Portfolio Weight Calculation: Risk Parity, HRP, Minimum Variance, and Maximum Diversification

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PortfolioWeights.mqh computes portfolio weights from the returns of its components, which can be symbols or the daily results of multiple Expert Advisors. It offers five classic long-only methods, a covariance calculation with Ledoit-Wolf shrinkage, and details the risk contribution of each component. This tool utilizes MQL5's matrix and vector types and requires no external DLLs.

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Usage

matrix returns(days, assets); // Period data in rows, asset data in columns // ... populate returns matrix ... matrix cov; double shrink = CPortfolioWeights::LedoitWolf(returns, cov); // or CPortfolioWeights::Covariance(returns, cov) int order[]; vector w = CPortfolioWeights::RiskParity(cov); // Weights sum to 1 vector h = CPortfolioWeights::HierarchicalRiskParity(cov, order); vector rc = CPortfolioWeights::RiskContributions(cov, w);

Methods

InverseVolatility
: Assigns weights inversely proportional to each component's volatility. RiskParity
: Achieves equal risk contribution, meaning each component contributes equally to the portfolio's variance. This method uses cyclical coordinate descent (Griveau-Billion, Richard, and Roncalli, 2013). HierarchicalRiskParity
: Components are ordered using a single-linkage tree based on the distance metric sqrt((1 - correlation) / 2). Weights are then allocated down this ordered list, inversely proportional to the variance of each sub-group. The 'order[]' array returns the tree's ordering (Lopez de Prado, 2016). MinimumVariance
: Aims to minimize the portfolio's overall variance, with an option to set a cap on individual component weights. MaximumDiversification
: Maximizes the ratio of weighted component volatilities to the overall portfolio volatility (Choueifaty and Coignard, 2008). LedoitWolf
: Calculates the sample covariance matrix, shrinking its correlations towards zero using the optimal intensity determined by Ledoit and Wolf (2004). This calculation is performed on returns scaled to unit variance. For datasets with few periods and many components, where sample correlations can be noisy, the shrunk covariance provides more stable weights. Both optimization methods are solved precisely using an active-set quadratic programming approach (handling bounds and a single equality constraint), rather than iterative search.

Example

The script PortfolioWeightsExample.mq5 demonstrates the functionality. It takes a list of symbols (or the first 8 from Market Watch), calculates their daily log returns over a specified number of days, and outputs the weights for each method along with its diversification ratio and the risk contributions for the risk parity mix (refer to picture 1).

Validation

On a dataset of 750 periods from 8 correlated series, the shrinkage intensity matched scikit-learn's LedoitWolf implementation. The hierarchical method's tree order aligned with scipy's single linkage, and its weights corresponded to a Python version using bisection within 1e-15 precision for risk parity contributions. The minimum variance (with and without caps) and maximum diversification weights were found to be within 2e-8 of scipy's SLSQP optimizer results.

Files

Place PortfolioWeights.mqh in the MQL5\Include\PortfolioWeights directory. Place PortfolioWeightsExample.mq5 in the MQL5\Scripts\PortfolioWeights directory.

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#property copyright "RobotFX"
#property version     "1.00"
#property script_show_inputs
#include <PortfolioWeights\PortfolioWeights.mqh>
input string InpSymbols = "";
input int    InpDays    = 500;
input bool   InpShrink  = true;
void OnStart()
  {
   string symbols[];

.......

• This tool is provided for educational and testing purposes only.
• Past performance does not guarantee future results.
• Trading involves substantial risk of loss. Use on a demo account first.
• Results may vary depending on market conditions, broker, and settings.
• We recommend thorough backtesting and forward testing before using with real funds.