Quantitative Models and Construction CPPI Model - **Model Name**: CPPI (Constant Proportion Portfolio Insurance) [35] - **Construction Idea**: Dynamically adjust the allocation between risk assets and risk-free assets based on the gap between current portfolio value and the preset protection target [35] - **Construction Process**: - Calculate the protection target at time t: $ F_{t}=G\times e^{-r(T-t)} $ where $ G $ is the protection amount at the end of the protection period, $ r $ is the risk-free rate, and $ T-t $ is the remaining time [35] - Determine the amount of funds available for risk assets: $ C_{t}=V_{t}-F_{t} $ where $ V_{t} $ is the portfolio value at time t [36] - Adjust risk asset allocation using a risk multiplier $ m $ and an upper limit $ b $: $ \mathrm{E}_{t}=m i n\{m C_{t},b V_{t}\} $ $ \mathrm{E}_{t}=m a x\{m i n\{m C_{t},b V_{t}\},0\} $ $ B_{t}=V_{t}-E_{t} $ where $ E_{t} $ is the amount allocated to risk assets, and $ B_{t} $ is the amount allocated to risk-free assets [37][38] - Monthly rebalancing based on the last trading day’s closing price [39] - **Evaluation**: CPPI effectively reduces asset volatility and drawdowns but may slightly lower annualized returns due to increased allocation to risk-free assets [45] - **Parameters**: - Protection ratio $ \lambda $: [60%, 70%, 80%] - Risk multiplier $ m $: [2, 3] - Risk asset upper limit $ b $: [70%, 80%, 90%] - Risk-free asset annualized return: based on the previous year’s actual return of money market funds [52][43] Risk Budgeting Model - **Model Name**: Risk Budgeting Model [68] - **Construction Idea**: Allocate risk budgets to assets based on their risk characteristics (volatility, upside volatility, or momentum) [70] - **Construction Process**: - Optimize the risk budget allocation using the SLSQP algorithm: $ O b j e c t i v e\,f u n c t i o n=\sum_{i=1}^{n}(R C_{i}-R B_{i})^{2} $ where $ R C_{i} $ is the actual risk contribution of asset $ i $, and $ R B_{i} $ is the risk budget proportion [68] - Three allocation methods: - Volatility ranking: Higher volatility assets receive higher risk budgets - Upside volatility ranking: Higher upside volatility assets receive higher risk budgets - Momentum ranking: Higher past returns receive higher risk budgets [70] - **Evaluation**: Volatility and upside volatility rankings provide higher elasticity but larger drawdowns, while momentum ranking offers more stable returns [77] Daily Net Value Monitoring Mechanism - **Model Name**: Daily Net Value Monitoring Mechanism [79] - **Construction Idea**: Monitor daily portfolio net value to mitigate short-term market shocks [79] - **Construction Process**: - Trigger pre-warning when rolling N-day maximum drawdown exceeds threshold $ \theta $ and net value falls below M-day moving average [80] - Exit pre-warning when net value crosses above M-day moving average [81] - Adjust portfolio to 95% bonds + 5% money market during pre-warning, and revert to risk budgeting weights after stabilization [79][80] - **Evaluation**: Effectively reduces drawdowns and improves risk-return ratios without significantly impacting returns [88] --- Model Backtesting Results CPPI Model - **Annualized Return**: 4.4% to 14.6% depending on asset type [46] - **Volatility**: Reduced by 7.7% to 11.4% compared to original assets [46] - **Maximum Drawdown**: Improved by 7.5% to 19.3% [46] Risk Budgeting Model - **Maximum Drawdown Constraint (3%)**: - Best combination: Annualized return 6.82%, maximum drawdown -2.91%, Sharpe ratio 2.207, Calmar ratio 2.344 [95][96] - **Maximum Drawdown Constraint (5%)**: - Best combination: Annualized return 7.66%, maximum drawdown -4.97%, Sharpe ratio 2.010, Calmar ratio 1.541 [106][108] - **No Maximum Drawdown Constraint**: - Best combination: Annualized return 8.15%, maximum drawdown -6.36%, Sharpe ratio 1.622, Calmar ratio 1.281 [120][121] Daily Net Value Monitoring Mechanism - **Impact on Risk Budgeting Models**: - Improves Calmar ratio by up to 1.101 for 3% drawdown constraint [88] - Reduces pre-warning frequency to less than 6 times/year [94] --- Supplementary Testing Sensitivity Analysis - **3% Drawdown Constraint**: Parameter adjustments have minimal impact on annualized returns; all combinations maintain Calmar > 1 and Sharpe > 1.5 [133][134] - **5% Drawdown Constraint**: Parameter adjustments have minimal impact on annualized returns; all combinations maintain Calmar > 0.8 and Sharpe > 1.5 [135][136] - **No Drawdown Constraint**: Most combinations maintain Calmar > 1 and Sharpe > 1.4, indicating low risk of overfitting [137][138] Validation of CPPI + Daily Monitoring - **Comparison with Original Assets**: - Original assets fail to meet 3% drawdown constraint - CPPI + Daily Monitoring significantly improves Calmar ratio compared to original risk budgeting models [140]