Active Portfolio Rebalancing using Multi-objective Metaheuristics

Abstract

Active Portfolio Rebalancing deals with devising a new asset allocation by buying and selling portions of the original portfolio invested in, as and when the need arises, so that the risk of the rebalanced portfolio reverts back to its original state. However, the problem of finding the optimal buy-sell weights to rebalance the portfolio can turn complex when the original portfolio invested in was already governed by multiple objectives and complex constraints defined by the investor, and the rebalancing of the portfolio adds more constraints and (or) objectives to the problem model.This paper discusses such an Active Portfolio Rebalancing model to obtain the optimal rebalanced portfolio, with the multi-objectives of maximizing its Diversification Ratio and its Expected Portfolio Return, subject to the non-linear constraints of Risk Budgeting and other investor preferential constraints stipulated for the original portfolio, besides the additional constraints involving transaction costs for rebalancing and the rebalanced portfolio risk. The portfolio rebalancing model, which is a multi-objective non-convex non-linear constrained fractional programming problem, turns difficult for direct solving using traditional methods and hence employs Multi-objective Metaheuristics to arrive at the optimal weights of assets to buy-sell to rebalance the portfolio. The experimental studies have been undertaken over high risk long-only equity portfolios of SP BSE 200 Index (Bombay Stock Exchange, India Period: March 1999-March 2009) and Nikkei 225 Index (Tokyo Stock Exchange, Japan, Period: March 1999-March 2009) over historical periods that included both upturns and downturns in the markets.