Max Sharpe vs Risk Parity vs HRP
Three optimization methods. Same assets. Same data. Three different portfolios. This worked example shows how each method thinks about the problem differently and produces a distinct allocation from the same inputs.
The inputs
We use a 6-asset portfolio with J.P. Morgan 2026 LTCMA estimates: US Large Cap, International Developed, Emerging Markets, US Aggregate Bonds, Gold, and Bitcoin. All three methods receive the same expected returns, volatilities, and correlation matrix.
| Asset | Return | Volatility |
|---|---|---|
| US Large Cap | 7.90% | 14.80% |
| Intl Developed | 8.70% | 16.10% |
| Emerging Markets | 8.10% | 18.70% |
| US Agg Bonds | 4.60% | 5.70% |
| Gold | 5.50% | 16.00% |
| Bitcoin | 15.00% | 42.50% |
The results
| Asset | Max Sharpe | Risk Parity | HRP |
|---|---|---|---|
| US Large Cap | 15% | 12% | 18% |
| Intl Developed | 22% | 11% | 15% |
| Emerging Markets | 8% | 9% | 12% |
| US Agg Bonds | 30% | 55% | 38% |
| Gold | 7% | 10% | 11% |
| Bitcoin | 18% | 3% | 6% |
| Expected Return | 8.4% | 5.6% | 6.7% |
| Volatility | 13.1% | 6.2% | 8.5% |
| Sharpe Ratio | 0.40 | 0.40 | 0.42 |
Illustrative allocations using J.P. Morgan 2026 LTCMA. Actual optimizer output depends on constraint settings. Run the optimizer yourself for exact results.
How each method thinks
Maximum Sharpe Ratio
Chases the best risk-adjusted return. Loads up on high-return assets (Bitcoin at 18%, international equities at 22%) and uses bonds mainly as a volatility dampener. Produces the highest return but also the highest volatility. Sensitive to input assumptions: if Bitcoin's expected return drops from 15% to 10%, the allocation changes dramatically.
Risk Parity
Ignores expected returns entirely. Equalizes each asset's contribution to total risk. Because bonds are far less volatile than equities or Bitcoin, Risk Parity allocates 55% to bonds to make their risk contribution equal to the others. Bitcoin gets only 3% because its volatility is so high that even a small allocation contributes substantial risk. Lowest volatility of the three.
Hierarchical Risk Parity
Groups assets by how similarly they behave (equity cluster, safe haven cluster, alternatives cluster) and allocates within and across clusters. Produces a middle ground: more diversified than Max Sharpe, higher returning than Risk Parity. Most robust to changes in input assumptions because it avoids matrix inversion.
Which should you use?
- •You trust the return assumptions: Max Sharpe. It is mathematically optimal given the inputs.
- •You distrust return forecasts: Risk Parity. It uses only volatilities and correlations, which are more stable than return estimates.
- •You want robustness: HRP. Best when correlations are noisy or your asset universe is large.
- •You want conviction: Run all three and compare. If all three agree on an asset, that signal is strong.
Run all three methods on your portfolio
Switch between Max Sharpe, Min Variance, Risk Parity, HRP, and Black-Litterman in one click.
Open the optimizerFrequently asked questions
What is the difference between Max Sharpe and Risk Parity?
Maximum Sharpe Ratio finds the portfolio with the best risk-adjusted return using expected returns, volatilities, and correlations. Risk Parity ignores expected returns entirely and instead equalizes each asset's contribution to total portfolio risk. Max Sharpe concentrates in high-return assets; Risk Parity produces more balanced, often bond-heavy allocations.
What is Hierarchical Risk Parity (HRP)?
HRP is a machine learning-based portfolio optimization method that clusters assets by how similarly they behave, then allocates within and across clusters using inverse-variance weighting. Unlike traditional optimization, it does not require expected return estimates and avoids inverting the covariance matrix, making it more robust to estimation error.
Which optimization method is best?
There is no universally best method. Max Sharpe is optimal when you trust your return assumptions. Risk Parity is better when you distrust return forecasts and want balanced risk exposure. HRP is most robust when correlations are noisy or unstable. Many practitioners use multiple methods and compare the outputs.