On multiobjective combinatorial optimization and dynamic interim hedging of efficient portfolios

A dynamic portfolio policy is one that periodically rebalances an optimally diversified portfolio to account for time‐varying correlations. In order to sustain target‐level Sharpe performance ratios between rebalancing points, the efficient portfolio must be hedged with an optimal number of contingent claim contracts. This research presents a mixed‐integer nonlinear goal program (MINLGP) that is directed to solve the hierarchical multiple goal portfolio optimization model when the decision maker is faced with a binary hedging decision between portfolio rebalance periods. The MINLGP applied to this problem is formed by extending the separable programming foundation of a lexicographic nonlinear goal program (NLGP) to include branch‐and‐bound constraints. We establish the economic efficiency of applying this normative approach to dynamic portfolio rebalancing by comparing the risk‐adjusted performance measures 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 does its nonhedged and naively diversified counterpart.