Quantitative Models and Construction Methods 1. Model Name: "百元转股溢价率" (Premium Rate per 100 Yuan Conversion) - **Model Construction Idea**: This model aims to compare the valuation of convertible bonds and their underlying stocks by calculating a time-series comparable valuation indicator, "百元转股溢价率" (Premium Rate per 100 Yuan Conversion), and using rolling historical percentiles to measure the relative allocation value[4][15]. - **Model Construction Process**: - Fit the relationship curve between the conversion premium rate and conversion value in the cross-sectional space at each time point - Substitute a conversion value of 100 into the fitted formula to obtain the "百元转股溢价率" - Formula: $$y_{i}=\alpha_{0}+\,\alpha_{1}\cdot\,{\frac{1}{x_{i}}}+\epsilon_{i}$$ where \(y_{i}\) represents the conversion premium rate of the \(i\)-th bond, and \(x_{i}\) represents the conversion value of the \(i\)-th bond[44] - **Model Evaluation**: Provides a relative valuation perspective for comparing convertible bonds and their underlying stocks[15] 2. Model Name: "修正 YTM – 信用债 YTM" (Adjusted YTM - Credit Bond YTM) - **Model Construction Idea**: This model isolates the impact of conversion terms on the yield-to-maturity (YTM) of convertible bonds to assess the relative allocation value between debt-heavy convertible bonds and credit bonds[5][15]. - **Model Construction Process**: - Adjust the YTM of debt-heavy convertible bonds by considering the probability of conversion and maturity - Formula: $$\text{Adjusted YTM} = \text{Convertible Bond YTM} \times (1 - \text{Conversion Probability}) + \text{Expected Annualized Return of Conversion} \times \text{Conversion Probability}$$ - Conversion probability is calculated using the Black-Scholes (BS) model, incorporating stock price, strike price, stock volatility, remaining maturity, and discount rate - Calculate the median difference between the adjusted YTM of convertible bonds and the YTM of credit bonds of the same rating and maturity: $$\text{"Adjusted YTM - Credit Bond YTM Median"} = \text{median}\{X_1, X_2, ..., X_n\}$$ where \(X_i\) represents the difference for the \(i\)-th convertible bond[45][46] - **Model Evaluation**: Highlights the cost-effectiveness of debt-heavy convertible bonds compared to credit bonds[5] 3. Model Name: Convertible Bond Style Rotation Model - **Model Construction Idea**: This model captures market sentiment using momentum and volatility deviation indicators to construct a convertible bond style rotation portfolio, with bi-weekly rebalancing[6][27]. - **Model Construction Process**: - Calculate the following sentiment indicators for each convertible bond: - 20-day momentum - Volatility deviation - Rank the indicators in reverse order and sum the rankings to determine the market sentiment capture indicator for each style index: $$\text{Market Sentiment Capture Indicator} = \text{Rank (20-day Momentum)} + \text{Rank (Volatility Deviation)}$$ - Allocate portfolio weights based on the rankings, with a preference for the style index with the lowest indicator value. If rankings are equal, allocate weights equally. If all three styles are selected, allocate 100% to the balanced low-valuation style[28] - **Model Evaluation**: Demonstrates superior performance compared to the equal-weighted convertible bond index, with a focus on balanced low-valuation styles[27][33] --- Quantitative Factors and Construction Methods 1. Factor Name: 转股溢价率偏离度 (Conversion Premium Deviation) - **Factor Construction Idea**: Measures the deviation of the conversion premium rate from its fitted value, enabling comparability across different parities[19][20]. - **Factor Construction Process**: $$\text{Conversion Premium Deviation} = \text{Conversion Premium Rate} - \text{Fitted Conversion Premium Rate}$$ - The number of convertible bonds determines the fitting quality[20] - **Factor Evaluation**: Provides a robust measure for identifying valuation discrepancies in convertible bonds[20] 2. Factor Name: 理论价值偏离度 (Theoretical Value Deviation, Monte Carlo Model) - **Factor Construction Idea**: Quantifies the price expectation gap by considering various convertible bond terms (e.g., conversion, redemption, downward revision, put options) through Monte Carlo simulation[19][20]. - **Factor Construction Process**: $$\text{Theoretical Value Deviation} = \frac{\text{Convertible Bond Closing Price}}{\text{Theoretical Value}} - 1$$ - Simulate 10,000 paths at each time point using the Monte Carlo model, with the same credit term interest rate as the discount rate[20] - **Factor Evaluation**: Effectively captures valuation discrepancies, particularly for equity-heavy convertible bonds[19][20] 3. Factor Name: 转债综合估值因子 (Comprehensive Convertible Bond Valuation Factor) - **Factor Construction Idea**: Combines the rankings of the above two factors to enhance valuation analysis across all domains (equity-heavy, balanced, debt-heavy)[19][20]. - **Factor Construction Process**: $$\text{Comprehensive Convertible Bond Valuation Factor} = \text{Rank (Conversion Premium Deviation)} + \text{Rank (Theoretical Value Deviation)}$$ - **Factor Evaluation**: Demonstrates superior performance in identifying undervalued convertible bonds across different styles[19][20] --- Backtesting Results of Models 1. Convertible Bond Style Rotation Model - **Annualized Return**: 23.38% - **Annualized Volatility**: 16.48% - **Maximum Drawdown**: -15.54% - **IR**: 1.42 - **Calmar Ratio**: 1.50 - **Monthly Win Rate**: 65.12%[33] --- Backtesting Results of Factors 1. 转股溢价率偏离度 Factor - **Equity-Heavy Convertible Bonds**: Enhanced excess return of 0.9% over the past 4 weeks[22] - **Balanced Convertible Bonds**: Enhanced excess return of 1.2% over the past 4 weeks[22] - **Debt-Heavy Convertible Bonds**: Enhanced excess return of -0.3% over the past 4 weeks[22] 2. 理论价值偏离度 Factor - **Equity-Heavy Convertible Bonds**: Enhanced excess return of 0.9% over the past 4 weeks[22] - **Balanced Convertible Bonds**: Enhanced excess return of 1.2% over the past 4 weeks[22] - **Debt-Heavy Convertible Bonds**: Enhanced excess return of -0.3% over the past 4 weeks[22] 3. 转债综合估值因子 Factor - **Equity-Heavy Convertible Bonds**: Enhanced excess return of 0.9% over the past 4 weeks[22] - **Balanced Convertible Bonds**: Enhanced excess return of 1.2% over the past 4 weeks[22] - **Debt-Heavy Convertible Bonds**: Enhanced excess return of -0.3% over the past 4 weeks[22]