# Hierarchical Risk Parity (HRP) Optimization

Hierarchical Risk Parity (HRP) is a new portfolio optimization method that incorporates elements of graph theory and machine learning algorithms. Unlike traditional portfolio optimization techniques, HRP focuses on grouping similar assets together based on their underlying characteristics and relationships with the primary goal to create a diversified portfolio that is less sensitive to market fluctuations. By intelligently weighting groups of assets and distributing risk evenly among them, HRP seeks to create a more robust investment portfolio. The HRP method offers advantages over traditional methods like Markowitz's Critical Line Algorithm by being less sensitive to market volatility and less dependent on precise estimates of asset returns.

Mean-Variance Optimization (MVO)

This foundational model of portfolio theory balances risk and return, aiming for the highest expected return for a given risk level using historical data. However, its reliance on statistical estimates can lead to over-concentration in certain assets.

Risk Parity

Instead of focusing on capital allocation like MVO, this model equally distributes risk across all assets or asset classes in a portfolio. It results in more diversified portfolios and is less sensitive to market changes compared to MVO.

Hierarchical Risk Parity (HRP)

Combining aspects of MVO and risk parity, HRP uses a hierarchical clustering algorithm to allocate risk within asset clusters. This approach leads to enhanced diversification and is effective in managing market instabilities.

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## Optimization settings

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Position Weight Constraints

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## Optimal Asset Allocation

## Portfolio Performance

## Allocation Over Time

## Portfolio Drawdowns

## Portfolio Volatility

## Asset Correlations Table

## Risk Parity Portfolios Advantages

Risk parity portfolios aim to allocate risk equally across various asset classes, rather than allocating capital based on expected returns. This approach offers several advantages:

- Diversification: Risk parity encourages true diversification by spreading risk across different asset classes, rather than concentrating it in one or two high-performing sectors.
- Resilience to Market Conditions: Because risk is more evenly distributed, these portfolios tend to be more resilient in various market conditions, including downturns.
- Reduced Volatility: The focus on risk allocation rather than return allocation often results in reduced portfolio volatility, which can be particularly beneficial during turbulent market conditions.
- Predictable Risk Profiles: The risk exposure of each asset class in a risk parity portfolio is easier to predict and manage, making the portfolio more robust over time.

## Performance and Risks

Risk parity portfolios often exhibit more consistent performance compared to portfolios that focus solely on maximizing returns, especially in volatile markets.

- Lower Tail Risk: The strategy tends to minimize the impact of severe losses from any single asset class, thus reducing the portfolio's tail risk.
- Lower Return Potential: On the flip side, by being risk-averse, risk parity portfolios may miss out on higher returns from riskier assets, especially in bull markets.
- Leverage: To achieve equal risk contribution from low-risk assets like bonds, risk parity portfolios often require the use of leverage, which can introduce its own set of risks.

Overall, risk parity portfolios offer a balanced approach that focuses on risk distribution, which can lead to more stable and resilient performance, albeit often at the expense of higher returns.