Hierarchical Risk Parity with regime detection using Topological Data Analysis (TDA) Submission for the Itaú Quant Challenge 2025 — Top 4% (40/953)
Atlas is a long-only quantitative allocation framework that uses Topological Data Analysis and Machine Learning to navigate different market regimes. Unlike traditional models based solely on linear correlations — which tend to break down exactly when you need them most, during crises — Atlas uses Persistent Homology to detect structural market turbulence and TDA/Mapper to cluster assets by topological behavior. From there, a Meta-Blend (ML ensemble) dynamically determines the optimal factor weights (Momentum, Quality, Carry) for the current regime, and Hierarchical Risk Parity (HRP) builds the final portfolio.
Period: 09/14/2017 to 10/06/2025 (Ibovespa Universe) Validation: Walk-Forward Analysis (504d Train / 126d Test)
Atlas consistently outperformed both the benchmark (Ibovespa) and the CDI risk-free rate, delivering strong risk-adjusted returns with downside protection via an automated kill-switch.
Equity Curves (Walk-Forward vs. Ibovespa):
Key Performance Indicators (KPIs):
| Metric | Atlas (Walk-Forward) | Ibovespa |
|---|---|---|
| CAGR | 0.316 | 0.209 |
| Sharpe | 1.181 | 0.549 |
| Sortino | 1.903 | 0.813 |
| Vol | 0.166 | 0.234 |
| MaxDD | -0.199 | -0.254 |
| AvgTimeUnderWater | 20.400 | 30.800 |
| MaxTimeUnderWater | 270.000 | 500.000 |
| Calmar | 1.590 | 0.821 |
| HitRate | 0.542 | 0.515 |
| Turnover | 0.017 | NaN |
KPIs per out-of-sample (OOS) window from the walk-forward analysis:
| Metric | WF 01 | WF 02 | WF 03 | WF 04 | WF 05 | WF 06 | WF 07 | WF 08 | WF 09 |
|---|---|---|---|---|---|---|---|---|---|
| CAGR | 1.284 | 0.059 | -0.031 | 0.553 | 0.221 | 0.413 | 0.187 | 0.187 | 0.312 |
| Sharpe | 5.080 | 0.254 | -0.360 | 1.698 | 0.706 | 1.302 | 0.522 | 0.547 | 0.882 |
| Sortino | 11.760 | 0.401 | -0.448 | 5.643 | 1.307 | 2.051 | 0.836 | 0.818 | 1.281 |
| Vol | 0.161 | 0.176 | 0.167 | 0.197 | 0.110 | 0.184 | 0.147 | 0.158 | 0.173 |
| MaxDD | -0.039 | -0.099 | -0.132 | -0.033 | -0.053 | -0.097 | -0.058 | -0.069 | -0.094 |
| AvgTimeUnderWater | 6.820 | 19.000 | 0.000 | 14.750 | 9.200 | 21.400 | 12.560 | 6.860 | 11.670 |
| MaxTimeUnderWater | 29.000 | 37.000 | 0.000 | 45.000 | 23.000 | 57.000 | 36.000 | 19.000 | 60.000 |
| Calmar | 32.776 | 0.591 | -0.234 | 16.515 | 4.126 | 4.275 | 3.222 | 2.693 | 3.310 |
| HitRate | 0.691 | 0.540 | 0.489 | 0.519 | 0.516 | 0.553 | 0.517 | 0.532 | 0.526 |
| Turnover | 0.022 | 0.021 | 0.029 | 0.016 | 0.008 | 0.011 | 0.017 | 0.007 | 0.017 |
Walk-forward outperformance vs. Ibovespa (cumulative excess return):
Relative KPIs (Atlas vs. Ibovespa):
| Metric | Atlas vs Ibovespa |
|---|---|
| Annualized Alpha | 0.158 |
| Beta | 0.269 |
| Excess Annual Return | 0.064 |
| Tracking Error | 0.231 |
| Information Ratio | 0.277 |
| Correlation | 0.377 |
Traditional quant models rely on linear correlations — but correlations converge to 1 during crises, precisely when diversification is needed most. Atlas addresses this with three core engines:
Instead of using simple volatility, Atlas measures the shape of the market's data cloud.
- How it works: Vietoris-Rips filtration tracks the persistence of topological "holes" in the market's return space.
- Practical effect: When the topological structure breaks — a signal of systemic stress — the algorithm automatically activates Risk-Off mode, reducing exposure before volatility spikes.
Assets are grouped not just by sector or correlation, but by topological behavior.
- The differentiator: The Mapper algorithm projects assets onto a graph, identifying which stocks are "peripheral" (idiosyncratic/safe) and which are "central" (systemic/risky).
- Application: The portfolio tilts toward peripheral assets during periods of uncertainty.
An ensemble model (Ridge/ElasticNet) that dynamically learns the optimal mix of factors (Momentum, Quality, Carry) for the current regime detected by the topology.
The project was built with software engineering rigor to be fully auditable and reproducible.
- Ingestion: Data loading and universe filtering (Liquidity/Hysteresis).
- TDA Engine: Computation of Persistence Landscapes and Mapper graphs.
- ML Layer: Meta-Blend training with Purged K-Fold Cross Validation.
- Portfolio Optimization: HRP guided by the topological structure.
- Risk Guards: Drawdown-based kill-switch and turnover control.
Environment managed via uv or pip. Requires Python 3.10+.
# 1. Setup
python -m venv .venv
source .venv/bin/activate # or .venv\Scripts\activate on Windows
pip install -e ".[dev]"
# 2. Run Full Backtest
python -m src.main --mode backtest --config configs/base.yaml
# 3. Generate PDF Report
python -m src.reports.build_pdf --config configs/base.yaml
Run the full pipeline from a script or notebook without the CLI:
from pathlib import Path
from src.backtest.engine import run_backtest
from dataio.config import load_config
from dataio.loaders import get_panel
cfg = load_config("configs/base.yaml")
panel = get_panel(cfg["dates"]["start"], cfg["dates"]["end"])
result = run_backtest(cfg, panel=panel)
print(result["kpis"])
equity_path = Path("reports") / "equity_curve_example.csv"
result["equity_curve"].to_csv(equity_path)
print(f"Equity curve saved to: {equity_path}")
You can also run everything via notebooks/full_pipeline.ipynb, which reproduces the official pipeline used to generate the reported results.
Visualization of the topological evolution (Mapper) over time:
.
├── configs/ # YAML files (model hyperparameters)
├── src/
│ ├── features/ # TDA (Mapper/PH) and feature engineering
│ ├── models/ # Meta-models (ElasticNet/Ridge)
│ ├── backtest/ # Execution engine and HRP
│ └── risk/ # Risk management and kill-switches
├── artifacts/ # Generated outputs (caches, saved models)
└── reports/ # PDFs, metric CSVs, and final charts
To ensure results are not due to overfitting or p-hacking:
- Deflated Sharpe P-Value: 11.6% — meaning 88.4% confidence that Sharpe > 0 is not noise.
- Sensitivity Analysis: Model maintains stable performance across a wide range of
target_vol(12–14%). - Realistic Costs: Simulation includes non-linear slippage and brokerage fees.
© 2025 Atlas Project.
Licensed under the MIT License. You are free to use, modify, and distribute this software with attribution. See LICENSE for the full text.
Interested in similar work — quantitative modeling, backtesting, or risk analysis? Feel free to reach out via LinkedIn or email.