金融工程专题：宏观因子的周期轮动与资产配置

Quantitative Models and Construction Methods 1. Model Name: HP Filter - Model Construction Idea: The HP filter is used to decompose a time series into trend and cyclical components, aiming to remove long-term trends and short-term noise from macroeconomic factors[10][9] - Model Construction Process: The HP filter solves the following optimization problem to balance trend smoothness and data fit: $\operatorname*{min}\left\{\sum_{t=1}^{T}(y_{t}-g_{t})^{2}+\lambda\sum_{t=2}^{T-1}[(g_{t+1}-g_{t})-(g_{t}-g_{t-1})]^{2}\right\}$ - $y_t$: Original time series data - $g_t$: Trend component - $\lambda$: Smoothing parameter, where larger $\lambda$ results in a smoother trend In this report, a larger $\lambda$ is used to remove long-term trends, and a smaller $\lambda$ is applied to filter out noise, resulting in a mid-cycle series for further analysis[10] - Model Evaluation: The HP filter aligns with classical macroeconomic analysis frameworks but suffers from endpoint bias and cannot identify different frequency cycles[3][42] 2. Model Name: Fourier Transform - Model Construction Idea: Fourier Transform decomposes a time series into a combination of sine waves with different frequencies, amplitudes, and phases, enabling the identification of dominant cycles in macroeconomic data[25][26] - Model Construction Process: The Fourier Transform is defined as: $F(f)=\int_{-\infty}^{\infty}f(x)e^{-i2\pi f(x)}\,\mathrm{d}x$ - $f(x)$: Time series data - $F(f)$: Frequency domain representation Since most macroeconomic data are non-stationary, the HP filter is first applied to remove long-term trends, producing a stationary series. The Fourier Transform is then used to extract the main cycles and fit the periodic series[25][26] - Model Evaluation: Suitable for analyzing historical data and identifying economic cycle patterns, but assumes constant periodic structures over time, which may reduce short-term fit[3][42] 3. Model Name: Hybrid Filtering - Model Construction Idea: Combines the strengths of HP filtering and Fourier Transform to achieve both extrapolation capability and flexibility in cycle fitting[42] - Model Construction Process: - Apply Fourier Transform to identify periodic patterns in macroeconomic data - Use HP filtering to observe short-term trends in macroeconomic factors - Combine the results to create a series that retains both periodicity and trend information[42] - Model Evaluation: Balances the advantages of both methods, providing better adaptability for macroeconomic data analysis[42] 4. Model Name: Merrill Lynch Clock Model - Model Construction Idea: Divides the economic cycle into four phases based on economic growth and inflation, using PMI YoY growth as a proxy for economic growth and PPI YoY growth for inflation[68][72] - Model Construction Process: - Recovery: PMI YoY up, PPI YoY down → 60% stocks, 40% bonds - Expansion: PMI YoY up, PPI YoY up → 60% commodities, 40% stocks - Stagflation: PMI YoY down, PPI YoY up → 60% cash, 40% commodities - Recession: PMI YoY down, PPI YoY down → 60% bonds, 40% cash[72] - Model Evaluation: Achieves higher returns and Sharpe ratio compared to a balanced allocation model, with a monthly win rate of 56.49%[68][70] 5. Model Name: Monetary-Credit Model - Model Construction Idea: Adapts the Merrill Lynch Clock for the Chinese market by focusing on monetary and credit conditions, using M2 YoY growth for monetary policy and social financing YoY growth for credit conditions[76] - Model Construction Process: - Loose Monetary & Loose Credit: M2 YoY up, social financing YoY up → 60% stocks, 40% commodities - Tight Monetary & Loose Credit: M2 YoY down, social financing YoY up → 60% commodities, 40% stocks - Tight Monetary & Tight Credit: M2 YoY down, social financing YoY down → 60% cash, 40% bonds - Loose Monetary & Tight Credit: M2 YoY up, social financing YoY down → 60% bonds, 40% stocks[76] - Model Evaluation: Slightly lower annualized returns than the Merrill Lynch Clock but demonstrates more stable excess returns since 2020[76][85] --- Model Backtesting Results 1. HP Filter - Annualized Excess Return: 1.43%-3.16% for stock index timing[57][58] - Annualized Excess Return: 4.84%-9.91% for stock-bond timing[60][61] 2. Fourier Transform - Core Cycle: Identified a 38-44 month cycle across all macroeconomic factors, suggesting a 3-4 year mid-cycle pattern[26][83] 3. Merrill Lynch Clock Model - Annualized Return: 11.71% - Annualized Excess Return: 5.82% - Sharpe Ratio: 1.037 - Monthly Win Rate: 56.49%[68][70] 4. Monetary-Credit Model - Annualized Return: 9.93% - Annualized Excess Return: 4.04% - Sharpe Ratio: 0.589 - Monthly Win Rate: 56.90%[76][79] --- Quantitative Factors and Construction Methods 1. Factor Name: PMI YoY Growth - Construction Idea: Represents economic growth trends[9][83] - Construction Process: Derived from the year-over-year growth rate of the Purchasing Managers' Index (PMI)[9][83] 2. Factor Name: PPI YoY Growth - Construction Idea: Represents inflation trends[9][83] - Construction Process: Derived from the year-over-year growth rate of the Producer Price Index (PPI)[9][83] 3. Factor Name: M1 YoY Growth - Construction Idea: Reflects changes in narrow money supply[9][83] - Construction Process: Derived from the year-over-year growth rate of M1[9][83] 4. Factor Name: M2 YoY Growth - Construction Idea: Reflects changes in broad money supply[9][83] - Construction Process: Derived from the year-over-year growth rate of M2[9][83] 5. Factor Name: Social Financing YoY Growth - Construction Idea: Represents credit supply conditions[9][83] - Construction Process: Derived from the year-over-year growth rate of total social financing[9][83] 6. Factor Name: 1-Year Treasury Yield YoY Difference - Construction Idea: Reflects interest rate trends[9][83] - Construction Process: Calculated as the year-over-year difference in 1-year treasury yields[9][83] 7. Factor Name: Industrial Production YoY Growth - Construction Idea: Represents industrial output trends[9][83] - Construction Process: Derived from the year-over-year growth rate of industrial production[9][83] 8. Factor Name: Corporate Profit YoY Growth - Construction Idea: Reflects corporate profitability trends[9][83] - Construction Process: Derived from the year-over-year growth rate of corporate profits[9][83] --- Factor Backtesting Results Stock Index Timing - Annualized Excess Return: 1.43%-3.16% for factors like M1 YoY, PPI YoY, and PMI YoY[57][58] Stock-Bond Timing - Annualized Excess Return: 4.84%-9.91% for factors like M1 YoY, PPI YoY, and PMI YoY[60][61]