Load-Following Forward Contracts.

• Author: Brown, David P.

1. INTRODUCTION

   Electricity is commonly purchased and sold in wholesale (spot) markets. The price of electricity can vary widely in such markets, depending on prevailing demand and supply conditions. Forward contracts can avoid the volatility of wholesale market prices by specifying in advance the unit price at which electricity will ultimately be supplied. Forward contracts are prevalent in the electricity sector and elsewhere. Holmberg and Willems (2015, p. 237) report that the total value of all transactions governed by forward contracts exceeded 20% of the world's gross domestic product in 2008. (1)

   In addition to reducing exposure to volatile wholesale prices, forward contracts can reduce the wholesale price of electricity. This is the case because a supplier's forward commitment reduces the amount of electricity it sells in the wholesale market. The supplier's corresponding reduced exposure to the wholesale price of electricity reduces its concern with any reduction in this price, thereby encouraging the supplier to expand its supply of electricity. The resulting increased supply promotes a lower wholesale price of electricity.

   This well known effect of forward contracts has been demonstrated formally in settings where buyers and sellers can sign swap forward contracts (SFCs). A SFC obligates a supplier to deliver a specified amount of the commodity in question in return for a fixed payment by the buyer (Allaz and Vila, 1993). Forward contracts assume other forms in practice. For example, a load-following forward contract (LFFC) obligates a seller to deliver a specified fraction of the buyer's ultimate demand for the product at a pre-determined unit price. To illustrate, under a LFFC, an electric distribution company (or retailer) that is committed to serve the demand of its retail customers might agree to pay an electricity supplier a pre-specified unit price for 10% of the customers' realized demand for electricity. (2) The distribution company might purchase the remaining 90% of its customers' demand at the prevailing spot price.

   Electric distribution companies in many parts of North America employ LFFCs to procure the electricity required to serve customers who do not explicitly choose their preferred retail supplier of electricity. (3) Retail suppliers of electricity in Australia employ LFFCs to help fulfil their mandate to secure via forward contract a specified fraction of the maximum demand for electricity they anticipate. (4) Some retail service contracts also take the form of LFFCs. In markets with retail competition where vertically-integrated producers (VIPs) compete against competitive retailers, the VIPs often agree to supply electricity to customers at a fixed price for a specified period of time. Such contracts effectively commit the VIP to supply the entire realized demand of its customers at the specified fixed price.

   LFFCs differ from SFCs by automatically tailoring a seller's forward commitment to the realized demand for its product. In particular, an electricity generator that signs a LFFC commits itself to remove more output from exposure to the wholesale price as realized demand increases. The generator thereby commits itself to compete particularly aggressively in the wholesale market when demand is high and less aggressively when demand is low. Such tailoring of competitive aggression to realized demand can be valuable for a generator because increased wholesale output can be particularly profitable when demand is pronounced. This is the case because high demand promotes a relatively high wholesale price, and thus a relatively large profit margin for the generator.

   The ability of LFFCs to tailor a generator's competitive aggression to realized demand can promote their widespread adoption. We show that in a setting designed to reflect conditions that prevail in the wholesale electricity market in Alberta, Canada, generators adopt LFFCs exclusively when they have the option to sign LFFCs, SFCs, or both. The equilibrium adoption of LFFCs serves to increase expected consumer surplus and total surplus above the levels that arise in the absence of forward contracting. (5) However, equilibrium expected consumer surplus and total surplus fall below the levels that would arise if SFCs were the only feasible forward contracts. The reduced consumer surplus and total surplus reflect two primary considerations. First, LFFCs induce relatively limited competitive aggression when realized demand is low. The limited aggression promotes a relatively high wholesale price. Second, because LFFCs automatically tailor a generator's competitive aggression to realized demand, generators often can achieve profit-maximizing levels of aggression with a relatively limited expected forward coverage (i.e., a relatively small ratio of expected forward sales to expected total sales). The resulting reduced level of expected forward coverage promotes a relatively high expected wholesale price and associated relatively small levels of expected consumer surplus and total surplus.

   Our analysis builds upon many studies that examine the effects of forward contracting on wholesale market competition. These studies include Allaz and Vila (1993)'s seminal investigation of SFCs. Like Allaz and Vila and much of the ensuing literature, we assume industry participants are risk neutral in order to focus on the strategic role of forward contracting rather than its risk-hedging properties. (6,7)

   Several studies examine the strategic role that financial instruments other than SFCs can play. For example, Willems (2006) permits firms to sign SFCs and call options before engaging in Cournot competition. The author finds that, in equilibrium, call options enhance the pro-competitive effect of forward contracts. (8) Holmberg and Willems (2015) allow firms to choose SFCs and a portfolio of call options before competing via supply functions in the wholesale market. In this setting, firms commit to produce less output as the prevailing wholesale price increases. This commitment to downward-sloping supply functions enhances profit by reducing the intensity of wholesale market competition. (9,10)

   Other studies identify additional means by which forward contracts can limit the intensity of competition. Mahenc and Salanie (2004) demonstrate how firms can purchase forward quantities to commit themselves to subsequently set higher prices for their differentiated products. Liski and Montero (2006) and Green and Le Coq (2010) conclude that forward contracting can reduce the critical discount factor above which collusive agreements are sustainable in infinitely-repeated games.

   Our analysis complements these studies in three primary ways. First, to the best of our knowledge, we are the first to analyze formally the endogenous choice of LFFCs and SFCs. We thereby contribute to the literature that examines how an expanded set of forward contracts affects strategic firm behavior and associated industry outcomes. Second, our analysis provides a nuanced view of how expanded forward contracting affects the intensity of wholesale market competition. We show that LFFCs can simultaneously produce relatively intense competition when market demand is high while inducing relatively limited competition when demand is low. Third, our analysis can help policymakers better understand the benefits and costs of LFFCs which, as noted above, are employed in electricity markets around the world.

   Our analysis proceeds as follows. Section 2 describes our model. Section 3 explains how LFFCs affect equilibrium outcomes by altering generators' reactions functions. Section 4 examines the effects of LFFCs numerically in a setting designed to reflect conditions in Alberta's wholesale electricity market. Section 5 concludes.

2. MODEL ELEMENTS

   We consider a setting with two electricity generators (G1 and G2) and one aggregate electricity consumer. Gi produces electricity at constant marginal cost [c.sub.i] > 0 (i [member of] {1,2}). (11) The consumer's demand function and inverse demand function for electricity are, respectively

   Q(P,s) = a + [epsilon] - bP and P(Q, [epsilon]) = a + [[[epsilon]] / [b]] [[1]/[b]] Q (1)

   where [??] denotes quantity, P denotes price, a and b are constants, and a > [bc.sub.i] > 0 for i [member of] {1,2}. [epsilon] [member of] [[epsilon], [epsilon]] is the realization of a random demand parameter with zero mean and strictly positive variance. H([epsilon]) is the cumulative distribution function for [epsilon].

   The generators sell electricity in a wholesale market. They also can sign forward contracts before the wholesale market operates. A swap forward contract (SFC) imposes a financial obligation on a generator to deliver one unit of electricity at fixed price [p.sup.s] > 0 immediately after the wholesale price of electricity is determined. A load-following forward contract (LFFC) imposes a financial obligation on a generator to deliver a load strip at a fixed unit price for electricity, [p.sup.L], immediately after the wholesale price of electricity is determined. A load strip is the fraction [alpha] [member of] (0,1) of the realized consumption of electricity. (12)

   [q*.sub.i]([epsilon]) is Gi's equilibrium output when demand parameter [epsilon] is realized. (13) Q*([epsilon]) = [q*.sub.1]([epsilon]) + [q*.sub.2],([epsilon]) and P*([epsilon]) = P(Q*([epsilon]),[epsilon]) are the corresponding total output and wholesale price of electricity, respectively. When Gi signs [S.sub.i] SFCs and [L.sub.i] LFFCs, its equilibrium profit when [epsilon] is realized is:

   [Please download the PDF to view the mathematical expression] (2)

   [q.sub.i] - [L.sub.i][alpha]Q - [S.sub.i] is the amount of Gi's output that is exposed to (i.e., ultimately sold at) the wholesale price. [p.sup.s] [S.sub.i] + [p.sup.L] [L.sub.i] [alpha]Q is Gi's revenue from forward sales of electricity.

   The forward positions of generators are observed publicly. Furthermore, forward...