Benchmark Beating with the Increasing Convex Order

ArXiv ID: 2311.01692 “View on arXiv”

Authors: Unknown

Abstract

In this paper we model benchmark beating with the increasing convex order (ICX order). The mean constraint in the mean-variance theory of portfolio selection can be regarded as beating a constant. We then investigate the problem of minimizing the variance of a portfolio with ICX order constraints, based on which we also study the problem of beating-performance-variance efficient portfolios. The optimal and efficient portfolios are all worked out in closed form for complete markets.

Keywords: Increasing Convex Order (ICX), Mean-Variance Theory, Portfolio Selection, Variance Minimization, Beating-Performance-Efficient Portfolios, Equities/General Portfolio Management

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper develops advanced stochastic order theory (ICX order) with extensive proofs and quantile formulations, but provides no empirical data, backtesting, or implementation details, focusing purely on theoretical optimization in complete markets.

  flowchart TD
    A["Research Goal: Model Benchmark Beating<br>using Increasing Convex Order ICX"] --> B["Methodology: ICX Order Constraints<br>Mean Constraint = Beating a Constant"]
    B --> C["Data: Complete Markets<br>Full Covariance & Return Data"]
    C --> D["Computational Process: Minimize Portfolio Variance<br>Subject to ICX Constraints"]
    D --> E["Outcome 1: Closed-Form Optimal Portfolios"]
    D --> F["Outcome 2: Beating-Performance-Variance<br>Efficient Portfolios"]
    E --> G["Final Result: Complete analytical solutions<br>for equities/general portfolio management"]
    F --> G