Hedging with futures: Efficacy of GARCH correlation models to European electricity markets

Int. Fin. Markets, Inst. and Money 20 (2010) 135–148

Contents lists available at ScienceDirect

Journal of International Financial Markets, Institutions & Money j o ur na l ho me pa ge : w w w . e l s e v i e r . c o m / l o c a t e / i n t f i n

Review

Hedging with futures: Efficacy of GARCH correlation models to European electricity markets Giovanna Zanotti a,∗, Giampaolo Gabbi b, Manuela Geranio c a b c

Bergamo University, SDA Bocconi Faculty, Italy Siena University, SDA Bocconi Faculty, Italy Bocconi University, Italy

a r t i c l e

i n f o

Article history: Received 12 February 2009 Accepted 8 December 2009 Available online 14 December 2009 JEL classification: C5 G2 Q4 Keywords: Hedge ratios Futures GARCH Correlation Electricity

a b s t r a c t European electricity markets have been subject to a broad deregulation process in the last few decades. We analyse hedging policies implemented through different hedge ratios estimation. More specifically we compare naïve, ordinary least squares, and GARCH conditional variance and correlations models to test if GARCH models lead to higher variance reduction in a context of high time varying volatility as the case of electricity markets. Our results show that the choice of the hedge ratio estimation model is central on determining the effectiveness of futures hedging to reduce the portfolio volatility. © 2009 Elsevier B.V. All rights reserved.

Contents 1. 2. 3.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The electricity markets in Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Naïve one to one hedge ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. OLS estimated hedge ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. GARCH hedging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

136 137 138 139 139 139

∗ Corresponding author. E-mail addresses: [email protected], [email protected] (G. Zanotti), [email protected] (G. Gabbi), [email protected] (M. Geranio). 1042-4431/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.intfin.2009.12.001

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4. 5. 6. 7.

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3.3.1. Constant conditional correlations models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2. Dynamic correlations models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimal hedge ratio estimation and hedging performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction Since the second half of the 1990s, European electricity markets have experienced a wide liberalization process and have changed their structure from a regulated monopoly to a competitive open market. At the end of 1996, the first EU Directive on electricity (1996/92/EC), later replaced by the second Directive (2003/54/EC), set the initial common rules for the creation of an internal competitive electricity market. Three are the pillars of these directives. The first pillar is the unbundling of monopoly position. The directives state that in order to increase competition within the market, generation, transmission and distribution activities must be kept separated. Only generation and distribution should be liberalized and subject to competition. The second pillar is the principle of the Third Party access. The owner of the network is obliged to give access to all deliveries requests and should operate with transparent and non-discriminatory criteria. The third pillar is about the opening of the demand side. The notions of eligible customers and Single Buyer were introduced. Eligible consumers are wholesale customers that have the right to access the market and buy energy at the most convenient price. The Single Buyer creates competition among producers and represents retail consumers in the market. Compared with other traded commodities such as gold, coffee or crude oil, electricity poses two distinct challenges. Firstly, it is not possible to store electricity in any significant quantity so there is a need to match instantaneous demand with instantaneous generation. Secondly, the demand and supply are inelastic. This causes energy prices being characterized by extremely high volatility, seasonal jumps and daily effect. These huge prices changes cannot be controlled using inventories. To hedge price volatility futures contracts may be used. Implementing a hedging strategy with futures requires several steps: define the delivery date of the futures to be used for hedging; identify the optimal amount to hedge; estimate the optimal hedge ratio. In this paper we test if hedging with electricity futures actually allow to reduce the volatility of portfolio returns and we investigate the best model to estimate the hedge ratio. The traditional assumption that the minimum risk hedge ratio is the same irrespective of when hedging is undertaken has in fact been proved not to hold for markets characterized by high volatility, irregular correlation between spot and futures returns, limited and imperfect arbitrage opportunities, non-storability of the underlying. Compared to previous literature we estimate hedging efficacy for three of the most liquid electricity European futures markets: Nord Pool, EEX, and Power Next. Furthermore we test the hedging performance of not previously tested model such, the GARCH Dynamic Conditional Correlation (GARCH-DCC) and the Exponential Smoothing Conditional Correlation (Exp-DCC). If the dynamic correlation is an important issue to consider these models should lead to better hedging performances. Electricity markets with their high volatility seem good test for our hypothesis. Our results show that hedging may be ineffective when markets are characterized by high time varying volatility and when traditional hedging strategies, based on a static hedge ratio, are applied. A reduction of hedging errors is estimated when dynamic volatility and correlation approaches are implemented. The paper is organized as follows. Section 2 introduce the fundamental characteristics of the European electricity markets. In Section 3 we describe the methodology. Section 4 reviews the literature. Sections 5 and 6 present data and findings. Section 7 concludes.

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Table 1 Electricity market opening and eligible consumption ThW by annual consumption in European Countries (2006 and 2007). Country

Austria Belgium Bulgaria Cyprus Czech Republic Denmark Estonia Finland France Germany Greece Hungary Ireland Italy Latvia Lithuania Luxembourg Netherlands Poland Portugal Romania Slovakia Slovenia Spain Sweden United Kingdom

Market opening (%)

Consumption (TWh)

2006

2007

2006

2007

100.0 87.4 60.0 30.8 100.0 100.0 13.0 100.0 69.0 100.0 70.0 37.1 100.0 73.0 76.0 74.0 84.0 100.0 80.0 100.0 n/a 80.0 75.0 100.0 100.0 100.0

100.0 100.0 100.0 31.8 100.0 100.0 13.0 100.0 100.0 100.0 90.1 22.3 100.0 100.0 100.0 74.0 100.0 100.0 100.0 100.0 n/a 100.0 100.0 100.0 100.0 100.0

62.0 89.9 n/a n/a n/a 35.8 n/a 90.0 478.4 567.0 54.6 n/a n/a 337.5 n/a 8.9 n/a 112.0 149.8 49.2 53.0 n/a 13.7 268.0 157.8 352.8

61.7 90.1 n/a n/a n/a 35.7 n/a 90.3 480.3 569.2 55.3 n/a n/a 339.9 n/a 9.1 n/a 112.0 154.2 50.1 54.1 n/a 13.9 276.3 157.4 350.1

Source: Commission of the European Communities, report on progress in creating the internal gas and electricity market, Brussels, 11 March 2009.

2. The electricity markets in Europe Following the EU Directive on electricity (96/92/EC and 2003/54/EC) most European countries have opened to competitive mechanisms (Table 1). Two markets were in fact already in existence. The first European Exchange for electricity trading, the Electricity Pool in England and Wales, was created in 1990, followed by the Nordic Power Exchange (Nord Pool), founded in 1993. With the approval of above-mentioned European Directives, electricity markets appeared in many other European countries, as Table 2 shows. Table 2 The European Energy Exchanges. Country

Date

Name

United Kingdom

1990–1999 2001 1990 1993–1996 1998 2000 2000 2000 2001 2001 2002 2004 2005

Electricity Pool UK Power Exchange (UKPX) now APX Power UK Amsterdam Power Exchange (APX) Nord Pool Scandinavia OMEL Leipzig Power Exchange (KPX) European Power Exchange (EEX) Polish Power Exchange (PPX) Powernext Power Market operator EXAA Gestore del Mercato Elettrico (GME) Belpex – Belgian Power Exchange

The Netherlands Norway Spain Germany Poland France Slovenia Austria Italy Belgium

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Table 3 European Energy Exchanges features. Country

Austria Belgium Bulgaria Cyprus Czech Republic Denmark Estonia Finland France Germany Greece Hungary Ireland Italy Latvia Lithuania Luxembourg Netherlands Norway Poland Portugal Romania Slovakia Slovenia Spain Sweden United Kingdom

Total share of 3 largest producers (%)

Volumes traded at spot market power exchanges (% of consumption)

2006

2007

2006

2007

52.2 93.0 56.4 100.0 73.5 75.0 99.0 67.0 93.0 68.5 99.0 67.0 72.0 66.3 95.0 84.0 74.8 62.0 43.7 62.8 75.0 65.1 84.8 89.8 60.3 79.0 37.5

52.0 99.9 56.4 100.0 76.9 75.0 99.0 68.0 93.0 85.4 n/a 67.0 n/a 61.2 93.0 84.0 80.0 61.0 40.0 50.9 72.5 63.7 85.2 92.7 76.0 78.0 41.0

2.70 0.59 n/a n/a n/a 96.09 n/a 42.00 6.19 15.60 102.75 n/a n/a 58.22 n/a 18.88 n/a 17.14 n/a 1.11 0.00 7.74 n/a 0.01 51.90 70.22 4.33

3.73 8.43 n/a n/a n/a 99.16 n/a 45.85 9.20 21.48 105.70 n/a n/a 65.11 n/a 21.98 n/a 18.48 n/a 1.60 43.63 9.32 n/a 0.01 80.06 85.32 4.71

Source: Regulators’ data.

European Energy Exchanges share some common characteristics. All the systems are nonmandatory, since producers and consumers may choose either to interact on the market or to enter bilateral contracts for the delivery of electricity in the short and in the long term. All the systems have a demand side bidding system. Finally, markets have chosen to set the electricity price based on the marginal price rule: 24 auctions, one for each hour, are held the day before the delivery and the last unit dispatched fixes the closing price for all the market participants. Nevertheless important differences still exist among the Directives implementation status and the productivity structure for several countries. Directive 2004/54 requires each member country to implement both legal and functional unbundling for transmission and distribution so to increase competition, reduce costs and lead to non-discriminatory network access. But in some countries a governance overlapping between the Transmission System Operator (TSO) and some suppliers, usually the former monopolist, still survives. Differences also exist in the productivity structure reflecting different cost and prices volatility, generally due to hydro and nuclear ratio production for each country. Moreover, energy markets show disparities (Table 3) in terms of total share of the three largest producers, total trading and total consumption ratio (Commission of the European Communities, 2009). The liberalization process and the growing number of markets and players have grown the attention of electricity producers and distributors on financial performances and risk management, which is particularly needed to stabilize the competitive open market drivers over prices and returns. This makes imperative to optimize the market risk depending on the observed volatility. 3. Methodology Most of the tools used to transfer the market risk are based on derivatives. When the price is for quoted assets, futures contracts help to hedge the risk, generally reducing other risk factors, such

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as liquidity and counterpart. The hedge ratio specifies how many futures contract should be either bought or sold to hedge the underlying position in order to minimize the portfolio variance. Several ways to estimate the hedge ratio have been proposed. 3.1. Naïve one to one hedge ratio The most naïve approach to futures hedging is the one to one (zero basis) hedge ratio, implying that for any given spot position, an equal amount of futures positions are undertaken. This hedge ratio is very easy to calculate: each spot contract is offset by exactly one future contract. However it assumes that the covariance between futures and spot returns equals the variance of futures returns. 3.2. OLS estimated hedge ratio In most applications, to recognize the existence of possible different volatilities in spot and futures markets, the optimal futures position is calculated by minimizing the variance of the spot-future portfolio. Let rst represents the actual return on a spot position held from time t − 1 to time t. Similarly let rft represents the actual return on a futures position. The expected return, E(rpt ), of a portfolio comprising one unit of the spot position and ˇ unit of the futures contract may be written as E(rpt ) = E(rst ) − ˇt−1 E(rft )

(1)

where ˇ is the hedge ratio determined at time t − 1 for employment in time t. The variance of the portfolio may be written as 2 2 2 = st + ˇt−1 ft2 − 2ˇt−1 cov(rst , rft ) pt 2 , 2 where pt st

(2)

and ft2

represent the conditional variances of the portfolio, of the spot and of the futures positions and cov(rst , rft ) is the conditional covariance between the spot and the futures position. Therefore, the optimal number of futures contract in the hedger portfolio is equal to ∗ =− ˇt−1

cov(rst , rft ) ft2

(3)

The optimal hedge ratio is given by the fraction of the covariance between spot and futures returns and the variance of futures returns. If the conditional variance–covariance matrix is time invariant then the constant optimal hedge ratio may be obtained as the estimated slope coefficient in the OLS regression where spot returns are the dependent variable and futures returns are the independent variable: rst = ˛ + ˇrft + εt

(4)

where rst and rft are, respectively, the spot and futures returns for period t, and the OLS estimator of ˇ provides an estimate for the minimum-variance hedge ratio. In this case the hedging is static the hedge ratio is estimated once and applied to the all hedging period. In our paper we also apply a Dynamic OLS Hedging. In this case the regression is re-estimated n-times over n time intervals. This strategy generates a spot-future portfolio with a vector of hedge ratios depending on time. 3.3. GARCH hedging A major problem with the OLS hedge ratio is the assumption that variance–covariance matrix of returns are constant over time. This hypothesis may be difficult to accept for high volatile energy markets. We employ GARCH models to make the conditional variances and covariances time varying and check whether the model improves the hedging effectiveness. Various approaches have been suggested for the modelling of the correlations between two assets. The simplest and most used model is the rolling window correlation methodology. Even if widely used, this methodology, due to its fixed time interval and equal weights given to all the observations, may ignore structural change

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of volatility. GARCH time varying variances and covariances models are an alternative to model the heteroskedasticity often found in time series. Numerous extensions of GARCH models have been proposed and there is not a unique answer to the ideal specification of a multivariate GARCH. On one hand, a GARCH model should be flexible and able to represent the actual dynamics of variances and covariances. On the other hand, as the flexibility and the number of parameters increase, the complexity of the estimation increases as well. A standard multivariate GARCH model may be defined as 1/2

rt = Ht

t

(5)

where rt is a stochastic vector process with dimension N × 1 such that Ert = 0. Ht is the conditional covariance matrix of rt and t is an i.i.d vector error process such that Et t = I. This is a general multivariate GARCH framework with no linear dependence structure in rt . The most general expression of multivariate GARCH model, the VEC model of Bollerslev et al. (1988) is a generalization of the univariate GARCH, where every conditional variance and covariance is a function of lagged conditional variances and covariances, lagged squared returns and cross-products of returns. The VEC is a very general and flexible model, but flexibility comes with three main disadvantages: the number of parameters to estimate is very large, unless N is small; there exist only rather restrictive conditions in which the conditional covariance matrices are positive definite; parameters estimation is computationally demanding. Subsequent literature worked on developing models to overcome the VEC limits. Here we present and discuss pros and cons of alternatives GARCH models used in our estimations. 3.3.1. Constant conditional correlations models This model is based on the decomposition of the conditional covariance matrix into conditional standard deviations and correlations. The Constant Conditional Correlation (CCC) model of Bollerslev (1990) assumes that the conditional correlation matrix is time invariant and can be expressed as Ht = Dt RDt

(6)

where Dt is a N × N matrix of time varying standard deviations and R is a N × N time invariant correlation matrix. The constant correlation assumption makes the model easier to estimate and ensures the semidefiniteness property. We estimate the conditional covariance, based on information regarding the fixed correlation and the product of the two conditional standard deviations. However the CCC model presents two major drawbacks. First, the assumption of constant correlation is against the empirical evidence that correlations increase during crisis or high volatility periods. Second, the difficulty on capturing interactions among assets in the model. 3.3.2. Dynamic correlations models Engle and Sheppard (2001) proposed a new class of models that are easy to estimate as the CCC with the benefit of non-constant correlations. Engle (2002) demonstrates that this family of multivariate GARCH models are superior to moving average methods alternatively used to estimate volatility. The dynamic correlation structure of this model (DCC) differs from CCC in allowing R, the correlation matrix, to be time varying: Ht = Dt Rt Dt

(7)

where D represents the matrix of the conditional volatility and R is the matrix of conditional correlation. The model estimates conditional volatilities and correlations in two steps. In the first step, univariate volatility models are assigned for each variable and conditional volatility estimation are obtained. In the second step, standardized residuals resulting from the first estimation are used to estimate a time varying correlation matrix. In the GARCH-DCC model, the covariance proxy q can be modelled with a GARCH (1,1) qi,j,t = ¯ i,j + ˛(εi,t−1 , εj,t−1 − ¯ i,j ) + ˇ(qi,j,t−1 − ¯ i,j )

(8)

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To estimate the correlation matrix at each point in time we could also use exponential smoothing, as follows: qi,j,t = (1 − )(εi,t−1 , εj,t−1 ) + (qi,j,t−1 )

(9)

where q is a proxy of covariance among normalized returns. The appeal of these approaches is that they model conditional variances and correlations instead of straightforward modelling the conditional covariance matrix. 4. Literature review Several papers have investigated the optimal hedge ratio estimation methodology starting with the Figlewski paper published in 1984. Baillie and Myers (1991) estimate the optimal hedge ratio for six different commodities. They show how a bivariate GARCH model can improve hedge ratios estimation in commodity markets and how the assumption of a constant hedge ratio is costly, in terms of higher return variance. Kroner and Sultan (1993) estimate the risk minimizing futures hedge ratios with a bivariate Error Correction Model with a GARCH error structure, showing that the GARCH model provides greater risk reduction than traditional models. Bera et al. (1997) show how the use of random coefficient autoregressive model allows to improve hedging performance compared to traditional OLS models. The analysis is applied to spot and futures prices of corn and soybeans. Yang and Awoke (2003) examine the risk hedging effectiveness of different models for major storable and non-storable agricultural commodity futures markets over the period 1997–2001. Using the bivariate GARCH approach they find a strong effectiveness for all storable commodities, unfortunately weaker for non-storable commodities. Lien et al. (2002) compare the performance of hedge ratios estimated using different models on three currency futures contracts, five commodity futures and two stock index futures contracts in the period 1988–1998. Their results show that in general GARCH strategy cannot outperform the OLS hedge strategy. Rossi and Zucca (2002) suggest that GARCH hedging strategy is more effective than the traditional methods when applied to a portfolio of Italian fixed income government bonds hedged with futures contracts traded at Liffe. Brooks et al. (2002) estimate optimal hedge ratio for the FTSE 100 index and FTSE 100 futures over the period 1985–1999. They find that asymmetric models yield improvements in forecast accuracy in sample but not on hedging performances out of sample. Copeland and Zhu (2006) compute dynamic hedge ratios for contracts on the major stock market index of six countries (Australia, Germany, Japan, Korea, UK and USA) from 1995 to 2005. The results are extremely mixed so authors conclude that the more sophisticated model benefits are likely to be very small or even negative. Ahmed (2007) in a study applied to US Treasury Market demonstrates that time varying hedge ratio have superior hedging performances compared to the traditional duration-based constant ratio. Time varying hedge ratio, estimated using CCC-GARCH shows a clear advantage in minimizing the variance of portfolio returns over a period of 10 years. Ku et al. (2007) apply dynamic conditional correlations GARCH models to estimate fluctuations that distinguish futures markets. DCC shows the best hedging performance both in the Japanese and the British futures markets. Kenourgios et al. (2008) show that, compared to OLS, the Error Correction Model provides better results in terms of risk reduction, forecasts and stability of the estimated hedge ratio. They apply their analysis to stock portfolios and the S&P500 futures contract for the period 1992–2002. Chiang et al. (2007) implement a model based on DCC to study whether there is a contagion effect in Asian equity markets. They show that the DCC model is able to catch the dynamic behaviour of stock return correlations, more than other approaches. With a similar approach, Savva (2009) estimates price, volatility linkage effects and correlation coefficients from the US equity market to the European ones and vice versa, after the euro introduction. DCC models are preferable to alternative methods for the skewness characterizing the stock returns. Focusing on electricity markets there are some papers investigating the effectiveness of hedging strategies performed using different hedge ratios model estimation or that apply GARCH models to investigate statistical properties of electricity prices. Escribano et al. (2002) use six different GARCH models to study mean reversion, GARCH behaviour and time-dependent jumps of spot electricity prices of five markets (Argentina, Australia, New Zealand,

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Nord Pool, and Spain). Bystrom (2003) analyses variances and covariances of Nord Pool electricity price returns over the period 1996–1999. He compares traditional models with the constant correlation bivariate GARCH and the Orthogonal GARCH model (Ding, 1994). Short term hedging of electricity spot prices with electricity futures reduces the variability of the portfolio returns. However the traditional hedging models perform as well as more elaborated models when the performances of hedging are evaluated on the basis of their ability to reduce the portfolio variance. Malo and Kanto (2005) compare the hedging performances of a broader range of multivariate GARCH models to check the robustness of the selected models. Wickens and Wimschulte (2007) make evident that EEX electricity prices suffer of biases, generally due to the spot price level and the remaining time to maturity of futures. According to the authors, there is not an outstanding model able to reduce residuals in forecasting price changes. Koopman et al. (2007) show how conditional GARCH models allow to model the day of the week periodicity in the autocovariance function of electricity spot prices on Nord Pool, EEX, Powernext and APX. Torró (2008) demonstrates that Nord Pool electricity prices are characterized by particular statistical features, particularly a low correlation between spot and futures prices, due to high volatility and kurtosis, and no storability property of the underlying which avoids the cash-and-carry relation. This means that hedging strategies could generate ineffective performances, unless more sophisticated models are applied. Torró obtains a better performance employing the Ederington and Salas (2008) model, in order to minimize the hedge ratio variance by the spot price forecast, assuming the spot price changes in the electricity market are partially predictable. 5. Data As described in previous sections, the liberalization process is fairly recent in Europe. We analyse those markets – Nord Pool, EEX and Powernext – whose data are available both for the spot and futures markets. In most European markets, a futures derivatives market began very recently or it still does not exist. Nord Pool spot returns are computed from daily system prices. System prices are an equally weighted average of 24 hourly prices. The system price is the spot reference rate for derivatives contract traded at Nord Pool market. The derivatives traded at Nord Pool are base load futures, forwards, options and contract for differences. Day and week futures and monthly, quarterly and yearly forwards with a maximum time horizon of 4 years are traded on this market. We estimated daily returns from monthly forward. The length of time series available for the Nord Pool goes from 2nd January 2004 to 14th February 2006. The reason for this choice is that even if spot and derivatives trading started in Nord Pool well before 2003, at the end of 2003 a new product structure was introduced. Blocks contract were replaced with monthly contracts and seasons contract with quarterly contracts. In the case of EEX market we used daily Phelix base spot prices from 2nd July 2002 to 14th February 2006. The Phelix base load index is the average of all the hourly auctions on the spot market of EEX for the German/Austrian market area. The Phelix is the reference price for futures contract traded at EEX. On the EEX Derivatives market, only base load and peak load futures contracts are traded. The available expirations are the current month, the next 11 quarters and the next 6 years. Base load and peak load futures are traded. While EEX futures have been traded since March 2001, Phelix futures contracts were introduced in July 2002. Finally, daily system prices and monthly futures returns from 18th June 2004 to 14th February 2006 were used for Powernext. In the French Market the activity of buying and selling electricity has been strongly encouraged since 2003. However it is only on July 2004 that the French legislative environment led to 100% opening of the power market for professional end-users. Derivatives traded in the French Market are three monthly, four quarterly and 3 yearly contracts. For all the three spot markets, base load daily settlement prices Monday to Friday were used. We removed the weekends since futures are not traded on Saturdays and Sundays. For the futures markets, a first step was to select the future contract. Each day a number of futures contract with different maturities are available and can be chosen as hedging instruments. In our analysis we used as hedging instruments futures contract with 1 month to expiration. This because

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Table 4 Market descriptive statistics. SD

Kurtosis

Panel A: Nord Pool market Spot 0.00741 Futures 0.000209

Mean

Skewness

Q(6)

0.053121 0.023967

12.02119 11.20506

0.521946 1.133039

31.961 10.749

53.213 40.460

Panel B: EEX market Spot 0.001106 Futures 0.001128

0.325185 0.041377

11.85761 30.96759

0.579756 1.984044

157.78 9.9622

218.80 24.137

Panel C: Powernext market Spot 0.002234 Futures 0.001871

0.168953 0.029464

8.819029 11.32722

0.143896 −0.401778

50.567 9.2490

Q(18)

67.299 21.294

Panels A–C report summary statistics of the logarithmic of spot and futures prices for the Nord Pool (Panel A), the EEX (Panel B) and the Powernext (Panel C) markets. The mean is the daily mean return. The standard deviation is the daily standard deviation of returns. Q() is the Ljung–Box test for autocorrelation. 95% and 99% critical values for Ljung–Box are 37.65 and 44.31.

monthly futures contract are the shorter term instruments available on all the three analysed markets. Short term instruments are generally more liquid than long term and more correlated with underlying spot. To create a time series of futures prices and avoid delivery or thin markets effect we roll over to the next 1 month futures contract 1 week before the expiration of the previous future contract. Table 4 gives summary statistics of the spot and futures returns for the three markets. Daily returns are constructed as the first difference of logarithmic prices. Some point is worth noting. The volatility is incredibly high but different on the three markets with Nord Pool the first born, more efficient and liquid market being the less volatile. Another possible explanation of different volatilities between the three markets could be the different production structure as discussed in the introduction. Another important point is that the spot and the futures volatility within the same market are really different with the spot volatility being significantly higher than the futures volatility. Furthermore the volatility is clearly not constant over time (as shown in Figs. 1–3) leading to the idea of using time varying models in hedge ratio choices. Both returns series show high kurtosis and skewness. This suggests that both spot and futures return are not normally distributed. All the summary statistics showed signs of variations across different periods suggesting that there might be a need to incorporate time varying parameter. The Ljung–Box test for autocorrelation shows autocorrelation for spot returns and in some case for futures return as well. In order to check if the spot and futures prices are unit root in time series we perform the ADF tests. Results obtained shows that the test statistics are more negative than the critical values, and hence

Fig. 1. GARCH (1,1) Nord Pool conditional volatility of spot and futures returns.

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Fig. 2. GARCH (1,1) EEX conditional volatility of spot and futures returns.

the null hypothesis of a unit root in returns is convincingly rejected in favor of alternate hypothesis of stationarity. 6. Optimal hedge ratio estimation and hedging performance To evaluate the hedging performances we consider a one-period model. At the beginning of the period the economic agent is long the underlying asset. To hedge his position and reduce risk exposure he sells futures contract. The number of futures contracts is chosen so to minimize the variance of the hedged portfolio. We estimated the hedge ratio in six different ways: the naïve one to one hedge ratio where we offset each spot contract by one futures contract; the static OLS hedge ratio were we regress the spot return over the futures return; the dynamic OLS hedge ratio estimated continuously updating the moving averages (50 days period); a constant correlation model (CCC); finally, two dynamic time varying correlations models: GARCH-DCC and exponential DCC. Data are divided in 2 sub-samples: the in-sample (test) period and the out-of-sample period. For each market we ran our first analysis considering an equally weighted in and out-of-sample period. Table 5 reports the results obtained. To check the robustness of our estimation we also considered a 1/3, 2/3 ratio between the in-sample and the out-of-sample periods. The results obtained are not different from those reported in Table 5. To compare the performances of hedging strategies based on different hedge ratios estimation we compute daily spot and future returns. Then we estimate the hedge ratio. For the static OLS the

Fig. 3. GARCH (1,1) Powernext conditional volatility of spot and futures returns.

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Table 5 Portfolio returns, standard deviations and volatility reduction. Mean return

Variance

% Variance reduction

Panel A: Nord Pool market Spot un-hedged position Naïve 1–1 OLS static hedge OLS dynamic hedge CCC GARCH-DCC Exp-DCC

0.177% −0.031% 0.128% 0.130% 0.110% 0.132% 0.117%

0.388% 0.419% 0.381% 0.396% 0.377% 0.378% 0.379%

−7.346% 2.015% −1.813% 3.123% 2.801% 2.445%

Panel B: EEX market Spot un-hedged position Naïve 1–1 OLS static hedge OLS dynamic hedge CCC GARCH-DCC Exp-DCC

0.098% −0.035% 0.047% 0.142% 0.061% 0.099% 0.069%

3.664% 3.545% 3.579% 3.814% 3.514% 3.536% 3.537%

3.371% 2.373% −3.926% 3.472% 3.634% 3.593%

Panel C: Powernext market Spot un-hedged position Naïve 1–1 OLS static hedge OLS dynamic hedge CCC GARCH-DCC Exp-DCC

0.262% 0.089% 0.309% 0.236% 0.259% 0.260% 0.264%

3.355% 3.422% 3.375% 3.497% 3.354% 3.355% 3.355%

−1.938% −0.576% −4.046% 0.021% 0.007% 0.005%

Panels A–C report the mean return and the standard deviation of un-hedged and hedged portfolios. Volatility reduction is calculated as percentage difference between the hedged and un-hedged portfolio. A negative sign indicates a standard deviation increase. A positive sign indicates a standard deviation reduction.

hedge ratio is calculated over the test period and used to build the hedged portfolio. For the dynamic models the hedge ratio is updated daily. Finally we calculate the performance of the hedge as variance reduction, compared to spot un-hedged position, obtained through different hedge ratios estimation method. In Table 5, Panels A–C show the average portfolio returns, standard deviations and the percentage of variance reduction. The best hedging strategy could be defined as the one that allows the highest variance reduction and the lowest return reduction. However, since the average return of the portfolio depends on the underlying trend of the spots and futures return, we believe that variance reduction is a much valid ranking criteria. Some interesting results may be derived from Table 5. First naïve or OLS hedges do not perform better than other hedges. Vice versa it appears that in some case traditional hedging may consistently increase the portfolio variance. With reference to EEX, this may occur because the in-sample correlation of spot and futures returns is negative leading to a hedge ratio that for the static model is −0.577. However the out-of-sample correlation becomes positive and explain the unsuccessful hedging strategy and the increase of volatility. This first observation leads us to conclude that taking into consideration time varying variations seems to be important. In the case of Nord Pool the best performing model is the CCC. As stated in Table 6, Nord Pool is the market with the lowest standard deviation of conditional correlation. In this case the CCC seems able to capture the time varying nature of spot and futures returns. For EEX, the market recording the highest standard deviation of conditional correlation, the best performing hedging strategy are instead based on GARCH dynamic correlations models. Dynamic correlations models perform better than other hedging models also in Powernext where the standard deviation of the conditional correlation is lower than EEX but still significantly higher than Nord Pool.

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Table 6 Daily standard deviations of conditional correlations.

All period Sub-period 1 Sub-period 2

Nord Pool

EEX

Powernext

0.056% 0.069% 0.041%

0.082% 0.097% 0.051%

0.072% 0.040% 0.083%

The most interesting conclusion is that only time varying GARCH models lead for all the three markets to a significant and constant variance reduction. To further increase the statistical significance of our results, we split the out-of-sample period in two sub-periods and we tested the hedging performances over the two sub-periods. We considered 10 samples of different sub-periods lengths. In the case of the first sample 25% of the total data are in the first sub-period and the remaining 75% in the second. Then we change the mix by 5%, until the last sample where 70% of the total data are in sub-period one and the remaining 30% in sub-period 2. We estimated the average standard deviation and the average variance reduction in the 10 sub-periods. Table 7, Panels A–C report our findings. This analysis further stresses the importance of implementing hedging strategies based on time varying variances and correlations models. In fact, only GARCH dynamic models allow for all markets and all periods to reduce the variance of the hedged portfolio. Furthermore, the performance of dynamic hedging model compared to traditional hedging models increase on high volatile market moment and when the standard deviation of correlation is higher, that is when hedging is most important. The sub-period analysis leads us to another conclusion: dynamic GARCH models perform significantly better than other models in case of high standard deviation of returns and of conditional correlations. EEX results clearly confirm this conclusion.

Table 7 Portfolio returns, standard deviations and volatility reduction in two sub-periods. Variance

% Variance reduction

Sub-period 1

Sub-period 2

Sub-period 1

Sub-period 2

Panel A: Nord Pool market Spot un-hedged position Naïve 1–1 OLS static hedge OLS dynamic hedge CCC GARCH-DCC Exp-DCC

0.412% 0.434% 0.401% 0.421% 0.397% 0.401% 0.402%

0.386% 0.434% 0.382% 0.392% 0.349% 0.347% 0.349%

−5.282% 2.559% −2.322% 3.587% 2.717% 2.400%

−12.610% 0.852% −1.764% 9.643% 10.001% 9.412%

Panel B: EEX market Spot un-hedged position Naïve 1–1 OLS static hedge OLS dynamic hedge CCC GARCH-DCC Exp-DCC

9.393% 9.068% 9.221% 9.648% 9.890% 9.013% 8.970%

3.905% 3.872% 3.857% 4.077% 3.855% 3.854% 3.855%

3.463% 1.829% −2.709% 4.397% 4.045% 4.503%

0.852% 1.218% −4.395% 1.283% 1.297% 1.266%

Panel C: Powernext market Spot un-hedged position Naïve 1–1 OLS static hedge OLS dynamic hedge CCC GARCH-DCC Exp-DCC

2.230% 2.293% 2.243% 2.274% 2.230% 2.230% 2.230%

4.782% 4.878% 4.805% 5.014% 4.780% 4.781% 4.782%

−2.842% −0.597% −1.973% 0.007% 0.004% 0.009%

−2.022% −0.491% −4.853% 0.027% 0.008% 0.003%

Panels A–C report the variance and the variance reduction over 10 sub-samples generated splitting the data for each market from one to another. The sub-period 1 grows from 25 to 70% with steps of 5%; vice versa, the sub-period 2 decreases from 75 to 30%.

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7. Conclusions In this paper we analyze the performance of different hedging models and provide a hedging effectiveness of dynamic hedge ratios. We estimated the hedge ratio and calculated the reduction obtained by the futures hedging compared to the spot un-hedged positions using six different models. From the results obtained some interesting conclusions may be driven. First, for the periods and the market we analysed it has been possible to reduce the variance of electricity markets using futures hedging. The only market where the hedging does not lead to a variance reduction is the Powernext market that also appears as the most recent and less liquid markets. In the other two cases our results show that trading in futures allows to reduce the risk of electricity portfolios and to control the risk of adverse movements on electricity prices. Second, results provide a clear indication of the superior performance of the time varying hedge ratio as compared with traditional hedge ratios. Hedging is not independent from the model chosen to estimate the hedge ratio. Time varying variances and correlations models reduces the volatility of the hedge portfolio wherever sometime traditional OLS led to an increase of risk. Furthermore the GARCH models obtain the maximum hedging effectiveness when volatility is relatively high. Acknowledgements The authors are grateful to Roberto Reno’ for providing helpful comments. Special thanks are due to Paolo Negri for dedicated research assistance. We thank anonymous referees and participants in 2007 International Symposium on Forecasting (New York), 2008 Multinational Finance Conference (Orlando), 2008 Northern Finance Association (Calgary), 2008 Aarhus School of Business working paper presentations, 2009 Energy and Value Conference (Istanbul), Giampaolo Gabbi acknowledges financial support from the Siena University Research Programme. The usual disclaimer applies. References Ahmed, S., 2007. Effectiveness of time-varying hedge ratio with constant conditional correlation: an empirical evidence from the US treasury market. ICFAI Journal of Derivatives Markets 4, 22–30. Baillie, R.T., Myers, R.J., 1991. Bivariate GARCH estimation of the optimal commodity futures hedge. Journal of Applied Econometrics 6, 109–124. Bera, A.K., Garcia, P., Roh, J.-S., 1997. Estimation of time-varying hedging ratios for corn and soybeans: BGARCH and random coefficient approaches. OFOR Paper 97-06. Bollerslev, T., 1990. Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model. Review of Economics and Statistics 72, 498–505. Bollerslev, T., Engle, R., Wooldridge, J.M., 1988. A capital asset pricing model with time varying covariances. Journal of Political Economy 96, 116–131. Brooks, C., Henry, O.T., Prsand, G., 2002. The effect of asymmetries on optimal hedge ratio. Journal of Business 75, 333–352. Bystrom, H.N.E., 2003. The hedging performance of electricity futures on the Nordic power exchange. Applied Economics 35, 1–11. Chiang, T.C., Jeon, B.N., Li, H., 2007. Dynamic correlation analysis of financial contagion: evidence from the Asian Markets. Journal of International Money and Finance 26, 1206–1228. Commission of the European Communities, 2009. Report on Progress in Creating the Internal Gas and Electricity Market, Brussels. Copeland, L., Zhu, Y., 2006. Hedging Effectiveness in the Index Futures Market. Cardiff Business School working paper. Ding, Z., 1994. Time Series Analysis of Speculative Returns. PhD thesis. University of California, San Diego. Ederington, L.H., Salas, J.M., 2008. Minimum variance hedging when spot price changes are partially predictable. Journal of Banking and Finance 32, 654–663. Engle, R.F., 2002. Dynamic conditional correlation—a simple class of multivariate GARCH models. Journal of Business and Economic Statistics 20, 339–350. Engle, R.F., Sheppard, K., 2001. Theoretical and empirical properties of Dynamic Conditional Correlation MVGARCH. Working paper No. 2001-15, University of California, San Diego. Escribano, A., Pena, J.I., Villaplana, P., 2002. Modeling electricity prices: international evidence. Universidad Carlos III de Madrid Working Paper 02/07. Kenourgios, D., Samitas, A., Drosos, P., 2008. Hedge ratio estimation and hedging effectiveness: the case of the S&P 500 stock index futures contract. International Journal of Risk Assessment and Management 9, 121–134. Koopman, S.J., Ooms, M., Carnero, M.A., 2007. Periodic seasonal Reg-ARFIMA-GARCH models for daily electricity spot prices. Journal of the American Statistical Association 102, 16–27. Kroner, K.F., Sultan, J., 1993. Time varying distribution and dynamic hedging with foreign currency futures. Journal of Financial and Quantitative Analysis 28, 535–551. Ku, Y.H., Chen, H., Chen, K., 2007. On the application of the dynamic conditional correlation model in estimating optimal time-varying hedge ratios. Applied Economics Letters 14, 503–509.

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