Quantitative Models and Construction Methods Model 1: Convertible Bond Valuation Model - **Model Name**: Convertible Bond Valuation Model - **Model Construction Idea**: The model aims to compare the valuation of convertible bonds with their underlying stocks using a time-series comparable valuation metric called "100 Yuan Conversion Premium Rate" and the median of "Adjusted YTM - Credit Bond YTM" to measure the relative allocation value between debt-biased convertible bonds and credit bonds[4][5][15] - **Model Construction Process**: - **100 Yuan Conversion Premium Rate**: Fit the relationship curve between the conversion premium rate and conversion value in the cross-sectional space at each time point, and substitute the conversion value = 100 into the fitting formula to obtain the "100 Yuan Conversion Premium Rate" - Formula: $$ y_{i}=\alpha_{0}+\,\alpha_{1}\cdot\,{\frac{1}{x_{i}}}+\epsilon_{i} $$ where \( y_{i} \) is the conversion premium rate of the i-th convertible bond, and \( x_{i} \) is the conversion value of the i-th convertible bond[43] - **Adjusted YTM - Credit Bond YTM**: Adjust the YTM of debt-biased convertible bonds by stripping out the impact of conversion terms - Formula: $$ \text{Adjusted YTM} = \text{Convertible Bond YTM} \times (1 - \text{Conversion Probability}) + \text{Expected Conversion Annualized Yield} \times \text{Conversion Probability} $$ The conversion probability is calculated using the BS model, substituting the closing price of the underlying stock, option exercise price, stock volatility, remaining term, and discount rate to calculate the conversion probability \( N(d2) \)[44] - **Model Evaluation**: The model provides a systematic approach to evaluate the relative allocation value of convertible bonds compared to their underlying stocks and credit bonds[15] Model 2: Convertible Bond Comprehensive Valuation Factor - **Model Name**: Convertible Bond Comprehensive Valuation Factor - **Model Construction Idea**: The model combines the deviation of the conversion premium rate and the theoretical value deviation (Monte Carlo model) to construct a comprehensive valuation factor for convertible bonds[6][19] - **Model Construction Process**: - **Conversion Premium Rate Deviation**: - Formula: $$ \text{Conversion Premium Rate Deviation} = \text{Conversion Premium Rate} - \text{Fitted Conversion Premium Rate} $$ - **Theoretical Value Deviation (Monte Carlo Model)**: - Formula: $$ \text{Theoretical Value Deviation} = \frac{\text{Convertible Bond Closing Price}}{\text{Theoretical Value}} - 1 $$ The Monte Carlo model fully considers the conversion, redemption, downward revision, and repurchase terms of convertible bonds, simulating 10,000 paths at each time point and using the same credit term interest rate as the discount rate to calculate the theoretical value of the convertible bond[20] - **Comprehensive Valuation Factor**: - Formula: $$ \text{Convertible Bond Comprehensive Valuation Factor} = \text{Rank}(\text{Conversion Premium Rate Deviation}) + \text{Rank}(\text{Theoretical Value Deviation (Monte Carlo Model)}) $$ - **Model Evaluation**: The comprehensive valuation factor performs well in the overall, balanced, and debt-biased convertible bonds, while the theoretical value deviation (Monte Carlo model) performs better in equity-biased convertible bonds[19][20] Model 3: Convertible Bond Style Rotation Model - **Model Name**: Convertible Bond Style Rotation Model - **Model Construction Idea**: The model uses convertible bond momentum and volatility deviation as market sentiment capture indicators to construct a convertible bond style rotation portfolio, with bi-weekly rebalancing[7][26] - **Model Construction Process**: - **Market Sentiment Capture Indicators**: - Formula: $$ \text{Convertible Bond Style Market Sentiment Capture Indicator} = \text{Rank}(\text{Convertible Bond 20-Day Momentum}) + \text{Rank}(\text{Volatility Deviation}) $$ - **Style Rotation Position Calculation**: - Example Calculation: | | Convertible Bond Equity-Biased Low Valuation | Convertible Bond Balanced Low Valuation | Convertible Bond Debt-Biased Low Valuation | | --- | --- | --- | --- | | Equal Weight Index | 1 | 2 | 3 | | Volatility Deviation Ranking | 2 | 1 | 3 | | Market Sentiment Capture Indicator | 3 | 3 | 6 | | Style Rotation Position | 50% | 50% | 0% | - **Model Evaluation**: The style rotation model effectively captures market sentiment and allocates positions accordingly, showing superior performance compared to the equal-weight index[26][27][28] Model Backtesting Results Convertible Bond Valuation Model - **100 Yuan Conversion Premium Rate**: Rolling three-year percentile at 98.70%, rolling five-year percentile at 94.90%[4][15] - **Adjusted YTM - Credit Bond YTM**: Current median at -2.36%[5][15] Convertible Bond Comprehensive Valuation Factor - **Equity-Biased Convertible Bond Low Valuation Index**: - Annualized Return: 26.10% - Annualized Volatility: 20.55% - Maximum Drawdown: -22.94% - IR: 1.27 - Calmar Ratio: 1.14 - Monthly Win Rate: 62.22%[23] - **Balanced Convertible Bond Low Valuation Index**: - Annualized Return: 14.80% - Annualized Volatility: 11.82% - Maximum Drawdown: -15.95% - IR: 1.25 - Calmar Ratio: 0.93 - Monthly Win Rate: 62.22%[23] - **Debt-Biased Convertible Bond Low Valuation Index**: - Annualized Return: 13.37% - Annualized Volatility: 9.43% - Maximum Drawdown: -17.78% - IR: 1.42 - Calmar Ratio: 0.75 - Monthly Win Rate: 57.78%[23] Convertible Bond Style Rotation Model - **Convertible Bond Style Rotation**: - Annualized Return: 25.27% - Annualized Volatility: 16.68% - Maximum Drawdown: -15.89% - IR: 1.51 - Calmar Ratio: 1.59 - Monthly Win Rate: 65.56%[32] - **Convertible Bond Low Valuation Equal Weight Index**: - Annualized Return: 14.71% - Annualized Volatility: 10.97% - Maximum Drawdown: -15.48% - IR: 1.34 - Calmar Ratio: 0.95 - Monthly Win Rate: 61.11%[32] - **Convertible Bond Equal Weight Index**: - Annualized Return: 9.75% - Annualized Volatility: 11.66% - Maximum Drawdown: -20.60% - IR: 0.84 - Calmar Ratio: 0.47 - Monthly Win Rate: 60.00%[32]