Options and insurance each has a niche, but price collars are cheaper and more adaptable to market risk and customer behavior.
During the summers of 1998 and 1999, wholesale prices in the Midwest soared to $7,000 or more per megawatt, in comparison to a more typical summer price of $30 to $50 per megawatt. In a competitive environment, electricity suppliers - that is generators, utilities, marketers, etc. - will offer a variety of pricing products ranging from flat rates to real-time pricing (RTP). By varying degrees, price risk will be passed to the end-user. Consequently, consumers will demand risk management alternatives.
A price collar is a way for the electricity merchant and customer to agree on how to share price risk.[fn.1] With a collar, there is a ceiling on the maximum hourly price. In return, the customer accepts a floor on the minimum hourly price. The collar offers an alternative to the extremes of flat rates and RTP.
While customers can use other risk management tools, such as options, to effectively smooth rates, price collars permit the customer to use unlimited quantities at all prices. Options, by contrast, are for fixed quantities. Most customers desire unlimited quantities.
The focus here is on how to establish the floor of a price collar, with particular attention given to price elasticity and the effects of customer response as predicted by economic principles. Accounting for such effects leads to upward adjustments in the floor price needed by the merchant to break even. The key issue is that the merchant who ignores price elasticity will lose money.
Adverse selection is another factor that, if ignored, could result in losses to the merchant. If the floor of a price collar is based on the price responsiveness of the average customer and then is offered to all takers, those who have above-average elasticities will opt for the collar and those with below-average elasticities will decline the collar. The result is that the merchant will suffer a loss. In order to break even, the merchant will need to distinguish among customers based on price-response capability and charge a higher floor to customers with above-average price elasticities.
Already, consumers have a number of choices for managing risk. In 1996, trading of electricity options began on the West Coast. It since has been introduced on the East Coast, as well. Puts and calls allow the purchaser to hedge against low and high prices respectively. Electricity insurance recently was introduced. Enron offers derivatives that provide coverage against high electric prices associated with extreme temperatures. CIGNA Property & Casualty, just purchased by ACE Limited, offers insurance against high prices due to generation outages.
Price collars offer a simple alternative, especially for the retail customer. Risk management is accomplished through pricing, rather than turning to a derivative market. Here we compare collars, options and insurance as risk management tools. The remainder of the paper addresses the pricing of collars.[fn.2]
Risk Management Tools: Not Created Equal
Each of the three approaches - options, insurance and price collars - has a niche in the market. No one approach is likely to be superior in all situations. Some investigators claim that options alone will be sufficient and that there is no need for separate examination of insurance or price collars because they are equivalent to options. Were these claims correct, then any price collar or insurance policy could be priced using the Black-Scholes model applied to an equivalent option.[fn.3]
There are, however, at least two fundamental differences between collars and options. As mentioned, options are for fixed contractual quantities while price collars allow unlimited consumption at the ceiling price. The price of a contract that allows unlimited consumption is not the price that would be given by an option pricing formula.[fn.4] In this respect, a price collar would entail more risk for the merchant and consequently cost more than an option.
Second, options have upside potential. Mike O'Sheasy demonstrated that as spot prices exceed the option strike price, holders could decide to exercise the option prior to expiration. ("Real-Time Pricing - Supplanted by Price-Risk Derivatives?" Public Utilities Fortnightly, March 1, 1997, pp. 31-35.) In this respect, because options entail more risk for the merchant, price collars should be priced lower than options. Naturally, there are other differences. Options require greater customer knowledge and a willingness to trade financial derivatives. Price collars have no explicit premium costs, they do not require knowledge of financial derivative markets and they are simpler.
Insurance also has its place in the market. Insurance protects against downside risk by indemnifying against unfavorable states of nature. Enron offers temperature derivatives, should prices rise with extreme temperatures. The customer negotiates a "strike" temperature and corresponding price. At temperatures above the "strike," Enron pays the difference, if any, between the market price and the "strike" price. CIGNA Property & Casualty offers PowerBackersm, a product that insures against generation outages. If a generator goes offline and the generating company buys replacement generation in the market, the insurer will indemnify the customer, provided the market price exceeds a level agreed to by the customer and insurer.
While insurance protects against downside risk, it does not offer upside potential. The risk to the merchant is lower and, therefore, the cost of insurance is lower than a corresponding call option. [fn.5]
There is an important concern about the economic efficiency of price collars. Because ceiling and floor prices are not necessarily equal to marginal cost, the cap would appear to cause too much electric use at high-priced times, and the floor would cause too little consumption at low-priced hours. The usual criticism is in the context of a risk-less world. Just as farmers sell in a forward market to avoid risk, customers choose a price cap to limit upside risk. Efficiency depends upon the consumer's tolerance of risk. Even flat rates may be efficient if a customer is willing to pay to avoid all risk.
Table 1 summarizes the key characteristics of the three risk management alternatives.
There is a role for price collars to reduce risk. In addition to offering simplicity and protection with unlimited consumption, they are an extension of a familiar product. Utilities offer flat rates through equal pay plans to avoid summer and winter monthly spikes. Future electricity markets will see third parties with long histories in risk management offer these new pricing products at competitive rates.
How to Allow for Demand Response
In the following examples, demand and cost conditions are simplified for presentation purposes; however, the concepts should provide direction for pricing collars in a competitive market.
Inelastic Demand. Figure 1 presents a price collar contract with the assumption that demand is not price-responsive. The price ceiling is Pc and the floor is Pf. For simplicity, it is assumed that the collar is for a summer day with only one hour during the high-priced peak period and one hour during the low-priced off-peak period. Notice that demand shifts with temperature, so that consumption (Q) is higher during the peak period when prices are high due to hot temperatures. In this initial case, quantity demanded is perfectly inelastic with respect to price.
In figure 1, Pl s and Phs are the probabilistic low and high spot prices, Ql and Qh are corresponding quantities consumed, and A and B are the supplier's probabilistic loss and gain depending on the actual price.
If it is assumed that the entire contract is represented by figure 1, where the customer selects a price ceiling of Pc , then the merchant would set the price floor, Pf, by equating the area represented by loss A to the area represented by the desired gain, B. Using this equality, the price floor that allows the supplier to break even is[fn.6]
Pf = Pl S +(Ph S - PC)(Qh __Ql ).
With inelastic demand, the only unknown in this equation is Pf. Off-peak quantity does not change even though Pf exceeds Pls.
Elastic Demand. Figure 2 depicts downward-sloping demands. For a given price ceiling, the merchant's loss (A) is larger than for the inelastic case. The per-unit loss is unchanged, but the merchant now loses on a larger number of units. For a given price floor, the merchant now gains less (B'). Per-unit gain would be the same as before, but the gain is now for a smaller number of units. So in order to break even, the merchant must increase floor price to increase per-unit gain. But the increase in per-unit gain will have to more than offset the decrease in quantity that accompanies the higher price.
In figure 2, the merchant's loss increases for a given price ceiling. Total loss A' is the sum of the original loss A and the additional loss of rectangle C. The additional loss is due to an increase in quantity demanded when the customer purchases at price ceiling Pc instead of the higher spot price Phs. Similarly, total gain is now B'. To make up for the larger loss, the merchant must increase price floor Pf. But because demand Df is downward-sloping, the increase in floor price causes a decrease in quantity sold at the floor price. Rectangle D represents revenues that were earned when demand was inelastic, but no longer are earned by the merchant when demand slopes down.
Merchants need to be aware of price elasticity during peak high-demand hours and off-peak low-demand hours. If those elasticities differ from zero, the floor price for a given ceiling will have to increase as compared to the inelastic case. Merchants who face downward-sloping demands but ignore demand elasticity will lose money.
Because consumption varies with price, determination of the floor price is more complicated than in the fixed-quantity case. The approach is to compute earnings lost due to the price ceiling, then find the floor price that recovers the loss. From figure 2, earnings lost (EL) is derived by
EL = (Phs - Pc) *Qc.
Qc is derived from the peak arc elasticity condition:
(Pc - Phs)
(1 + ________ hc)
(Pc + Phs)
Qc = Qhs ____________ .
(Pc - Phs)
(1 - ________ hc)
(Pc + Phs)
In a similar manner, earnings desired (ED) to make up this loss is derived by
ED = (Pls - Pf) *Qf.
Qf is derived from the off-peak arc elasticity condition:
(Pls - Pf)
(1 - ________ hf)
(Pf + Pls)
Qf = Qls ____________ .
(Pls - Pf)
(1 + ________ hf)
(Pf + Pls)
Now Pf may be found by trial and error to achieve the equality of EL and ED. Table 2 displays Pf for several examples, as well as the earlier case of perfectly inelastic demands.[fn.7]
Note in example 2 that the merchant would lose $72 by continuing to set the floor at $0.04 per kilowatt-hour.[fn.8] For a large industrial customer with much greater consumption than in the example, losses could be substantial. It is important, therefore, that the merchant consider price-responsiveness during high- and low-temperature hours. In all cases where consumers respond to price, table 2 shows that the price ceiling must be higher than for the fixed-quantity case. An increase in (the absolute value of) elasticity in either period increases the floor price.
Change in Price Ceiling. Suppose the customer decided that these floor prices were too high and so decided to choose a higher price ceiling. Table 3 shows the price floors that correspond to a price ceiling of $0.25 instead of $0.20 per kilowatt-hour.
The price floor is now lower than in table 2 in all cases. Again, the price floor increases when demand is price-sensitive, but by a smaller amount than in the previous case.
The Free-Rider Problem: How to Keep
the Attractive Customers
A price collar effectively ensures the customer against high prices. As with insurance, however, the merchant must be aware of the potential problem of adverse selection. This problem occurs if the insurance policy attracts high-payout customers while discouraging low-payout customers.
The merchant offering a price collar also could lose money due to adverse selection, as mentioned. Customers with above-average demand elasticities would find a price collar developed with the assumption of an average elasticity more attractive than customers with below-average elasticities. For example, if hc=-1 (Qc=3,000) and hf=-0.45 (Qf=6,000), then the break-even price floor for a ceiling price Pc=$0.20 would be Pf=$0.07 per kilowatt-hour. (This example is not shown in table 2.) Consequently, a merchant that offers a price floor of $0.05 per kilowatt-hour would attract above-average elasticity customers who would increase hot-hour usage and decrease low-temperature usage more than the average elasticity customer, resulting in losses for the merchant. Furthermore, customers with below-average elasticities would not choose the rate; hence there is no earnings offset to the losses from the high elasticity customers. If the merchant can distinguish these two groups of customers, it may be able to charge each group a different price floor.
Peter Schwarz, Ph.D., is professor and chair of the Department of Economics at the University of North Carolina-Charlotte, and senior economist, energy resource planning, Research Triangle Institute. He specializes in real-time pricing.
Tom Taylor, Ph.D., is a senior economist in the Rates and Regulatory Affairs Department at Duke Energy Corp. He led the development of Duke's hourly pricing program and has focused on pricing for industrial customers.
1 The term "merchant" is used throughout this paper to represent any party who purchases electricity on the spot market and offers, for a fee, to sell that electricity at a rate that reduces or eliminates price risk. Consequently, the cost of electricity to the merchant is equal to the spot price.
2 In Britain, generating companies purchase contracts for differences (CfDs) to manage the risk of buying in the real-time wholesale market and selling at flat rates to customers. See Green and Newbery, "Competition in the British Electricity Spot Market," Journal of Political Economy, Vol. 100, No. 5, pp. 929-953, 1992.
3 Oren, Gupta and Tiesberg and Tiesberg argue that price collars are equivalent to options. See Proceedings: EPRI Conference on "Innovative Approaches to Electric Pricing: Managing the Transition to Market-Based Prices," TR-106232, Research Project 2343, March 1996, for the Oren and Gupta papers. See Tiesberg and Tiesberg, "The Value of Commodity Purchase Contracts with Limited Price Risk," Energy Journal, Vol. 12, pp. 109-135, 1991. The equivalence of insurance and options is in Merton, Robert, "An Analytic Derivation of the Cost of Deposit Insurance and Loan Guarantees: An Application of Modern Option Pricing Theory," Journal of Banking and Finance, Vol. 1, pp. 3-11, 1977.
4 EPRI, "Pricing the Riskiest Retail Electricity Product - Flip-the-Switch," Technical Brief, September 1996.
5 This information is from Restructuring Today, July 15, 1999, and a conversation with Kurt Husar of CIGNA Property & Casualty. Husar also noted that in actuality, the delivery of electricity from an option may take up to two days.
6 Under more realistic assumptions than those of figure 1, contracts are likely to be developed under conditions where there is variability in the number of peak and off-peak hours, spot prices and levels of consumption. The general form of the equation of figure 1 to calculate the floor price under such conditions is
Sh PhsQh - Pc Sl Qh
Pf = S PlsQl + ______________ .
Note that other aspects of the development of floor prices typically considered in the finance literature may be incorporated, such as forming expectations for spot prices, present values of appropriate quantities, etc. Our purpose here is to illustrate the effects of price elasticity, a concept that generally is not incorporated in other approaches.
7 As discussed in endnote 6, contracts are likely to be developed under conditions where there is variability in the number of peak and off-peak hours, spot prices and levels of consumption. The general form of the equation of figure 2 to calculate the floor price under such conditions isS (Phs -Pc ) * Qc =S(Pf - Pls ) * Qf ,
where Qc and Qf are defined in the text. Trial and error may be used to find a value of Pf that solves the equation. The solutions of the examples use Microsoft Excel's Solver tool.
8 At $0.05 per kilowatt-hour, off-peak sales were 8,000 kilowatt-hours, profit per unit was $0.03, and off-peak profit was $240. At $0.04, off-peak sales increase to 8,400, but per unit profit drops to $0.02, and off-peak profit to $168, a decrease of $72.
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