Turnover of investment portfolio via covariance matrix of returns

ArXiv ID: 2412.03305 “View on arXiv”

Authors: Unknown

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.

Keywords: Portfolio Turnover Estimation, Algorithmic Trading Strategies, Covariance Matrix of Returns, Turnover Modeling, Liquidity Management, Equities (USA Market)

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: 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.

  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"]