Paper: arXiv 2605.02326

Authors: Yangzhou Chen, Shuaida He, Xin Chen

Abstract

Large-scale portfolio choice is highly sensitive to estimation error, making the preliminary asset selection essential in empirical implementation. Existing selection rules typically rely on scalar returns or low dimensional high frequency summaries, and thus discard intraday risk dynamics that may be relevant for risk adjusted allocation. We propose Metric Dependence Screening (MDS), an asset selection procedure that incorporates high frequency information as object valued data. Each asset day observation is represented as a point-curve object combining daily return with an intraday risk state curve, equipped with a weighted product metric that preserves both reward information and within day risk dynamics. MDS ranks assets by a Fréchet variation based dependence score, measuring how much a risk adjusted target explains the metric dispersion of the asset representations. This yields a simple two stage portfolio procedure: MDS first reduces the investable universe, and standard mean-variance or minimum variance allocation is then applied. We develop a target slicing estimator and establish concentration, sure selection, and rank consistency guarantees under $α$-mixing time series dependence and ultrahigh dimensionality. Simulations show that MDS performs well across both Euclidean and non-Euclidean settings. Using high frequency data for $2938$ Chinese A-share stocks from July 2023 to December 2025, we demonstrate that MDS improves out of sample portfolio performance over return based and scalar dependence based benchmarks, highlighting the value of preserving intraday risk dynamics.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10 (capped from 8.0: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper combines sophisticated Fréchet geometry and functional data analysis with rigorous asymptotic theory, while simultaneously conducting a large-scale empirical test on nearly 3000 Chinese A-share stocks.

Research Flowchart

  flowchart TD
    A[<b>Goal:</b> Improve large-scale portfolio choice via asset selection] --> B(<b>Data:</b> Daily returns & Intraday high-frequency curves)
    B --> C[<b>Method:</b> Metric Dependence Screening - MDS]
    C --> D{<b>Process:</b> Apply Fréchet variation based score}
    D --> E[<b>Reduction:</b> Screen assets to subset]
    E --> F[<b>Allocation:</b> Mean-Variance/Min-Variance optimization]
    F --> G[<b>Outcomes:</b> Superior empirical performance & theoretical guarantees]

Cited References (62)

  1. Fréchet Regression with Mondrian Forests: Finite-Sample Guarantees and Ensemble Benefits (2026)
  2. LaTeX: A Document Preparation System (1994)
  3. Out of sample forecasts of quadratic variation (2008)
  4. Intraday periodicity and volatility persistence in financial markets (1997)
  5. The distribution of realized stock return volatility (2001)
  6. Modeling and forecasting realized volatility (2003)
  7. Econometric analysis of realized volatility and its use in estimating stochastic volatility models (2002)
  8. Power and bipower variation with stochastic volatility and jumps (2004)
and 54 more
  1. On the sensitivity of mean-variance-efficient portfolios to changes in asset means: some analytical and computational results (1991)
  2. The sampling error in estimates of mean-variance efficient portfolio weights (1999)
  3. Single index Fr 'e chet regression (2023)
  4. Generalized autoregressive conditional heteroskedasticity (1986)
  5. Intraday periodicity, long memory volatility, and macroeconomic announcement effects in the US Treasury bond market (2000)
  6. Strategic asset allocation: portfolio choice for long-term investors (2002)
  7. Sure explained variability and independence screening (2017)
  8. The effect of errors in means, variances, and covariances on optimal portfolio choice (1993)
  9. Empirical properties of asset returns: stylized facts and statistical issues (2001)
  10. Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? (2009)
  11. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation (1982)
  12. Sure independence screening for ultrahigh dimensional feature space (2008)
  13. A selective overview of variable selection in high dimensional feature space (2010)
  14. Sure independence screening in generalized linear models with NP-dimensionality (2010)
  15. Vast portfolio selection with gross-exposure constraints (2012)
  16. Sure independence screening (2018)
  17. Ultrahigh dimensional feature selection: beyond the linear model (2009)
  18. The economic value of volatility timing (2001)
  19. An empirical Bayes approach to efficient portfolio selection (1986)
  20. Portfolio selection with parameter and model uncertainty: A multi-prior approach (2007)
  21. When will mean-variance efficient portfolios be well diversified? (1992)
  22. Measuring statistical dependence with Hilbert-Schmidt norms (2005)
  23. A kernel statistical test of independence (2007)
  24. Using generalized correlation to effect variable selection in very high dimensional problems (2009)
  25. Quantile-adaptive model-free variable screening for high-dimensional heterogeneous data (2013)
  26. The Fr 'e chet correlation coefficient for heterogeneous random objects (2026)
  27. Risk reduction in large portfolios: Why imposing the wrong constraints helps (2003)
  28. On distance covariance in metric and Hilbert spaces (2019) — link
  29. Estimation for Markowitz efficient portfolios (1980)
  30. Bayes-Stein estimation for portfolio analysis (1986)
  31. Optimal portfolio choice with parameter uncertainty (2007)
  32. Honey, I Shrunk the Sample Covariance Matrix (2004)
  33. Improved estimation of the covariance matrix of stock returns with an application to portfolio selection (2003)
  34. Riemannian geometry of symmetric positive definite matrices via Cholesky decomposition (2019)
  35. Feature screening via distance correlation learning (2012)
  36. Distance covariance in metric spaces (2013)
  37. The Kolmogorov filter for variable screening in high-dimensional binary classification (2013)
  38. PORTFOLIO SELECTION (1952)
  39. Portfolio selection: efficient diversification of investments (2008)
  40. Measuring volatility with the realized range (2007)
  41. The Markowitz optimization enigma: Is ‘optimized’optimal? (1989)
  42. Ball covariance: A generic measure of dependence in banach space (2020)
  43. Fr 'e chet regression for random objects with Euclidean predictors (2019)
  44. A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics (2005)
  45. Capital asset prices: A theory of market equilibrium under conditions of risk (1964)
  46. Mutual fund performance (1966)
  47. Measuring and testing dependence by correlation of distances (2007)
  48. Brownian distance covariance (2009)
  49. Forward regression for ultra-high dimensional variable screening (2009)
  50. Asset selection based on high frequency Sharpe ratio (2022)
  51. Fr 'e chet sufficient dimension reduction for random objects (2022)
  52. A tale of two time scales: Determining integrated volatility with noisy high-frequency data (2005)
  53. Dimension reduction for Fr 'e chet regression (2024)
  54. Model-free feature screening for ultrahigh-dimensional data (2011)

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