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Minimizing costs using dynamic programming.
Institutional money managers develop risk models and optimal portfolios to match a desired risk/reward profile. Utility functions express risk preferences and implicitly reflect the views of fund trustees or directors.
Once a manager determines a target portfolio, maintaining this balance of assets is non-trivial. A manager must rebalance actively because different asset classes can exhibit different rates of return. Managers also must rebalance if weights in the target portfolio are altered. This occurs when the model for expected returns of asset classes changes or the risk profile changes.
Most academic theory ignores frictional costs, and assumes that a portfolio manager can simply readjust holdings dynamically without any problems. In practice, trading costs are non-zero and affect the decision to rebalance. Transaction costs involve commissions and market impact as well as cost of personnel and technological resources. If the transaction costs exceed the expected benefit from rebalancing, no adjustment should be made, but without any quantitative measure for this benefit, we cannot accurately determine whether or not to trade.
Conventional approaches to portfolio rebalancing include periodic and tolerance band rebalancing (see Donahue and Yip [2003] and Masters [2003]). With periodic rebalancing, the portfolio manager adjusts to the target weights at a consistent time interval (e.g., monthly or quarterly). The drawback with this method is that trading decisions are independent of market behavior. Thus, rebalancing may occur even if the portfolio is nearly optimal.
Tolerance band rebalancing requires managers to rebalance whenever any asset class moves beyond some predetermined tolerance band (e.g., ±5%). When this occurs, the manager fully rebalances to the target portfolio. While this method reacts to market movements, the threshold for rebalancing is fixed, and the process of rebalancing involves trading all the way back to the optimal portfolio.
Research on dynamic strategies for asset allocation has established a so-called no-trade region around the optimal target portfolio weights (see Perold and Sharpe [1995] and Leland [1999]). If the proportions allocated to each asset at any given time lie within this region, trading is not necessary. If current asset ratios lie outside the no-trade region, though, Leland [1999] has shown that it is optimal to trade but only to bring the weights back to the nearest edge of the...