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Robo-Advising in Motion: A Model Predictive Control Approach

Tomasz R. Bielecki, Igor Cialenco

TL;DR

This paper addresses dynamic asset allocation for robo-advisors using Model Predictive Control (MPC) to overcome the limitations of static, one-period strategies. It integrates a Hidden Markov Model (HMM) with Black–Litterman (BL) priors to forecast mean returns and covariances, while enforcing practical constraints such as turnover limits and transaction costs. Two optimization criteria are studied in a rolling-horizon setting: dynamic mean-variance (MV) and dynamic mean-risk-budgeting (MRB), with convex approximations for tractability. Numerical experiments on 8 ETFs over 2009–2024 show that MPC-based MV with HMM-BL forecasts yields flexible and diversified portfolios, whereas MRB produces smoother, more robust allocations; the results illuminate trade-offs between adaptability and stability and offer practical guidance on constraint design for robo-advising systems.

Abstract

Robo-advisors (RAs) are automated portfolio management systems that complement traditional financial advisors by offering lower fees and smaller initial investment requirements. While most existing RAs rely on static, one-period allocation methods, we propose a dynamic, multi-period asset-allocation framework that leverages Model Predictive Control (MPC) to generate suboptimal but practically effective strategies. Our approach combines a Hidden Markov Model with Black-Litterman (BL) methodology to forecast asset returns and covariances, and incorporates practically important constraints, including turnover limits, transaction costs, and target portfolio allocations. We study two predominant optimality criteria in wealth management: dynamic mean-variance (MV) and dynamic risk-budgeting (MRB). Numerical experiments demonstrate that MPC-based strategies consistently outperform myopic approaches, with MV providing flexible and diversified portfolios, while MRB delivers smoother allocations less sensitive to key parameters. These findings highlight the trade-offs between adaptability and stability in practical robo-advising design.

Robo-Advising in Motion: A Model Predictive Control Approach

TL;DR

This paper addresses dynamic asset allocation for robo-advisors using Model Predictive Control (MPC) to overcome the limitations of static, one-period strategies. It integrates a Hidden Markov Model (HMM) with Black–Litterman (BL) priors to forecast mean returns and covariances, while enforcing practical constraints such as turnover limits and transaction costs. Two optimization criteria are studied in a rolling-horizon setting: dynamic mean-variance (MV) and dynamic mean-risk-budgeting (MRB), with convex approximations for tractability. Numerical experiments on 8 ETFs over 2009–2024 show that MPC-based MV with HMM-BL forecasts yields flexible and diversified portfolios, whereas MRB produces smoother, more robust allocations; the results illuminate trade-offs between adaptability and stability and offer practical guidance on constraint design for robo-advising systems.

Abstract

Robo-advisors (RAs) are automated portfolio management systems that complement traditional financial advisors by offering lower fees and smaller initial investment requirements. While most existing RAs rely on static, one-period allocation methods, we propose a dynamic, multi-period asset-allocation framework that leverages Model Predictive Control (MPC) to generate suboptimal but practically effective strategies. Our approach combines a Hidden Markov Model with Black-Litterman (BL) methodology to forecast asset returns and covariances, and incorporates practically important constraints, including turnover limits, transaction costs, and target portfolio allocations. We study two predominant optimality criteria in wealth management: dynamic mean-variance (MV) and dynamic risk-budgeting (MRB). Numerical experiments demonstrate that MPC-based strategies consistently outperform myopic approaches, with MV providing flexible and diversified portfolios, while MRB delivers smoother allocations less sensitive to key parameters. These findings highlight the trade-offs between adaptability and stability in practical robo-advising design.
Paper Structure (26 sections, 55 equations, 20 figures, 4 tables)

This paper contains 26 sections, 55 equations, 20 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminaries on Model Predictive Control
  3. SMPC for Robo-Advisors
  4. Mean-variance portfolio selection problem
  5. MV receding horizon SMPC
  6. Mean-risk-budgeting (MRB) portfolio selection
  7. MRB receding horizon SMPC
  8. Convex approximation to the MRB criterion
  9. Forecasting of conditional moments of asset returns via Hidden Markov Models and the Black-Litterman Methods
  10. Risk profiling, allocation targets and trading constraints
  11. Risk profiling
  12. Allocation target constraints
  13. Transaction costs
  14. Initial portfolio
  15. Numerical experiment on market data
  16. ...and 11 more sections

Figures (20)

  • Figure 1: Historical asset prices, scaled to 100 at the first observation. The shaded area represents the trading period, January 16 2020 to December 31, 2024.
  • Figure 2: Forecasted market regimes by HMM model, gray shaded area corresponds to 'contraction' regime. Dark blue curve represents the average prices of all assets.
  • Figure 3: Correlation matrix of asset returns.
  • Figure 3: Portfolio weights for the mean-variance strategies MV-Est-MPC (top row) and MV-BL (bottom row) with risk aversion coefficient $\gamma\in\{0.01, 0.1, 1, 5, 10\}$.
  • Figure 4: Portfolio weights for the mean-variance strategies MV-Est-MPC (top row) and MV-BL (bottom row) with risk aversion coefficient $\gamma\in\{0.5, 0.7, 1, 1.5, 2\}$.
  • ...and 15 more figures

Theorems & Definitions (4)

  • Remark 3.1
  • Remark 3.2
  • Remark 4.1
  • Remark 4.2