This paper derives a new method for comparing the weak-form efficiency of markets. The author derives the formula of the Sharpe ratio from the ARMA-GARCH model and finds that the Sharpe ratio just depends on the coefficients of the AR and MA terms and is not affected by the GARCH process. For empirical purposes, the Sharpe ratio can be formulated with a monotonic increasing function of R-squared if the sample size is large enough. One can utilize the Sharpe ratio to compare weak-form efficiency among different markets. The results of stochastic simulation demonstrate the validity of the proposed method. The author also constructs empirical AR-GARCH models and computes the Sharpe ratio for S&P 500 Index and the SSE Composite Index.

中文翻译：

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如何比较市场效率？基于 ARMA-GARCH 预测的夏普比率

本文推导出一种比较市场弱形式效率的新方法。作者从ARMA-GARCH模型推导出夏普比率的公式，发现夏普比率只取决于AR和MA项的系数，不受GARCH过程的影响。出于经验目的，如果样本量足够大，可以使用 R 平方的单调递增函数来制定夏普比率。可以利用夏普比率来比较不同市场之间的弱形式效率。随机模拟的结果证明了所提出方法的有效性。作者还构建了经验 AR-GARCH 模型并计算了标准普尔 500 指数和上证综合指数的夏普比率。