Degree of (In)Efficiency in the Stock Market: Do Price-Earnings Ratios Matter?

Keywords: Efficient Markets, Long Memory, Price-Earnings Ratio, Brazilian Companies

Abstract

Employing an innovative approach based on fractional integration, this study examines the potential heterogeneity in long memory (persistence) behavior among stocks of two groups of companies listed on stock markets: those with higher price-earnings (P/E) ratios and those with lower P/E ratios. This empirical investigation offers a novel contribution to the ongoing economic literature on market efficiency and long memory dynamics, in the period spanning January 2016 to December 2022, based on Brazil's daily stock prices. The fractionally integrated parameter is used to check long memory and, for both returns and volatility, the results reveal that P/E ratios alone do not significantly influence the degree of persistence, as both groups display similar long memory patterns. Notably, the occurrence of persistent volatility is more attributable to external shocks, such as the COVID-19 crisis, than to valuation metrics, such as the P/E ratio. Furthermore, the stock market's degree of (in)efficiency is time-varying and exhibits mean reversion (i.e., it is transient), indicating transitory inefficiencies.

References

Abbritti, M., Gil-Alana, L. A., Moreno, A., and Lovcha, Y. (2016). Term structure persistence. Journal of Financial Econometrics, 14(2):331–352.

Amorim, D. P. L. and Camargos, M. A. (2021). Reversão à média em um índice preço-lucro e sub/sobrevalorização no mercado de ações brasileiro. Revista Contabilidade e Finanças, 32(86):301–313.

Baillie, R. T. (1996). Long memory processes and fractional integration in econometrics. Journal of Econometrics, 73(1):5–59.

Baillie, R. T., Bollerslev, T., and Mikkelsen, H. O. (1996). Fractionally integrated generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 74(1):3–30.

Ball, R. (1978). Anomalies in relationships between securities’ yields and yield-surrogates. Journal of Financial Economics, 6(2-3):103–126.

Basu, S. (1977). Investment performance of common stocks in relation to their price-earnings ratios: A test of the efficient market hypothesis. The Journal of Finance, 32(3):663–682.

Bennett, V. M. and Gartenberg, C. M. (2016). Changes in persistence of performance over time. Research Paper 2016-41, Duke I&E. Retrieved from: https://ssrn.com/abstract=2839630.

Bhattacharya, S. N., Bhattacharya, M., and Guhathakurta, K. (2018). The comparative dynamics of developed and emerging stock markets: A long memory perspective. Theoretical Economics Letters, 8(8):1493–1509.

Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31(3):307–327.

Bollerslev, T. and Mikkelsen, H. O. (1996). Modeling and pricing long-memory in stock market volatility. Journal of Econometrics, 73(1):151–184.

Booth, G. G., Kaen, F. R., and Koveos, P. E. (1982). R/S analysis of foreign exchange rates under two international monetary regimes. Journal of Monetary Economics, 10(3):407–415.

Breidt, F. J., Crato, N., and de Lima, P. (1998). The detection and estimation of long memory in stochastic volatility. Journal of Econometrics, 83(1-2):325–348.

Cajueiro, D. O. and Tabak, B. M. (2004). The Hurst exponent over time: Testing the assertion that emerging markets are becoming more efficient. Physica A: Statistical Mechanics and its Applications, 336(3-4):521–537.

Campbell, J. Y. and Shiller, R. J. (1988). Stock prices, earnings, and expected dividends. The Journal of Finance, 43(3):661–676.

Caporale, G. M., Gil-Alana, L., and Plastun, A. (2019). Long memory and data frequency in financial markets. Journal of Statistical Computation and Simulation, 89(10):1763–1779.

Cavalcante, J. and Assaf, A. (2004). Long-range dependence in the returns and volatility of the Brazilian stock market. European Review of Economics and Finance, 3:5–22.

Chan, L. K. C., Hamao, Y., and Lakonishok, J. (1991). Fundamentals and stock returns in Japan. The Journal of Finance, 46(5):1739–1764.

Chan, N. H. and Wei, C. Z. (1988). Limiting distributions of least squares estimates of unstable autoregressive processes. The Annals of Statistics, 16(1):367–401.

Charfeddine, L. (2016). Breaks or long-range dependence in the energy futures volatility: Out-of-sample forecasting and VaR analysis. Economic Modelling, 53:354–374.

Charfeddine, L. and Guégan, D. (2012). Breaks or long memory behavior: An empirical investigation. Physica A: Statistical Mechanics and its Applications, 391(22):5712–5726.

Corazza, M. and Malliaris, A. G. (2002). Multifractality in foreign currency markets. Multinational Finance Journal, 6:387–401. Retrieved from https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1084659.

Costa, R. L. and Vasconcelos, G. L. (2003). Long-range correlations and nonstationarity in the Brazilian stock market. Physica A: Statistical Mechanics and its Applications, 329(1-2):231–248.

Crato, N. and de Lima, P. (1994). Long-range dependence in the conditional variance of stock returns. Economics Letters, 45(3):281–285.

Crato, N. and Ray, B. K. (2000). Memory in returns and volatilities of futures’ contracts. Journal of Futures Markets, 20(6):525–543.

Daniel, K. and Titman, S. (1997). Evidence on the characteristics of cross-sectional variation in stock returns. The Journal of Finance, 52(1):1–33.

Dickey, D. A. and Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49(4):1057–1072.

Diebold, F. X. and Inoue, A. (2001). Long memory and regime switching. Journal of Econometrics, 105(1):131–159.

Ding, Z., Granger, C. W. J., and Engle, R. F. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance, 1(1):83–106.

dos Santos, M. A., Fávero, L. P. L., Brugni, T. V., and Serra, R. G. (2024). Adaptive markets hypothesis and economic-institutional environment: A cross-country analysis. Revista de Gestão, 31(2):215–236.

dos Santos Maciel, L. (2023). Brazilian stock-market efficiency before and after COVID-19: The roles of fractality and predictability. Global Finance Journal, 58:100887.

Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4):987–1007.

Fama, E. F. (1991). Efficient capital markets: II. The Journal of Finance, 46(5):1575–1617.

Fama, E. F. (1998). Market efficiency, long-term returns, and behavioral finance. Journal of Financial Economics, 49(3):283–306.

Geweke, J. and Porter-Hudak, S. (1983). The estimation and application of long memory time series models. Journal of Time Series Analysis, 4(4):221–238.

Glenn, L. A. (2007). On randomness and the NASDAQ composite. Available at SSRN: http://ssrn.com/abstract=1124991.

Greene, M. T. and Fielitz, B. D. (1977). Long-term dependence in common stock returns. Journal of Financial Economics, 4(3):339–349.

Henry, Ó. T. (2002). Long memory in stock returns: Some international evidence. Applied Financial Economics, 12(10):725–729.

Hull, J. C. (2021). Options, futures, and other derivatives. Pearson Education Limited, London, 11th edition.

Hull, M. and McGroarty, F. (2014). Do emerging markets become more efficient as they develop? Long memory persistence in equity indices. Emerging Markets Review, 18:45–61.

Hurvich, C. M., Deo, R., and Brodsky, J. (1998). The mean squared error of Geweke and Porter-Hudak’s estimator of the memory parameter of a long-memory time series. Journal of Time Series Analysis, 19(1):19–46.

Jacobsen, B. (1995). Are stock returns long term dependent? Some empirical evidence. Journal of International Financial Markets, Institutions and Money, 5(2/3). Retrieved from https://papers.ssrn.com/sol3/papers.cfm?abstract_id=7459.

Jaffe, J., Keim, D. B., and Westerfield, R. (1989). Earnings yields, market values, and stock returns. The Journal of Finance, 44(1):135–148.

Kim, C. S. and Phillips, P. C. B. (2006). Log periodogram regression: The nonstationary case. Discussion Paper 1587, Cowles Foundation.

Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., and Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? Journal of Econometrics, 54(1-3):159–178.

Lakonishok, J., Shleifer, A., and Vishny, R. W. (1994). Contrarian investment, extrapolation, and risk. The Journal of Finance, 49(5):1541–1578.

Lee, D. K. C. and Robinson, P. M. (1996). Semiparametric exploration of long memory in stock prices. Journal of Statistical Planning and Inference, 50(2):155–174.

Lekhal, M. and El Oubani, A. (2020). Does the adaptive market hypothesis explain the evolution of emerging markets efficiency? Evidence from the Moroccan financial market. Heliyon, 6(7):e04429.

Lo, A. W. (1991). Long-term memory in stock market prices. Econometrica, 59(5):1279–1313.

Lo, A. W. (2004). The adaptive markets hypothesis. The Journal of Portfolio Management, 30(5):15–29.

Lo, A. W. (2005). Reconciling efficient markets with behavioral finance: The adaptive markets hypothesis. Journal of Investment Consulting, 7(2):21–44. Retrieved from https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1702447.

Lu, Y. K. and Perron, P. (2010). Modeling and forecasting stock return volatility using a random level shift model. Journal of Empirical Finance, 17(1):138–156.

Maheswaran, S. (1990). Predictable short-term variation in asset prices: Theory and evidence. Working paper, Carlson School of Management, University of Minnesota.

Maheswaran, S. and Sims, C. A. (1992). Empirical implications of arbitrage-free asset markets. Discussion Paper 1251, Cowles Foundation.

Malkiel, B. G. (2003). The efficient market hypothesis and its critics. Journal of Economic Perspectives, 17(1):59–82.

Mandelbrot, B. B. (1972). Statistical methodology for nonperiodic cycles: From the covariance to R/S analysis. In Annals of Economic and Social Measurement, volume 1, pages 259–290. NBER. Retrieved from http://www.nber.org/chapters/c9433.pdf.

Molinares, F. F., Reisen, V. A., and Cribari-Neto, F. (2009). Robust estimation in long-memory processes under additive outliers. Journal of Statistical Planning and Inference, 139(8):2511–2525.

Monte, E. Z. (2023). A long-memory analysis for the CBOE Brazil ETF volatility index. International Journal of Emerging Markets, 18(11):5155–5171.

Nicholson, S. F. (1960). Price-earnings ratios. Financial Analysts Journal, 16(4):43–45.

Perron, P. and Qu, Z. (2010). Long-memory and level shifts in the volatility of stock market return indices. Journal of Business & Economic Statistics, 28(2):275–290.

Peters, E. E. (1991). Chaos and order in the capital markets: A new view of cycles, prices, and market volatility. John Wiley & Sons, Inc.

Peters, E. E. (1994). Fractal market analysis: Applying chaos theory to investment and economics. John Wiley & Sons, Inc.

Phillips, P. C. B. and Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2):335–346.

Ray, B. K. and Tsay, R. S. (2000). Long-range dependence in daily stock volatilities. Journal of Business & Economic Statistics, 18(2):254–262.

Reisen, V. A. (1994). Estimation of the fractional difference parameter in the ARIMA(p,d,q) model using the smoothed periodogram. Journal of Time Series Analysis, 15:335–350.

Resende, M. and Teixeira, N. (2002). Permanent structural changes in the Brazilian economy and long memory: A stock market perspective. Applied Economics Letters, 9(6):373–375.

Serletis, A. and Rosenberg, A. A. (2007). The Hurst exponent in energy futures prices. Physica A: Statistical Mechanics and its Applications, 380:325–332.

Shimotsu, K. (2010). Exact local Whittle estimation of fractional integration with unknown mean and time trend. Econometric Theory, 26(2):501–540.

Shimotsu, K. and Phillips, P. C. B. (2005). Exact local Whittle estimation of fractional integration. The Annals of Statistics, 33(4):1890–1933.

Sims, C. A. (1984). Martingale-like behavior of prices and interest rates. Discussion Paper 205, Center for Economic Research, Department of Economics, University of Minnesota.

Stărică, C. and Granger, C. (2005). Nonstationarities in stock returns. The Review of Economics and Statistics, 87(3):503–522.

Taleb, N. N. (2008). Fooled by randomness: The hidden role of chance in life and in the markets. Random House, New York.

Taylor, S. (1986). Modelling financial time series. Wiley.

Tiao, G. C. and Tsay, R. S. (1983). Consistency properties of least squares estimates of autoregressive parameters in ARMA models. The Annals of Statistics, 11(3):856–871.

Tsay, R. S. (2010). Analysis of financial time series. Wiley, 3rd edition.

Velasco, C. (2000). Non-Gaussian log-periodogram regression. Econometric Theory, 16(1):44–79. Retrieved from https://www.jstor.org/stable/3533159.

Vera-Valdés, J. E. (2022). The persistence of financial volatility after COVID-19. Finance Research Letters, 44:102056.

Woo, K.-Y., Mai, C., McAleer, M., and Wong, W.-K. (2020). Review on efficiency and anomalies in stock markets. Economies, 8(1):1–51.

Published
2025-09-11
How to Cite
Monte, E. Z., & Moreira, R. R. (2025). Degree of (In)Efficiency in the Stock Market: Do Price-Earnings Ratios Matter?. Econometric Research in Finance, 10(1), 1-24. https://doi.org/10.33119/ERFIN.2025.10.1.1
Section
Articles
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