Dynamic Rolling Risk–Return‑Volume Insight: Ten Highly Liquid S&P 500 Constituents
Introduction
The chart visualizes rolling risk–return–volume dynamics for ten highly liquid S&P 500 constituents — AAPL, AMZN, AVGO, GOOG, GOOGL, META, MSFT, NVDA, PLTR, and TSLA — selected, over the April 2025–March 2026 period, by ranking all index members on the Amihud (2002) illiquidity ratio — a widely used measure of price impact per unit of trading volume — and retaining the ten most liquid stocks. Intraday OHLCV data for that period were sourced from EODHD (eodhd.com) at 5‑minute resolution and then aggregated to the 15‑, 30‑, and 60‑minute frequencies. These data are used in their entirety in the author’s paper on cross‑sectional topological anomaly scores and intraday return predictability in the S&P 500 (Ozimek, 2026).
Figure 1. Dynamic rolling risk–return‑volume bubble chart for ten highly liquid US equities (April 2025–March 2026)
Note: Returns are per-bar percentage changes of the closing price. Standard deviation is computed from those returns within the rolling window. Volume is the integer number of shares traded per bar. Bubble diameter is proportional to the square root of mean volume inside the window, normalized to the global maximum across all bars for the chosen timeframe, so that sizes remain comparable across window positions. The Window length slider sets the number of bars the rolling window spans. The Window position slider moves the window forward and backward through the sample, shifting both axes and bubble sizes simultaneously; pressing ▶ animates this movement continuously, with Step controlling how many bars are skipped per frame and Interval controlling the pause between frames in milliseconds.
Source: Author’s own elaboration based on EODHD (eodhd.com) intraday OHLCV data.
Financial insight
Animating the window reveals how the risk–return profile of each stock evolves through time. During calm market periods the bubbles cluster in a narrow band of low standard deviation and modest positive returns; as the window enters a stress episode — such as a sharp macro shock or a volatility surge — bubbles scatter rightward, reflecting elevated intraday dispersion. Stocks that simultaneously shift upward and rightward are repricing quickly but still generating positive returns, while those drifting downward and rightward are absorbing losses under rising volatility. Bubble size captures trading intensity: swelling bubbles indicate that heavy volume accompanies the move, suggesting the repricing is broad‑based rather than a thin‑market artefact. Isolating a single stock allows one to trace its own risk–return path over the full sample, while comparing two stocks side by side exposes divergences in how they absorb the same market environment.
How to Trade That?
Watching the bubble cloud evolve raises a natural question: is there structure in the motion, or merely noise? What does the motion reveal — patterns, anomalies, trading intuitions? Whether these visual impressions survive rigorous statistical testing — and whether the anomaly score framework developed in the companion paper can formalize them — is precisely the question the interactive tool is designed to provoke. No trading rule is implied here; the chart is an invitation to look, to ask better questions, and to be sparked to dig deeper.
This topic is also discussed on LinkedIn.
References
Amihud, Y. (2002). Illiquidity and stock returns: Cross-section and time-series effects. Journal of Financial Markets, 5(1), 31–56.
EODHD. End of Day Historical Data. https://eodhd.com/
Ozimek, K. (2026). Cross-sectional topological anomaly scores and intraday return predictability in the S&P 500: A BallMapper, decoder-conditional VAE, and Function-on-Function regression approach. arXiv preprint arXiv:2606.08586 [q‑fin.ST]. https://doi.org/10.48550/arXiv.2606.08586
