How are Electricity Futures Contracts Priced? A Preliminary Investigation

Transcription

1 Title: How are Electricity Futures Contracts Priced? A Preliminary Investigation Author: Russell Poskitt and Stephen Tomlinson Department of Accountancy, Finance and Information Systems University of Canterbury Private Bag 4800 Christchurch New Zealand Phone: Fax: R.Poskitt@afis.canterbury.ac.nz 1

2 How are Electricity Futures Contracts Priced? A Preliminary Investigation ABSTRACT: This paper examines the relevance of the cost of carry model to the pricing of the electricity futures contract in New Zealand. Analysis of the data indicates that the spot price is substantially more volatile than the futures price. OLS regression analysis provides little evidence in support of the cost of carry model, using either levels data or first difference data. The evidence strongly suggests the futures price moves independently of the theoretical futures price derived from the cost of carry model. There is some evidence that the futures prices is driven by past levels of the spot price. 1. INTRODUCTION During 1995 the New Zealand Government embarked on a programme to reform the New Zealand electricity market. The objective of the reform package was to change the nature of the electricity market from a fixed price, engineering-driven market to a trading environment with a competitive market structure. The New Zealand Government believed that a competitive market structure was the best way of ensuring that energy services would continue to be available at the least cost to the economy as a whole. The new wholesale electricity market commenced operation on 1 October 1996 under the aegis of the Electricity Market Company Limited (EMCO). Under EMCO rules spot market participants have until 12 p.m. to submit the price and quantity of bids/offers for all of the 48 half-hour trading period in the forthcoming trading day. The clearing prices and volumes for 2

3 each half-hour period are determined by the intersection of the supply and demand curves for that period. In response to the creation of a new market for buying and selling wholesale electricity, an electricity futures contract was listed on the New Zealand Futures and Options Exchange (NZFOE) on 18 November 1996, although the first contract was not traded until 17 January The unit size for the electricity futures contract is 250 Megawatt hours (Mwh) of electrical energy, with prices quoted in dollars per Mwh. The underlying asset is 250 Mwh of electricity at the North Island reference point (Haywards 220 kv bus). Table 1 summarises the number of trades in electricity futures contracts since its inception to 30 September There were only 517 trades in the 9 month period, illustrating a lack of depth in the market. Of these trades, 98 (19%) were in the current month contract, more than any other settlement period. Table 1 Summary Statistics: Number of Trades Contract Jan Feb Mar Apr May Jun Jul Aug Sep Total Current Current Current Current Current Current Current Current Current Current Current Current TOTAL Table 2 summarises the number of electricity futures contracts traded to 30 September Note that only 3387 contracts were traded in the 9 month period. The noticeable decline in 3

4 trading from July 1997 through to September 1997 may indicate that the contract is not gaining acceptance as a risk management tool. Table 2 Summary Statistics: Volume of Contracts Traded Contract Jan Feb Mar Apr May Jun Jul Aug Sep Total Current Current Current Current Current Current Current Current Current Current Current Current TOTAL The advent of electricity futures has generated considerable debate amongst energy consultants and academics (Amundsen and Singh, 1992; Powell, 1993; Tussing and Hatcher, 1994; Banks, 1997). Much of the controversy concerns the imperfect nature of the spot market. Critics doubt whether futures trading will succeed when the generation and transmission of electricity is concentrated in the hands of several suppliers. Brianza et al. (1987) observe that in the 1930s the futures markets for fertiliser were closed as soon as national cartels of fertiliser producers were formed in Europe. Each year the cartels announced price schedules for the coming agricultural season, suppressing the need for a futures market. Prior to the electricity market reforms in 1995, the Electricity Corporation of New Zealand (ECNZ) held 96% of the electricity generating capacity available for public supply in New Zealand. This prompted the Wholesale Electricity Market Development Group (WEMDG) to note that ECNZ is, to all intents and purposes, the only generator with which wholesale buyers can contract to purchase electricity (WEMDG, 1994). However, following a forced sell down 4

5 of ECNZ's assets, ECNZ now holds approximately 60% of the electricity generating capacity in New Zealand. The other major generator is Contact Energy Ltd, a state owned enterprise set up in 1995 to promote competition in electricity generation, which holds 27% of the generating capacity in New Zealand. Other generators account for the remaining 13% capacity. In addition to the progressive sell down of ECNZ's generating capacity, certain constraints have been placed on ECNZ's operations. These include constraints in constructing new generating capacity and a requirement for ECNZ to offer much of its generating capacity to customers in the form of long-term supply contracts. The purpose of these constraints is to reduce ECNZ's ability to influence the spot market. These constraints will remain in effect until ECNZ's market share of generation falls below 45%. The New Zealand Government's attempts to promote competition in the electricity market should reduce imperfections in the spot market caused by a lack of competition. A second issue concerns the ability of the New Zealand Government to intervene in the electricity market should a severe shortage emerge. Given the long history of state ownership of electricity generation in New Zealand, it is unlikely that regulating electricity supply by price in the event of crisis would be politically acceptable. Currently, the New Zealand Government has not publicly stated what would happen if a severe shortage of electricity was to occur. A third issue concerns the ability of futures trading to thrive in the face of stiff competition from forward contracts and contracts-for-differences. Banks (1997) notes that the key derivatives product to emerge in the UK is the contract-for-differences, or electricity swap, and predicts that this product will eventually replace the electricity futures contract traded on the New York Mercantile Exchange (NYMEX). 5

6 A fourth issue, which is the subject of this paper, is the pricing of electricity futures contracts. The cost of carry model (Working, 1949) is the dominant explanation for the pricing of futures contracts. However, it is argued that the unique characteristics of electricity, in particular the inability of traders to store the commodity or sell it short, mean that the traditional arbitrage-free spot/futures pricing relationship cannot hold. In this paper we conduct several tests of the cost of carry model to determine the relevance of this model to the pricing of the electricity futures contract. This paper is organised as follows. In Section 2 we outline the cost of carry model of futures pricing and the limitations of this model. We describe the tests we propose to use in Section 3, and summarise the spot and futures market data in Section 4. In Section 5 we report the results of the empirical tests of the cost of carry model, and in Section 6 we make a number of observations and conclusions. 2. THEORETICAL DEVELOPMENT The dominant explanation of the spot/futures pricing relationship is the cost of carry model. According to Working (1949), the time t price of a futures contract for settlement at time T, F t, must equal the time t price of the commodity, S t, plus the costs of carry, C, over the period T-t. This relationship can be expressed as follows: F = S + C t t (1) When the holder of the commodity enjoys the convenience yield, y, or the ability to profit from short-run price variations, the cost of carry model is specified as follows: 6

7 F = S + C y (2) t t Unfortunately, it is not possible to estimate the convenience yield and for this reason, the convenience yield has been excluded from the analysis in the paper. The relevance of the cost of carry model to the pricing of electricity futures contracts is a contentious issue (Banks, 1997; Godlewska et al., 1997). Godlewska et al. (1997) claim that the cost of carry reflects the cost of shifting capacity from today to tomorrow but fail to explain how this is determined. They acknowledge that the cost of carry relationship is more complicated to specify in the electricity industry but claim that it is more valuable to those who get it right. Banks (1997) is generally dismissive of the cost of carry model but acknowledges that it may be relevant in markets where hydro accounts for the majority of electricity generation on the grounds that storage can occur in hydro systems. This suggests that the cost of carry model is a valid model for pricing electricity futures in New Zealand since hydro accounts for approximately 72% of electricity generation capacity in New Zealand. However, it is electricity not water that is being traded and there is a significant difference between storing water and storing electricity. The cost of carry relationship for a storable commodity in equation (1) is derived from conventional arbitrage-free arguments. When F t exceeds S t +C arbitrageurs can earn riskless profits by executing cash and carry arbitrage. That is, arbitrageurs borrow and buy the underlying commodity in the spot market, simultaneously selling futures contract on the commodity in the futures market. On settlement date the respective spot and futures market positions are unwound, the loan is repaid and the arbitrageur profits from the arrangement. The selling pressure in the futures market and the buying pressure in the spot market should lead to the 7

8 restoration of the spot/futures relationship in equation (1) with the result that the arbitrage opportunity disappears. Similarly, when F t is less than S t +C arbitrageurs can earn riskless profits by executing reverse cash and carry arbitrage. Arbitrageurs sell the underlying commodity short in the spot market, simultaneously lending the proceeds and buying futures contracts on the commodity in the futures market. The spot and futures market positions are unwound on settlement date, the loan is repaid and the arbitrageur profits from the transaction. Again, buying pressure in the futures market and the selling pressure in the spot market should lead to the restoration of the spot/futures relationship in equation (1) and the elimination of the arbitrage opportunity. One crucial problem with applying the cost of carry model to the pricing of electricity futures is that electricity is not storable. It is difficult to envisage how arbitrageurs could execute the sequence of spot market transactions required in cash and carry arbitrage with electricity since electricity cannot be stored. Thus, it would be possible for the futures price, F t, to exceed the theoretical level defined by the sum of the spot price plus the costs of carry, S t +C. Furthermore, reverse cash and carry arbitrage would be difficult to implement since it is not possible for arbitrageurs to short electricity, although it is plausible for a monopoly supplier to sell more electricity in the spot market and simultaneously buy futures contracts. Even then, however, the capacity of end users to absorb additional electricity is limited. Thus, it would be possible for the futures price, F t to trade below S t +C. The above arguments suggest that the cost of carry model is a weak representation of how electricity futures are priced. The debate over the relevance of the cost of carry model to the pricing of electricity futures can only be resolved by empirical evidence. 8

9 3. METHODOLOGY We use equation (1) is conjunction with actual spot prices and estimates of the cost of carry model to estimate theoretical futures prices, denoted by F *. Contract mispricing is measured by the difference between the actual and theoretical futures prices or the differential, F - F *. One simple test of the cost of carry model is a test of the null hypothesis that the mean differential is not significantly different from zero. The relevance of the cost of carry model can also be assessed by estimating a model of the form: * F = α + α F + u t 0 1 t t (3) where u t is the random error term. The absence of arbitrage opportunities requires that α 0 = 0 and α 1 = 1. The applicability of the cost of carry model is assessed by testing the statistical acceptability of this joint restriction on the coefficients of equation (3). Equation (3) must be estimated using data in first difference form rather than in levels form if the levels data are I(1) and not cointegrated. The use of non-stationary levels data would make conventional estimation techniques such OLS and hypothesis tests unreliable (Granger and Newbold, 1974; Phillips, 1986). The first difference form of the cost of carry model is as follows: * F = α + α F + u t 0 1 t t (4) Again, the applicability of the cost of carry model is assessed by testing the statistical acceptability of the joint restriction α 0 = 0 and α 1 = 1. The absence of arbitrage opportunities 9

10 requires that the futures price change in step with the theoretical futures price derived from the spot price and the cost of carry. 10

11 4. DATA We used spot market data provided by EMCO and futures contract data provided by the NZFOE. EMCO provided Haywards price and volume data for each half-hour period since 1 October The NZFOE provided transaction price and volume data for each electricity futures contract traded since the contract's inception. A time series was created for the current futures contract by splicing together the closing prices for successive futures contracts. Unfortunately, many data points are missing due to the intermittent nature of trading. Carrying costs were estimated from overnight cash rate data supplied by Dow Jones Telerate. Table 3 reports summary statistics for the spot and futures prices. Over the sample period the average daily spot price ranged from a low of $10.72 to a high of $ It is clear from the data that the daily average spot price is relatively volatile with a mean absolute daily change of 8.9%. The daily price change exceeded plus or minus 10% on 102 or 28% of trading days. Table 3 Summary Statistics: Spot and Futures Prices Standard Mean Price Deviation ($) ($) (%) Mean Daily Change Mean Absolute Daily Change (%) Contract Sample Size Spot Futures n.a. n.a. Unfortunately the relatively thin trading in the futures contract made it difficult to compute a full set of comparative statistics from the futures data. However the data available suggests that the futures price is substantially less volatile than the spot price. The standard deviation of the futures price is approximately 45% of the standard deviation of the spot price. Summary statistics on the basis are reported in Table 4. The mean level of the basis across daily closing prices in all futures contracts is $6.14, with a standard deviation of $ When the 11

12 sample is restricted to the current futures contract the mean level of the basis drops to $0.46 with a standard deviation of $6.49. Table 4 Summary Statistics: Spot/Futures Basis Near contract All contracts Sample size Mean $0.46 $6.14 Standard deviation $6.49 $11.76 Mean absolute basis $4.33 $9.22 Mean absolute % basis * 8.8% 20.0% Maximum basis $27.79 $42.69 Minimum basis -$ $38.09 Range $43.28 $80.78 * As a percent of the futures price The t test is employed to test the null hypothesis that the basis is not significantly different from zero. The t statistics of 0.49 for the near futures sample and 9.13 for the full sample indicate that the zero basis null hypothesis can only be rejected for the full sample. These results also suggest that the basis in the more distant maturities is significantly positive. Table 5 Frequency Distribution of Spot/Futures Basis Current contract All contracts Number % Number % Size of basis > $ $25 to $ $20 to $ $15 to $ $10 to $ $5 to $ $0 to $ $0 to -$ $5 to -$ $10 to -$ $15 to -$ $20 to -$ $25 to -$29.99 < -$

13 The frequency distribution of the spot/futures basis is reported in Table 5. This data shows that there is a positive bias in the basis, with instances of a positive basis outnumbering instances of a negative basis by two-to-one in both the current futures contract sample and the full sample. This suggests there is a pronounced tendency for the spot price to exceed the futures price. To determine the sign and significance of the relationship between the basis and the term to maturity we estimate an OLS regression model of the form Bt = β0 + β1 TTMt + ut (5) where B t is the basis at time t and TTM t is the term to maturity at time t. The OLS estimate of β 1 is and the standard error of the estimate is The t statistic for the null hypothesis β 1 = 0 is 6.97 which is significantly different from zero at the 0.01 significance level. The estimation results suggest that the basis declines as the term to maturity approaches. We test for non-stationarity of spot prices using the Dickey Fuller (DF) and Augmented Dickey Fuller (ADF) unit root tests. Intermittent trading in futures prevents us from carrying out unit root tests on the futures price. Table 6 reports the t statistic for the coefficient of the lagged dependent variable for levels and first differences of the spot price series. Table 6 Unit Root Tests for Stationarity of Spot Price DF and ADF Statistics Data Test 1 Test 2 Test 3 Test 4 + Levels ** ** First differences ** ** ** ** * ** The DF and ADF tests for a unit root in a variable y t involve regressing the first difference of the variable, y t on: y t-1 (Test 1); a constant term and y t-1 (Test 2); a constant term, a time trend and y t-1 (Test 3); and a constant term, a time trend, y t-1 and lagged terms in y t (Test 4). Additional lagged terms are added until their contribution is insignificantly different from zero. The null hypothesis of a unit root is rejected if the coefficient of y t-1 is significantly different from zero. The MacKinnon critical values for rejection of the null hypothesis at the 0.05 and 0.01 significance levels are and for Test 1, and for Test 2 and and for Tests 3 and 4. Significant at the 0.05 level. Significant at the 0.01 level 13

14 + Optimal lags lengths are 5 for levels data and 4 for first-difference data. 14

15 The null hypothesis of a unit root in the levels data cannot be rejected in either test 1 or test 4 at the 0.05 significance level. These results provide some evidence that spot prices in levels form are stationary. Additional tests are performed to determine whether the first differences are stationary. The test statistics strongly reject the null hypothesis of a unit root in the first differences of the spot price. That is, the first difference of the spot price is stationary. 5. RESULTS Tables 7 and 8 report the regression results for the cost of carry model in levels and firstdifference form respectively. The t statistics reported beneath the coefficient estimates test the individual null hypotheses α 0 = 0 and α 1 = 0. The last two columns report the test statistics for the tests of the null hypothesis α 1 = 1 and the joint null hypothesis α 0 =0 and α 1 = 1. Table 7 OLS Regression Results Cost of Carry Model - Levels Data (Equation (3)) α 0 α 1 α 2 R 2 Adj. DW statistic t statistic H0: α 1 = 1 Model A (13.78) ** (10.37) ** ** F statistic H0: α 0 = 0 & α 1 = ** Model B (0.48) ** (4.92) ** (8.90) ** ** Model C (53.90) ** n.a n.a. ** Significant at the 0.01 level. Equation (3) is separately estimated with and without a constant term. When the constant term is included (Model A), the low Durbin Watson statistic suggests the presence of positive serial correlation. The model is re-estimated (Model B) with a correction for first-order serial correlation but the OLS estimates of α 0 and α 1 are individually significantly different from 0 and 1 respectively and the joint null hypothesis is strongly rejected. When the constant term is 15

16 suppressed (Model C) the OLS estimate of α 1 is much closer to 1 and the null hypothesis that α 1 = 1 cannot be rejected at the 0.05 significance level. When the cost of carry model is estimated using first differences data the results are equally unsupportive. In Model D the OLS estimates of α 0 and α 1 are again significantly different from 0 and 1 respectively and joint null hypothesis is strongly rejected. Moreover the OLS estimate of α 1 is not significantly different from 0 in either Model D or Model E. These results suggest that the futures prices moves largely independently of changes in the theoretical futures price. Table 8 OLS Regression Results Cost of Carry Model - First Differenced Data (Equation (4)) α 0 α 1 R 2 Adj. DW statistic t statistic H0: α 1 = 1 F statistic H0: α 0 = 0 & α 1 = 1 Model D (1.00) (0.96) ** 80.7 ** Model E (0.71) n.a. n.a ** n.a. ** Significant at the 0.01 level. The results obtained to date do not support the traditional cost of carry explanation of futures pricing for electricity futures contracts. We are unsure what is driving the futures price but offer several suggestions. One explanation is that the futures price is being driven by the prices of electricity forward or hedge contracts. As yet we have not been able to obtain any forward hedge price data from ECNZ to determine whether or not this is the case. Nevertheless, this would seem unlikely since the forward price is set at a fixed premium to the spot price. A second and possibly more useful explanation is that the current futures price represents the market's consensus opinion of the expected spot price on the futures maturity date. This is the famous expectations hypothesis of futures pricing. 16

17 Of particular interest is the expectations formation process i.e. how do market participants form their expectation of the spot price on the futures maturity date? One possibility is that market participants are basing their expectations of the future spot price on the current spot price. This seems unlikely given the volatility of the spot/futures basis. Another possibility is that expectations of the future spot price are based on past levels of the spot price. Such a model of expectations formation would explain the remarkable stability of the futures price in the face of rather sharp fluctuations in the spot price. Table 9 reports summary statistics on the difference between (i) the near futures price and the current spot price, and (ii) the near futures price and the 30-day moving average of the spot price. Table 9 Summary Statistics Futures - Spot Futures - 30DMA Spot Sample size Mean -$0.46 $0.86 Standard deviation $6.49 $1.30 Mean absolute difference $4.33 $1.23 Mean absolute % difference * 8.8% 2.5% Maximum positive difference $15.49 $3.29 Maximum negative difference -$ $1.84 Range $43.28 $5.13 * As a percent of the futures price The traditional test of the expectations hypothesis would involve testing for a statistically significant difference between the futures price one month from maturity and the spot price on maturity date. However, lack of data prevents us from testing whether the spot price is an accurate predictor of the futures price. The data suggest that the futures price is a more accurate predictor of the 30-day moving average spot price than the current spot price. For example, the mean absolute difference of $1.23 (or 2.5%) compares more than favourably with the mean 17

18 absolute basis of $4.33 (or 8.8%) and the range of the differentials is much lower: $5.13 versus $ This is confirmed by Figure 1 below. We test the null hypothesis that the mean difference is insignificantly different from 0. The t statistics of 0.28 and indicate that the null hypotheses cannot be rejected at conventional significance levels. This suggests that the current futures price is an unbiased estimate of both the 30-day moving average spot price and the current spot price. We believe the t test result for the current spot price reflects the low power of the t test and is of doubtful significance given the variability of the spot/futures basis. The relationship between the futures price and the 30-day moving average spot price appears promising. Why should the futures price have such a long memory? We suggest the reason lies in the nature of electricity. Electricity is a product that is purchased continuously, unlike other commodities such as wool which are purchased at discrete intervals in time. This means that market participants may be more concerned with the average 18

19 price of electricity over a period of time than with the price of electricity at a particular point in time, such as the futures maturity date. 6. OBSERVATIONS AND CONCLUSIONS This paper examines the relevance of the cost of carry model to the pricing of the electricity futures contract. Preliminary data analysis revealed that the spot price was substantially more volatile than the futures price. Unit roots tests provide some evidence that the spot price is stationary. Not surprisingly, the spot/futures basis is found to be quite volatile, ranging between -$15.49 and $27.79 for the near contract. OLS regression analysis finds little evidence in support of the cost of carry model, using either levels data or first difference data. In fact, the slope coefficient is found to be insignificantly different from zero in the first differences model, which suggests that the futures price moves largely independently of the theoretical futures price derived from the cost of carry model. We suggest that the futures price may be driven by the price of forward hedge contracts offered by ECNZ, or alternatively, that the futures price may represent the market's consensus forecast of the futures spot price. We further speculate that market participants base their expectations of the future spot price on past levels of the spot price. We find evidence that the current futures price is an unbiased estimate of the 30-day moving average of the spot price and attribute this to the fact that electricity is purchased continuously. As a result, we surmise that it is the average price of electricity over a specified period that is important to market participants, not the price of electricity at a single point in time. 19

20 References Amundsen, E.S. and Singh, B. (1992), Developing futures markets for electricity in Europe, Energy Journal, vol. 13, pp Banks, F.E. (1997), Economic Theory and Electricity Futures Markets, Department of Economics, University of Uppsala. Brianza, T. Phlips, L. and Richard, J.-F. (1987), Futures markets, inventories and monopoly, Core Discussion Paper No. 8725, Centre for Operations Research and Econometrics, Catholic University of Louvain. Godlewska, A., Mello, A.S., and Parsons, J.E. (1997) Price behavior in electricity futures: the story so far, Public Utilities Fortnightly, 1 January 1997, pp Granger, C.W.J. and Newbold, P. (1974), Spurious regression in econometrics, Journal of Econometrics, vol. 2, pp Gujarati, D.N. (1995), Basic Econometrics, McGraw-Hill, New York. Phillips, P.C.B. (1986), Understanding spurious regressions in econometrics, Journal of Econometrics, vol. 33, pp Powell, A. (1993), Trading forward in an imperfect market: the case of electricity in Britain, The Economic Journal, vol. 103, pp Tussing, A.R. and Hatcher, D.B. (1994), Prospects for an electricity futures market, Resources Policy, vol. 20, pp

21 Wholesale Electricity Market Development Group (1994), Final Report of New Zealand Wholesale Electricity Market Development Group, August Working, H. (1949), The theory of price of storage, American Economic Review, vol. 39, pp