Portfolio diversification with varying investor abilities

ArXiv ID: 2311.06519 “View on arXiv”

Authors: Unknown

Abstract

We introduce new mathematical methods to study the optimal portfolio size of investment portfolios over time, considering investors with varying skill levels. First, we explore the benefit of portfolio diversification on an annual basis for poor, average and strong investors defined by the 10th, 50th and 90th percentiles of risk-adjusted returns, respectively. Second, we conduct a thorough regression experiment examining quantiles of risk-adjusted returns as a function of portfolio size across investor ability, testing for trends and curvature within these functions. Finally, we study the optimal portfolio size for poor, average and strong investors in a continuously temporal manner using more than 20 years of data. We show that strong investors should hold concentrated portfolios, poor investors should hold diversified portfolios; average investors have a less obvious distribution with the optimal number varying materially over time.

Keywords: portfolio diversification, quantile regression, investor skill, optimal portfolio size, risk-adjusted returns, Equities

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced statistical methods, quantile regression, and concepts from statistical mechanics to analyze optimal portfolio size, indicating high mathematical complexity. It demonstrates strong empirical rigor by using over 20 years of daily equity data, conducting thorough regression experiments, and providing specific, backtest-ready insights on portfolio optimization across varying investor skill levels.

  flowchart TD
    A["Research Question:<br>What is the optimal portfolio size<br>for investors with varying skill?"] --> B["Data Input:<br>20+ years of equity returns"]
    B --> C["Methodology Step 1:<br>Annual Diversification Analysis<br>(Poor/Average/Strong Investors)"]
    B --> D["Methodology Step 2:<br>Quantile Regression on Risk-Adjusted Returns<br>(vs. Portfolio Size)"]
    B --> E["Methodology Step 3:<br>Continuous Temporal Optimization"]
    C --> F["Computational Process:<br>Define investor ability by percentiles<br>(10th/50th/90th risk-adjusted returns)"]
    D --> F
    E --> F
    F --> G["Key Findings/Outcomes:<br>• Strong Investors: Concentrated Portfolios<br>• Poor Investors: Highly Diversified Portfolios<br>• Average Investors: Optimal size varies over time"]