Quantitative Models and Construction Methods 1. Model Name: Optimal Factor Timing Portfolio - Model Construction Idea: The model integrates numerous factors and predictors to construct a timing strategy, leveraging shrinkage techniques to avoid overfitting to historical data and spurious opportunities[2][3][17] - Model Construction Process: 1. Use the Ledoit and Wolf (2003) covariance matrix shrinkage estimator to ensure robustness even with thousands of timing portfolios. The shrinkage intensity is calculated following Schäfer and Strimmer (2005)[3][25] 2. Apply a modified version of Kozak, Nagel, and Santosh (2020) shrinkage method to estimate portfolio weights, introducing skepticism toward unrealistically high Sharpe ratio opportunities. The weight formula is: where $\hat{\Sigma}{t}$ is the covariance matrix, $\hat{\mu}{t}$ is the mean return vector, and $\lambda$ controls the shrinkage degree[27][28][29] 3. Rescale portfolio weights to ensure the absolute sum of weights equals 1 in each period, focusing on factor rotation while avoiding extreme leverage[3][30] - Model Evaluation: The shrinkage techniques effectively mitigate estimation errors and prevent overfitting, ensuring robust out-of-sample performance even in high-dimensional settings[3][30][80] --- Model Backtesting Results 1. Optimal Factor Timing Portfolio (Fama-French Factors) - Mean Return: 4.71% - Standard Deviation: 5.81% - Sharpe Ratio: 0.81 - Appraisal Ratio: 0.79 - Worst 12-Month Return: -5.62%[40][41] 2. Optimal Factor Timing Portfolio (Large-Cap Fama-French Factors) - Mean Return: 3.65% - Standard Deviation: 6.49% - Sharpe Ratio: 0.56 - Appraisal Ratio: 0.54 - Worst 12-Month Return: -13.70%[40][41] 3. Optimal Factor Timing Portfolio (Jensen Factors, Small Predictor Set) - Mean Return: 2.97% - Standard Deviation: 2.01% - Sharpe Ratio: 1.48 - Appraisal Ratio: 1.51 - Worst 12-Month Return: -1.79%[40][41] 4. Optimal Factor Timing Portfolio (Jensen Factors, Large Predictor Set) - Mean Return: 2.73% - Standard Deviation: 1.91% - Sharpe Ratio: 1.43 - Appraisal Ratio: 1.46 - Worst 12-Month Return: -3.17%[40][41] --- Quantitative Factors and Construction Methods 1. Factor Name: Interaction of Factors and Predictors - Factor Construction Idea: Factor timing portfolios are constructed by interacting lagged predictors with factor returns, transforming the time-series prediction problem into a cross-sectional mean-variance optimization problem[17][19][23] - Factor Construction Process: 1. Define factor timing portfolios as: where $X_{t-1}$ are lagged predictors and $F_{t}$ are factor returns[19][20] 2. The expected return of the timing portfolio is: indicating that timing returns depend on the predictive power of $X_{t-1}$ for $F_{t}$[21][22] 3. Construct $KJ$ timing portfolios for $K$ factors and $J$ predictors, always including the original factors as a baseline[22][23] - Factor Evaluation: The interaction approach effectively captures time-varying factor exposures, enabling robust timing strategies across diverse factor-predictor combinations[23][80] --- Factor Backtesting Results 1. Fama-French Factors (Standard Version) - Mean Return: 4.71% - Standard Deviation: 5.81% - Sharpe Ratio: 0.81 - Appraisal Ratio: 0.79 - Worst 12-Month Return: -5.62%[40][41] 2. Fama-French Factors (Large-Cap Version) - Mean Return: 3.65% - Standard Deviation: 6.49% - Sharpe Ratio: 0.56 - Appraisal Ratio: 0.54 - Worst 12-Month Return: -13.70%[40][41] 3. Jensen Factors (Small Predictor Set) - Mean Return: 2.97% - Standard Deviation: 2.01% - Sharpe Ratio: 1.48 - Appraisal Ratio: 1.51 - Worst 12-Month Return: -1.79%[40][41] 4. Jensen Factors (Large Predictor Set) - Mean Return: 2.73% - Standard Deviation: 1.91% - Sharpe Ratio: 1.43 - Appraisal Ratio: 1.46 - Worst 12-Month Return: -3.17%[40][41]
“学海拾珠”系列之二百三十八：高维环境下的最优因子择时
Huaan Securities·2025-06-12 10:40