Transcript Electricity portfolio management

Electricity portfolio
management
-A dynamic portfolio approach to hedging
economic risk in electricity generation
Stein-Erik Fleten
Stein W. Wallace
Norwegian University of Science and
Technology
William T. Ziemba
University of British Columbia
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Outline
• Background
– The portfolio management problem
– The market and its products
• Presentation of the proposed model
• Example and results
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Background
• Electricity production deregulated in 1991
• Transmission is still regulated
• Producers face
– Volume (inflow) uncertainty
– Price uncertainty
• These are correlated
– Cold weather means high demand and low
inflow yielding high prices
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Our interests
• A risk averse hydro-power producer
• Forward, futures and option markets exist
• Bilateral contracts are numerous
• Weaknesses of todays’ systems
– Difficult to integrate production and trading in
futures, forwards, options and other contract
categories
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Hydropower portfolio
management
• Producers use the flexibility in hydro
generation and in the contract portfolio to
maximize expected profits with some
regard to risk
• The important stochastic variables: Spot
market prices and inflows to reservoirs and
power stations
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Markets
Our view on the present situation:
• The underlying market is a duopoly with
outsiders
• Market power is used, but very carefully
• Most firms behave as if the market was
perfect
• Forward and futures markets are
functioning
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– They are financial in nature
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– Bilateral contracts are financial (+ physical)
Markets
Producer
Vattenfall AB
Statkraft SF
Sydkraft AB
Stockholm Energi AB
Gullspångs Kraft AB
Norsk Hydro
Oslo Energi
BKK
Stora Kraft AB
Lyse Kraft
Sum
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Average production
68420 GWh
33834
29170
12070
10727
10400
8233
5357
5300
5290
188801
Market share
27.2
13.4
11.6
4.8
4.3
4.1
3.3
2.3
2.3
2.2
75.5
Large producers
Hydro
TWh/year
250
Nuclear
Conventional thermal (fossil
)
200
150
100
50
0
Vattenfall Statkraft
Swe
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Nor
Sydkraft
Swe
Fortum
Fin
Elsam and
Other
Elkraft
producers
Den
Supply
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Forwards/futures
• Contracts without flexibility
– Fixed load profile: Constant power level
• Varying time intervals
– Next week
– ...
– A full year three years from now
• Means of payment
– forwards: during delivery
– futures: mark to market
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Futures contracts
Price CAD/MWh
$40
$30
$20
May 98
August 98
July 99
$10
0
19
11
29 39
1998
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7
17
27
1999
37
47
5
15 25
2000
35
45
Options
• European options on futures
• Asian options on spot price
• But: This is an oligopoly with outsiders!
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Load factor contracts
(options)
• Bilateral contracts with flexibility.
–
–
–
–
–
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One year
5000h of maximal load (out of 8760h)
at least 1/3 in summer
at most 2/3 in winter
(always profitable to use)
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Why risk aversion?
• Modigliani & Miller 1958
• Is hedging cheaper for the company or for
its owners?
• Who are the owners?
• External financing is usually cheaper than
internal funds
• Bankruptcy costs and financial distress
• Leverage and tax advantages
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Current methodology
1: Production planning
2: Trading for hedging
– financial risk management through forward
contracts
• Not integrated
• Contracting decisions at future stages are
not considered
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Separation theorem
• No production uncertainty or basis risk:
Production planning can be done
independently from hedging and depend
only on the forward/futures price
• Speculative/hedging decisions still
depend on subjective beliefs and attitude
toward risk
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Breakdown of separation
• Basis risk: f.ex. due to spatial risk
• Production uncertainty: f.ex. due to
imperfect correlation between inflow and
spot price
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Current methodology (cont.)
Two model-views on the
future
Now (t = 0)
t=1
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Model characteristics
• Theory and methodology from portfolio
management in finance
• Multistage stochastic program
• Research computer model is implemented
at NTNU
• Advanced prototype is developed at
SINTEF Energy Research
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Basic model
• Risk = the danger of not achieving preset
profit targets at different dates in the future
• Shortfall = the extent to which the
achieved profit is below the specified profit
target
• Maximise expected profit less of expected
shortfall costs given production constraints
and contract rebalancing constraints,
including power balance
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Variables
• Production in individual reservoirs
• Buying and selling
–
–
–
–
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forward contracts
futures
options
load factor contracts
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Shortfall cost function
example
Shortfall cost function
Cost MNOK
50
40
30
20
10
0
300
22
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320
330
340
350
360
profit MNOK
Objective function
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Balance constraints
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Solution procedures
• Linear constraints and objective function
• Multistage stochastic program
• Development phase: Linear program
– AMPL with CPLEX 6.0
– (MSLiP 8.3)
• SINTEF Energy Research uses SDDP
(Pereira 1989)
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Solution procedures
• Problem: Lack of convexity in the states
– Random prices correlated over time
• Standard in hydro scheduling: SDDP
– Philosophy of dynamic programming
– Uses cuts instead of tables as in DP
– Uses sampling
• Now is used SDDP on top of normal DP
– Gjelsvik & Wallace 1996
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Generating scenarios
• Example: 5 periods (5 stages), with 4
outcomes in each stage
• The scenario tree:
stage 1
stage 2
stage 3
stage 4
stage 5
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Generating scenarios
• The tree is constructed by sequential
nonlinear optimization using the method
described in K. Høyland and S. W. Wallace
(1997)
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Generating scenarios
• Portfolio having 11 reservoirs, 7 plants
• Inflow to two rivers
• Market price
– forward price
– option price
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Example portfolio
• Reservoir capacity 1490 GWh, starts 65%
full
• Generation capacity 595 MW
• Initial contracts: has sold a lot, is now short
• “Revenue periods” at stages 3 to 5
• Four forwards; for stages 2-5, 16 options
• One load factor contract
• Target revenue for last stage is 261 Mkr
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Input data - inflow
14000
Max
75 %
Average
25 %
Min
12000
Inflow [GWh]
10000
8000
6000
4000
2000
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52
49
46
43
40
37
34
31
28
25
22
19
16
13
10
7
4
1
0
Inflow
Input data is averaged for the periods
25 %
Avg
75 %
Max
Min
140
Inflow [GWh]
120
100
80
60
40
20
0
0
33
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20
30
40
50
Generated inflow data
Min_gen
25%_gen
Avg_gen
75%_gen
Max_gen
140
Inflow [GWh]
120
100
80
60
40
20
0
0
34
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20
30
40
50
Comparison
140
Avg_gen
Avg
Inflow [GWh]
120
100
80
60
40
20
0
0
35
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20
30
40
50
Samkjøringsmodellenprices
800
Max
75%
Average
25%
Min
Price [NOK/MWh]
700
600
500
400
300
200
100
0
1
36
11 21 31 41 51 61 71 81 91 101 111 121 131 141 151
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Averaged price data from
Samkjøringsmodellen
800
700
Price [NOK/MWh]
600
Average
Average of average
500
400
300
200
100
151
145
139
133
127
121
115
109
97
91
85
79
73
67
61
55
49
43
37
31
25
19
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103
37
7
1
0
Comparison
300
250
NOK/MWh
200
25%_gen
Avg_gen
75%_gen
Max_gen
Min_gen
Min_sam
25%_sam
Avg_sam
75%_sam
Max_sam
150
100
50
0
1
38
11
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31
41
51
61
71
81
91
101
Cum. prob.
Revenue distribution:
1st quarter
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
100
Risk neutral
Risk averse
Expected value 138 121
St. dev.
13 2.6
E[Shortfall cost] 0.8 3.6
110
120
130
140
M NOK
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150
160
170
180
Revenue distr.: 2+3rd
quarter
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Expected value 236 201
St. dev.
131 37
E[Shortfall cost] 15 13
Risk neutral
Risk averse
0
40
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100
150
200
250
Million NOK
300
350
400
Cumulative probabilities
Revenue distr.: final year
1
0.8
Risk averse
Risk neutral
0.6
0.4
Expected value 265 309
St. dev.
131 131
E[Shortfall cost] 151 5.7
0.2
0
-200
0
200
400
Revenue [MNOK]
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600
800
Cumulative probabilities
Revenue distr. at horizon
1
Expected value
St.
0.8 dev.
E[Shortfall cost]
0.6
639 631
329 139
151 23
0.4
0.2
Risk averse
Risk neutral
0
-100
100
300
500
700
Cumulative revenue [MNOK]
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900
First week decision
Reservoir
Disch. Mm3 % of max Risk neutral %
Finnabu/Vasstøl
6
34
71
Grubbedalstjørn/Djupetjørn
0.0
0
0
Isvann/Holmevann
15
100
0
Kaldevann
0.0
0
0
Kvanndalsfoss
11
56
56
Middyrvatn
6.5
100
100
Nupstjørn
1.5
100
100
Røldalsvann
37
100
100
Sandvann
9.2
100
100
Valldalen
33
100
100
Votna
11
100
100
Generation GWh
89
89
85
Spot purchases GWh
76
79 GWh
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How much to buy on
contracts
Delivery period Price GWh GWh/Week MW
3 187
0
0
0
4 167 3391
130 776
5 176
0
0
0
• Write 200 MW Call for stage 5 at X = 235
NOK/MWh, Write 200 MW Put for stage 3 at X = 170
NOK/MWh,
Buy 22.3 MW Put for stage 5 at X = 145 NOK/MWh
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E(profit)
Portfolio results
640
638
636
634
632
630
628
626
0
20
40
60
80
100
E(shortfall costs)
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120
140
160
180
Portfolio results
• Compare a normal run with a myopic version:
– production is scheduled first, risk neutral, then kept
constant
– then find the “optimal” first stage contract decisions,
disregarding possibilities of contracting in the future
– loop until last stage
• Result: 2.4% reduction in objective function value
• Recommended first stage trade in the myopic
approach has futures volumes that are 3 x what is
optimal, and option volumes that are 31% higher.
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•
•
•
•
•
•
SDDP test case at Norsk
Hydro
Two year horizon, weekly resolution ( 104 stages)
Entire portfolio, underlying data (60 scenarios)
Forward contracts, dynamic resolution
Options are simulated, not dynamically traded
Quarterly reporting, four “revenue periods” per year
Problem: Increasing risk weight in objective lowers risk but
increases expected profit
• 20 iterations takes 8 hours CPU time on a DEC Alpha 4100
• Model is being extensively tested with existing systems for
risk management and hydro scheduling at Norsk Hydro
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Accumulated probability of profit year 1999
1
Risk neutral
Risk averse
0.8
0.6
0.4
0.2
0
0
100
200
300
400
500
600
700
Accumulated probability of profit year 2000
1
Risk neutral
Risk averse
0.8
0.6
0.4
0.2
Profit [MNOK]
0
48
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100
200
300
400
500
600
700
Comparison
• Can solve large problems
• Assumes stochastic independence in the
backward recursion
• Spurious trading gains
• No forward price uncertainty for maturities
of more than 6 months
• Spatial risk more difficult to incorporate
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Future work
• Solve larger problems
• (Thermal production)
• Data collection / preparation, stability
analysis
• Derivative pricing, discounting
• Taxes
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Conclusion
• Myopic models will give too much trade
• Utilizing such a model can add value to
portfolio management
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