Methods for Measuring Changes in Stock Market Efficiency
Summary
The document surveys empirical approaches for assessing how stock market efficiency changes over time, distinguishing broad market measures from firm-level analysis. For firm-specific questions, it identifies event studies as a common procedure and points to methodological literature. For broad markets, it lists tests and proxies including ARMA model tests, variance ratios, Hurst exponents, approximate entropy, an efficiency index, and market-model R-squared.
The discussion is a reference-oriented overview rather than a comparison of performance. It cites review work and original studies, but does not provide implementation details, empirical results, or criteria for choosing a single best measure. The measures capture different properties and rely on different assumptions, so the document leaves selection to the research question and market context; it does not establish that any one proxy is universally superior.
Key ideas
- Event studies are presented as a common method for studying firm-specific market efficiency.
- Variance ratio tests assess deviations from random-walk behavior in market prices.
- The listed broad-market proxies include ARMA tests, Hurst exponents, approximate entropy, an efficiency index, and market-model R-squared.
- The document provides references but does not compare the measures empirically or recommend one as universally best.
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Full text
# What are the main market efficiency measures in the stock market? # What are the main market efficiency measures in the stock market? I'm going to test for the effect of the change in market efficiency on the stock market portfolio, and, I want to know what are the main measures known in the academic literature in order to compare them and to choose the "best" one for a given market. Till now, I found the following measures to test for market efficiency in the broad market-specific case: - Variance Ratio (Lo & MacKinlay, 1988) - Approximate Entropy (Pincus, 1991) - The Hurst exponent (Peters, 1994) - Mkt Delay (Pagano & Schwartz, 2002) For the firm-specific case, I found that the event-study procedure is the most common to test the market efficiency. Could you suggest other measures or other procedures to test for market efficiency in the stock market, in addition to the ones I cited above, or, alternatively, suggest which is the best one by providing a reference? ## Answer by Quantopik (score 3) https://quant.stackexchange.com/a/18516 There are different methodologies to detect a change in the market efficiency, both in the market and firm-specific cases. In the FIRM-SPECIFIC case, the most common procedure is the event study methodology; you can find how to construct an event-study case explained in Kothari & Warner (2006), who collected all the event study methodology implemented till 2006 in the academic literature; below, you can find the paper reference and relative link: > Kothari, S. P., and Jerold B. Warner. "The econometrics of event studies." > Available at SSRN 608601 (2004). In the BROAD MARKET case, there exist different measures/proxy for the market efficiency exploited in the academic literature to test and measure the effects of the change in market efficiency on the markets. Below, you can find a list of the proxies developed in the academic literature to test/measure the level of market efficiency and the relative references in chronological order. As regards the review about market efficiency test and measuring: > Bollerslev, Tim, and Robert J. Hodrick. Financial market efficiency tests. No. w4108. National bureau of economic research, 1992. Lim, Kian‐Ping, and Robert Brooks. "The evolution of stock market efficiency over time: a survey of the empirical literature." Journal of Economic Surveys 25.1 (2011): 69-108. As regards the market efficiency test: - ARMA() Model test > Amihud, Yakov, and Haim Mendelson. "Trading mechanisms and stock returns: An empirical investigation." The Journal of Finance 42.3 (1987): 533-553. - Variance Ratio Test/MEC() > Lo, Andrew W., and A. Craig MacKinlay. "Stock market prices do not follow > random walks: Evidence from a simple specification test." Review of financial > studies 1.1 (1988): 41-66. - Hurst Exponent Over-Time > Peters, Edgar E. Fractal market analysis: applying chaos theory to investment and economics. Vol. 24. John Wiley & Sons, 1994. Cajueiro, Daniel O., and Benjamin M. Tabak. "The Hurst exponent over time: testing the assertion that emerging markets are becoming more efficient." Physica A: Statistical Mechanics and its Applications 336.3 (2004): 521-537. As regards the market efficiency measures: - Approximate Entropy > Pincus, Steven M. "Approximate entropy as a measure of system complexity." Proceedings of the National Academy of Sciences 88.6 (1991): 2297-2301. Look at here to know more about the statistical properties of the approximate entropy measure. - Efficiency Index > L. Kristoufek and M. Vosvrda. Measuring capital market efficiency: Global and local correlations structure. Physica A, 392:184–193, 2013. - Market Model $R^2$ > Bramante, Riccardo, Diego Zappa, and Giovanni Petrella. "On the interpretation and estimation of the market model R-square." Electronic Journal of Applied Statistical Analysis 6.1 (2013): 57-66. THIS ANSWER WILL BE UPDATED; ANY HINT, ADVISES OR IDEA WILL BE APPRECIATED
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