Nonlinear Trading Rules for Portfolio Management

Abstract

The author continues his study of dynamic portfolio management published in an earlier issue of this journal. The approach considers each asset in isolation and finds the best trading policy for the asset within a prespecified class of policies. An earlier article considered linear trading rules and developed the notion of a target portfolio—a position we would prefer to hold given a single cost-free trade. The target is in motion, driven by changes in a collection of signals that are assumed to be correlated with future asset returns. In this article, the author expands the class of policies to include piecewise linear policies for three defined ranges (buy, hold, sell) and defined responses in the buy and sell regions. The policy driver is the difference between the target position and the current position, known as the backlog. If the backlog is small enough in absolute value, we are in the no-trade zone, and the policy prescription is hold. If the backlog is larger than the positive no-trade zone, the policy buys a fraction of excess and thus moves part of the way toward the boundary of the no-trade zone. The situation is symmetric in the sell case. The policy is defined by two parameters: the size of the no-trade zone and the fraction of the excess that is purchased (sold). The focus on one asset and a two-parameter policy class allows one to find good solutions to an otherwise intractable problem. The state space for the problem is the position of the asset and the values of the signals. The technique is scalable: Problems have been solved with over 3,000 assets and over 30 signals per asset. The resulting policy can then be folded into a single-stage multiasset optimization, in effect embedding the optimal dynamic policy into the static optimization.