Longitudinal review of portfolios with minimum variance approach before during and after the pandemic

ArXiv ID: 2507.15111 “View on arXiv”

Authors: Genjis A. Ossa, Luis H. Restrepo

Abstract

This study investigates the impact of the pandemic on the most traded stocks in the Colombian stock market for the date of January 17, 2024. Based on the daily data of the most traded companies in Colombia for said date and covering a period general from 2015 to 2023, in a summarized way our analysis reveals that in the period 2015-2019, the return reached 5.70%, with a relatively low risk of 18.45%. However, in the following period 2016 -2020, although the yield decreased to 5.40%, the risk experienced a significant increase, reaching 24.64%. The beta also showed variations, being lowest in 2015-2019 with 0.61 and increasing to 1.02 in 2016-2020. The capital market line (LMC) in the constructed portfolios has a downward trend, indicating that the portfolio offers an expected rate of return lower than the risk-free rate. This finding is supported by the Sharpe index, which shows negative values throughout the periods studied.

Keywords: Colombian Stock Market, Pandemic Impact Analysis, Risk-Return Trade-off, Beta Analysis, Sharpe Index

Complexity vs Empirical Score

• Math Complexity: 2.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Philosophers
• Why: The paper uses basic statistical formulas (mean, standard deviation, beta) and standard financial theory (CAPM, Modern Portfolio Theory) without advanced derivations. It applies these to a limited dataset (Colombian stocks, 2015-2023) with descriptive results but no code, backtests, or implementation details.

  flowchart TD
    A["Research Goal:<br>Analyze Pandemic Impact on<br>Colombian Stock Portfolios"] --> B["Data Selection<br>Most Traded Stocks 2015-2023"]
    B --> C["Methodology:<br>Minimum Variance Portfolio Optimization"]
    C --> D{"Computational Phases"}
    D --> E["Pre-Pandemic 2015-2019"]
    D --> F["Pandemic 2016-2020"]
    E --> G["Returns: 5.70%<br>Risk: 18.45%<br>Beta: 0.61<br>Sharpe: Negative"]
    F --> H["Returns: 5.40%<br>Risk: 24.64%<br>Beta: 1.02<br>Sharpe: Negative"]
    G & H --> I["Outcome:<br>CML Downward Trend<br>Portfolio underperforms<br>risk-free rate"]