwise). For all the other notations see Table 5.
VAR (2) VAR (1)  As discussed in section 4 (see equations (4.6) and the discussion therein), inference based on the traditional reduced form VAR setup might be ambiguous to some extent owing to the fact that it does not include the contemporary futures price term, and because the spot price and futures prices for the same delivery period constitute perhaps the most interesting relationship between the two series, it should actually be taken into account in the VAR model. Hence, as the final step, to shed more light on the pricing dynamics we regressed the spot price against its own lags, and lagged and contemporary values of the futures price series. The results from this stage are presented in Table 7.  Table 6. Hence, at least in terms of statistical significance, our argument in favor of using the contemporaneous values in pricing the Finnish electricity market EPADs seems strongly valid. The F-tests on Granger causality confirm that when the series for contemporary futures price is included to the model, the futures prices Granger cause the spot price. This mitigates the relevance of our earlier results that suggested market inefficiency based on the role of past prices in evaluating the futures prices for the next period.
In conclusion, there is a clear bi-directional causality between the futures and spot prices in the Finnish market. This is illustrated in Figure 12. On one hand, −1 − , −1 (the previous spot price) influences −1, (the contemporaneous futures price, or market's expectation for the spot price in next month's delivery period), and on the other hand −1, also has predictive power over − , (the contemporaneous spot price). The connection between them seems to be based on the fact that the spot prices are serially correlated. This implies that the market's expectation of the next month's spot price may be at least partially influenced by the spot price in the previous period, and at the same time, the futures market need not be as inefficient as would seem at the first glance.

Conclusions and suggestions for further research
In recent years, the electricity market spot prices have been systematically higher in Finland than in other Nordic countries. This has exposed the Finnish market participants to significant basis risks when using only the Nordic system futures for hedging. We examined the pricing of Finnish EPADs that are used to hedge the price difference between the Finnish spot price and the Nordic system price. More specifically, we analyzed whether the monthly EPADs prices are biased estimates of the future area price difference and whether the bias can be attributed to market inefficiency or a risk premium.
Our results imply that on average the futures prices before the delivery period have exceeded the Finnish area spot price difference in the respective delivery period. This result is clearly intuitive as Finland is a net importer of electricity and as a consequence, there are less natural sellers of Finnish EPADs than buyers and since the area price difference risk is biased upwards.
The positive bias is also in line with the results from Redl et al. (2009) and Lucia & Torro (2011) from different electricity markets.
The bias seems to vary between seasons, and is significantly different from zero only when excluding the extreme observations of winter 2009 -2010 from the sample. Again, Lucia & Torro (2011) obtained a similar result for the weekly Nordic system futures. A possible reason for the seasonality might be that electricity consumption varies seasonally which might cause the systematic mismatch of hedging demand between natural sellers and buyers of Finnish EPADs to vary also. Alternatively, the market participant's perceived risk may be greater in autumn and winter than in summer leading to positive premium during winter and autumn and negative in summer.
Both risk considerations and market inefficiency seem to explain the bias. However, we document little support for the findings of previous studies, that have linked the bias to abnormal electricity supply and demand conditions (Weron & Zator, 2014) or different kind of risk proxies derived from realized spot price distributions in the preceding period (Marchhoff & Wimschulte, 2009). Instead, one of our strongest results is that the bias has increased after 2012. This could be attributed to the decrease in Russian imports, which may have widened the imbalance between the electricity consumers and generators that naturally hedge the Finnish area price leading to a positive futures premium in the futures market. The fact that the bias, similar to the electricity consumption pattern, exhibits seasonality, might also suggest that it may to some extent be explained by risk considerations.
Finally, we document a strong bi-directional causality relationship between the Finnish area price difference and the EPADs, which could hint that the bias may at least partly stem from a somewhat inefficient, backward-looking futures market that utilizes the realized area spot price difference to forecast the next period's area spot price difference. Redl et al. (2009) found similar results for the earlier data on Nordic system and EEX futures. The bi-directional relationship might also contribute to the seasonality of the futures premium as the area price difference exhibits also some seasonality. However, due to the fact that the area spot price differences are serially correlated it is impossible to state that the futures market is completely inefficient even when it incorporates past information to futures prices for the next's period price.
The results show that the Finnish market participants should pay attention to their area price hedging policies and timing as the futures market has somewhat positive bias that varies within seasons, and since the market seems to clearly be backward-looking. Due to the fact that this study has solely focused on the Finnish EPADs and monthly contracts and the EPADs are unique to each bidding area which by themselves have unique fundamentals, it is unclear how widely the results can be generalized to other bidding areas. However, it seems reasonable to assume that they may well exhibit similar peculiarities for example in terms of the past spot prices affecting the futures market.