Paper: arXiv 2412.03305

Abstract

An investment portfolio consists of $n$ algorithmic trading strategies, which generate vectors of positions in trading assets. Sign opposite trades (buy/sell) cross each other as strategies are combined in a portfolio. Then portfolio turnover becomes a non linear function of strategies turnover. It rises a problem of effective (quick and precise) portfolio turnover estimation. Kakushadze and Liew (2014) shows how to estimate turnover via covariance matrix of returns. We build a mathematical model for such estimations; prove a theorem which gives a necessary condition for model applicability; suggest new turnover estimations; check numerically the preciseness of turnover estimations for algorithmic strategies on USA equity market.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper features advanced mathematical modeling, including theorems and eigenvalue-based derivations for turnover estimation, warranting a high math complexity score. It is strongly grounded in empirical finance, with a dedicated section for backtesting on USA equity markets, quantitative validation of estimations, and practical considerations like trade crossing and transaction costs, indicating high empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Effective Portfolio Turnover Estimation"] --> B["Methodology<br>Covariance Matrix Model"]
  B --> C["Data Input<br>USA Equity Market Algorithmic Strategies"]
  C --> D["Computational Process<br>Model Theorem & Numerical Simulation"]
  D --> E["Outcome 1<br>Proof of Necessary Condition"]
  D --> F["Outcome 2<br>Novel Turnover Estimations"]
  D --> G["Outcome 3<br>Verified Estimation Preciseness"]