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

The problem of interest in this paper is the optimization of portfolios of real and contractual assets, including derivative instruments, subject to a Value-at-Risk (VaR) constraint. The focus in this paper is on translating VaR definitions for one 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, or valuations of, 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. Our focus will be on electricity trading, an arena in which the portfolio optimization problem under VaR constraints is well developed. The paper characterizes computationally efficient methods for solving the VaRconstrained multi-period optimal portfolio problem, and shows its relationship to efficient frontier analysis in standard portfolio theory. * Corresponding author