On multiobjective combinatorial optimization and dynamic interim hedging of efficient portfolios

This research introduces a new mixed-integer nonlinear goal program (MINLGP) with branch and bound constraints and a separable programming foundation. The motivation for creating the MINLGP algorithm is to advance the ability of portfolio managers facing multiple and hierarchical goals to simultaneously solve for an efficient portfolio with an optimal number of contingent claim contracts in order to hedge temporal portfolio volatility. Upon establishing convexity characteristics, the MINLGP is executed in a dynamic trading strategy to compare performance characteristics of a hedged optimal portfolio to those of a naively diversified portfolio. We find that a hedged equally weighted small portfolio and a hedged efficiently diversified small portfolio perform similarly when comparing risk-adjusted return metrics. However, when percentile risk measures are used to measure performance, the hedged optimally diversified portfolio clearly produces less expected catastrophic loss than that of the non-hedged and naively diversified counterpart at a predetermined confidence level.