Time-consistency in managing a commodity portfolio: A dynamic risk measure approach
We address the problem of managing a storable commodity portfolio, that includes physical assets and positions in spot and forward markets. The vast amount of capital involved in the acquisition of a power plant or storage facility implies that the financing period stretches over a period of several quarters or years. Hence, an intertemporally consistent way of optimizing the portfolio over the planning horizon is required. We demonstrate the temporal inconsistency of static risk objectives based on final wealth and advocate the validity in our setting of a new class of recursive risk measures introduced by Epstein and Zin [Epstein, G., Zin, S., 1989. Substitution, risk aversion, and the temporal behavior of consumption and asset returns: A theoretical framework. Econometrica, 57 (4) 937-969] and Wang [Wang, T., 2000. A class of dynamic risk measures University of British Columbia]. These risk measures provide important insights on the trade-offs between date-specific risks (i.e., losses occurring at a point in time) and time-duration risks represented by the pair (return, risk) over a planning horizon; in a number of situations, they dramatically improve the efficiency of static risk objectives, as exhibited in numerical examples.
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- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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- 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.
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- James E. Smith, 1998. "Evaluating Income Streams: A Decision Analysis Approach," Management Science, INFORMS, vol. 44(12-Part-1), pages 1690-1708, December.
- Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-969, July.
- Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
- Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
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