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

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 - 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 multiperiod 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.