The Natural Number of Forward Markets for Electricity
9th Annual POWER Conference on Electricity Industry Restructuring
March 19, 2004
Hiroaki Suenaga and Jeffrey WilliamsDepartment of Agricultural and Resource Economics
University of California, Davis
2
Common observations about electricity:
(1) Extremely volatile prices in spot wholesale markets• short-run capacity constraints
• retail prices inflexible
• pronounced seasonality in demand
• short-run weather shocks
• electricity not storable
(2) Underdeveloped forward wholesale markets• most efforts by exchanges have failed
• California PX restrained to one-day-ahead
• generally, private bilateral trades
3
Our propositions:
• Because of electricity’s very properties, long-dated forward markets for electricity are essentially redundant.
• The NYMEX natural gas futures market duplicates an electricity futures market.
4
How to demonstrate that some price is redundantif it cannot be observed?
• An idealized world for trading electricity• full profile of forward prices
• forward prices are best possible forecasts by construction
• companion forward prices for a fuel
• An analogy with corn• considerable price variation recently
• well developed futures market
5
Progressions of Prices of Corn Futures Contracts
9.88 cents
7.63
3.60
150
200
250
300
350
400
450
5001 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Business days (5/15 - 6/13)
Cents per
bushel
July '96 Dec '96 Dec '97Correlation
of price changes
.45
.81
.40
Std. Dev.of pricechanges
5
Progressions of Prices of Corn Futures Contracts
9.88 cents
7.63
3.60
2.59
2.67
2.34
150
200
250
300
350
400
450
5001 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Business days (5/15 - 6/13)
Cents per
bushel
July '96 Dec '96 Dec '97 July '01 Dec '01 Dec '02Correlation
of price changes
.45
.81
.40
.996
.95.93
Std. Dev.of pricechanges
6
Profiles of Corn Futures Prices in Mid June
150
200
250
300
350
400
450
500
0 3 6 9 12 15 18
Months ahead from mid June
Cents per
bushel
1996
6
Profiles of Corn Futures Prices in Mid June
150
200
250
300
350
400
450
500
0 3 6 9 12 15 18
Months ahead from mid June
Cents per
bushel
1996 2001
6
Profiles of Corn Futures Prices in Mid June
150
200
250
300
350
400
450
500
0 3 6 9 12 15 18
Months ahead from mid June
Cents per
bushel
1996 1997 1998 1999 2000 2001
7
Idealized Market Model (Spot Market)
• Generating and retailing firms trade wholesale electricity for a full constellation of delivery hours and days, far into the future.
• All firms are competitive and risk-neutral.
• Aggregate supply:
PSt = b wt Qc-1(1 + MC e1,t) e1,t = MC e1,t -1 + u1,t
where wt = price of primary input (fuel)
b, c, MC, MC = parameters
u1,t ~ iid N(0,1)
• Retail demand is exogenously determined (QAt).
Equilibrium spot price in any hour: Pt = b wt QAtc-1(1 + MC e1,t)
8
Exogenous Variables
• Demand (load)
QAt = QDT(t; )(1 + QA e2, t) e2,t = QA e2, t-1 + u2, t
• Fuel Pricewd = w0, d + w vd e3,d e3,d = w e3, d-1 + u3, d
w0, d = w0(d; )
vd = v(d; )
u2,t, u3,t ~ iid N(0,1)
A total of 25 parameters with 3 stochastic factors (a shock to the load, a shock to the fuel price, and a shock to the cost of generation).
9
Seasonal and Diurnal Variations in Deterministic Load: QDTt
131
61
9112115
118121
124127
130133
1361
15
913
1721
0
20
40
60
80
100
120
140
160
Load
Day count
Hour of day
10
Seasonal cycles in fuel price and price variance
w 0(d ; )
v (d ; )
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
1 31 61 91 121
151
181
211
241
271
301
331
361
Day count (d ) from January 1
11
Simulated data - 3 price relationships
(1) Examine forward profiles – For each delivery hour t, generate as many forward prices, Ft,t-k, as the number of k. Each is the best, unbiased forecast by construction (Ft,t-k = Et-k[Pt]).
If the profiles consistently attenuate to a stable price, forward prices beyond that time ahead are redundant.
(2) Examine spreads
If the spread between the forward prices of two distinct delivery hours is stable, one price can be deduced from the other.
(3) Compare the forecasting ability of the forward price of primary input (wt,t-k) with that of the forward electricity price (Ft,t-k).
If the price movements of the two commodities are highly correlated, one forward price can be deduced from the other.
12
Representative time series of simulated spot prices
One realization of the spot electricity price standardized to the seasonal average (July 24, Hour 18 - Aug 1, Hour 18)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
7/24, H18 7/25, H18 7/26, H18 7/27, H18 7/28, H18 7/29, H18 7/30, H18 8/1, H18
Delivery hour
base
12
Representative time series of simulated spot prices
One realization of the spot electricity price standardized to the seasonal average (July 24, Hour 18 - Aug 1, Hour 18)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
7/24, H18 7/25, H18 7/26, H18 7/27, H18 7/28, H18 7/29, H18 7/30, H18 8/1, H18
Delivery hour
base SD=.20
12
Representative time series of simulated spot prices
One realization of the spot electricity price standardized to the seasonal average (July 24, Hour 18 - Aug 1, Hour 18)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
7/24, H18 7/25, H18 7/26, H18 7/27, H18 7/28, H18 7/29, H18 7/30, H18 8/1, H18
Delivery hour
base c=5
12
Representative time series of simulated spot prices
One realization of the spot electricity price standardized to the seasonal average (July 24, Hour 18 - Aug 1, Hour 18)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
7/24, H18 7/25, H18 7/26, H18 7/27, H18 7/28, H18 7/29, H18 7/30, H18 8/1, H18
Delivery hour
base AR=.98
13
(1) Progressions of an electricity forward price
Movements of forward price (standardized to the seasonal average) within one week of delivery period (Aug. 1, Hour 18)
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
168 144 120 96 72 48 24 0
Hours Ahead
base
13
(1) Progressions of an electricity forward price
Movements of forward price (standardized to the seasonal average) within one week of delivery period (Aug. 1, Hour 18)
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
168 144 120 96 72 48 24 0
Hours Ahead
base SD=.20
13
(1) Progressions of an electricity forward price
Movements of forward price (standardized to the seasonal average) within one week of delivery period (Aug. 1, Hour 18)
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
168 144 120 96 72 48 24 0
Hours Ahead
base c=5
13
(1) Progressions of an electricity forward price
Movements of forward price (standardized to the seasonal average) within one week of delivery period (Aug. 1, Hour 18)
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
168 144 120 96 72 48 24 0
Hours Ahead
base AR=.98
14
Variation across realizations in a forward priceStandard deviation (variation over 1,000 realizations)
of forward price standardized to the seasonal average within one week of delivery (Aug. 1, Hour 18)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
168 144 120 96 72 48 24 0
Hours Ahead
Base
14
Variation across realizations in a forward priceStandard deviation (variation over 1,000 realizations)
of forward price standardized to the seasonal average within one week of delivery (Aug. 1, Hour 18)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
168 144 120 96 72 48 24 0
Hours Ahead
Base SD=.2 c=5 AR=.98
15
(2) Spreads among forward prices for three distinct delivery periods (Hour 18, Aug. 1, 2, and 8) - Base parameter case
Progressions of forward prices (July 24, Hour 18 - Aug 8, Hour 18)
0
10
20
30
40
50
60
70
80
90
7/24, H18 7/26, H18 7/28, H18 7/30, H18 8/2, H18 8/4, H18 8/6, H18 8/8, H18
Trading hour
8/1, H18 8/2, H18 8/8, H18
16
(3) Forecasting ability
• Regression Models
(1) ln Pt = a0 + b0 ln Ft,t-k + e0,t
(2) ln Pt = a2 + b2 ln wt,t-k + c2 ln QFt,t-k + e2,t
Load forecast, QFt,t-k, in (2) allows the market heat rate to be non-constant and vary by season.
• If the R2 for (2) is close to the R2 for (1), the forward price of fuel predicts the spot electricity price as accurately as the electricity forward.
If so, the benefit from a separate forward market for electricity would be small.
17
R-squared for regressions explaining the electricity spot priceRegressor = Electricity forward
Estimated over 8,640 hours (approx. one year)
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
312244872168
Hours ahead
R2
base (F)
17
R-squared for regressions explaining the electricity spot price - Comparison
Estimated over 8,640 hours (approx. one year)
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
312244872168
Hours ahead
R2
base (F) base (w, QF)
17
R-squared for regressions explaining the electricity spot price - Sensitivity
Estimated over 8,640 hours (approx. one year)
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
312244872168
Hours ahead
R2
base (F) high SD for supply (F) high AR for supply (F)base (w, QF) high SD for supply (w, QF) high AR for supply (w, QF)
18
One-Month-Ahead Forecasting Ability of Corn Futures Contracts (1996-2001)
0
100
200
300
400
500
600
0 100 200 300 400 500 600
July Futures as of Mid June
July Futures at Expiration in Mid July(Cents per
bushel)
R2 = 0.97
19
Six-Month-Ahead Forecasting Ability of Corn Futures Contracts (1996-2001)
0
50
100
150
200
250
300
350
400
0 50 100 150 200 250 300 350 400
December Futures as of Mid June
December Futures at Expiration in Mid Dec(Cents per
bushel)
R2 = 0.52
20
Eighteen-Month-Ahead Forecasting Ability of Corn Futures Contracts (1996-2001)
0
100
200
300
400
500
600
0 100 200 300 400 500 600
July Futures as of Mid June
July Futures at Expiration
in Mid July
0
50
100
150
200
250
300
350
400
0 50 100 150 200 250 300 350 400
December Futures as of Mid June One Year Previously
December Futures at Expiration in Mid Dec(Cents per
bushel)
R2 = 0.31
21
Thirty-Month-Ahead Forecasting Ability of Corn Futures Contracts (1996-2001)
0
50
100
150
200
250
300
350
400
0 50 100 150 200 250 300 350 400
Dec Futures as of Mid June
December Futures at Expiration
in Mid Dec
0
50
100
150
200
250
300
350
400
0 50 100 150 200 250 300 350 400
December Futures as of Mid June Two Years Previously
December Futures at Expiration in Mid Dec(Cents per
bushel)
22
Conclusions
• Forecasting ability of electricity forward prices inevitably low.
• Local electricity forward price profiles well represented by:• Local spot markets plus forwards perhaps as far as a week
ahead.
• Regional month-ahead energy forward market, such as natural gas.
• National benchmark long-dated energy forward market, such as the NYMEX natural gas.
• Complex varieties of contracting likely• Local long-dated forward “basis” agreements.
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