Determinants of the Forward Premium in Electricity Markets

Transcription

1 Determinants of the Forward Premium in Electricity Markets Álvaro Cartea, José S. Penalva, Eduardo Schwartz Universidad Carlos III, Universidad Carlos III, UCLA June, 2011

2 Electricity: a Special Kind of Market Electricity is a non-storable commodity (or uneconomical to store) Consequently subject to abrupt changes in prices: large upward spikes in prices (downward spikes too) Strong mean reversion of spikes As soon as it is produced it must be consumed: Price can become negative How can physical players (Producers and retailers) hedge their exposures? What instruments do we expect to help hedging needs

3 Electricity Prices: PJM

4 The Market for Electricity Exhibits marked seasonal patterns Seasonal demand (highly inelastic) Seasonal fuel prices (Gas prices) Market structure: Relatively few producers Few retailers who buy wholesale electricity from producers and sell at fixed price to end consumers System operator who is in charge of balancing the market at every instant in time: engineering and financial duty

5 Electricity Futures Impossible to hedge by buying and holding electricity Main hedging instrument are futures and forward contracts Futures are traded through an exchange Forwards are bilateral agreements (account for a large proportion of electricity sold forward in markets like UK)

6 Our Questions What are the key determinants that drive electricity futures and forward prices? What are the main drivers behind deviations of futures and forward prices from the expected spot price of electricity Hedging pressure from retailers and producers? Pressure from outside investors? What is the role of outside investors in the futures market?

7 Existing Literature No-Arbitrage models Schwartz (1997), Schwartz and Smith (2000), Lucía and Schwartz (2002), Cartea and Figueroa (2005), Geman and Roncoroni (2006) Equilibrium and Hybrid models Barlow (2002), Bessembinder and Lemmon (2002), Pirrong and Jermakyan (2008), Cartea and Villaplana (2008), Coulon and Howison (2009) Forward risk premium Longstaff and Wang (2004), Lucia and Torró (2008), Benth, Cartea and Figueroa (2008), Bühler and Müller-Merbach (2007), Biegler-König, Benth and Kiesel (2011)

8 Main Results Empirical measures of hedging pressures of producers and retailers support the model s predictions (sign) Results suggest that there is a mistiming of producer and retailer hedging pressures Financial market variables have a significant impact on the forward premium Results suggest that the impact of outside investors is felt through capital movements associated with financial cycles

9 The Players and their Spot Profits The Model The Equilibrium Forward Premium Distributional Proxies Producers of electricity (N P = 1) produce q i MWh of electricity at a total cost of TC i (q i ) spot market profits are: Π Pi = Sq i TC i (q i ) where S is the spot price of electricity Electricity retailers (N R = λ) sells q j MWh of electricity to final consumers at a fixed price P per MWh spot market profits are: Π Rj = q j (P S) Outside investors (N O = γ) obtain risky profits from their other investments, Π O

10 Objective Functions The Financials of Electricity The Model The Equilibrium Forward Premium Distributional Proxies Each of the three types of agents, x {Pi,Rj,O}, purchase q fx futures contracts for delivery at date t = 2 at a price of f each. They decide their purchases of futures to maximize E[Π x ] A x 2 V[Π x] where Π x = Π x + (f S)q }{{ fx }, profits from position in futures and Π x represents profits without futures contracts. For example, recall that Π Pi = Sq i TC i (q i ) and Π Rj = q j (P S).

11 Demand for Futures The Financials of Electricity The Model The Equilibrium Forward Premium Distributional Proxies The corresponding demand functions for the three types of agents are obtained from the FOC: f E[S] A x 2 (2q fxv[s] + 2Cov [Π x,s]) = 0 q fx = 1 A x f E[S] V[S] Note that when + Cov [Π x,s] V[S] }{{}. Hedging pressure component q fx > 0: agent x {Pi,Rj,O} sells futures contracts, q fx < 0: agent x {Pi,Rj,O} buys futures contracts. If Cov [Π x,s] > 0 (< 0) the hedging component requires to sell (buy) futures contracts.

12 Equilibrium Forward Premium The Model The Equilibrium Forward Premium Distributional Proxies In equilibrium the total demand for futures is equal to zero: q fpi + λq frj + γq fo = 0 Let A 1 = A 1 Ri + λa 1 Pj + γa 1 O so that we can write The equilibrium forward premium f E[S] = A ( Cov [Π Pi,S] + λcov [ Π Rj,S] + γcov [Π 0,S] ).

13 What drives hedging demands? The Model The Equilibrium Forward Premium Distributional Proxies Producers >0Sell forwards {}}{ Cov [Π Pi,S] = Cov [Q i S TC i (Q i ),S] { >0 }} <0 Sell fewer forwards to hedge costs {{}}{ = Cov [Q i S,S] }{{} Sell forwards to hedge revenue Cov [TC i (Q i ),S] }{{} >0. Retailers ] Cov [Π Rj,S = Cov [ Q j (P S),S ] }{{} sign indeterminate = Buy fewer forwards to hedge revenue <0 {}}{ P Cov [ Q j,s ] {}}{ Cov [ Q j S,S ]. }{{}}{{} >0 Buy forwards to hedge costs

14 Outside investors The Financials of Electricity The Model The Equilibrium Forward Premium Distributional Proxies Outside Investors Cov [Π O,S] The presence of outside investors affects the premium through their hedging demand, which depends on what is happening to their portfolios Cov(S,Π x ) = V(S) V(Π x )ρ S,x.

15 The Offsetting Effect of Revenue The Model The Equilibrium Forward Premium Distributional Proxies Both retailers and producers include Cov [QS, S] in their hedging demands, but Cov [Q i S,S] = λcov [Q i S,S] thus these risks are internally diversified because producer s revenues are the same as retailers costs. Hence we can write Cov [Π Pi,S]+λCov [ Π Rj,S] = Cov [TC i (Q i ),S]+λPCov [Q j,s]. Incentivises vertical integration

16 Drivers of the Forward Premium The Model The Equilibrium Forward Premium Distributional Proxies The equilibrium forward premium f E[S] = A Cov [TC i (Q i ),S] λp Cov [ Q j,s ] γ V(S) V(Π }{{} x )ρ S,x. }{{} >0 >0 Producers: The first term on the right-hand side increases the premium because Producers are selling fewer forwards to hedge costs. Retailers: The second term on the right-hand side decreases the premium because Retailers are buying fewer forwards to hedge revenues.

17 The Model The Equilibrium Forward Premium Distributional Proxies Equilibrium Determination of the Spot Market The nature of the electricity market allows us to establish a direct relationship between price and quantity in the electricity market The electricity market is characterized by demand: retailers are obliged to satisfy the demand for electricity from final consumers at a fixed price. Thus, demand is inelastic and subject to shocks related to external factors such as the weather [and overall economic activity] supply: electricity is difficult to store in large quantities so that the demand for electricity has to be produced almost simultaneously (the electricity grid works with 5 minute production intervals). Production flexibility depends on the nature of the plant (both its production process: nuclear, gas,...; but also the age of the plant/technological development of its machinery).

18 Demand The Financials of Electricity The Model The Equilibrium Forward Premium Distributional Proxies We assume retailers are all the same Retailers face inelastic demands which are described stochastic factors such as the weather. The weather effects are nonlinear, as extreme weather conditions (too hot or too cold) lead to increased demand for electricity. This is captured by measuring daily temperatures, C, and constructing two measures: Heating degree days: max{0,c 65F } Cooling degree days: max{0,65f C}

19 Supply The Financials of Electricity The Model The Equilibrium Forward Premium Distributional Proxies Producers have to cover a fixed cost, F, plus a variable cost that changes with the level of production. Let Φ(q) = TC i (q)/ q denote the marginal cost of production so that TC i (q i ) = F + qi Φ(q)dq, where we assume the marginal cost is increasing and convex [it becomes increasingly costly to ramp up production] Thus, the supply function is given by the inverse of the marginal cost function, Φ 1 (s).

20 Equilibrium The Financials of Electricity The Model The Equilibrium Forward Premium Distributional Proxies In the spot market (assuming symmetry amongst producers, and amongst retailers) supply has to equal demand: q Pi = λq Rj Thus, the equilibrium price is equal to the marginal cost of producing the electricity demanded by consumers S = Φ 1 ( Q D).

21 The Model The Equilibrium Forward Premium Distributional Proxies Distributional Proxies: Volatility of Spot Price We first consider the direct effects of changes in the distribution of the spot price: its second, V[S], and third, S 3 [S], centered moments. Let I (S) = Φ 1 (S), and I (S) = I/ S. V[S] (f E[S]) = A 1 + λ I ( S)(p S) < 0.

22 The Model The Equilibrium Forward Premium Distributional Proxies Distributional Proxies: Spot Price Skewness S 3 [S] (f E[S]) = A 1 + λ ( 1 2 I ( S)(p S) 1 ) 2 I ( S) > 0.

23 Constructing the Underlying Driving Factors of the Forward Premium Data: electricity spot prices and demand for PJM Western hub hourly LMP (Location Marginal Pricing) Western hub hourly load data The Western hub changed dramatically on Oct 1, 2004 as AEP RFC (ECAR) and Dayton Power & Light RFC (ECAR) joined the hub, substantially increasing its size

24 Forward data The Financials of Electricity Constructing the Underlying Driving Factors of the Forward Premium PJM Peak Calendar-Month LMP Swap Futures NYMEX Peak day: Monday through Friday, excluding North American Electric Reliability Council holidays. Peak hour: hour ending 0800 to hour ending 2300 Contract quantity: a flow of 2.5 Mega-watt Hours (MWh) per hour for each peak hour of the contract month. The daily flow is 40 MWh. One contract shall equal the daily flow multiplied by the number of peak days remaining in the contract month not including the current business day. Prices shall be quoted in U.S. dollars and cents per MWh. Delivery under the PJM Peak Calendar-Month LMP Swap Futures contract shall be by cash settlement Data from Ecowin: 1-pos starting September 2004 to January 2011.

25 Modelling approach The Financials of Electricity Constructing the Underlying Driving Factors of the Forward Premium Constructing the forward premium: construct the price of the underlying security and its expected value E[S t t 1] fix a forward price and horizon Explanatory variables: expected demand shocks: determining factors expected supply factors: price of inputs expected variance and covariance of prices and quantities expected investor hedging: market factors

26 Constructing the Underlying Driving Factors of the Forward Premium Building expected spot price (quick overview) Take 30 year temperature (Philadelphia airport) year data Hourly Load (take into account non-linear effects) Daily Gas spot price (Henry Hub) Coal prices

27 Forward Premia Stats Constructing the Underlying Driving Factors of the Forward Premium 14 Prior EEX (Euro) UK ( ) PJM ($) Mean Volatility Max Min Prior EEX (Euro) UK ( ) PJM ($) Mean Volatility Max Min Table: Statistics of the Forward Premia: EEX, UK and PJM

28 Forward Premia 4 Days Prior

29 Forward Premia 14 Days Prior

30 Driving Factors The Financials of Electricity Constructing the Underlying Driving Factors of the Forward Premium Proxies for Producers hedging demand Gas prices Covariance Gas Price with Spot Electricity Price Proxies for Retailers hedging demand Covariance Spot and Load Covariance Spot and Revenue

31 Market factors The Financials of Electricity Constructing the Underlying Driving Factors of the Forward Premium Market-based risk, commonly used to explain the equity market risk premium see Goyal and Welch (2004) VIX Corporate bond premia Risky corporate bonds Long-term bond returns Market returns fixed income shares Commodity prices gas Brent commodity index

32 Electricity Market Variables Constructing the Underlying Driving Factors of the Forward Premium F BusDay,month (t 1) E[Spot month t ] = α + βx BusDay,month (t 1) PJM Coefficient Coefficient Constant *** *** Cov(Spot,Load) 1.98*** -7.38** Cov(Spot,Rev) 1.57*** Cov(Spot,Gas) Spot Gas price 2.07*** 1.60** Coal Adjusted R-sqd f E[S] = A Cov [TC i (Q i ),S] λp Cov [ Q j,s ] γ V(S) V(Π }{{} x )ρ S,x. }{{} >0 >0 Table: PJM 4 days prior to delivery

33 Financial Market Variables Constructing the Underlying Driving Factors of the Forward Premium F BusDay4,month (t 1) E[Spot month t ] = α + βx BusDay4,month (t 1) PJM Coefficient Coefficient Constant Cov(Spot,Load) -8.09*** -7.83*** Cov(Spot,Rev) 1.69*** 1.65*** Spot Gas price 2.28*** 2.35*** Coal 1year TBill Default Spread (AAA-1yrTBill) S&P Nasdaq Index 0.00 Adjusted R-sqd Table: PJM 4 days prior to delivery

34 Commodity Markets EEX Constructing the Underlying Driving Factors of the Forward Premium F BusDay14,month (t 1) E[Spot month t ] = α + βx BusDay14,month (t 1) EEX Coefficient (14 days) Coefficient (17 days) Constant ** ** Cov(Spot,Load) Cov(Spot,Rev) 0.23* 0.15 Cov(Spot,Gas) Spot Gas price year TBill 7.55** 6.67** Default Spread (AAA-1yrTBill) 7.53** 6.65** Eurostoxx ** 0.10** Eurostoxx ** -0.93** Adjusted R-sqd Table: EEX Explanatory Regression with Commodities

35 Main Results Empirical measures of hedging pressures of producers and retailers support the model s predictions (sign) Results suggest that there is a mistiming of producer and retailer hedging pressures Financial market variables have no explanatory power in isolation Financial market variables have a significant impact on the forward premium in the joint analysis with electricity market variables Results suggest that the impact of outside investors is felt through capital movements associated with financial cycles

36 Determinants of the Forward Premium in Electricity Markets Álvaro Cartea, José S. Penalva, Eduardo Schwartz Universidad Carlos III, Universidad Carlos III, UCLA June, 2011