The Dual Approach to Portfolio Evaluation: A Comparison of the Static, Myopic and Generalized Buy-and-Hold Strategies

We use the recently proposed duality approach to study the performance of static, myopic and generalized buy-and-hold (GBH) trading strategies. Our interest in static and GBH strategies is motivated by the fact that these strategies are intuitive and straightforward to implement in practice. The myopic strategy, while more difficult to implement, is often close to optimal and so we use it to obtain tight bounds on the performance of the true optimal dynamic trading strategy. We find that while this optimal dynamic strategy often significantly outperforms the GBH strategy, this is not true in general when no-borrowing or no-short sales constraints are imposed on the investor. This has implications for investors when a dynamic trading strategy is too costly or difficult to implement in practice. For the class of security price dynamics under consideration, we also show that the optimal GBH strategy is always superior to the optimal static strategy. We also demonstrate that the dual approach is even more tractable than originally considered. In particular, we show it is often possible to solve for the theoretically satisfying upper bounds on the optimal value function that were suggested when the dual approach was originally proposed.