金融工程研究报告：指数抽样复制：分组抽样方案及实践

Quantitative Models and Construction Methods - Model Name: Convertible Bond Index Sampling Replication Model Construction Idea: The model aims to replicate the performance of the benchmark convertible bond index by maintaining consistency in key characteristics such as stock-bond nature, industry distribution, and market capitalization distribution. It uses a simplified grouping and sampling method to achieve effective replication with reduced complexity[2][13][19] Model Construction Process: 1. Define the sample space as all publicly issued convertible bonds listed on the Shanghai and Shenzhen exchanges, with a listing period exceeding 10 working days and a bond balance of at least 30 million yuan[19] 2. Categorize convertible bonds into three types based on their "flat premium rate" (calculated as $ \text{Flat Premium Rate} = \frac{\text{Convertible Value}}{\text{Pure Bond Value}} - 1 $): - Bond-oriented: Flat premium rate < -20% - Balanced: Flat premium rate between -20% and 20% - Stock-oriented: Flat premium rate > 20%[13][19] 3. Group the convertible bonds by flat premium rate and industry classification (based on Shenwan Level 1 industry), resulting in 93 subgroups (3 flat premium categories × 31 industries)[19] 4. Within each subgroup, rank the bonds by the market capitalization of their underlying stocks and select approximately 20% of the bonds near the median market capitalization (10% above and below the median)[19][20] 5. Adjust holdings quarterly, equally weight the selected bonds, and account for transaction costs (0.12% on both sides)[20] Model Evaluation: The model is simple, easy to implement, and achieves good replication results with a tracking error of approximately 2% since the second half of 2023[2][20] Model Backtesting Results - Convertible Bond Index Sampling Replication: - Annualized Tracking Error: Approximately 2% since 2023H2[2][20] - Impact of Sampling Ratio: Increasing the sampling ratio reduces tracking error. For example, sampling 40% of the bonds results in a tracking error of 1.5% since 2022[25][27] - Liquidity: The daily average trading volume of the sampling portfolio accounts for approximately 17% of the benchmark index's trading volume since 2020, ensuring sufficient liquidity[32] Quantitative Factors and Construction Methods - Factor Name: Flat Premium Rate Factor Construction Idea: The flat premium rate measures the stock-bond nature of convertible bonds, which significantly impacts their price behavior. It categorizes bonds into three types based on their risk-return characteristics[13][19] Factor Construction Process: - Formula: $ \text{Flat Premium Rate} = \frac{\text{Convertible Value}}{\text{Pure Bond Value}} - 1 $ - Classification: - Bond-oriented: Flat premium rate < -20% - Balanced: Flat premium rate between -20% and 20% - Stock-oriented: Flat premium rate > 20%[13][19] Factor Evaluation: Different types of convertible bonds exhibit distinct risk-return profiles, with bond-oriented bonds being the most stable and stock-oriented bonds having the highest elasticity[13][15] Factor Backtesting Results - Flat Premium Rate Factor: - Bond-oriented Convertible Bonds: - Annualized Return: 9.6% - Annualized Volatility: 8.7% - Maximum Drawdown: 12.1% - Sharpe Ratio: 1.10[15] - Balanced Convertible Bonds: - Annualized Return: 9.1% - Annualized Volatility: 12.9% - Maximum Drawdown: 20.2% - Sharpe Ratio: 0.74[15] - Stock-oriented Convertible Bonds: - Annualized Return: 11.5% - Annualized Volatility: 21.7% - Maximum Drawdown: 38.3% - Sharpe Ratio: 0.61[15]