1. 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 Fleten Stein W. Wallace Norwegian University of Science and Technology William T. Ziemba University of British Columbia

2. 8-May-15 www.iot.ntnu.no/~fleten/ 2 Outline Background –The portfolio management problem –The market and its products Presentation of the proposed model Example and results

3. 8-May-15 www.iot.ntnu.no/~fleten/ 3 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-15 www.iot.ntnu.no/~fleten/ 4 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-15 www.iot.ntnu.no/~fleten/ 5 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-15 www.iot.ntnu.no/~fleten/ 6 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-15 www.iot.ntnu.no/~fleten/ 7 Markets

8. 8-May-15 www.iot.ntnu.no/~fleten/ 8 Large producers Swe Nor Swe Fin Den (fossil )

9. 8-May-15 www.iot.ntnu.no/~fleten/ 9 Supply

10. 8-May-15 www.iot.ntnu.no/~fleten/ 10 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-15 www.iot.ntnu.no/~fleten/ 11 Futures contracts

12. 8-May-15 www.iot.ntnu.no/~fleten/ 12 Options European options on futures Asian options on spot price But: This is an oligopoly with outsiders!

13. 8-May-15 www.iot.ntnu.no/~fleten/ 13 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-15 www.iot.ntnu.no/~fleten/ 14 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-15 www.iot.ntnu.no/~fleten/ 15 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-15 www.iot.ntnu.no/~fleten/ 16 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-15 www.iot.ntnu.no/~fleten/ 17 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-15 www.iot.ntnu.no/~fleten/ 18 Current methodology (cont.) Now (t = 0) t = 1 Two model-views on the future

19. 8-May-15 www.iot.ntnu.no/~fleten/ 19 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-15 www.iot.ntnu.no/~fleten/ 20 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-15 www.iot.ntnu.no/~fleten/ 21 Variables Production in individual reservoirs Buying and selling –forward contracts –futures –options –load factor contracts

22. 8-May-15 www.iot.ntnu.no/~fleten/ 22 Shortfall cost function example

23. 8-May-15 www.iot.ntnu.no/~fleten/ 23 Objective function

24. 8-May-15 www.iot.ntnu.no/~fleten/ 24 Balance constraints

25. 8-May-15 www.iot.ntnu.no/~fleten/ 25 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-15 www.iot.ntnu.no/~fleten/ 26 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-15 www.iot.ntnu.no/~fleten/ 27 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-15 www.iot.ntnu.no/~fleten/ 28 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-15 www.iot.ntnu.no/~fleten/ 29 Generating scenarios Portfolio having 11 reservoirs, 7 plants Inflow to two rivers Market price –forward price –option price

30. 8-May-15 www.iot.ntnu.no/~fleten/ 30

31. 8-May-15 www.iot.ntnu.no/~fleten/ 31 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-15 www.iot.ntnu.no/~fleten/ 32 Input data - inflow

33. 8-May-15 www.iot.ntnu.no/~fleten/ 33 Inflow Input data is averaged for the periods

34. 8-May-15 www.iot.ntnu.no/~fleten/ 34 Generated inflow data

35. 8-May-15 www.iot.ntnu.no/~fleten/ 35 Comparison

36. 8-May-15 www.iot.ntnu.no/~fleten/ 36 Samkjøringsmodellen- prices

37. 8-May-15 www.iot.ntnu.no/~fleten/ 37 Averaged price data from Samkjøringsmodellen

38. 8-May-15 www.iot.ntnu.no/~fleten/ 38 Comparison

39. 8-May-15 www.iot.ntnu.no/~fleten/ 39 Revenue distribution: 1st quarter Expected value 138 121 St. dev. 13 2.6 E[Shortfall cost] 0.8 3.6

40. 8-May-15 www.iot.ntnu.no/~fleten/ 40 Revenue distr.: 2+3rd quarter Million NOK Expected value 236 201 St. dev. 131 37 E[Shortfall cost] 15 13

41. 8-May-15 www.iot.ntnu.no/~fleten/ 41 Revenue distr.: final year Expected value 265 309 St. dev. 131 131 E[Shortfall cost] 151 5.7

42. 8-May-15 www.iot.ntnu.no/~fleten/ 42 Revenue distr. at horizon

43. 8-May-15 www.iot.ntnu.no/~fleten/ 43 First week decision

44. 8-May-15 www.iot.ntnu.no/~fleten/ 44 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-15 www.iot.ntnu.no/~fleten/ 45 Portfolio results

46. 8-May-15 www.iot.ntnu.no/~fleten/ 46 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-15 www.iot.ntnu.no/~fleten/ 47 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-15 www.iot.ntnu.no/~fleten/ 48

49. 8-May-15 www.iot.ntnu.no/~fleten/ 49 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-15 www.iot.ntnu.no/~fleten/ 50 Future work Solve larger problems (Thermal production) Data collection / preparation, stability analysis Derivative pricing, discounting Taxes

51. 8-May-15 www.iot.ntnu.no/~fleten/ 51 Conclusion Myopic models will give too much trade Utilizing such a model can add value to portfolio management