分红对期指的影响20250418

Quantitative Models and Construction Methods - Model Name: Theoretical Pricing Model for Stock Index Futures Model Construction Idea: This model calculates the theoretical price of stock index futures by considering the impact of dividends, risk-free interest rates, and the time to maturity. It assumes no arbitrage conditions in the market[34][35] Model Construction Process: 1. Discrete Dividend Distribution: - Assume the futures price at time $t$ is $F_t$, the spot price is $S_t$, the maturity date is $T$, and the present value of dividends during $T-t$ is $D$. The risk-free rate over $T-t$ is $r$. - If there are $m$ dividend payments at times $t_1, t_2, ..., t_m$, with amounts $D_1, D_2, ..., D_m$, the present value of dividends is: $\mathbf{D} = \sum_{\mathrm{i=1}}^{\mathrm{m}} \mathbf{D}_{\mathrm{i}} / (1 + \phi)$ Here, $\phi$ represents the risk-free rate between two dividend payments. - The theoretical futures price is: $F_t = (S_t - D)(1 + r)$ 2. Continuous Dividend Distribution: - When dividends are distributed continuously, the theoretical futures price is: $F_t = S_t e^{(r-d)(T-t)}$ Here, $d$ is the annualized dividend yield, and $r$ is the annualized risk-free rate[34][35] Quantitative Factors and Construction Methods - Factor Name: Dividend Impact Factor Factor Construction Idea: This factor estimates the impact of dividends on stock index futures by predicting the dividend payout of index constituents and their contribution to the index[22][25] Factor Construction Process: 1. Estimate Net Profit: Use annual reports, earnings forecasts, and other financial data to estimate the net profit of index constituents[25][26] 2. Calculate Total Dividend: Assume the dividend payout ratio remains constant. For companies without prior dividends, assume no dividends. For companies with negative profits, set the dividend ratio to zero[29] 3. Calculate Dividend Impact on Index: - Dividend Yield = Total Dividend / Latest Market Value - Dividend Impact on Index = Stock Weight × Dividend Yield - Adjust stock weights based on price changes using the formula: $\mathrm{w_{it} = \frac{w_{i0} \times (1+R)}{\sum_{1}^{n} w_{i0} \times (1+R)}}$ Here, $w_{i0}$ is the initial weight, and $R$ is the price change[27] 4. Predict Impact on Futures Contracts: Aggregate the dividend impact for all constituents before the contract's expiration date[31] Backtesting Results of Models - Theoretical Pricing Model: - For the May contracts of major indices, the annualized hedging costs (excluding dividends) are: - CSI 300: 9.63% - CSI 500: 17.67% - CSI 1000: 19.08%[10][11][12] Backtesting Results of Factors - Dividend Impact Factor: - Remaining dividend impact on May contracts: - SSE 50: 0.00% - CSI 300: 0.20% - CSI 500: 0.07% - CSI 1000: 0.14%[13]