Chapter 21

Optimal Rebalancing

Intuition is nothing but the outcome of earlier intellectual experience.

—Albert Einstein

Fluctuations in the prices of risky assets affect overall portfolio value as well as the relative allocation of assets within the portfolio. Periodic rebalancing policies are therefore designed to preserve targeted allocations of risky and safe assets relative to their respective weights in a benchmark portfolio. Targeted allocations (for example, a 60/30/10 mix of stocks, bonds, and cash) are ultimately a statement of the portfolio's exposure to risk and, therefore, weight adjustments are necessary to prevent drift in risk due to underlying price volatility. Rebalancing also serves to minimize movements in the durations of portfolios of fixed income securities due to yield volatility, indicating that even portfolios of safe assets (for example, Treasury issues) are not immune to risk.

The objective is to rebalance to add value but minimize the risk of not meeting liabilities. Clearly, a do-nothing, buy-and-hold strategy will not control for risk. Calendar rebalancing may add value and minimize risk at the time rebalancing occurs, but the temporal nature of this rule-based policy means it cannot serve to optimally control risk and add value over time because of its arbitrary timing. Dynamic policies (constant mix and various forms of portfolio insurance) provide upside or downside protection, depending on the time series properties of asset prices (for example, rising, falling, mean reverting, or volatile periods), but the inherent randomness in asset prices prevent any one dominant policy. Hence, these policies are essentially regimes that work best in a compatible market. Without the ability to forecast asset prices, they are essentially reactionary policies.

Transactions costs complicate the problem—rebalancing must now trade off the benefits (adding value, reducing risk) against the costs of doing so—but they also serve to recast the problem as one in which the decision is the outcome of an optimization problem whose objective it is to maximize the net benefits of rebalancing. At the simplest level, the setup provides some insight into solving for trigger solutions, that is, the optimal time at which the decision is made to rebalance. For example, when the benefits of rebalancing (reduced risk, say) are quadratic in the drift from the target weight(s) and costs are linear, then the trigger point (expressed as a function of the magnitude in the drift of the current portfolio weight from the target) is easily solved (it is the maximal amount of drift allowed that signal a rebalancing). How much rebalancing is an appropriate response, when triggered to do so? In a quadratic setup, it is always half the trigger point. For example, if rebalancing is triggered at 6 percent drift (the difference between the portfolio weight and the target), then rebalancing will proceed back to 3 percent drift and not all the way back to benchmark. Why? Because the costs of rebalancing produce a drag on the benefits, both explicitly and implicitly.