On Drawdown-Modulated Feedback Control in Stock Trading

TL;DR

This paper introduces a novel feedback control method to manage drawdown risk in stock trading, ensuring wealth drops stay within predefined limits, and applies it to optimize investment strategies with historical data.

Contribution

The paper develops the Drawdown Modulation Lemma and a drawdown-modulated feedback control scheme for risk management in stock trading, extending Kelly optimization with drawdown constraints.

Findings

Guarantees drawdown limits with probability one

Introduces a new optimal investment strategy under drawdown constraints

Demonstrates effectiveness with historical stock data

Abstract

Control of drawdown, that is, the control of the drops in wealth over time from peaks to subsequent lows, is of great concern from a risk management perspective. With this motivation in mind, the focal point of this paper is to address the drawdown issue in a stock trading context. Although our analysis can be carried out without reference to control theory, to make the work accessible to this community, we use the language of feedback systems. The takeoff point for the results to follow, which we call the Drawdown Modulation Lemma, characterizes any investment which guarantees that the percentage drawdown is no greater than a prespecified level with probability one. With the aid of this lemma, we introduce a new scheme which we call the drawdown-modulated feedback control. To illustrate the power of the theory, we consider a drawdown-constrained version of the well-known Kelly Optimization Problem which involves maximizing the expected logarithmic growth of the trader's account value. As the drawdown parameter dmax in our new formulation tends to one, we recover existing results as a special case. This new theory leads to an optimal investment strategy whose application is illustrated via an example with historical stock-price data.