Tensor dynamic conditional correlation model: A new way to pursuit “Holy Grail of investing”

ArXiv ID: 2502.13461 “View on arXiv”

Authors: Unknown

Abstract

Style investing creates asset classes (or the so-called “styles”) with low correlations, aligning well with the principle of “Holy Grail of investing” in terms of portfolio selection. The returns of styles naturally form a tensor-valued time series, which requires new tools for studying the dynamics of the conditional correlation matrix to facilitate the aforementioned principle. Towards this goal, we introduce a new tensor dynamic conditional correlation (TDCC) model, which is based on two novel treatments: trace-normalization and dimension-normalization. These two normalizations adapt to the tensor nature of the data, and they are necessary except when the tensor data reduce to vector data. Moreover, we provide an easy-to-implement estimation procedure for the TDCC model, and examine its finite sample performance by simulations. Finally, we assess the usefulness of the TDCC model in international portfolio selection across ten global markets and in large portfolio selection for 1800 stocks from the Chinese stock market.

Keywords: Tensor Dynamic Conditional Correlation (TDCC), Style Investing, Portfolio Selection, Conditional Correlation Matrix, Time Series Analysis, General Financial Data / Equities

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail
  • Why: The paper introduces a novel tensor GARCH model with advanced multi-way conditional heteroskedasticity specifications and trace-normalization, requiring deep mathematical treatment. It is heavily implementation-focused, with simulations, a large-scale empirical application (1800 stocks), and clear portfolio selection backtests.
  flowchart TD
    A["Research Goal: Pursue "Holy Grail of investing"<br>via Style Investing & Correlation Dynamics"] --> B["Data Input: Tensor-Valued<br>Style Return Time Series"]
    B --> C["Methodology: TDCC Model<br>with Trace & Dimension Normalization"]
    C --> D["Computation: Estimation &<br>Simulation Validation"]
    D --> E["Application 1: International<br>Portfolio Selection (10 Markets)"]
    D --> F["Application 2: Large Portfolio<br>Selection (1800 Stocks)"]
    E --> G["Key Outcomes: Effective<br>Dynamic Correlation Modeling"]
    F --> G