A Global Optimal Theory of Portfolio beyond R-$σ$ Model

ArXiv ID: 2601.00281 “View on arXiv”

Authors: Yifan Liu, Shi-Dong Liang

Abstract

The deviation of the efficient market hypothesis (EMH) for the practical economic system allows us gain the arbitrary or risk premium in finance markets. We propose the triplet $(R,H,σ)$ theory to give the local and global optimal portfolio, which eneralize from the $(R,σ)$ model. We present the formulation of the triplet $(R,H,σ)$ model and give the Pareto optimal solution as well as comparing it with the numerical investigations for the Chinese stock market. We define the local optimal weights of the triplet $(\mathbf{“w”}{“R”},\mathbf{“w”}{“H”},\mathbf{“w”}_σ)$, which constructs the triangle of the quasi-optimal investing subspace such that we further define the centroid of the triangle or the incenter of the triangle as the optimal investing weights, which optimizes the mean return, the arbitrary or risk premium and the volatility risk. By investigating numerically the Chinese stock market as an example we demonstrate the validity of the formulation and obtain the global optimal strategy and quasi-optimal investing subspace. The theory provides an efficient way to design the portfolio for different style investors, conservative or aggressive investors, in finance market to maximize the mean return and arbitrary or risk premium with a small volatility risk.

Keywords: Triplet (R,H,σ) Theory, Portfolio Optimization, Pareto Optimal Solution, Arbitrary/Risk Premium, Efficient Market Hypothesis, Equities

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper presents a mathematically dense theory involving Lagrangian functions, Kuhn-Tucker conditions, and geometric concepts like incenters and centroids, scoring high in math complexity. However, the empirical section relies on a single-case study of the Chinese stock market without detailed backtesting frameworks or robust performance metrics, indicating low empirical rigor.

  flowchart TD
    A["Research Goal:<br/>Generalize the (R,σ) model to<br/>find global optimal portfolio"] --> B["Develop Triplet Theory<br/>(R, H, σ)"]
    B --> C["Input: Chinese Stock Market Data"]
    C --> D["Compute Local Optimal Weights<br/>(w_R, w_H, w_σ)"]
    D --> E["Construct Quasi-Optimal<br/>Investing Subspace"]
    E --> F["Find Global Optimal via<br/>Pareto/Geometric Solution<br/>(Centroid/Incenter)"]
    F --> G["Outcomes:<br/>Global Optimal Strategy<br/>(Max Return & Premium, Min Risk)"]
    G --> H["Conclusion:<br/>Valid theory for diverse investor styles<br/>(Conservative vs. Aggressive)"]