蒙特卡洛回测：从历史拟合转向未来稳健

Quantitative Models and Construction Methods - Model Name: Monte Carlo Backtesting Model Construction Idea: Shift from historical path fitting to future robustness testing by generating multiple random paths to evaluate strategy performance across diverse scenarios [1][10] Model Construction Process: 1. Generate thousands of random price paths that follow historical statistical characteristics (e.g., return distribution, volatility, correlation) but differ from the original historical path [10] 2. Perform stress tests on strategies across these simulated paths to observe performance under various market conditions [10] 3. Calculate risk metrics such as Sharpe ratio, maximum drawdown, and value-at-risk (VaR) based on the distribution of strategy returns [10] Model Evaluation: Effectively reduces overfitting to specific historical paths and provides a more comprehensive robustness assessment [10][46] - Model Name: Non-Parametric Monte Carlo Simulation Model Construction Idea: Use historical data directly without assuming any parametric distribution, preserving cross-sectional correlation [2][13] Model Construction Process: 1. Method 1: Multi-Asset Time-Series Return Joint Rearrangement - Extract daily returns of all assets as a "data block" - Randomly sample and sequentially concatenate these blocks to form simulated paths [18] 2. Method 2: Multi-Asset Time-Series Return Block Bootstrap - Divide historical returns into fixed-length overlapping/non-overlapping blocks - Randomly sample blocks and concatenate them to form simulated paths [19] Model Evaluation: Preserves cross-sectional correlation but disrupts time-series structures like volatility clustering and autocorrelation [14][20] - Model Name: Residual Bootstrap (Factor Model-Based) Model Construction Idea: Separate systematic risk and idiosyncratic risk using factor models, then randomize residuals for simulation [2][23] Model Construction Process: 1. Construct risk factors (e.g., market, size, value, momentum) and calculate historical daily returns [23] 2. Perform cross-sectional regression to estimate factor exposures (β) and extract residual returns [23] 3. Randomly shuffle residuals while preserving cross-sectional correlation [23] 4. Reconstruct paths using historical factor returns and randomized residuals [23] Model Evaluation: Useful for analyzing alpha and risk exposure but limited by the explanatory power of the factor model [24][25] - Model Name: Geometric Brownian Motion (GBM) Simulation Model Construction Idea: Assume asset returns follow a normal distribution and simulate paths using drift and volatility parameters [2][28] Model Construction Process: $d S_{i}(t)=\mu_{i}S_{i}(t)d t+\sigma_{i}S_{i}(t)d W_{i}(t),i=1,\ldots,n$ - $\mu_{i}$: Drift rate (expected return) - $\sigma_{i}$: Volatility - $W_{i}(t)$: Standard Brownian motion Discretized path: $S_{i}^{(j)}(t_{k})=X_{i}(0)\,e x p[(\,k\Delta t+\sum_{l=1}^{k}\sum_{p=1}^{n}L_{i p}Z_{l,p}^{(j)}\,]$ - $L$: Cholesky decomposition of covariance matrix - $Z_{l,p}^{(j)}$: Independent standard normal random variables [28] Model Evaluation: Accurately replicates volatility and correlation but fails to capture tail risks and price jumps [28][47] Model Backtesting Results - Monte Carlo Backtesting: - Historical price path Sharpe ratio: 0.96 (25-day window) - Simulated path Sharpe ratio: 0.19 (25-day window, GBM method) [45][46] - Non-Parametric Monte Carlo Simulation: - Historical price path Sharpe ratio: 0.96 (25-day window) - Simulated path Sharpe ratio: 0.22 (15-day window, joint rearrangement method) [45][46] - Residual Bootstrap: - Historical price path Sharpe ratio: 0.96 (25-day window) - Simulated path Sharpe ratio: 0.19 (25-day window) [45][46] - Geometric Brownian Motion (GBM): - Historical price path Sharpe ratio: 0.96 (25-day window) - Simulated path Sharpe ratio: 0.19 (25-day window) [45][46] Quantitative Factors and Construction Methods - Factor Name: Momentum and Volatility Dual Factor Factor Construction Idea: Combine momentum and volatility factors using Z-score normalization and equal weighting [35] Factor Construction Process: $S c o r e_{i}=0.5*Z S c o r e_{i,m o m}+0.5*Z S c o r e_{i,v o l}$ - Momentum and volatility calculated over different window lengths (N ∈ [15, 20, 40]) [35] Factor Evaluation: Provides a balanced scoring mechanism for style rotation strategies [35][37] Factor Backtesting Results - Momentum and Volatility Dual Factor: - Historical price path cumulative return: 535% (25-day window) - Simulated path cumulative return: 62.25% (15-day window, GBM method) [38][42]