Asset allocation using a Markov process of clustered efficient frontier coefficients states

Paper: arXiv 2604.03946

Authors: Nolan Alexander, William Scherer, Jamey Thompson

Abstract

We propose a novel asset allocation model using a Markov process of states defined by clustered efficient frontier coefficients. While most research in Markov models of the market characterize regimes using return and volatility, we instead propose characterizing these states using efficient frontiers, which provide more information on the interactions of underlying assets that comprise the market. Efficient frontiers can be decomposed to their functional form, a square-root second-order polynomial defined by three coefficients, to provide a dimensionality reduction of the return vector and covariance matrix. Each month, the proposed model hierarchically clusters the monthly coefficients data up to the current month, to characterize the market states, then defines a Markov process on the sequence of states. To incorporate these states into portfolio optimization, for each state, we calculate the tangency portfolio using only return data in that state. We then take the expectation of these weights for each state, weighted by the probability of transitioning from the current state to each state. To empirically validate our proposed model, we employ three sets of assets that span the market, and show that our proposed model significantly outperforms benchmark portfolios.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents an innovative framework that compresses mean-variance dimensions into efficient frontier polynomial coefficients before applying Markov regime-switching via hierarchical clustering. It features strong empirical validation across multiple market asset sets, though exact reproducibility is slightly constrained by missing explicit code links.

Research Flowchart

  flowchart TD
    A["Research Goal: Improve Asset Allocation using Efficient Frontier Markov Regimes"] --> B["Inputs: Historical Monthly Asset Returns (3 Market Datasets)"]
    B --> C["Dimensionality Reduction: Fit Monthly Efficient Frontiers & Extract 3 Polynomial Coefficients"]
    C --> D["State Identification: Hierarchical Clustering of Historical Coefficients into Market Regimes"]
    D --> E["Markov Modeling: Estimate Transition Probabilities & Calculate State-Specific Tangency Portfolios"]
    E --> F["Portfolio Optimization: Compute Expected Weights via Transition Probability Matrix"]
    F --> G["Key Outcome: Proposed Model Significantly Outperforms Benchmark Portfolios"]