Quantitative Models and Construction - **Model Name**: FIFAA (Flexible Indeterminate Factor Asset Allocation) **Model Construction Idea**: Combines quantitative academic rigor with subjective forward-looking flexibility, using historical data (ex-post) and subjective views (ex-ante) to derive asset-factor exposure and optimize portfolio allocation[2][15][74] **Model Construction Process**: 1. **Factor Selection**: Select tradable, low-correlation macroeconomic factors with clear economic logic. Factors include global equities (economic growth), U.S. Treasuries (interest rate/defensive), credit, inflation protection, and currency protection[15][16][20] 2. **Asset-Factor Mapping**: Use LASSO regression to calculate historical beta exposure, then adjust using subjective views derived from professional investor interviews. Subjective single-factor beta is converted into multi-factor beta using matrix transformations[16][35][39] - Formula for historical beta regression: $$y\,=\,X W\,=\,w_{1}x_{1}+\cdots+w_{n}x_{n}$$[32] Loss function for Ridge regression: $$L(w)\,=\,\sum_{i=1}^{n}(y_{i}-\sum w_{j}x_{i j})+\lambda\sum w_{j}^{2}$$[33] Subjective beta transformation: $$\beta_{f}^{*}\,=\,(1\quad F_{f})\,{\binom{\beta_{f}}{\beta_{!f}}}$$[35] $$\beta=F^{-1}\beta^{*}$$[39] 3. **Factor Exposure Optimization**: Optimize factor exposure based on subjective risk/reward judgment or quantitative methods[17] 4. **Portfolio Optimization**: Maximize expected returns while minimizing factor exposure differences. Constraints include absolute exposure differences ≤ 10% of the larger exposure value[44] - Optimization formula: $$m a x(w^{T}r)$$ $$s.\,t.\,w^{T}I\;=\;1$$ $$a b s(w^{T}\beta_{i}-w^{T}\beta_{j})<0.1*m a x(a b s(w^{T}\beta_{i}),a b s(w^{T}\beta_{j}))$$[44] 5. **Rebalancing**: Allow slight deviations in factor exposure to reduce transaction costs and frequency[18] **Model Evaluation**: Provides higher returns and risk-adjusted performance compared to equal-weighted portfolios. Simplified implementation demonstrates practical feasibility[2][74] Model Backtesting Results - **Default Parameters**: - Historical beta optimization: Annualized return 13.63%, annualized volatility 11.47%, max drawdown -18.97%[49][50] - Adjusted beta optimization: Annualized return 15.43%, annualized volatility 16.46%, max drawdown -33.86%[49][50] - Equal-weight portfolio: Annualized return 10.32%, annualized volatility 11.91%, max drawdown -25.27%[49][50] - **Different Adjustment Coefficients**: - Coefficient range (0.1-0.5): Annualized return varies between 15.16%-15.43%, annualized volatility between 15.73%-16.46%, max drawdown between -30.51% to -37.50%[57][59] - **Different Expected Returns**: - Neutral expected return scenarios (5%, 10%, 15%): Annualized return ranges from 13.63%-15.90%, annualized volatility from 11.47%-16.45%, max drawdown from -18.97% to -36.67%[69][70][71][72] Quantitative Factors and Construction - **Factor Name**: Macroeconomic Factors (Economic Growth, Interest Rate, Inflation) **Factor Construction Idea**: Represent macroeconomic trends using tradable indices to ensure simplicity and reduce calculation errors[15][20][30] **Factor Construction Process**: - Economic growth: Represented by stock indices (e.g., Wind All A Index, S&P 500)[30] - Interest rate: Represented by bond indices (e.g., China Bond Treasury Wealth Index)[30] - Inflation: Composite of commodity indices (e.g., Nanhua Industrial, Agricultural, Energy, and Black Metal indices)[20][30] **Factor Evaluation**: Tradable and low-correlation factors ensure practical applicability and reduce subjective judgment uncertainty[15][16][20] Factor Backtesting Results - **Macroeconomic Factor Correlation Matrix**: - Wind All A vs. S&P 500: 0.15 - Wind All A vs. China Bond Treasury: -0.12 - Wind All A vs. Commodity Composite: 0.30[28][30] - **Factor Performance**: - Economic growth factor (Wind All A): Annualized return 13.63%-15.43% depending on optimization method[49][50][69] - Inflation factor (Commodity Composite): Adjusted beta optimization shows higher returns during inflationary periods[49][50][69]