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Large-Scale Asset Selection via Metric Dependence with Enriched High Frequency Information

This paper proposes Metric Dependence Screening (MDS), a novel asset selection procedure that leverages high-frequency intraday risk dynamics represented as point-curve objects to improve large-scale portfolio performance by effectively reducing estimation error and enhancing out-of-sample returns compared to traditional scalar-based methods.

Original authors: Yangzhou Chen, Shuaida He, Xin Chen

Published 2026-05-05

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CC BY 4.0

Original authors: Yangzhou Chen, Shuaida He, Xin Chen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a chef trying to create the perfect soup. You have a pantry with thousands of ingredients (stocks), but you only have a small pot (your investment budget). If you try to mix everything at once, the flavors clash, and the soup becomes a disaster. This is the problem of large-scale portfolio selection: when you have too many choices, it's easy to make mistakes because you can't perfectly predict which ingredients will taste good together.

Most chefs (investors) currently look at a simple summary of each ingredient: "How much did this carrot cost yesterday?" or "Did it grow fast?" They ignore the texture, the color changes during cooking, or how the flavor evolved minute-by-minute.

This paper introduces a new way to choose ingredients called Metric Dependence Screening (MDS). Here is how it works, broken down into simple concepts:

1. The Old Way vs. The New Way

The Old Way (Scalar Summaries): Traditional methods look at an asset like a stock as a single number, like its daily return. It's like judging a movie only by its final rating. You miss the plot twists, the character development, and the pacing.
The New Way (Point-Curve Objects): The authors suggest treating each stock not as a single number, but as a story.
- The "Point": The daily return (the final score).
- The "Curve": The intraday risk (how the price moved during the day). Did it spike wildly at 10 AM and settle down? Did it drift slowly?
- The Analogy: Instead of just knowing a runner finished a race in 10 seconds, MDS looks at their entire race path: where they sprinted, where they stumbled, and how they recovered. This "curve" captures the intraday risk dynamics that a simple number misses.

2. The "Metric" (The Ruler)

To compare these complex "stories" (point-curve objects), the authors invented a special ruler called a weighted product metric.

Imagine you are comparing two runners. You care about their finish time (reward) and how smooth their run was (risk).
This ruler measures the distance between two stocks by looking at both their daily returns and the shape of their intraday price curves simultaneously. It ensures you don't ignore the "shape" of the risk just because you are looking at the "size" of the reward.

3. The Screening Process (The Taste Test)

The goal is to pick the best ingredients for a "risk-adjusted" soup.

The Target: The authors create a "Target Series" based on a high-frequency Sharpe ratio (a measure of how much reward you get for the risk taken). Think of this as the "perfect flavor profile" you are aiming for.
The Score (Fréchet Variation): MDS asks: "If I know the flavor profile of my target soup, how much does that help me predict the story of this specific ingredient?"
- If knowing the target helps you understand the ingredient's story very well, that ingredient gets a high score.
- If the ingredient's story is random noise and the target tells you nothing about it, it gets a low score.
The Result: The method ranks all 2,938 stocks and picks the top ones (e.g., the top 60). This shrinks the massive pantry down to a manageable list of high-quality candidates.

4. The Two-Stage Kitchen

Once the top ingredients are selected, the paper suggests a simple two-step cooking process:

Stage 1 (Screening): Use MDS to filter the 2,938 stocks down to a small, high-quality group (e.g., 60 stocks).
Stage 2 (Cooking): Use standard, proven recipes (like Mean-Variance optimization) to mix these 60 stocks into a portfolio.

Why this works: By filtering out the "bad" or "noisy" ingredients first, the second stage doesn't have to guess as much. It reduces the chance of the chef making a mistake due to too many confusing options.

5. What the Data Shows

The authors tested this on 2,938 Chinese A-share stocks using 5-minute data from July 2023 to December 2025.

The Result: Portfolios built using MDS made more money and had better risk-adjusted returns (higher Sharpe ratios) than portfolios built using traditional methods (which only looked at daily returns or simple summaries).
The Key Takeaway: By preserving the "shape" of the intraday risk (the curve) instead of throwing it away, the method found better ingredients that performed more consistently in the real world.

Summary

Think of MDS as a smart filter that doesn't just ask "How much did you make today?" but also asks "How did you behave while making it?" By listening to the full story of the stock's daily movement, it builds a better, more stable portfolio than methods that only listen to the headline.

Technical Summary: Large-Scale Asset Selection via Metric Dependence with Enriched High Frequency Information

1. Problem Statement

Large-scale portfolio construction is inherently sensitive to estimation errors, particularly when the number of assets ( $p$ ) is large relative to the sample size ( $n$ ). While two-stage procedures (screening followed by optimization) are standard to mitigate this, existing asset selection rules typically rely on scalar returns or low-dimensional summaries of high-frequency data (e.g., daily returns, realized volatility).

The authors argue that reducing intraday price paths to scalar summaries discards valuable "intraday risk dynamics," such as the timing and concentration of volatility bursts. When assets have similar daily returns but divergent intraday risk profiles, scalar-based screening may fail to distinguish them, leading to suboptimal candidate sets for the second-stage optimizer. The core problem is how to incorporate high-frequency, object-valued intraday information into the asset screening process without aggressive dimensionality reduction that loses shape information.

2. Methodology: Metric Dependence Screening (MDS)

The paper proposes Metric Dependence Screening (MDS), a two-stage procedure that treats high-frequency asset information as random objects in a metric space rather than Euclidean vectors.

A. Asset Representation (Point-Curve Objects)
Instead of using a scalar return, each asset $i$ on day $t$ is represented as a point-curve object $X_{i,t} = (R_{i,t}, v_{i,t}) \in \mathcal{X}$ , where:

$R_{i,t}$ is the daily return.
$v_{i,t}$ is a smoothed curve representing the intraday absolute log-price-change magnitude over the trading day.
The space $\mathcal{X}$ is equipped with a weighted product metric:
$d_{\mathcal{X}}(x, x')^2 = (r - r')^2 + w \|v - v'\|_{L^2}^2$
This metric preserves both reward information (the point component) and intraday risk dynamics (the curve component).

B. Target Variable
A risk-adjusted target series $Y_t$ is constructed based on high-frequency Sharpe ratios. Stocks are ranked by their daily high-frequency Sharpe ratio, the top 10% are selected, and a value-weighted return of this subset forms $Y_t$ . This aligns the screening objective with risk-adjusted portfolio allocation rather than raw return prediction.

C. The Screening Score
MDS ranks assets using a Fréchet variation-based dependence score.

Population Definition: The score $\rho$ measures the proportion of the metric dispersion of $X$ explained by the target $Y$ . It is defined as:
$\rho = 1 - \frac{E[V(Y)]}{V_F}$
where $V_F$ is the global Fréchet variance of $X$ , and $V(Y)$ is the conditional residual variation given $Y$ . A higher $\rho$ indicates that the risk-adjusted target explains more of the asset's metric dispersion.
Estimation: Since direct nonparametric estimation of conditional Fréchet means in metric spaces is difficult, the authors propose a target slicing estimator. The range of $Y$ is partitioned into cells; within each cell, empirical Fréchet means and variances are computed. The final score is a plug-in estimator of the explained variation ratio.

D. Two-Stage Pipeline

Stage 1: Rank all $p$ assets by their estimated MDS scores and select a reduced subset (e.g., top $d$ assets).
Stage 2: Apply standard mean-variance or minimum variance optimization on the selected subset.

3. Theoretical Contributions

The paper establishes rigorous theoretical guarantees for MDS under $\alpha$ -mixing time series dependence and ultrahigh dimensionality ( $p \gg n$ ).

Concentration: The authors derive exponential tail bounds for the deviation of the estimated score from the population score, accounting for the bias introduced by target slicing and the estimation error of Fréchet means in metric spaces.
Sure Screening: Under a minimal signal strength condition, the method guarantees that all truly relevant assets are included in the screened set with probability approaching one.
Rank Consistency: The empirical ranking asymptotically preserves the population ordering between active (relevant) and inactive (irrelevant) assets, ensuring that the top- $d$ selection rule is consistent.

4. Empirical Results

The authors evaluate MDS using 5-minute intraday data for 2,938 Chinese A-share stocks from July 2023 to December 2025.

Benchmarks: MDS is compared against:
- D-SEVIS: A dependence screening method based on scalar summaries (Wang et al., 2022).
- MTM: A momentum-based ranking strategy.
Performance: Across various weighting schemes (Equal Weight, Score-Squared, Global Optimization, and Shrinkage Global Optimization) and selection sizes ( $d=30, 60, 90$ $d = 30, 60, 90$ ), MDS consistently outperforms the benchmarks.
- Returns: MDS portfolios achieved higher accumulated net values (e.g., 1.90 vs. 1.22 for D-SEVIS under the best configuration).
- Risk-Adjusted Returns: MDS yielded significantly higher Sharpe ratios (exceeding 1.0 in optimal settings) compared to D-SEVIS and negative Sharpe ratios for MTM.
- Drawdowns: MDS maintained comparable or lower maximum drawdowns than the benchmarks, indicating that the performance gains were not driven by excessive downside risk.
Simulations: Monte Carlo experiments in both Euclidean and non-Euclidean (Wasserstein space) settings confirmed that MDS remains effective under serial dependence and ultrahigh dimensionality, particularly excelling in non-linear and non-Euclidean scenarios where traditional scalar methods struggle.

5. Significance and Claims

The paper claims that MDS offers a unified framework for asset selection that bridges the gap between complex, object-valued high-frequency data and conventional portfolio construction.

Conceptual Shift: It moves beyond scalarization, treating intraday paths as functional objects to preserve "within-day shape information" (e.g., volatility bursts) that is often lost in standard summaries.
Methodological Innovation: It adapts Fréchet-based dependence measures to the screening context, providing a metric-space alternative to linear correlation or distance covariance that is specifically tailored for risk-adjusted allocation.
Practical Value: The empirical results demonstrate that preserving intraday risk dynamics in the screening stage leads to tangible, economically meaningful improvements in out-of-sample portfolio performance, validating the hypothesis that intraday risk states contain predictive power for risk-adjusted returns.

The authors conclude that while the framework is currently applied to intraday absolute log-price changes, it is generalizable to other high-frequency risk signatures and offers a robust approach for large-scale asset selection in modern, data-rich financial markets.