Investment Theory and Risk Management, + Website

Trigger Strategies and No-Trade Regions

Trigger strategies are attractive because they are outcomes to an optimization problem, meaning that they minimize the possibly unnecessary (and redundant) costs of rebalancing on a purely calendar basis. But they are also static, meaning that they assume costs and benefits are constant through time. To understand this better, consider a setup for which costs are constant but benefits are measured as a Value-at-Risk (VaR) dollar amount portfolio risk exposure. VaR is a function of the correlations in the portfolio returns, the returns themselves, and the value of the portfolio, at each point in time. Clearly, this quantity is not constant, and in fact, may be highly volatile. In such a setting, the optimal solution to the problem of choosing a time to rebalance, as well as the degree of rebalancing, is one that maximizes the net benefits of doing so over all points in time. It is a dynamic strategy. As such, it is not so much a problem of knowing when to rebalance; technically, maximizing the net benefits occurs at each point, so rebalancing is really a continuous process—it is a random variable. Rather, it is knowing how much to rebalance in each period. In this type of problem—an optimal control problem—the objective is to maximize the function (say, net benefits) over time, that is, to solve for the optimal rebalancing path that maximizes the objective function continuously. What is attractive about this approach is that it combines the ...