Hierarchical Risk Parity
HRP by Marcos Lopez de Prado. Uses hierarchical clustering on correlation matrix to build a tree structure, then allocates weights recursively. Avoids covariance matrix inversion.
At a glance
What the backtest shows
- Beat buy-and-hold on 1 of 1 markets by annual return over 5 years.
- Had a smaller maximum drawdown than buy-and-hold on 0 of 1 markets.
- Best market by Sharpe ratio: HRP (Sharpe 0.95, CAGR 19.8%).
Equity curve
Score and risk profile
Each bar is a percentile against every strategy on the same market and window (100 = best).
How it held up in sell-offs (HRP)
| Period | Strategy | Buy & hold |
|---|---|---|
| Q4 2018 sell-off | -22.0% | -15.9% |
| COVID crash (Feb–Mar 2020) | -48.8% | -26.0% |
| 2022 bear market | +12.6% | -4.4% |
| Market above its 200-day average (annualized) · 69% | +7.3% | +6.9% |
| Market below its 200-day average (annualized) · 31% | -13.2% | +1.7% |
Sell-off dates follow the US stock market. Above/below the 200-day average uses the previous day's position, so there is no look-ahead.
Out-of-sample check (HRP)
| Check | Value |
|---|---|
| Chosen parameters on their 3-year training windows (average Sharpe) | 0.28 |
| Same parameters in the following 6 months, when traded (Sharpe) | 0.17 |
| Default parameters over the same months (Sharpe) | 0.45 |
| Parameter re-selections / changes | 28 / 7 |
| Parameter settings with a positive Sharpe (full history) | 3 of 3 |
| Sharpe across settings: worst / median / best | 0.15 / 0.20 / 0.37 |
Out-of-sample periods start on 2013-01-04. Training-window figures are flattered by picking the best of 3 settings; the out-of-sample figure is what the strategy actually earned. A large drop, or a result that depends on one setting, points to overfitting. How walk-forward testing works.
Results by market (5 years)
| Market | CAGR | Buy & hold CAGR | Sharpe | Max drawdown | Buy & hold max DD | Volatility | Arena Score |
|---|---|---|---|---|---|---|---|
| HRPHierarchical Risk Parity | 19.8% | 13.8% | 0.95 | -22.8% | -16.5% | 21.0% | 55 |
Strategy metrics use daily returns without trading costs. Buy-and-hold figures are for the same market and window. Rows are sorted by Sharpe ratio.
HRP across time windows
Rules
Entry
1. Cluster assets by correlation distance 2. Quasi-diagonalize covariance matrix 3. Recursive bisection for weights
Exit
Monthly rebalance
Indicators
Correlation matrix Hierarchical clustering
Inputs
Lookback = 60 Linkage = single
Risk
No matrix inversion needed
Strategy evidence
- HRP · Inspect evidence 2026-11-10
Only available, validated bundles appear below. Missing evidence is not a passing validation result.
Evidence coverage
1 / 1 declared strategy–market pairs validated
Notes
- Marcos Lopez de Prado (2016)
- More stable than mean-variance optimization
- Uses inverse variance at leaf level
Related strategies
Embed this score
Add the live badge to a blog post, README or forum signature. It updates with the daily data.
<a href="https://quantarenas.com/strategy/port-05-hierarchical-risk-parity/"><img src="https://quantarenas.com/badge/port-05-hierarchical-risk-parity.svg" alt="Hierarchical Risk Parity Arena Score on Quant Arena" height="20"></a>
[](https://quantarenas.com/strategy/port-05-hierarchical-risk-parity/)
Backtests are historical simulations on daily data and do not include commissions or slippage. They do not guarantee future results and are not investment advice. See the methodology for how every strategy is tested.