How to compare market efficiency? The Sharpe ratio based on the ARMA-GARCH forecast
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Financial Innovation
RESEARCH
Open Access
How to compare market efficiency? The Sharpe ratio based on the ARMA-GARCH forecast Lin Liu*
and Qiguang Chen
* Correspondence: [email protected] Peking University, Beijing 100871, China
Abstract 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. Keywords: ARMA, GARCH, Measurement of market efficiency, Sharpe ratio, Stochastic simulation Mathematics subject classification: 60G10, 62 M10 JEL classification: G10, G14, G17, C22
Introduction Since Fama (1970) published his influential paper, there has been a thorough assessment of market efficiency. Various methods have been proposed over the decades to test the efficient market hypothesis (EMH), but the empirical results vary according to the specific markets chosen, periods of time, and even the selected methods. For instance, like the frictionless state in physics, the efficient market could just be viewed as an ideal state with no real existence in the world. However, it could serve as a useful benchmark for measuring relative efficiency of markets over space and time. In fact, it is more relevant to measure the relative efficiency of markets from the empirical perspective. Just as Campbell et al. (1997) pointed out, “The notion of relative efficiency—the efficiency of one market measured against another—may be a more useful concept than the all-or-nothing view taken by much of the traditional marketefficiency literature.” © The Author(s). 2020 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Liu and Chen Financial Innovation
(2020) 6:38
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