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8-May-15 www.iot.ntnu.no/~fleten/ 1 Electricity portfolio management -A dynamic portfolio approach to hedging economic risk in electricity generation Stein-Erik.

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Presentation on theme: "8-May-15 www.iot.ntnu.no/~fleten/ 1 Electricity portfolio management -A dynamic portfolio approach to hedging economic risk in electricity generation Stein-Erik."— Presentation transcript:

1 8-May 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

2 8-May Outline Background –The portfolio management problem –The market and its products Presentation of the proposed model Example and results

3 8-May 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

4 8-May 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

5 8-May 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

6 8-May 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 –They are financial in nature –Bilateral contracts are financial (+ physical)

7 8-May Markets

8 8-May Large producers Swe Nor Swe Fin Den (fossil )

9 8-May Supply

10 8-May 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

11 8-May Futures contracts

12 8-May Options European options on futures Asian options on spot price But: This is an oligopoly with outsiders!

13 8-May Load factor contracts (options) Bilateral contracts with flexibility. –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)

14 8-May 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

15 8-May 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

16 8-May 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

17 8-May Breakdown of separation Basis risk: f.ex. due to spatial risk Production uncertainty: f.ex. due to imperfect correlation between inflow and spot price

18 8-May Current methodology (cont.) Now (t = 0) t = 1 Two model-views on the future

19 8-May 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

20 8-May 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

21 8-May Variables Production in individual reservoirs Buying and selling –forward contracts –futures –options –load factor contracts

22 8-May Shortfall cost function example

23 8-May Objective function

24 8-May Balance constraints

25 8-May 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)

26 8-May 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

27 8-May 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

28 8-May Generating scenarios The tree is constructed by sequential nonlinear optimization using the method described in K. Høyland and S. W. Wallace (1997)

29 8-May Generating scenarios Portfolio having 11 reservoirs, 7 plants Inflow to two rivers Market price –forward price –option price

30 8-May

31 8-May 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

32 8-May Input data - inflow

33 8-May Inflow Input data is averaged for the periods

34 8-May Generated inflow data

35 8-May Comparison

36 8-May Samkjøringsmodellen- prices

37 8-May Averaged price data from Samkjøringsmodellen

38 8-May Comparison

39 8-May Revenue distribution: 1st quarter Expected value St. dev E[Shortfall cost]

40 8-May Revenue distr.: 2+3rd quarter Million NOK Expected value St. dev E[Shortfall cost] 15 13

41 8-May Revenue distr.: final year Expected value St. dev E[Shortfall cost]

42 8-May Revenue distr. at horizon

43 8-May First week decision

44 8-May How much to buy on contracts 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

45 8-May Portfolio results

46 8-May 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.

47 8-May 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

48 8-May

49 8-May 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

50 8-May Future work Solve larger problems (Thermal production) Data collection / preparation, stability analysis Derivative pricing, discounting Taxes

51 8-May Conclusion Myopic models will give too much trade Utilizing such a model can add value to portfolio management


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