Multi-period portfolio selection with drawdown control

  • Peter Nystrup
  • Stephen Boyd
  • Erik Lindström
  • Henrik Madsen
S.I.: Application of O. R. to Financial Markets


In this article, model predictive control is used to dynamically optimize an investment portfolio and control drawdowns. The control is based on multi-period forecasts of the mean and covariance of financial returns from a multivariate hidden Markov model with time-varying parameters. There are computational advantages to using model predictive control when estimates of future returns are updated every time new observations become available, because the optimal control actions are reconsidered anyway. Transaction and holding costs are discussed as a means to address estimation error and regularize the optimization problem. The proposed approach to multi-period portfolio selection is tested out of sample over two decades based on available market indices chosen to mimic the major liquid asset classes typically considered by institutional investors. By adjusting the risk aversion based on realized drawdown, it successfully controls drawdowns with little or no sacrifice of mean–variance efficiency. Using leverage it is possible to further increase the return without increasing the maximum drawdown.


Risk management Maximum drawdown Dynamic asset allocation Model predictive control Regime switching Forecasting 



The authors are thankful for the helpful comments from the responsible editor Stavros A. Zenios and two anonymous referees.


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Authors and Affiliations

  1. 1.Department of Applied Mathematics and Computer ScienceTechnical University of DenmarkKgs. LyngbyDenmark
  2. 2.ANNOXHellerupDenmark
  3. 3.Department of Electrical EngineeringStanford UniversityStanfordUSA
  4. 4.Centre for Mathematical SciencesLund UniversityLundSweden

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