Dynamic Bond Portfolio Optimization with Transaction Costs Using a Markov Decision Process

Summary

This document presents a simulation-based method for managing bond portfolios over multiple periods while accounting for interest-rate risk and proportional trading costs. It models yield-curve movements with Dynamic Nelson-Siegel factors whose dynamics follow a vector autoregression, then approximates the joint yields across maturities with a time-varying discrete-state Markov chain. That chain supplies the states for a finite-horizon Markov Decision Process. The investor’s objective is to maximize expected terminal wealth, and backward induction yields the optimal rebalancing policy.

The framework addresses a practical weakness of static allocations: a portfolio concentrated in long-duration bonds may face losses and liquidity stress as rates rise. The document also examines error from truncating the transition probabilities. It reports that truncation has little effect on mean terminal wealth but can materially distort drawdown and tail-risk statistics. The summary does not provide detailed data, parameter choices, or broader validation, so those results do not establish how well the method transfers to other portfolios or market settings.

Key ideas

• The framework optimizes bond holdings across periods while charging proportional costs for rebalancing.
• Yield-curve factors are modeled with Dynamic Nelson-Siegel dynamics and a vector autoregression.
• A discrete Markov chain approximates the joint yield process and defines states for a finite-horizon decision problem.
• Backward induction produces a policy that maximizes expected terminal wealth.
• Truncating transition probabilities can preserve mean wealth while distorting drawdown and tail-risk measures.

Tags

# Multiperiod bond portfolio optimization with transaction costs using a Markov Decision process


# Multiperiod bond portfolio optimization with transaction costs using a Markov Decision process









Bank treasury portfolios must balance yield, liquidity, and interest-rate risk across bonds of different maturities. Static allocation rules are ill-suited to this task: portfolios concentrated in long-duration securities with no dynamic adjust- ment mechanism can accumulate large mark-to-market losses and liquidity stress under rising interest rates, as illustrated by the failure of Silicon Valley Bank in 2023. We develop a tractable simulation-based framework for multi-period bond port- folio optimization under interest-rate risk and proportional transaction costs. Yield-curve dynamics are modeled using the Dynamic Nelson-Siegel parameter- ization with Vector Autoregressive factor dynamics, from which we construct a time-inhomogeneous discrete-state Markov chain approximating the joint yield process across bond maturities. This chain forms the state space of a finite- horizon Markov Decision Process in which the investor maximizes expected terminal wealth subject to proportional rebalancing costs. The optimal portfolio policy is obtained by backward induction. We also quantify the approximation error introduced by truncating the transition kernel, and show that it leaves mean terminal wealth almost unchanged while substantially distorting drawdown and tail statistics.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.