building-risk-parity-portfolios

name	building-risk-parity-portfolios
description	Constructs risk parity allocation with equal risk contribution, leverage optimization, and asset class volatility targeting. Use when building risk parity, equalizing risk contribution, or designing leveraged balanced portfolios.
tags	["modeling","quantitative-capital-strategies","risk","portfolio"]
metadata	{"author":"casemark","practice_areas":["Quantitative Investing","Systematic Strategies","Factor Investing"],"document_types":["Model"],"skill_modes":["Modeling"]}

Building Risk Parity Portfolios

When To Use

• Constructing a multi-asset portfolio where each asset class contributes equally to total portfolio risk
• Designing leveraged balanced strategies (e.g., Bridgewater All Weather–style allocations)
• Rebalancing an existing risk parity book to reflect updated covariance estimates
• Comparing risk parity weights against market-cap or equal-weight benchmarks
• Building a volatility-targeted overlay that scales gross exposure to a constant risk budget

Inputs To Gather

• Asset universe: List of asset classes or instruments (e.g., equities, nominal bonds, TIPS, commodities, gold) with ticker-level mapping where applicable
• Return series: Total-return time series for each asset — minimum 10 years monthly, or 3 years daily; confirm frequency and currency [VERIFY]
• Covariance estimation method: Sample covariance, exponentially weighted (half-life), shrinkage (Ledoit-Wolf), or DCC-GARCH — confirm client preference
• Risk-free rate: Specify proxy (3-month T-bill, OIS, SOFR) and whether to subtract from returns before optimization [VERIFY]
• Target portfolio volatility: Annualized vol target for the levered portfolio (common range: 10–15%)
• Leverage constraints: Maximum gross exposure, borrowing cost assumption, margin/collateral rules [VERIFY]
• Rebalance frequency: Daily, weekly, monthly, or threshold-based (e.g., drift > 10% of target weight)
• Lookback window: Rolling window length for covariance estimation (e.g., 60-day, 252-day)

Workflow

1. Compute the covariance matrix

   • Calculate returns at the chosen frequency; annualize if needed (√252 for daily)
   • Apply the selected estimation method; if shrinkage, report shrinkage intensity
   • Validate: check that the matrix is positive semi-definite; flag near-singular conditions

2. Solve for risk parity weights

   • Define the objective: each asset's marginal risk contribution (MRC) equals 1/N of total portfolio volatility
   • MRC_i = w_i × (Σw)_i / σ_p — iterate until MRC_i ≈ MRC_j for all i, j
   • Use numerical optimization (e.g., sequential least squares or Newton's method on the risk-budget Lagrangian)
   • Confirm weights sum to 1.0 (unlevered) or to gross exposure target (levered)

3. Apply leverage scaling

   • Compute unlevered portfolio volatility σ_unlevered from the risk parity weights
   • Leverage multiplier = Target Vol / σ_unlevered
   • Adjusted weights = raw weights × leverage multiplier
   • Subtract borrowing cost from expected return: cost = (gross exposure − 1) × funding rate [VERIFY funding rate assumption]

4. Backtest and stress-test

   • Run rolling or expanding-window backtest; report annualized return, vol, Sharpe, max drawdown, and Calmar ratio
   • Conduct stress scenarios: 2008 GFC, 2013 taper tantrum, 2020 COVID, 2022 rates shock — report portfolio P&L under each
   • Compare against 60/40, equal-weight, and inverse-vol benchmarks

5. Sensitivity analysis

   • Vary lookback window (30d, 60d, 120d, 252d) — show weight stability and turnover impact
   • Vary covariance method — compare sample vs. shrinkage vs. EWMA weights
   • Shock individual asset vols by ±2σ and correlation matrix by ±0.10 — report weight and risk-contribution shifts

6. Document allocation model

   • Final weight table with risk contribution breakdown (absolute and percentage)
   • Gross and net exposure, leverage ratio, estimated borrowing cost drag
   • Rebalance rule specification and estimated annual turnover
   • All assumptions flagged explicitly; mark jurisdiction-dependent constraints with [VERIFY]

Output

Deliver a structured risk parity model package containing:

• Weight schedule: Asset-level weights, risk contributions, and leverage multiplier
• Covariance summary: Correlation heatmap, per-asset annualized vol, eigenvalue decomposition
• Backtest report: Equity curve, rolling Sharpe, drawdown chart, monthly return table
• Stress-test matrix: Scenario returns for the portfolio vs. benchmarks
• Sensitivity exhibits: Weight and turnover impact across parameter variations
• Methodology memo: Estimation method, optimization algorithm, rebalance logic, and all [VERIFY] items

Quality Checks

• Confirm each asset's percentage risk contribution is within ±0.5% of 1/N target after optimization convergence
• Verify portfolio vol matches the stated target (tolerance: ±25 bps annualized)
• Check that weights are non-negative (unless short selling is explicitly permitted) and sum correctly
• Validate that the covariance matrix has no negative eigenvalues
• Ensure backtest does not use future information (no look-ahead bias in rolling windows)
• Cross-check leverage multiplier against margin and regulatory constraints [VERIFY applicable margin rules]
• Confirm borrowing cost assumption reflects current market rates, not stale inputs