- The report discusses the concept of index futures arbitrage, which includes forward and reverse arbitrage strategies. Forward arbitrage occurs when the spot price is undervalued and the futures price is overvalued, while reverse arbitrage happens when the spot price is overvalued and the futures price is undervalued. The theoretical basis is that futures and spot prices converge on the delivery date[43] - The formula for forward arbitrage return is: $$P={\frac{(F_{\mathrm{t}}-S_{\mathrm{t}})-(S_{\mathrm{t}}+F_{\mathrm{t}}M_{\mathrm{f}})(1+r_{\mathrm{f}})^{\frac{T-t}{360}}-S_{\mathrm{t}}C s-F_{\mathrm{t}}C f)}{S_{\mathrm{t}}+F_{\mathrm{t}}M_{\mathrm{f}}}}$$ In this formula: - \(F_t\) and \(S_t\) represent the futures and spot prices at time \(t\) - \(M_f\) is the margin ratio for futures - \(C_s\) and \(C_f\) are transaction costs for spot and futures respectively - \(r_f\) is the risk-free interest rate[43] - The formula for reverse arbitrage return is: $$P={\frac{(S_{t}-F_{t})-(S_{t}M l+F_{t}M_{f})(1+r_{f})^{\frac{T-t}{360}}-S_{t}C s-F_{t}C f-S_{t}r^{\frac{T-t}{l360}})}{S_{t}M l+F_{t}M_{f}}}$$ In this formula: - \(M_l\) is the margin ratio for short selling - \(r_l\) is the annualized interest rate for short selling[43] - The report evaluates the risks associated with arbitrage strategies, including margin call risk, basis non-convergence risk, dividend risk, tracking error risk, and liquidity risk[44] - Dividend prediction methodology is outlined, where historical dividend patterns are used to forecast future dividend points. For companies with stable dividends over three years, the average dividend rate is used. For companies with unstable dividends but consistent profitability, the previous year's dividend rate is applied. For companies with no profitability or significant changes, a zero dividend rate is assumed[45][48] - The formula for calculating the dividend impact on index points is: $$\text{Dividend Points} = \sum \left( \text{Per Share Dividend} \times \text{Index Closing Price} \times \text{Component Stock Weight} \right) / \text{Component Stock Closing Price}$$ Alternatively: $$\text{Dividend Points} = \sum \left( \text{Forecast Dividend Rate} \times \text{Index Closing Price} \times \text{Component Stock Weight} \right)$$[49]