Market Completeness: How Options Affect Hedging and Investments in the Electricity Sector 1

Transcription

1 Market Completeness: How Optons Affect Hedgng and Investments n the Electrcty Sector 1 Bert Wllems TILEC and CenteR, Tlburg Unversty, the Netherlands b.r.r.wllems@uvt.nl Jors Morbee European Commsson 2, DG JRC, Insttute for Energy, the Netherlands; Center for Economc Studes and KULeuven Energy Insttute, KULeuven, Belgum jors.morbee@ec.europa.eu October 27, 2009 Abstract The hgh volatlty of electrcty markets gves producers and retalers an ncentve to hedge ther exposure to electrcty prces by buyng and sellng dervatves. Ths paper studes how welfare and nvestment ncentves are affected when an ncreasng number of dervatves are ntroduced. It develops an equlbrum model of the electrcty market wth rsk averse frms and a set of traded fnancal products, more specfcally: a forward contract and an ncreasng number of optons. We frst show that aggregate welfare (the sum of ndvdual frms' utlty) ncreases wth the number of dervatves offered, although most of the benefts are captured wth one to three optons. Secondly, power plant nvestments typcally ncrease because addtonal dervatves enable better hedgng of nvestments. However, the avalablty of dervatves sometmes leads to crowdng-out of physcal nvestments because frms lmted rsk-takng capabltes are beng used to speculate on fnancal markets. Fnally, we llustrate that players basng ther nvestment decsons on rsk-free probabltes nferred from market prces, may sgnfcantly overnvest when markets are not suffcently complete. 1 The authors would lke to thank the partcpants of the workshop on "Polcymakng Benefts and Lmtatons from Usng Fnancal Methods and Modellng n Electrcty Markets" n Oxford (July 2008) and semnar audences n Tlburg, Kev, Cologne and Ljubljana. Specal thanks to the dscussant Thomas Tangerås, as well as to three anonymous revewers. Furthermore, the authors would lke to thank the three anonymous referees of Energy Economcs, who provded helpful and constructve feedback. 2 The vews expressed are purely those of the author and may not n any crcumstances be regarded as statng an offcal poston of the European Commsson. 1

2 1 Introducton The specfc characterstcs of electrcal energy create a need for hedgng. Electrcty cannot be stored economcally, and therefore the prce for electrcty s determned by the supply and demand condtons at each gven hour. As demand for electrcal energy s very nelastc and of a stochastc nature and as generators face producton capacty constrants, spot prces are very volatle. Lberalzed electrcty markets are therefore typcally organzed around regonal spot markets for energy, whch determne hourly spot prces, complemented wth markets for long-term contracts, whch help coordnate the actons of the players and allow for hedgng of volume and prce rsks. The extent to whch a frm can hedge ts exposure, depends on the avalablty of markets, ther lqudty (determned by such parameters as tradng volume and bd-ask spread), and the presence of speculators who can absorb part of the rsk. These factors change as markets evolve from pure OTC to sophstcated spot and futures markets, and to more complete markets n whch there s a lqud trade of a broad set of dervatves. 3 Recognzng that electrcty markets are typcally very ncomplete, the objectve of ths paper s to analyze the effect of ncreasng market completeness on welfare and on nvestment ncentves n the electrcty sector. In our paper, market completeness s measured as the number of electrcty optons avalable to producers and retalers, n addton to a forward contract. Indeed, as more optons wth dfferent strke prces become avalable, frms have more nstruments to trade rsks and markets become more complete. 4 Ths paper develops an equlbrum model of the electrcty market, whch ncludes the producton process, spot market trades and trade of dervatves. For llustratve purposes, the model s calbrated on the German electrcty market, although an exact analyss of the German market s not the objectve of ths paper. Frst, the results show that addng opton markets s welfare-enhancng, but that most of the benefts are obtaned wth one to three optons. In partcular, f frms have strong 3 Note that vertcal ntegraton of electrcty producton and retal s an alternatve way of creatng a complete set of hedgng nstruments between producton and retal. 4 The paper assumes that demand shocks are the only source of rsk. In such a settng, the market s complete f optons at every strke prce can be traded. However, f there are also frm-specfc shocks, then addtonal dervatves should be added for the market to be complete. 2

3 averson of negatve shocks (shocks that would cause frm bankruptcy), then no equlbrum can be found unless opton contracts are avalable n order to protect retalers aganst bankruptcy under all condtons. Second, we analyze how nvestment decsons by small frms are affected when an ncreasng number of dervatves are traded. We show that market ncompleteness typcally leads to undernvestment. The effects are, however, dfferent for base load plants and peak load plants: the presence of forward contracts only (.e., no optons) s suffcent for nvestment n base load plants to reach the same level as n case of market completeness, but there wll be undernvestment n peak load plants untl there s a suffcent number of opton contracts (whch allow the nvestor to hedge market rsk assocated wth the nvestment). Increasng the number of dervatves may, however, also lead to crowdng-out of certan nvestments n power plants: f the nvestor can trade a fnancal contract that s hghly correlated wth the proft of a potental nvestment and the fnancal contract provdes a more attractve rsk-return rato, then the nvestor wll only nvest n the fnancal market, as ts rsk-takng capabltes are lmted. The amount of nformaton contaned n the equlbrum market prces, ncreases wth the number of fnancal products beng traded: t s shown that the qualty of power plant nvestment decsons that are based on rskfree probabltes nferred from market prces, mproves wth the number of contracts beng traded. If markets are not suffcently complete, players basng ther nvestment decsons on rsk-free probabltes may sgnfcantly overnvest. The model proposed n ths paper s complementary to the tradtonal fnancal models for dervatves prcng, whch are based on the no-arbtrage approach. In fact, t has been observed that t s dffcult to apply the tradtonal no-arbtrage approach to the case of electrcty dervatves, because the non-storablty of electrcty means that the well-known cost-of-carry relatonshp and delta-hedgng strategy cannot be mplemented, and hence prcng of electrcty forwards and optons cannot be done n the usual manner. 5 For that reason, Bessembnder and Lemmon (2002) adopt an equlbrum approach and explctly model the economc determnants of market clearng forward prces. Bessembnder and Lemmon s 5 Eydeland and Geman (1998) present a prcng model for power optons that reles on assumptons regardng the evoluton of forward power prces. They show that the approach s adequate to manage monthly and yearly power optons, but that t does not offer a safe soluton for daly optons. 3

4 (2002) model was only focused on forward contracts, and n our paper we extend ther model to nclude an ncreasng number of optons n addton to a forward contract. We then use the model to study the effects of ncreasng market completeness on welfare and on nvestment ncentves. The paper s organzed as follows. Frst, secton 2 provdes an overvew of relevant research on ncomplete markets, ncludng the applcablty to electrcty markets. Next, secton 3 descrbes the electrcty market model that s used to obtan the results of ths paper, whle secton 4 descrbes the model data. Secton 5 verfes the welfare effects of an ncreasng number of markets. Sectons 6 and 7 analyze the effect on nvestment ncentves, based on welfare consderatons (secton 6) and on rsk-free probabltes,.e. the fnance approach (secton 7). Fnally, secton 8 summarzes our conclusons. 2 Lterature revew The topc of ths paper s closely related to the lterature on ncomplete markets and fnancal nnovaton, as well as to the lterature on hedgng n electrcty markets. In ths secton we frst ntroduce the concept of ncomplete markets. Next, we dscuss the man results of the lterature. Fnally, we hghlght the relevance for electrcty markets and dscuss related work on hedgng n electrcty markets. We base our dscusson on market completeness manly on Staum (2008) and Duffe and Rah (1995). 2.1 Incomplete markets Markets are ncomplete when perfect rsk transfer between the agents s mpossble. There mght be several reasons why ths would be the case. Frst, the marketed set of assets may be nsuffcent to hedge the class of rsk one wshes to hedge. Ths type of ncompleteness deals wth the spannng role of securtes (see also Allen and Gale, 1994). Second, markets mght be mperfect due to the exstence of transacton costs and/or tradng constrants. For nstance, frms mght not be able to take a short poston n a traded securty. These costs and/or constrants make t effectvely mpossble to transfer rsk perfectly. In our paper we focus on the frst type of market ncompleteness: the mssng markets problem. 4

5 In practce, markets are never complete, as not all rsk factors are traded on a market. Hence, when mght market ncompleteness be relevant for hedgng or prcng decsons? We menton two stuatons n whch ths mght be the case. The frst stuaton s when some of the varables one would lke to hedge are derved from non-market prces, as s the case for weather dervatves. The second typcal stuaton of market ncompleteness occurs when the prce of an asset does not follow a standard random walk process where prces changes are nfntesmally small but contans large prce jumps. The problem wth prce jumps s that a hedgng strategy whch dynamcally adjusts a portfolo contanng the underlyng asset and a rsk-free bond, s no longer possble, as the payout s non-lnear n the sze of the shock. In order to complete the market one would need to add a forward market and a set of opton markets wth dfferent strke prces. 2.2 Research results on ncompleteness The frst man result of the lterature on welfare effects and prcng of addtonal assets s that welfare n an ncomplete market s lower than n a complete market because not all rsk s perfectly allocated n the market. 6 Ths s a rather ntutve result: as n an ncomplete market not all potental gans from trade are exhausted, total welfare can be mproved by a suffcent number of addtonal markets untl the market s complete. Ths smple ntuton does, however, not carry over to stuatons where only one addtonal market s added to the economy, wthout completng the market. Hart (1975) shows that addng a fnancal product mght make every one n the economy worse off. Extendng ths result, Elul (1995) and Cass and Ctanna (1998) show that n an economy wth many consumpton goods one can always fnd an asset that makes everyone worse off, or an asset that makes everyone better off, 6 In ths paper we assume that a Walrasan equlbrum exsts, even when markets are ncomplete. In a general equlbrum settng wth multple goods, (where securtes can contan dfferent bundles of goods), ths s not guaranteed. However, when we restrct ourselves to economes where fnancal clams only have a pay-off n terms of a sngle numerare good, exstence s guaranteed. On exstence of equlbra n a general equlbrum settng, see Duffe and Shafer (1985) and Duffe and Shafer (1986). 5

6 or an asset that makes any combnaton of ndvduals better or worse off. 7 Note that ntroducng all fnancal assets (completng the market) does not necessarly make everyone better off. Complete markets are Pareto effcent, but not necessarly Pareto domnant wth all possble ncomplete market allocatons. Wllen (2005) studes the mpact of market nnovaton n more detal and shows that, when agents have exponental utlty and rsk s normally dstrbuted, the effect of a fnancal nnovaton can be splt up n a portfolo effect and a prce effect. Elul (1999) studes the welfare effects of a fnancal nnovaton n a sngle-good market. Boyle and Wang (2001) study the prcng of a new dervatve n an ncomplete market. They show that one should not use the standard arbtrage assumptons typcally used n the fnancal (engneerng) lterature, as the prces of exstng assets may change once a new asset s added to the economy. 8 Instead, they recommend to make explct assumptons on the preferences of the agents n the economy and to use an equlbrum model to derve the prces of the dfferent assets. Staum (2008) and Carr et al. (2001) argue however that results of equlbrum models depend very much on the choce of the utlty functon, the ntal endowment of the frms, and the parameters of the probablty measure, and are therefore not useful for tradng decsons. 2.3 Incompleteness and hedgng n electrcty markets The electrcty market s an nterestng example of a very ncomplete market. Snce electrcty cannot be stored economcally and electrcty prces are very volatle, t s dffcult to hedge even the most basc forward contracts and optons, when they are 7 Smlar results were obtaned earler by Mlne and Shefrn (1987) n a specfc model set-up. Note that the results are not applcable here because our model assumes only one relevant good: money. 8 They also show that the condton of arbtrage-free prcng does not determne a unque prce for the newly created asset. 6

7 not traded drectly n the market. 9 Our paper focuses on the electrcty market and bulds further upon exstng studes on contractng and hedgng n ths market. 10 Frst of all, Bessembnder and Lemmon (2002) develop a partal equlbrum model of the spot market and one forward market. They derve analytcal solutons for forward and spot prces n a settng n whch frms are rsk averse, producton cost are convex, retal prces are fxed and demand s stochastc. Ther theoretcal predctons on rsk prema are verfed emprcally: the model correctly predcts when markets should be n backwardaton or n contango. Sddqu (2003) completes the Bessembnder and Lemmon (2002) model by ntroducng a forward market for ancllary servces (reserve capacty) and dervng analytcal results that lnk the forward prces of electrcty and ancllary servces wth the statstcal propertes of the spot prce. Our paper also extends the framework of Bessembnder and Lemmon (2002) and allows for multple fnancal products to be traded not just one forward contract. 11 Furthermore, our paper analyzes the effects of speculators tradng n a number of dervatves markets and studes an alternatve, more realstc formulaton of rsk averson. In addton, the effect on nvestments s analyzed. The usefulness of fnancal nstruments other than forwards to hedge rsks n electrcty markets s dscussed by Oum et al. (2007). They show that a regulated retal frm can use a combnaton of forwards, call optons and put optons to hedge ts volumetrc rsk, and draw attenton to the regulated frm s dffculty to hedge when regulators forbd trade n dervatves that look speculatve, such as weather dervatves, and rebuff contractng postons that requre the frm to pay a sum exante. The optmal hedgng strategy s found by optmzng the frm s utlty, 9 If t were possble to store electrcty economcally, then the forward contract could be hedged through a combnaton of stored electrcty and a loan. If, n addton, electrcty prces dd not have spkes, then electrcty optons could be hedged through a dynamcally adjusted portfolo of stored electrcty and a loan (.e., delta-hedgng). 10 In the revew we lmt ourselves wth the excepton of Oum et al. (2007) to studes that rely on equlbrum models of the electrcty market. The alternatve to equlbrum models s the study of one frm s contractng and producton decsons for an exogenously gven stochastc spot prce process and forward prce. 11 Wth a forward contract ths paper refers to a contract for future delvery of a fxed quantty of a good at a fxed prce. We wll not explctly specfy whether these contracts are traded over the counter (OTC), or whether they are traded as futures on a centralzed power exchange. 7

8 subjectve to the fnancng constrant. The results are derved for the CARA and the mean-varance utlty functons, wth an endogenously gven prce and quantty dstrbuton functon. In our paper we develop an equlbrum model of the market and show that opton contracts are mportant nstrument to transfer volumetrc rsks from generators to retalers, even more so when frms mght face lqudty constrants. 12 We also show the mportance of optons for nvestment decsons. Baldursson and von der Fehr (2007) study vertcal ntegraton, forward contractng and hedgng n an equlbrum electrcty market model. They show that vertcal ntegraton mght ncrease the equlbrum rsk prema n the market and lower overall welfare, compared wth forward contractng. The reason why ths happens n ther model s that they assume that a vertcally ntegrated frm has a smaller capacty to take up rsk than two separate enttes combned. Even though our model does not represent vertcal ntegraton explctly, the case of vertcal ntegraton n our model corresponds to the case n whch perfect rsk-transfer between producer and retaler s possble,.e., the case of market completeness. In such a settng, the mplct assumpton s that the vertcally ntegrated frm has the same capacty to take up rsk as the two separate frms combned. In our opnon, ths s a more realstc assumpton. We see the dfference between vertcal ntegraton and contractng by means of a forward contract, as follows: wthn the vertcally ntegrated frm, rsk sharng between generaton and retal s perfect, whle rsk sharng by tradng forward contracts s mperfect, leavng part of the rsk untraded The noton lqudty constrants n ths context refers to the constrants faced by an ndvdual frm n the fnancng of ts actvtes. We model these through a CRRA utlty functon, as descrbed further n the paper. Separately, there s the entrely dfferent ssue of lmted market lqudty, whch refers to the fact that n general, markets for energy dervatves are relatvely thn. As mentoned n the ntroducton, market lqudty s one of the elements of market completeness. In our paper, lmted market lqudty s therefore modeled by assumng that not all possble contracts are traded. An alternatve way of modelng lmted market lqudty s by assumng a large bd-ask spread. Our paper, however, does not consder transacton costs, hence we do not study market lqudty n ths way. 13 An addtonal dfference between vertcal ntegraton and tradng dervatves s that n a dervatves market, fnancal nvestors can reduce the rsk prema n the market. 8

9 Also Ad et al. (2006) study vertcal ntegraton, forward contractng, hedgng, and retal competton. They develop an equlbrum model n whch frms have a meanvarance utlty functon and show that both vertcal ntegraton and forward contractng allows for a better rsk sharng between retalers and generators and leads to lower retal prces, ncreased market share for small generators, and a reducton of the profts of retalers. Compared wth long-term contracts, vertcal ntegraton leads to perfect rsk sharng between generators and retalers. Addtonally, forward markets mght not develop under some parameters of the game n whch case no rsk s shared between upstream and downstream frms. The results of Ad et al. (2006) on the comparson of vertcal ntegraton and forward contractng are drven by the change of the utlty functon (and the mpled capacty of frms to take up rsks) and the qualty of rsk transfer between upstream and downstream frms (market completeness). In our paper we sngle out the effect of market completeness. We do not, however, study retal competton. Our paper assumes a perfectly compettve market and neglects strategc ssues assocated wth long-term contractng that have been reported n the lterature. Allaz and Vla (1993) study the role of forward contracts, not as a tool to hedge rsks, but as an nstrument used by olgopolsts to strategcally affect market outcomes. It s shown that n a Cournot settng, generaton frms sell forward contracts n order to commt to compete more aggressvely n the spot market. Hence forward contracts make markets more compettve. Wllems (2006) shows that a smlar mechansm s at work wth fnancal call optons: the market equlbrum s even more compettve than wth future contracts. Green (2003) studes the combned hedgng and strategc roles of forward contracts whle at the same tme examnng dfferent types of competton n the retal market. He shows that retal competton may lower the amount of forward contracts frms wll sgn. The current paper does not allow for retal competton, consumers cannot swtch retal suppler and assumes, as n Bessembnder and Lemmon (2002), that retal prces are fxed. Green (2007) models nvestment decsons and the technology choce n a long-term olgopolstc equlbrum model wth rsk averse frms n whch frms can sgn forward contracts. The settng of our paper allows us to analyze the relaton between market completeness and nvestment decsons of generators. 9

10 3 Model descrpton We extend the compettve market equlbrum model of the forward and spot markets developed by Bessembnder and Lemmon (2002). The man dfference wth ther model s that we allow for multple fnancal products to be traded on the market. We start wth a descrpton of the spot market and contnue wth a descrpton of the dervatves markets. We consder an electrcty sector wth dentcal retalers. Each of the producton cost wth a fxed and a varable component: N g dentcal generaton frms and N r N g generaton frms s assumed to have a total Q c F + a (1) c where Fa, and c are parameters that determne the shape of the cost functon, and Q s the producton level of an ndvdual frm. The total producton cost of the ndustry s gven by: c Q CQ ( ) = F+ a (2) c wth F = N F and c 1 a = a/ N and Q the total producton of the ndustry. g g Demand for electrcty D s nelastc and stochastc. The spot market s perfectly compettve, and the wholesale prce for electrcty P s determned by market clearng: c 1 = = (3) P C'( D) ad Each generaton frm produces D/ N g. As demand s a random varable, so s the spot prce. The combned proft of the generators s equal to spot market revenue mnus producton costs: π g = PD CD ( ) (4) 10

11 Retalers buy energy on the spot market and sell t at a fxed retal rate R to consumers. 14 Each retaler supples a volume D/ N r. The combned proft of the retalers s equal to: π r = ( R PD ) (5) Both retalers and generators profts are affected by the stochastc nature of demand. In the dervatves market, a dervatve {1,.., I} s traded at a prce F. The dervatve promses a payment T ( P ), whch s condtonal on the spot prce P. Ths paper assumes that the only dervatves whch are traded are call optons. Hence: T( P) = max( P S,0) (6) wth S the strke prce of opton. A dervatve wth strke prce zero corresponds to the standard forward contract. The combned proft j Π ( j= rg, ) that s made by retalers and generators, respectvely, when the retalers/generators buy a total of dervatves market, s equal to: k j dervatves n the I P = π ( P) + k ( T( P) F) (7) j j j = 1 The frms' proft s the sum of the proft they make n the spot market, and the proft they make on the dervatves they have bought. Both terms are stochastc as they depend on the realzaton of the demand level. We assume that retalers and generators are rsk averse, and that the utlty of ndvdual retalers and generators can be descrbed by a mean-varance utlty functon wth rsk averson parameter NA ( j= rg, ). The rsk averson parameter j contans N j to account for the fact that a larger number of frms would lead to a smaller average sze per frm, and therefore a proportonally smaller rsk-bearng capacty,.e. a hgher absolute rsk averson. When Ng = Nr, the rsk averson of all frms (both generators and retalers) s the same, a reasonable assumpton. If U r and 14 The fxed rate R s ether a regulated rate, or a fxed prce contract offered to customers n a deregulated market. The case of real-tme prcng, whch would allow retalers to transfer upward prce rsk to the consumers, s dscussed n secton 5. 11

12 U g represent the utlty of retalers and generators, respectvely, then each dentcal ndvdual frm wll maxmze ts utlty U / N : U j Π j NA j Π j = E Var j= rg, N j N j 2 N j Maxmzng (8) s equvalent to maxmzng the followng: j j A U j = E( Π j) Var( Π j) j= rg, (9) 2 whch has the ntutvely appealng beneft of not contanng N j anymore. One could say that the rsk averson parameter A measures the rsk averson of ether the generaton sector or the retal sector as a whole. We can proceed wth the analyss as f there was only one generator and one retaler. Aggregate market welfare W s equal to the sum of the utlty of retalers and generators: W = Ur + Ug. In the contractng stage, frm j maxmzes ts utlty U j, by choosng the amount of j j j dervatves k1,..., k,..., k t buys or sells. The equlbrum contract postons are I gven by: j 1 E( T) F 1 k =Σ Σ Cov{ π j, T} (10) A wth k j = ( k j 1,..., k j I ), the vector of equlbrum quanttes bought by player j, Σ= Cov{ TT, } the I by I covarance matrx of the contracts T = ( T1,..., T I ), F = ( F1,..., F I ) the dervatve prce vector, and Cov{ π j, T } the 1 by I covarance matrx of contracts and frm j s proft. Equaton (10) shows that the amount of contracts frm j buys s the sum of two terms. The frst term s the pure speculatve amount of contracts a frm would lke to buy. If a fnancal dervatve has an expected postve return, then the frm wll buy some of t, as long as t does not ncrease the varance of ts portfolo too much. The second term s the pure hedgng demand by the frm. A frm j wll buy dervatves n order to hedge ts proft rsk. It wll buy more of a certan dervatve, f t s more correlated wth the proft t wants to hedge, and f the mpact on the varance of the portfolo s smaller. In equlbrum the demand and supply of dervatve products should be equal. Hence, f there are no speculators actve n market we fnd: 12 (8)

13 k r g + k = 0 (11) and usng equaton (10) the equlbrum prce of dervatve s gven by: A F = E( T) Cov{ πg + πr, T} (12) 2 Hence, the prce of a dervatve s equal to the expected pay-off of the dervatve mnus a term whch reflects the fact that the dervatve s used to hedge the rsk of the ndvdual frms. The last term depends on the rsk averson of all the frms and the covarance of ndustry proft wth fnancal nstrument. It s worth notng that the prce of the dervatve does not depend on the number of products traded n the market. 15 If rsk neutral speculators are actve n dervatves market, then the rsk premum becomes zero, and the prce of the dervatve should be equal to ts expected value: F = E( T) (13) 4 Model data The model s calbrated on the German electrcty market, usng techncal and market data recorded n the frst two months of Note that the purpose of the calbraton s to allow us to perform smulatons that produce ntutvely relevant results. The numbers thereby serve as an llustraton ths paper does not clam to make exact statements about the mpact of opton trade on the German electrcty sector. The margnal producton cost curve C'( Q ) s calbrated on the actual German margnal producton cost curve, as explaned n Appendx A. Demand s assumed to be normally dstrbuted wth mean 60 GW (whch s the average of the observed sample) and standard devaton 17 GW. The standard devaton s chosen n such a way that the standard devaton of the resultng power prce (accordng to equaton (3)) corresponds to the standard devaton of the sample of observed prces. Gven the assumptons about supply and demand, we can derve the wholesale prce dstrbuton. The dstrbuton has a mean of 48 EUR/MWh and a standard devaton 15 In standard mean-varance settngs, rsk prcng s not affected. Specfcally, n quadratc or CARAnormal economes, the prce of any rsky securty relatve to the bond s unaffected by changes n the span. See Oh (1996). 13

14 of 35 EUR/MWh. Bessembnder and Lemmon (2002) show that as the ndustry margnal cost functon s convex, the prce dstrbuton s skewed. Retalers and generators have the same rsk averson parameter A = , whch has the unt (h/1000 EUR). Furthermore, we assume that the fxed cost parameter F = 1200 (expressed n 1000 EUR/h), and that retalers sell ther energy at a fxed prce of 58 EUR/MWh. Note that prces and quanttes are expressed n (EUR/MWh) and (GW), respectvely, and hence profts and total costs are expressed n (1000 EUR/h). 5 Welfare effects In ths secton, we use the model to calculate the optmal hedgng strategy of generators and retalers, and analyze the welfare effects of addng addtonal dervatves to the market. In the frst part of the smulatons we assume that no speculators are actve on the market, and hence supply and demand of fnancal contracts s only from retalers and generators. We consder four scenaros wth a dfferent number of dervatve markets present. In Scenaro 1, only a forward market exsts. In Scenaros 2 through 4, the forward market s supplemented wth one, three, and eleven addtonal opton markets, respectvely. 16 Table 1 shows the smulaton results for all scenaros. It shows for each of the twelve dervatve contracts the net amount traded by generators and retalers. Postve numbers represent long postons, negatve numbers represent short postons. The opton contracts have strke prces rangng from 0 to 143 EUR / MWh, wth the zero strke prce (contract 1) correspondng to the forward contract. The range of opton strke prces covers the 95% confdence nterval of prce levels. 16 The numercal model s wrtten as a Mxed Complementarty Problem (MCP) n GAMS. See Appendx B. 14

15 () S F Scenaro 1 Scenaro 2 Forward Forward + 1 Opton k g k r g Net Contract Poston k k Scenaro 3 Scenaro 4 Forward + 3 Optons All Contracts Welfare W r k k Table 1: Market equlbrum wthout speculaton g r k g k r The results show that f there are only forward contracts, frms overhedge ther postons. Generators sell 68 GW forward, whle n expected terms they wll only produce 60 GW. The ntutve explanaton for ths s that generators and retalers want to hedge volumetrc rsk (or quantty rsk), n addton to prce rsk. If there were only prce rsk (.e., the quantty of electrcty demanded would be determnstc), then forward contracts whch are specfcally suted for hedgng prce rsk would be suffcent. The number of forward contracts would exactly correspond to the determnstc demand quantty. However, n the settng of ths paper (and n realty), generators and retalers are exposed to both volumetrc rsk and prce rsk, because both quanttes and prces are stochastc. If no optons are traded, then volumetrc rsk can be hedged usng addtonal forwards, because prce and quantty are postvely related. Another way of explanng ths effect s that, because prce and quantty are postvely related, overall rsk exposure s convex n the underlyng state varable (demand) and hence the number of forward contracts exceeds expected demand. The prce of the forward contract s 45.3 EUR/MWh, whch s below the expected spot prce of 48 EUR/MWh. In Scenaros 2 to 4, extra fnancal nstruments are added to the market. Table 1 shows that once more nstruments become avalable, generators reduce the amount of standard forward contracts they sell and substtute these contracts wth opton contracts. The generators and the retalers reduce ther supply and demand of forward contracts. Although both demand and supply functons shft, the prce of the forward contract remans 45.3 EUR/MWh as shown n dervaton (12). As we 15

16 ponted out n footnote 15, ths effect s due to the use of the mean-varance utlty functon. The last row n Table 1 s the aggregate welfare, measured n certanty equvalents (1000 EUR/h). Increasng the number of contracts traded clearly ncreases market effcency. The ntroducton of one opton contract, when none exsted before, ncreases welfare by approxmately 50 %. Addng extra markets for opton contracts ncreases welfare further, but to a lesser extent. For nstance, ncreasng the number of opton markets from 3 to 11, ncreases welfare by 1.2 %. Hence rsk sharng between generaton and retal s close to optmal once one opton contract (or a few opton contracts) are traded. In fact, the welfare effects n Scenaro 2 (Forward + 1 Opton) can be mproved even further, by modfyng the strke prce of the one avalable opton contract. The strke prces of the opton contracts n the smulatons of Table 1 are chosen so that they span the 95% confdence nterval of prce levels. Scenaro 2 assumes that one opton s avalable, wth a strke prce roughly n the mddle of ths prce range. Fgure 1 shows how welfare would change when a dfferent strke prce s used. Welfare wth "Forward + 1 Opton" as a functon of strke prce Welfare (1000 EUR/h) All contracts Forw ard + 1 Opton Forw ard Strke prce of Opton (EUR/MWh) Fgure 1: Welfare obtaned wth "Forward + 1 Opton", for dfferent strke prces (compared wth welfare obtaned wth only a "Forward" and wth "All contracts") If the strke prce of the opton s very low, then welfare s equal to welfare obtaned wth a forward contract only, because the opton does not add any new hedgng possbltes. Welfare reaches a plateau optmum of 1280 (expressed n 1000 EUR/h) 16

17 when the strke prce s n the EUR/MWh range. However, for all strke prces n the EUR/MWh range, addng the one opton contract to the forward contract lfts welfare above 1200 (n 1000 EUR/h), thereby capturng more than 75% of the potental benefts of market completeness. Untl now, we have assumed that retalers sell at a fxed prce R, whch can be ether a regulated rate, or a fxed prce contract offered to customers n a deregulated market. Gven the contnuous development of more sophstcated meterng systems, t s nterestng to consder what would happen f real-tme prcng were possble. If all consumer contracts were based on real-tme prces, then ths would elmnate all rsk for the retalers. However, generators would stll have a desre to hedge. Smart retalers could therefore develop structured consumer contracts that take away rsks from the generators and transfer them to the consumers who are wllng to take on the rsks. Such consumers would be rewarded wth a lower expected power prce. In ts smplest form, such a structured contract could be smlar to a fxed prce contract. If optons are avalable on the wholesale market (n addton to forwards) then more sophstcated structures would be possble, thereby hedgng the generators' rsk better and better, and mprovng welfare. In practce, n order to preserve the demand ncentves created by real-tme prcng, such structured contracts are stll lkely to prce a consumer s ndvdual demand based on real-tme prces. However, at the end of each perod, consumers could expect a check that settles the structured part of the consumer contract,.e. the hedge, wth the amount of the check dependng on the overall demand and prce developments n the spot market n the course of the perod. 17 For the second part of the smulatons, we assume that speculators can actvely partcpate n the market, by takng postons n the electrcty dervatve markets and fnancally closng ther poston n the spot market. We assume they trade away the rsk prema n the market: the prce of the dervatves becomes equal to the expected value of the dervatve. As speculators provde extra lqudty to the market, the supply of dervatves by generators does no longer need to exactly balance the demand by retalers. The dfference of generators supply and retalers demand s 17 Borensten (2007) dscusses retal markets and hedgng n more detal. He shows how retal contracts can be developed that base the margnal prce of electrcty consumpton on the real tme prce, but at the same tme nclude a hedge whch reduces monthly bll volatlty. 17

18 the poston speculators take n the market. For the same four scenaros as before, Table 2 gves the net poston of generators and retalers. In Scenaro 1, only forward contracts exst, and generators sell 69.1 GW forward, retalers buy 67 GW, and speculators buy 2.1 GW. The results ndcate that the more dervatves markets are ntroduced, the larger the gap between supply and demand for forward contracts, and the larger the role played by speculators. In Scenaro 4, n whch there s one forward market and eleven opton markets, generators sell 34.2 GW, retalers sell 44.8 GW and speculators buy 79 GW. The ntroducton of speculators ncreases welfare, as the players can share ther rsk wth players outsde the market, the speculators. Hence, the addton of speculators does not change our prevous conclusons. Speculators play an actve role n the electrcty market by takng up market rsk and by decreasng the rsk prema n the market. As the number of markets ncreases, the amount of rsk that speculators take away from market partcpants ncreases, but the postve welfare effect of addtonal markets levels off after a few products. () S F Scenaro 1 Scenaro 2 Forward Forward + 1 Opton k g k r g Net Contract Poston k k Scenaro 3 Scenaro 4 Forward + 3 Optons All Contracts Welfare W r k k Table 2: Market equlbrum wth speculaton g r k g k r Fnally, for the thrd part of the smulatons, we repeat the prevous smulaton but we now use a dfferent assumpton for frms utlty functons: nstead of the utlty functons from equaton (7), we use the well-known CRRA utlty functon (.e., the utlty functon wth constant relatve rsk averson). As a result of the CRRA property, frms become very averse of potental shocks that would lead to very low or negatve profts. In other words, the CRRA utlty functon models a world n 18

19 whch frms want to avod the rsk of lqudty problems or bankruptcy. Practcally, we choose the coeffcent of relatve rsk averson to be 4, whch s n the mddle of the typcal 2-6 range (see e.g. Palsson, 1996). The smulaton results wth speculaton and CRRA utlty functons for producers and retalers are shown n Table 3. Generally speakng, the results are very smlar to the results of Table 2, although the retaler seems to have a slghtly ncreased preference for optons over forwards (as compared to Table 2). The most nterestng observaton s that wth the CRRA utlty functon, t s not possble to fnd a suffcently hedged soluton n the case when only forwards are present. In other words, f no optons are ntroduced, welfare remans nfntely low for CRRA utlty functons. The reason s that forwards alone do not allow the retaler and the generator to lmt ther exposure n all states-of-the-world. The ntuton for ths effect s the followng: snce a negatve result n one potental stateof-the-world s strongly penalzed by the CRRA functon, the retaler and the generator would lke to avod at all costs any outcomes n whch ther proft s below a certan threshold, n order to avod bankruptcy. The retaler faces a negatve shock when demand s hgh (t faces a hgh wholesale prce, and has to buy a large volume of power), and when demand s low (sales volume s too low to cover fxed costs). The generator faces a negatve shock when demand s very low (low prce and low volume). As the retaler wants to avod bankruptcy at all cost, ts demand for forward contracts s undetermned for any prce of forward contracts. Wth only the forward contract, the retaler s unable to hedge aganst both the rsk of havng hgh demand and the rsk of havng low demand. Based on these results for a CRRA utlty functon, t s clear that the ntroducton of optons s especally welfareenhancng f there s a strong rsk averson for negatve shocks that could lead to bankruptcy. A practcal mplcaton of ths phenomenon would be that a retaler alone would have dffculty to survve f no lqud opton market s avalable. Anecdotal evdence of ths effect s the case of Centrca n the UK. After the demerger of Brtsh Gas (Centrca, 12/2/1997), Centrca was essentally a gas retaler n the UK. At the end of 1997, Centrca entered the electrcty market as a pure retaler (wthout any generaton assets) and acqured ts frst electrcty customers (Centrca, 1/12/1997). Rather than stayng a stand-alone gas and electrcty retaler, Centrca started to nvest n gas-fred power generaton n 2001 (Centrca, 29/5/2001 and 24/8/2001). 19

20 Centrca stated the followng reason for the nvestments n power generaton: "As part of ts rsk management strategy the company has sad t plans to source per cent of ts future peak electrcty requrements from ts own generatng capacty. Ths strategy offers ncreased long term stablty and protecton aganst electrcty prce fluctuatons and spkes" (Centrca, 24/8/2001). In other words: the nvestment n gas-fred power generaton s meant prmarly to protect the retaler aganst electrcty prce volatlty n case of peak demand. From a fnancal perspectve, an nvestment n gas-fred power generaton (whch has relatvely low nvestment cost and relatvely hgh margnal cost) can be consdered as the purchase of a call opton on electrcty, wth a relatvely hgh strke prce 18. The absence of a market for such optons forces retalers to nvest n the physcal equvalent, because stayng unhedged s not a vable alternatve. () S F Scenaro 1 Scenaro 2 Forward Forward + 1 Opton Net Contract Poston Scenaro 3 Scenaro 4 Forward + 3 Optons All Contracts g r g r g r g r k k k k k k k k No soluton Welfare W "- " Table 3: Market equlbrum wth speculaton, wth CRRA utlty functons 6 Investment decsons by small frms Above we have shown that the welfare effect of addng contracts levels off after a relatvely small number of contracts. However, mplctly we have assumed that all producton frms have a dversfed portfolo of generaton plants. Indeed: we assume that there are N g dentcal producton frms, whch mples that the 18 Strctly speakng, a gas-fred power plant s an opton on a (clean) spark spread,.e., the dfference between the electrcty prce and the nput prces (gas, carbon emsson rghts). 20

21 producton cost curve of each frm s just a horzontally scaled verson of the aggregate producton cost curve of the generaton ndustry. In other words, the portfolo of each frm contans power plants wth relatvely low margnal costs (e.g., nuclear power plants), whch wll be run n nearly all demand scenaros, and power plants wth relatvely hgh margnal costs (e.g., gas-fred power plants), whch wll be run only f demand s hgh. As a result, all generaton frms are reasonably dversfed, and the demand/prce rsk s adequately dstrbuted across generaton frms. However, f some frms have only base load power plants and other frms have only peak load power plants, then some frms fnancal results are much more senstve to certan demand/prce scenaros. Intutvely, ths could make the potental socal value of a comprehensve set of fnancal contracts (whch would allow rsktransfer under accurately defned demand/prce scenaros) sgnfcantly hgher. In order to test the mpact of market completeness when frms have dfferent types of portfolos, we analyze how rsk tradng modfes nvestment behavor. Specfcally, we determne whether a small, non-dversfed frm would nvest n a sngle power plant wth margnal cost c and fxed nvestment cost F. 19 The small frm s assumed to be rsk averse, wth mean-varance utlty functon (as n the frst part of our smulatons). We assume no speculators n the market. The frm nvests n ths producton plant f the nvestment ncreases ts expected utlty. The expected utlty wthout nvestments s equal to U NI A = max E{ π} Var{ π} k1,..., ki 2 I wth π = k ( T( P) F) = 1 whle the expected utlty wth nvestments s equal to U INV A ( cf, ) = max E{ p} Var{ p} k1,..., ki 2 I wth p = k ( T( P) F) + (max{ p c,0} F) = 1 (14) (15) The frm nvests as long as NI INV U > U (, cf) (16) 19 Snce such a power plant s n fact (almost) equvalent to an opton contract, ths essentally means that we analyze the mplcatons of provdng one player wth one addtonal contract. 21

22 Equaton (16) defnes mplctly the maxmum fxed cost for whch the frm s wllng to nvest n new generaton capacty wth margnal cost c. Hence nvestment occurs as long as F < F cr () c (17) cr Therefore, the functon F () c represents the nvestment behavor of the frm. 20 cr F () c obvously depends on the number and types of fnancal contracts traded n the market, and on the rsk averson of the frm. Indeed, generally speakng, as more contracts are traded, the frm s able to better hedge the output of the producton plant, thereby reducng ts rsks. Ths makes t more nterestng for the frm to buld a power plant. In certan cases, there s, however, a non-monotonc relaton between market completeness and nvestments decsons, as wll see below. Let F () c denote the case of market completeness,.e., the frm's nvestment behavor f a full set of opton contracts s avalable. Fgure 2 compares the decson behavor of rsk averse frms n case of market ncompleteness wth the decson behavor n case of market completeness. More specfcally, the fgure shows the "adjustment factor" κ : cr F () c κ = (18) cr F () c When calculated for dfferent levels of market completeness, the factor κ descrbes how the frm s nvestment decsons change as markets become more complete. Those nvestments decsons are the proft-maxmzng decsons for the frm (condtonal on the avalable contracts). Note that the frm's rsk averson s chosen at a hgher level than before, because we analyze a small frm and the mean-varance utlty functon does not scale. If κ < 1, the frm nvests less n a partcular type of generaton than f markets were complete. If κ > 1, the frm nvests more n a partcular type of generaton than f markets were complete. cr 20 cr If we consder the power plant as an opton contract, then F () c s the maxmum prce (opton premum) the frm would be wllng to pay for ths opton contract. 22

23 1,2 Optmal Investment Decsons (Averson = 0.025) Adjustement Factor 1,0 0,8 0,6 0,4 No Contracts Forw ard Contracts Contracts 1 & 7 Contracts ,2 0, Margnal Cost Power Plant EUR/MWh Fgure 2: Optmal nvestment decsons. The effect of ncreasng market completeness s very dfferent for base load plants on the one hand, and peak load plants on the other hand. Once the forward contract s ntroduced, a frm wth a base load plant ( c 0) would be able to hedge ts poston completely. Addng addtonal dervatves to the market does not change the nvestment decsons for a base load power plant, as the frm already has perfect nformaton n evaluatng the value of the power plant usng the forward contract. Speculaton and nvestment decsons are decoupled: a frm wantng to nvest n a base load power plant can do so wthout takng any market rsk (.e., t can focus on the operatonal aspects), whle a speculator can decde to assume some base load market rsk wthout actually havng to buld a power plant. For peak load plants ( c large), the results are qute dfferent. Once the forward contract s ntroduced (and no optons), nvestment n certan peak load power plants wth very hgh margnal cost (hgher than 100 EUR/MWh n Fgure 2) may actually be less than f no contracts are traded. The reason for ths s that t may be more proftable for the frm to speculate on the forward market (wthout buldng a power plant), than to buld a power plant and use fnancal contracts to hedge ts portfolo. Hence, fnancal nvestments crowd out the nvestments n physcal assets: nvestment and speculaton decsons are coupled. As more and more contracts are ntroduced, we see that nvestment n peak generaton ncreases dramatcally, because there are better nstruments to hedge the rsk of the producton output of the 23

24 frm. 21 As a result, the nvestment decson and the speculaton decson become decoupled agan. The fgure also shows that for the technology wth margnal producton costs around 78 EUR/MWh, addng addtonal contract markets on top of contract number 7 does not change the results. Contract 7 has a strke prce of approxmately 78 EUR/MWh, hence the nvestment valuaton of the frm s perfect, regardless of any addtonal contracts beng added. Note that n certan cases the adjustment factor κ mght be larger than one, whch mples that a frm mght nvest more when markets are ncomplete than when markets are complete. Ths may happen when the nvestment ncreases the rsk of the exstng frms n the sector. In that case t would be cheaper for the frm to buy a fnancal opton wth an equvalent strke prce, than to nvest n physcal capacty. Such a fnancal opton would be avalable at a depressed prce,.e. a prce below ts expected value, because t reduces rsk of the exstng frms. Put otherwse, the avalablty of an extra dervatve market creates addtonal nvestments opportuntes for the frm. If those opportuntes are very proftable, then the frm uses ts captal to speculate on the dervatves market, nstead of nvestng t n new power plants. In other words, the opportunty cost of rsk-bearng captal has ncreased wth the avalablty of new nvestment opportuntes. Smlar to what we 21 It s mportant to note the dfference wth the Centrca case, n whch as mentoned n Secton 5 peak nvestment was due to a lack of tradable call optons. Before the nvestment, Centrca was a pure retaler, hence t had a natural short poston n peak electrcty. If tradable call optons had been avalable, such a retaler would have closed ts poston by takng a long poston (.e. buyng) n call optons. Snce these call optons were not avalable, Centrca nvested n physcal peak generaton n order to close ts poston. In contrast, Secton 6 studes the ncentves of a small generator, who s consderng makng an nvestment n power generaton, whch would gve t a natural long poston n peak electrcty. If tradable call optons are avalable, such a frm nvests n physcal peak generaton and closes ts poston by takng a short poston (.e. sellng) n call optons. If tradable call optons are not avalable, then the only way to keep a closed poston s to not nvest, whch leads to the undernvestment n peak generaton that one can observe n Fgure 2 for the case where no contracts or only forward contracts are traded. In summary, the avalablty of tradable call optons ncreases nvestment ncentves for generators, who then sell call optons to retalers. A lack of tradable call optons leads to undernvestment by generators and leaves retalers wth no other alternatve than to become an ntegrated generator-retaler themselves. 24