Market-Based Portfolio Variance

ArXiv ID: 2504.07929 “View on arXiv”

Authors: Unknown

Abstract

The variance measures the portfolio risks the investors are taking. The investor, who holds his portfolio and doesn’t trade his shares, at the current time can use the time series of the market trades that were made during the averaging interval with the securities of his portfolio and assess the current return, variance, and hence the current risks of his portfolio. We show how the time series of trades with the securities of the portfolio determine the time series of trades with the portfolio as a single market security. The time series of trades with the portfolio determine its return and variance in the same form as the time series of trades with securities determine their returns and variances. The description of any portfolio and any single market security is equal. The time series of the portfolio trades define the decomposition of the portfolio variance by its securities, which is a quadratic form in the variables of relative amounts invested into securities. Its coefficients themselves are quadratic forms in the variables of relative numbers of shares of its securities. If one assumes that the volumes of all consecutive deals with each security are constant, the decomposition of the portfolio variance coincides with Markowitz’s (1952) variance, which ignores the effects of random trade volumes. The use of the variance that accounts for the randomness of trade volumes could help majors like BlackRock, JP Morgan, and the U.S. Fed to adjust their models, like Aladdin and Azimov, to the reality of random markets.

Keywords: Portfolio Variance, Trade Volume Randomness, Time Series Analysis, Markowitz Optimization, Risk Decomposition

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced mathematical derivations, including quadratic forms and decomposition of portfolio variance based on time series of trades, indicating high mathematical density. However, it lacks empirical validation, backtests, or implementation details, relying solely on theoretical framework without data-driven evidence.

  flowchart TD
    A["Research Goal: Model Portfolio Variance <br> Accounting for Random Trade Volumes"] --> B["Data Input: <br> Time Series of Market Trades <br> (Securities & Portfolio)"]
    B --> C["Methodology: <br> Treat Portfolio as Single Market Security"]
    C --> D["Computation: <br> Calculate Return & Variance <br> Using Trade Time Series"]
    D --> E["Decomposition: <br> Quadratic Form in <br> Relative Investments"]
    E --> F["Finding 1: <br> Standard Markowitz Variance <br> (when trade volumes are constant)"]
    E --> G["Finding 2: <br> New Variance Metric <br> (accounts for random trade volumes)"]