DeterminantsoftheForwardPremiuminElectricity Markets · The Financials of Electricity The...

The Financials of ElectricityThe Theoretical Model

Empirical AnalysisConclusions

Determinants of the Forward Premium in ElectricityMarkets

Álvaro Cartea, José S. Penalva, Eduardo Schwartz

Universidad Carlos III, Universidad Carlos III, UCLA

June, 2011

Álvaro Cartea, José Penalva and Eduardo Schwartz The Forward Premium for Electricity



Electricity: a Special Kind of Market

Electricity is a non-storable commodity (or uneconomical tostore)

Consequently subject to abrupt changes in prices: large upwardspikes in prices (downward spikes too)Strong mean reversion of spikes

As soon as it is produced it must be consumed: Price canbecome negativeHow can physical players (Producers and retailers) hedge theirexposures?

What instruments do we expect to help hedging needs


Electricity Prices: PJM



The Market for Electricity

Exhibits marked seasonal patterns

Seasonal demand (highly inelastic)Seasonal fuel prices (Gas prices)

Market structure:

Relatively few producersFew retailers who buy wholesale electricity from producers andsell at fixed price to end consumersSystem operator who is in charge of balancing the market atevery instant in time: engineering and financial duty




Electricity Futures

Impossible to hedge by buying and holding electricity

Main hedging instrument are futures and forward contracts

Futures are traded through an exchangeForwards are bilateral agreements (account for a largeproportion of electricity sold forward in markets like UK)




Our Questions

What are the key determinants that drive electricity futuresand forward prices?What are the main drivers behind deviations of futures andforward 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?




Existing Literature

No-Arbitrage models

Schwartz (1997), Schwartz and Smith (2000), Lucía andSchwartz (2002), Cartea and Figueroa (2005), Geman andRoncoroni (2006)

Equilibrium and Hybrid models

Barlow (2002), Bessembinder and Lemmon (2002), Pirrongand Jermakyan (2008), Cartea and Villaplana (2008), Coulonand 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)




Main Results

Empirical measures of hedging pressures of producers andretailers support the model’s predictions (sign)Results suggest that there is a mistiming of producer andretailer hedging pressuresFinancial market variables have a significant impact on theforward premiumResults suggest that the impact of outside investors is feltthrough capital movements associated with financial cycles




The ModelThe Equilibrium Forward PremiumDistributional Proxies

The Players and their Spot Profits

Producers of electricity (NP = 1)

produce qi MWh of electricity at a total cost of TCi (qi )spot market profits are: Π∗Pi = Sqi −TCi (qi ) where S is thespot price of electricity

Electricity retailers (NR = λ )

sells qj MWh of electricity to final consumers at a fixed price Pper MWhspot market profits are: Π∗Rj = qj (P−S)

Outside investors (NO = γ)

obtain risky profits from their other investments, Π∗O





Objective Functions

Each of the three types of agents, x ∈ {Pi ,Rj ,O}, purchase qfxfutures contracts for delivery at date t = 2 at a price of f each.They decide their purchases of futures to maximize

E [Πx ]− Ax

2V [Πx ]

whereΠx = Π∗x + (f −S)qfx︸︷︷︸

profits from position in futures

,

and Π∗x represents profits without futures contracts. Forexample, recall that Π∗Pi = Sqi −TCi (qi ) and Π∗Rj = qj (P−S).





Demand for Futures

The corresponding demand functions for the three types ofagents are obtained from the FOC:

f −E [S ]− Ax

2(2qfxV [S ] +2Cov [Π∗x ,S ]) = 0

⇐⇒ qfx =1Ax

f −E [S ]

V [S ]+

Cov [Π∗x ,S ]

V [S ]︸︷︷︸Hedging pressure component

.

Note that when

qfx > 0: agent x ∈ {Pi ,Rj ,O} sells futures contracts,qfx < 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.





Equilibrium Forward Premium

In equilibrium the total demand for futures is equal to zero:

qfPi + λqfRj + γqfO = 0

Let A−1 = A−1Ri + λA−1Pj + γA−1O 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 ]

).





What drives hedging demands?

Producers

Cov [Π∗Pi ,S ] =

>0Sell forwards︷︸︸︷Cov [QiS−TCi (Qi ) ,S ]

=

>0︷︸︸︷Cov [QiS ,S ]︸︷︷︸

Sell forwards to hedge revenue

<0 Sell fewer forwards to hedge costs︷︸︸︷−Cov [TCi (Qi ) ,S ]︸︷︷︸

>0

.

Retailers

Cov[Π∗Rj ,S

]= Cov

[Qj (P−S) ,S

]︸︷︷︸sign indeterminate

=

Buy fewer forwards to hedge revenue︷︸︸︷P Cov

[Qj ,S

]︸︷︷︸>0

<0︷︸︸︷− Cov

[QjS ,S

]︸︷︷︸Buy forwards to hedge costs

.





Outside investors

Outside InvestorsCov [Π∗O ,S ]

The presence of outside investors affects the premium throughtheir hedging demand, which depends on what is happening totheir portfolios

Cov(S ,Πx) =√

V(S)√

V(Πx)ρS ,x .





The Offsetting Effect of Revenue

Both retailers and producers include Cov [QS ,S ] in theirhedging demands, but

Cov [QiS ,S ] = λCov [QiS ,S ]

thus these risks are internally diversified because producer’srevenues are the same as retailers costs. Hence we can write

Cov [Π∗Pi ,S ]+λCov[Π∗Rj ,S

]=−Cov [TCi (Qi ) ,S ]+λPCov [Qj ,S ] .

Incentivises vertical integration





Drivers of the Forward Premium

The equilibrium forward premium

f −E [S ] = A

Cov [TCi (Qi ) ,S ]︸︷︷︸>0

−λP Cov[Qj ,S

]︸︷︷︸>0

−γ√

V(S)√

V(Πx )ρS ,x

.

Producers: The first term on the right-hand side increases thepremium because Producers are selling fewer forwards tohedge costs.Retailers: The second term on the right-hand side decreasesthe premium because Retailers are buying fewer forwards tohedge revenues.





Equilibrium Determination of the Spot Market

The nature of the electricity market allows us to establish adirect relationship between price and quantity in the electricitymarketThe electricity market is characterized by

demand: retailers are obliged to satisfy the demand forelectricity from final consumers at a fixed price. Thus, demandis inelastic and subject to shocks related to external factorssuch as the weather [and overall economic activity]supply: electricity is difficult to store in large quantities sothat the demand for electricity has to be produced almostsimultaneously (the electricity grid works with 5 minuteproduction intervals). Production flexibility depends on thenature of the plant (both its production process: nuclear, gas,...; but also the age of the plant/technological development ofits machinery).





Demand

We assume retailers are all the sameRetailers face inelastic demands which are described stochasticfactors such as the weather.The weather effects are nonlinear, as extreme weatherconditions (too hot or too cold) lead to increased demand forelectricity.This is captured by measuring daily temperatures, C , andconstructing two measures:

Heating degree days: max{0,C −65F}Cooling degree days: max{0,65F −C}





Supply

Producers have to cover a fixed cost, F , plus a variable costthat changes with the level of production.Let Φ(q) = ∂TCi (q)/∂q denote the marginal cost ofproduction so that

TCi (qi ) = F +∫ qi

Φ(q)dq,

where we assume the marginal cost is increasing and convex [itbecomes increasingly costly to ramp up production]Thus, the supply function is given by the inverse of themarginal cost function, Φ−1 (s).





Equilibrium

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 ofproducing the electricity demanded by consumers

S = Φ−1(QD)

.





Distributional Proxies: Volatility of Spot Price

We first consider the direct effects of changes in thedistribution of the spot price:

its second, V[S ],and third, S3[S ], centered moments.

Let I (S) = Φ−1(S), and I ′(S) = ∂ I/∂S .

∂

∂V[S ](f −E [S ]) =− A

1+ λI ′(S̄)(p− S̄) < 0.





Distributional Proxies: Spot Price Skewness

∂

∂S3[S ](f −E [S ]) =− A

1+ λ

(12I ′′(S̄)(p− S̄)− 1

2I ′(S̄)

)> 0.




Constructing the UnderlyingDriving Factors of the Forward Premium

Data: electricity spot prices and demand for PJM

Western hub hourly LMP (Location Marginal Pricing)Western hub hourly load dataThe Western hub changed dramatically on Oct 1, 2004 asAEP RFC (ECAR) and Dayton Power & Light RFC (ECAR)joined the hub, substantially increasing its size





Forward data

PJM Peak Calendar-Month LMP Swap Futures–NYMEX

Peak day: Monday through Friday, excluding North AmericanElectric Reliability Council holidays.Peak hour: hour ending 0800 to hour ending 2300Contract quantity: a flow of 2.5 Mega-watt Hours (MWh) perhour for each peak hour of the contract month. The daily flowis 40 MWh. One contract shall equal the daily flow multipliedby the number of peak days remaining in the contract monthnot 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 SwapFutures contract shall be by cash settlement

Data from Ecowin: 1-pos starting September 2004 to January2011.





Modelling approach

Constructing the forward premium:

construct the price of the underlying security and its expectedvalue E [St |t−1]fix a forward price and horizon

Explanatory variables:

expected demand shocks: determining factorsexpected supply factors: price of inputsexpected variance and covariance of prices and quantitiesexpected investor hedging: market factors





Building expected spot price (quick overview)

Take 30 year temperature (Philadelphia airport) year dataHourly Load (take into account non-linear effects)Daily Gas spot price (Henry Hub)Coal prices





Forward Premia Stats

14 Prior EEX (Euro) UK (£) PJM ($)Mean 5.11 5.78 1.89

Volatility 15.46 17.62 13.10Max 54.51 88.05 53.83Min -22.73 -31.38 -18.01

4 Prior EEX (Euro) UK (£) PJM ($)Mean 4.18 5.37 1.28

Volatility 16.06 15.30 12.11Max 76.83 66.59 41.90Min -16.33 -30.30 -27.27

Table: Statistics of the Forward Premia: EEX, UK and PJM


Forward Premia 4 Days Prior

Forward Premia 14 Days Prior




Driving Factors

Proxies for Producers’ hedging demand

Gas pricesCovariance Gas Price with Spot Electricity Price

Proxies for Retailers’ hedging demand

Covariance Spot and LoadCovariance Spot and Revenue





Market factors

Market-based “risk”, commonly used to explain the equitymarket risk premium see Goyal and Welch (2004)

VIXCorporate bond premiaRisky corporate bondsLong-term bond returns

Market returns

fixed incomeshares

Commodity prices

gasBrentcommodity index





Electricity Market Variables

FBusDay ,month (t−1)−E [Spotmontht ] = α + βXBusDay ,month (t−1)

PJM Coefficient CoefficientConstant -19.23*** -17.30***

Cov(Spot,Load) 1.98*** -7.38**Cov(Spot,Rev) 1.57***Cov(Spot,Gas) -154.18 -65.63Spot Gas price 2.07*** 1.60**

Coal .04 .05Adjusted R-sqd 0.32 0.46

f −E [S ] = A

Cov [TCi (Qi ) ,S ]︸︷︷︸>0

−λP Cov[Qj ,S

]︸︷︷︸>0

−γ√

V(S)√

V(Πx )ρS ,x

.

Table: PJM 4 days prior to deliveryÁlvaro Cartea, José Penalva and Eduardo Schwartz The Forward Premium for Electricity




Financial Market Variables

FBusDay4,month (t−1)−E [Spotmontht ] = α + βXBusDay4,month (t−1)

PJM Coefficient CoefficientConstant 11.24 8.13

Cov(Spot,Load) -8.09*** -7.83***Cov(Spot,Rev) 1.69*** 1.65***Spot Gas price 2.28*** 2.35***

Coal1year TBill -2.64 -1.60

Default Spread (AAA-1yrTBill) -2.50 -1.92S&P500 -0.01 -0.02

Nasdaq Index 0.00Adjusted R-sqd 0.4963 0.4906

Table: PJM 4 days prior to delivery





Commodity Markets EEX

FBusDay14,month (t−1)−E [Spotmontht ] = α + βXBusDay14,month (t−1)

EEX Coefficient (14 days) Coefficient (17 days)Constant -13449** -11119**

Cov(Spot,Load) -1.90 -1.99Cov(Spot,Rev) 0.23* 0.15Cov(Spot,Gas)Spot Gas price -0.0061year TBill 7.55** 6.67**

Default Spread (AAA-1yrTBill) 7.53** 6.65**Eurostoxx 50 0.12** 0.10**Eurostoxx 400 -1.151** -0.93**Adjusted R-sqd 0.36 0.27

Table: EEX Explanatory Regression with Commodities




Main Results

Empirical measures of hedging pressures of producers andretailers support the model’s predictions (sign)Results suggest that there is a mistiming of producer andretailer hedging pressuresFinancial market variables have no explanatory power inisolationFinancial market variables have a significant impact on theforward premium in the joint analysis with electricity marketvariablesResults suggest that the impact of outside investors is feltthrough capital movements associated with financial cycles




Determinants of the Forward Premium in ElectricityMarkets

Álvaro Cartea, José S. Penalva, Eduardo Schwartz

Universidad Carlos III, Universidad Carlos III, UCLA

June, 2011


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