Risk Parity Construction AI Prompt

Construct and analyze a risk parity portfolio from this asset universe.

Assets: {{assets}}
Covariance matrix: {{covariance}}
Target volatility: {{target_vol}} (e.g. 10% annualized)

1. Risk contribution framework:
   Marginal risk contribution (MRC): MRC_i = (Σw)_i = ∂σ_p/∂w_i
   Total risk contribution (TRC): TRC_i = w_i × MRC_i
   Portfolio variance: σ²_p = w'Σw = Σ_i TRC_i
   Risk contribution percentage: RC%_i = TRC_i / σ²_p

   Risk parity condition: RC%_i = 1/N for all assets i

2. Numerical solution:
   Risk parity has no closed-form solution for N > 2 assets.
   Use gradient-based optimization:
   min Σ_i Σ_j (TRC_i - TRC_j)² subject to w'1 = 1, w ≥ 0

   Or alternatively, use Maillard et al. (2010) iterative algorithm:
   w_i ← w_i × σ_p / (N × MRC_i) → iterate until convergence

3. Risk parity portfolio analysis:
   - Report: asset weights, marginal risk contributions, percentage risk contributions
   - Verify: risk contributions are approximately equal across all assets
   - Compare weights to: equal-weight, min-variance, and 60/40 benchmark

4. Volatility targeting:
   - Scale the risk parity weights by: k = target_vol / σ_rp
   - This may require leverage if σ_rp < target_vol (common with bonds in the portfolio)
   - Report: leverage ratio, cost of leverage assumed (financing rate)

5. Sensitivity analysis:
   - How do weights change if equity volatility doubles? (Bonds get more weight)
   - How do weights change if bond-equity correlation goes from -0.3 to +0.3?
   - Risk parity is most sensitive to: changes in relative volatilities and correlation regime changes

6. Historical performance analysis:
   - Backtest the risk parity portfolio with monthly rebalancing
   - Compare to: equal-weight, 60/40, min-variance
   - Report: Sharpe ratio, Calmar ratio, max drawdown, monthly turnover
   - Notable: risk parity struggled in 2022 when bonds and equities both sold off simultaneously (positive correlation regime)

7. Limitations:
   - Risk parity is a risk-based, not return-based, allocation
   - It is implicitly long duration (bonds dominate in unlevered form)
   - Correlation instability undermines the equal risk contribution in practice

Return: risk parity weights with risk contribution verification, comparison table, sensitivity analysis, and backtest performance.