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Multi-Period VaR-Constrained Portfolio Optimization with Applications to the Electric Power Sector

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  • Paul R. Kleindorfer
  • Lide Li

Abstract

This paper considers the optimization of portfolios of real and contractual assets, including derivative instruments, subject to a Value-at-Risk (VaR) constraint, with special emphasis on applications in electric power. The focus is on translating VaR definitions for a longer period of time, say a year, to decisions on shorter periods of time, say a week or a month. Thus, if a VaR constraint is imposed on annual cash flows from a portfolio, translating this annual VaR constraint into appropriate risk management/VaR constraints for daily, weekly or monthly trades within the year must be accomplished. The paper first characterizes the multi-period VaR-constrained portfolio problem in the form Max {E Ð kV} subject to a set of separable constraints over the decision variables (the level of assets of different instruments contained in the portfolio), where E and V are, respectively, the expected value and variance of multi-period cashflows from operations covered by the portfolio. Then, assuming the distribution of multi-period cashflows satisfies a certain regularity condition (which is a generalization of the standard Gaussian assumption underlying VaR), we derive computationally efficient methods for solving this problem that take the form of the standard quadratic programming formulations well-known in financial portfolio analysis.

Suggested Citation

  • Paul R. Kleindorfer & Lide Li, 2005. "Multi-Period VaR-Constrained Portfolio Optimization with Applications to the Electric Power Sector," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1), pages 1-26.
  • Handle: RePEc:aen:journl:2005v26-01-a01
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    References listed on IDEAS

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    1. Finon, D., 2003. "Introducing Competition in the French Electricity Supply Industry: The Destabilisation of a Public Hierarchy in an Open Institutional Environment," Cambridge Working Papers in Economics 0314, Faculty of Economics, University of Cambridge.
    2. David M. Newbery, 2002. "Privatization, Restructuring, and Regulation of Network Utilities," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262640481, January.
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    4. Paul L. Joskow, 2003. "The Difficult Transition to Competitive Electricity Markets in the U.S," Working Papers 0308, Massachusetts Institute of Technology, Center for Energy and Environmental Policy Research.
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    Citations

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    Cited by:

    1. Zare, Kazem & Moghaddam, Mohsen Parsa & Sheikh El Eslami, Mohammad Kazem, 2010. "Electricity procurement for large consumers based on Information Gap Decision Theory," Energy Policy, Elsevier, vol. 38(1), pages 234-242, January.
    2. Glensk, Barbara & Madlener, Reinhard, 2011. "Dynamic Portfolio Selection Methods for Power Generation Assets," FCN Working Papers 16/2011, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
    3. Chi-Keung Woo, Ira Horowitz, Brian Horii, Ren Orans, and Jay Zarnikau, 2012. "Blowing in the Wind: Vanishing Payoffs of a Tolling Agreement for Natural-gas-fired Generation of Electricity in Texas," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1).
    4. Woo, C.K. & Moore, J. & Schneiderman, B. & Ho, T. & Olson, A. & Alagappan, L. & Chawla, K. & Toyama, N. & Zarnikau, J., 2016. "Merit-order effects of renewable energy and price divergence in California’s day-ahead and real-time electricity markets," Energy Policy, Elsevier, vol. 92(C), pages 299-312.
    5. Chi-Keung Woo, Ira Horowitz, Jay Zarnikau, Jack Moore, Brendan Schneiderman, Tony Ho, and Eric Leung, 2016. "What Moves the Ex Post Variable Profit of Natural-Gas-Fired Generation in California?," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    6. Debbie Dupuis, Geneviève Gauthier, and Fréderic Godin, 2016. "Short-term Hedging for an Electricity Retailer," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    7. Woo, C.K. & Sreedharan, P. & Hargreaves, J. & Kahrl, F. & Wang, J. & Horowitz, I., 2014. "A review of electricity product differentiation," Applied Energy, Elsevier, pages 262-272.
    8. G. Anandalingam & Robert W. Day & S. Raghavan, 2005. "The Landscape of Electronic Market Design," Management Science, INFORMS, vol. 51(3), pages 316-327, March.
    9. D. J. Wu & Paul R. Kleindorfer, 2005. "Competitive Options, Supply Contracting, and Electronic Markets," Management Science, INFORMS, vol. 51(3), pages 452-466, March.
    10. Deng, Shi-Jie & Xu, Li, 2009. "Mean-risk efficient portfolio analysis of demand response and supply resources," Energy, Elsevier, vol. 34(10), pages 1523-1529.
    11. Zon, Adriaan van & Fuss, Sabine, 2006. "Irreversible Investment under Uncertainty in Electricity Generation: A Clay-Clay-Vintage Portfolio Approach with an Application to Climate Change Policy in the UK," MERIT Working Papers 035, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    12. Woo, C.K. & Zarnikau, J. & Moore, J. & Horowitz, I., 2011. "Wind generation and zonal-market price divergence: Evidence from Texas," Energy Policy, Elsevier, vol. 39(7), pages 3928-3938, July.
    13. Geman, Hélyette & Ohana, Steve, 2008. "Time-consistency in managing a commodity portfolio: A dynamic risk measure approach," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 1991-2005, October.
    14. Min, Daiki & Chung, Jaewoo, 2013. "Evaluation of the long-term power generation mix: The case study of South Korea's energy policy," Energy Policy, Elsevier, vol. 62(C), pages 1544-1552.
    15. Roques, Fabien A. & Newbery, David M. & Nuttall, William J., 2008. "Fuel mix diversification incentives in liberalized electricity markets: A Mean-Variance Portfolio theory approach," Energy Economics, Elsevier, vol. 30(4), pages 1831-1849, July.
    16. Muñoz, José Ignacio & Sánchez de la Nieta, Agustín A. & Contreras, Javier & Bernal-Agustín, José L., 2009. "Optimal investment portfolio in renewable energy: The Spanish case," Energy Policy, Elsevier, vol. 37(12), pages 5273-5284, December.
    17. repec:eee:appene:v:204:y:2017:i:c:p:531-543 is not listed on IDEAS

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    JEL classification:

    • F0 - International Economics - - General

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