资产配置（二）：风险预算风险平价模型

Quantitative Models and Construction Methods 1. Model Name: Basic Risk Parity Model - Model Construction Idea: The model ensures that each asset in the portfolio contributes equally to the overall portfolio risk[20][23] - Model Construction Process: - Let the return vector of assets at time T be r and the weight vector be w - Covariance between assets is denoted as Σ, and the portfolio's return and volatility are: $\sigma(w) = \sqrt{w^T \Sigma w}$ - Marginal Risk Contribution (MRC) and Risk Contribution (RC) for asset i are: $MRC_i = \frac{\partial \sigma(w)}{\partial w_i} = \frac{(\Sigma w)_i}{\sqrt{w^T \Sigma w}}$ $RC_i = w_i \cdot MRC_i = w_i \cdot \frac{(\Sigma w)_i}{\sqrt{w^T \Sigma w}}$ - Total Risk Contribution (TRC) is: $TRC = \sum RC_i = \sqrt{w^T \Sigma w}$ - Risk parity requires: $RC_i = RC_j \; \text{for all} \; i, j$[23][24][25] - Model Evaluation: The model is effective in balancing risk contributions but may lead to conservative portfolios when asset volatilities differ significantly[5][20] 2. Model Name: Risk Budgeting Risk Parity - Model Construction Idea: Adjusts the risk budget to allocate higher weights to riskier assets, making the model more flexible for different risk preferences[5][33] - Model Construction Process: - Adjust the relative marginal contribution of assets to the benchmark: $RC_i : RC = k_i \; \text{for all} \; i$ - When assets are uncorrelated, the allocation becomes: $RC_i = \frac{k_i w_i^2 \sigma_i^2}{\sum k_i}$ - Risk budget and actual weights are related quadratically: $\text{If actual weight is } n \times \text{basic weight, then risk budget is } n^2$ - Static and dynamic risk budgeting rules: - Static: Fixed risk budgets for equities, commodities, and gold - Dynamic: Adjust risk budgets based on Sharpe ratios over the past 6 months[37][39][41] - Model Evaluation: Provides higher returns but increases risk. Dynamic budgeting improves returns further but has mixed effects on risk metrics[41] 3. Model Name: Macro Risk Parity Model - Model Construction Idea: Allocates risk based on shared macroeconomic factors rather than individual asset risks, addressing overlapping risk contributions among assets[10][64] - Model Construction Process: - General asset pricing model: $r = 1^T \times I \times f_{base} + B \times I \times F + \varepsilon$ - I: Dummy variable matrix indicating asset categories - f_base: Benchmark returns for major asset classes - F: Factor returns explaining intra-class differences - B: Factor exposures (sensitivity of assets to factors) - ε: Residual returns not explained by factors[64][66][68] - Systematic and idiosyncratic risk contributions: $RCF_i = w_{new,i} \cdot \frac{(\Sigma_f w_{new})_i}{\sqrt{w^T \Sigma w}}$ $RCE_i = w_{new,i} \cdot \frac{(E w_{new})_i}{\sqrt{w^T \Sigma w}} = \frac{w_{new,i}^2}{\sqrt{w^T \Sigma w}}$[74][75] - Model Evaluation: Effective in reducing leverage and addressing overlapping risks but requires precise macro risk modeling[12][115] --- Model Backtest Results 1. Basic Risk Parity Model - Annualized Return: 5.03% - Maximum Drawdown: -5.10% - Volatility: 2.58% - Sharpe Ratio: 1.90 - Monthly Win Rate: 71.11% - Monthly Profit-Loss Ratio: 3.44[28] 2. Risk Budgeting Risk Parity - Static Risk Budgeting: - Annualized Return: 5.80% - Maximum Drawdown: -9.30% - Volatility: 5.80% - Sharpe Ratio: 0.97 - Monthly Win Rate: 58.89% - Monthly Profit-Loss Ratio: 2.05 - Dynamic Risk Budgeting: - Annualized Return: 6.98% - Maximum Drawdown: -12.38% - Volatility: 6.29% - Sharpe Ratio: 1.07 - Monthly Win Rate: 63.33% - Monthly Profit-Loss Ratio: 2.30[46] 3. Macro Risk Parity Model - Basic Asset Classes: - Annualized Return: 5.03% - Maximum Drawdown: -5.10% - Volatility: 2.58% - Sharpe Ratio: 1.90 - Monthly Win Rate: 71.11% - Monthly Profit-Loss Ratio: 3.44 - Expanded Sub-Asset Classes: - Annualized Return: 7.35% - Maximum Drawdown: -11.49% - Volatility: 6.63% - Sharpe Ratio: 1.07 - Monthly Win Rate: 63.33% - Monthly Profit-Loss Ratio: 2.29[89] 4. Refined Asset Pool - Asset Risk Parity: - Annualized Return: 6.63% - Maximum Drawdown: -2.84% - Volatility: 2.83% - Sharpe Ratio: 2.27 - Monthly Win Rate: 75.51% - Monthly Profit-Loss Ratio: 5.99 - Macro Risk Parity: - Annualized Return: 8.03% - Maximum Drawdown: -3.59% - Volatility: 3.79% - Sharpe Ratio: 2.04 - Monthly Win Rate: 72.45% - Monthly Profit-Loss Ratio: 4.32[110]