Research on Optimal Portfolio Based on Multifractal Features

ArXiv ID: 2411.15712 “View on arXiv”

Authors: Unknown

Abstract

Providing optimal portfolio selection for investors has always been one of the hot topics in academia. In view of the traditional portfolio model could not adapt to the actual capital market and can provide erroneous results. This paper innovatively constructs a mean-detrended cross-correlation portfolio model (M-DCCP model), This model is designed to embed detrended cross-correlation between different simultaneously recorded time series in the presence of nonstationary into the reward-risk criterion. We illustrate the model’s effectiveness by selected five composite indexes (SSE 50, CSI 300, SSE 500, CSI 1000 and CSI 2000) in China A-share market. The empirical results show that compared with traditional mean-variance portfolio model (M-VP model), the M-DCCP model is more conducive for investors to construct optimal portfolios under the different fluctuation exponent preference and time scales preference, so as to improve portfolio’s performance.

Keywords: Mean-detrended cross-correlation, Portfolio optimization, Nonstationary time series, Detrended cross-correlation analysis, Risk measure, Equities

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail
  • Why: The paper is mathematically dense with advanced multifractal techniques, DCCA, and derivations, earning a high math score. It has a clear empirical test using real Chinese market data (five indices) and compares results to a benchmark, giving it solid but not exhaustive empirical rigor.
  flowchart TD
    A["Research Goal: Construct optimal portfolio<br>adapting to nonstationary markets"] --> B["Data: Five China A-share indexes<br>SSE 50, CSI 300, SSE 500, CSI 1000, CSI 2000"]
    B --> C["Methodology: M-DCCP Model<br>Embedding Detrended Cross-Correlation"]
    C --> D["Methodology: Mean-Variance Model<br>Traditional Benchmark"]
    C --> E{"Computational Process"}
    D --> E
    E --> F["Evaluation: Risk/Return analysis<br>across time scales & fluctuation exponents"]
    F --> G["Outcome: M-DCCP outperforms<br>traditional models for investors"]
    G --> H["Conclusion: Improved portfolio<br>performance in nonstationary markets"]