Computational Management Science

, Volume 9, Issue 3, pp 381–399 | Cite as

Optimal electricity generation portfolios

The impact of price spread modelling
  • Daniel ZieglerEmail author
  • Katrin Schmitz
  • Christoph Weber
Original Paper


It is common practice to base investment decisions on price projections which are gained from simulations using price processes. The choice of the underlying process is crucial for the simulation outcome. For power plants the core question is the existence of stable long-term cointegration relations. Therefore we investigate the impacts of different ways to model price movements in a portfolio selection model for the German electricity market. Three different approaches of modelling fuel prices are compared: initially, all prices are modelled as correlated random walks. Thereafter the coal price is modelled as random walk. The gas price follows the coal price through a mean-reversion process. Lastly, all prices are modelled as mean reversion processes with correlated residuals. The prices of electricity base and peak futures are simulated using historical correlations with gas and coal prices. Yearly base and peak prices are transformed into an estimated price duration curve followed by the steps power plant dispatch, operational margin and net present value calculation and finally the portfolio selection. The analysis shows that the chosen price process assumptions have significant impacts on the resulting portfolio structure and the weights of individual technologies.


Portfolio theory Decision making Stochastic processes 

Mathematics Subject Classification

Primary 91G99 Secondary 91G60 91G10 


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  1. Awerbuch S (1995) Market-based irp: it’s easy!. Electr J 8(3): 50–67CrossRefGoogle Scholar
  2. Awerbuch S (2000) Investing in photovoltaics: risk, accounting and the value of new technology. Energy Policy (28):1023–1035Google Scholar
  3. Awerbuch S (2004) Towards a finance-oriented valuation of conventional and renewable energy sources in ireland. Report, Sustainable Energy IrelandGoogle Scholar
  4. Awerbuch S, Berger M (2003) Applying portfolio theory to EU electricity planning and policy-making. Report number EET/2003/03, IEAGoogle Scholar
  5. Awerbuch S, Stirling A, Jansen J, Beurskens L (2006) Full-spectrum portfolio and diversity analysis of energy technologies. In: Leggio K, Bodde D, Taylor M (eds) Managing enterprise risk, elsevier global energy policy and economics series. Elsevier Science Ltd, Oxford, pp 202–222Google Scholar
  6. Bar-Lev D, Katz S (1976) A portfolio approach to fossil fuel procurement in the electric utility industry. J Finance 31(3): 933–947CrossRefGoogle Scholar
  7. Beltran H (2009) Modern portfolio theory applied to electricity resource planning. Master of sciences dissertation, University of Illinois at Urbana-ChampaignGoogle Scholar
  8. Black F, Scholes MS (1973) The pricing of options and corporate liabilities. J Political Econ 81(3): 637–654CrossRefGoogle Scholar
  9. Blyth W, Bradley R, Bunn D, Clarke C, Wilson T, Yang M (2007) Investment risks under uncertain climate change policy. Energy Policy 35(11): 5766–5773CrossRefGoogle Scholar
  10. Deng SJ (2005) Valuation of investment and opportunity-to-invest in power generation assets with spikes in electricity price. Manage Finance 31(6): 95–115. doi: 10.1108/03074350510769712 Google Scholar
  11. Dixit AK, Pindyck RS (1994) Investment under uncertainty. Princeton University Press, PrincetonGoogle Scholar
  12. EEX: Phelix baseload/peakload year future price data (2009).
  13. Fleten SE, Näsäkkälä E (2010) Gas-fired power plants: investment timing, operating flexibility and CO2 capture. Energy Econ 32(4): 805–816CrossRefGoogle Scholar
  14. Geman H, Shih YF (2009) Modeling commodity prices under the cev model. J Altern Invest 11(3): 65–84. doi: 10.3905/JAI.2009.11.3.065 CrossRefGoogle Scholar
  15. Haldrup N, Nielsen MØ (2006) A regime switching long memory model for eelectricity prices. J Econom. 135(1–2): 349–376CrossRefGoogle Scholar
  16. IEA (2008) World energy outlook 2008. International Energy Association (IEA) (2008)Google Scholar
  17. Irwin SH, Zulauf CR, Jackson TE (1996) Monte carlo analysis of mean reversion in commodity futures prices. Am J Agric Econom 78(2): 387–399CrossRefGoogle Scholar
  18. Jansen JC, Beurskens LW, van Tilburg X (2006) Application of portfolio analysis to the Dutch generating mix: reference case and two renewables cases: year 2030, SE and GE scenarioGoogle Scholar
  19. Johnson B, Barz G (1999) Selecting stochastic processes for modelling electricity prices. In: Jameson R (ed) Energy modelling and the management of uncertainty. Risk Books, London, pp 3–22Google Scholar
  20. Keles D, Hartel R, Möst D, Fichtner W (2012) Caes power plant investments under uncertain electricity prices. J Energy Markets 5(1): 53–84Google Scholar
  21. Kholodnyi VA (2005) Modeling power forward prices for power with spikes: a non-markovian approach. Nonlinear Anal Theory Methods Appl 63(5-7): 958–965CrossRefGoogle Scholar
  22. Konstantin P (2009) Praxisbuch Energiewirtschaft: Energieumwandlung, -transport und -beschaffung im liberalisierten Markt, 2 edn. Springer, BerlinGoogle Scholar
  23. Krey B, Zweifel P (2008) Efficient electricity portfolios for the united states and switzerland: an investor view.
  24. Lucia JJ, Schwartz ES (2002) Electricity prices and power derivatives : evidence from the nordic power exchange. In: Review of derivatives researchGoogle Scholar
  25. Madlener R, Wenk C (2008) Efficient investment portfolios for the swiss electricity supply sector. SSRN eLibraryGoogle Scholar
  26. Markowitz HM (1952) Portfolio selection. J Finance 7(1): 77–91Google Scholar
  27. Meade N (2010) Oil prices: brownian motion or mean reversion? a study using a one year ahead density forecast criterion. Energy Econ 32(6): 1485–1498CrossRefGoogle Scholar
  28. Merton RC (1973) Theory of rational option pricing. Bell J Econ 4(1): 141–183CrossRefGoogle Scholar
  29. Muche T (2009) A real option-based simulation model to evaluate investments in pump storage plants. Energy Policy 37(11): 4851–4862CrossRefGoogle Scholar
  30. Roques F, Newbery D, Nuttall W (2008) Fuel mix diversification incentives in liberalized electricity markets: A mean-variance portfolio theory approach. Energy Econ 30(4): 1831–1849CrossRefGoogle Scholar
  31. Roques F, Nuttall W, Newbery D (2006) Using probabilistic analysis to value power generation investments under uncertainty. Cambridge Working Papers in Economics 0650, Faculty of Economics, University of Cambridge.
  32. Rothwell G (2006) A real options approach to evaluating new nuclear power plants. Energy J 27: 37–53Google Scholar
  33. Sachverständigenrat: Die finanzkrise meistern—wachstumskräfte stärken. Jahresgutachten, Sachverständigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung (German Council of Economic Experts (2008)
  34. Schwartz ES (1997) The stochastic behavior of commodity prices: implications for valuation and hedging. J Finance 52(3): 923–973CrossRefGoogle Scholar
  35. Seifert J, Uhrig-Homburg M, Wagner M (2008) Dynamic behavior of CO 2 spot prices. J Environ Econ Manag 56(2): 180–194. doi: 10.1016/j.jeem.2008.03.003 CrossRefGoogle Scholar
  36. Weber C (2005) Uncertainty in the electric power industry: methods and models for decision support. Springer, BerlinGoogle Scholar
  37. Weber C (2007) Plants as real options: the importance of price models. In: Ostertag K, Llerena P, Richard A (eds) Option valuation for energy issues. ISI Schriftenreihe, Karlsruhe, pp 116–131Google Scholar
  38. Westner G, Madlener R (2010) The benefit of regional diversification of cogeneration investments in europe: a mean-variance portfolio analysis. Energy Policy 38(12): 7911–7920. doi: 10.1016/j.enpol.2010.09.011 CrossRefGoogle Scholar
  39. Westner G, Madlener R (2011) Development of cogeneration in germany: a mean-variance portfolio analysis of individual technology’s prospects in view of the new regulatory framework. Energy 36(8): 5301–5313. doi: 10.1016/ CrossRefGoogle Scholar
  40. Westner G, Madlener R (2011) Investment in new power generation under uncertainty: benefits of chp versus condensing plants in a copula-based analysis. Energy Econ 34: 1–380Google Scholar
  41. White B (2007) A mean-variance portfolio optimization of california’s generation mix to 2020Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Daniel Ziegler
    • 1
    Email author
  • Katrin Schmitz
    • 1
  • Christoph Weber
    • 1
  1. 1.Chair for Management Science and Energy EconomicsUniversity of Duisburg-EssenEssenGermany

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