On Drawdown-Modulated Feedback Control in Stock Trading

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.Comment: Proc. 20th IFAC World Congress (IFAC WC 2017), Toulouse, France, July 9-14, 2017 (accepted

Practical Implementation of the Kelly Criterion: Optimal Growth Rate, Number of Trades, and Rebalancing Frequency for Equity Portfolios

“…Their approach is based on the idea of minimizing the expected growth loss of the actual growth based on the plug-in estimates of the true growth rate. Almost at the same time, Hsieh and Barmish [21] claim that, when the optimal Kelly fraction increases, various risk measures become excessively large providing poor drawdown performances whilst the Kelly strategy, although being log-growth optimal, may be too aggressive in the short term. The authors also disagree with the use of the Taylor series to compute the optimal Kelly fraction, arguing that this solution may lead to performances lower than that of the true optimum.…”

Drawdown Measures: Are They All the Same?

“…For each of the constituent stocks, we obtain daily stock prices from Datastream. 12 Any prices denominated in currencies other than 11 Examples of fields include control theory (Hsieh and Barmish, 2017), insurance (Palmowski and Tumilewicz, 2017), energy markets (Charwand et al, 2017), and option pricing (Dassios and Lim, 2018).…”

Drawdown Measures: Are They All the Same?

“…For each of the constituent stocks, we obtain daily stock prices from Datastream. 12 Any prices denominated in currencies other than 11 Examples of fields include control theory (Hsieh and Barmish, 2017), insurance (Palmowski and Tumilewicz, 2017), energy markets (Charwand et al, 2017), and option pricing (Dassios and Lim, 2018). U.S. dollar (USD) are converted to USD using the spot exchange rate taken from Datastream.…”