Applied Economics, 2006, 38, 631–636
Capital market efficiency and the predictability of daily returns Jeffrey E. Jarrett* and Eric Kyper University of Rhode Island, Ballentine Hall/Management Science, 7 Lippitt Road, Kingston RI 02881, USA
Studies of the weak form of the capital market efficiency theorem infer that there are no predictable properties of the time series of prices of traded securities on organized markets. We examine the weak form of the efficient markets hypothesis with respect to daily closing prices to indicate evidence that daily closing prices have predictable properties. Furthermore, this study of individual securities prices of traded securities on organized markets corroborates previous findings of studies of stock market indexes both in the United States and in other nations’ bourses or stock exchanges. Often, these studies indicated that daily patterns are present in the times series of securities prices. The purpose of this paper is to clarify the existence of time series characteristics of daily stock prices of securities traded on organized exchanges. This study differs from previous studies where the focus was on index numbers of daily stock market prices rather than the actual prices of traded securities in the United States. Furthermore, this study is important because of the weak theory of market efficiency and its application to short-term forecasting of closing prices of traded securities.
I. Introduction Capital market efficiency is an important research topic since Fama (1955, 1970) explained these principles as a part of the efficient market hypothesis. Following Fama’s work many studies were devoted to investigating the randomness of stock price movements for the purpose of demonstrating the efficiency of capital markets. In recent years, other studies demonstrated market inefficiencies by identifying systematic and permanent variations in stock returns. Some of these systematic variations, or anomalies as they are referred to, are small firm effects, investment recommendations, and extraordinary returns to the time or the calendar effect.
These calendar or time effects do contradict the weak form of the efficient market hypothesis. The weak form refers to the notion that the market is efficient in past price and volume information and we do not predict stock price movements accurately using historical information. If no systematic patterns exist, stock prices are time invariant. Whenever the time series of daily prices of securities markets exist, market inefficiency is present and investors are able to earn abnormal rates of return not in line with the degree of risk they undertook (Francis, 1993). In addition, a large number of studies in the literature on predicting prices of traded securities confirm to some degree that patterns exist in stock market prices. We know that interest rates, dividend yields and
*Corresponding author. E-mail:
[email protected] Applied Economics ISSN 0003–6846 print/ISSN 1466–4283 online ß 2006 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/00036840600581422
631
J. E. Jarrett and E. Kyper
632 a variety of macroeconomic variables exhibit clear business cycle patterns. The emerging literature concerning studies of United States securities include Balvers et al. (1990), Breen et al. (1990), Campbell (1987), Fama and French (1989) and Pesaran and Timmermann (1994, 1995), and Granger (1992) provides a up to that time survey of methods and results. Studies in other places (the United Kingdom) include Clare et al. (1994), Clare at al. (1995), Black and Fraser (1995) and Pesaran and Timmermann (2000). Furthermore, Caporale and Gil-Alana (2002) pointed out that for US stock returns their degree of predictability depends on the process followed by the error term. Evidence of other market inefficiencies and an historical account of them, such as bubbles and crashers, are presented in Chancellor (1999). Campbell and Lo (1997) explore the empirical evidence of such inefficiencies. Shiller (1989) indicates the importance of excess volatility and other nonlinearities in time series data has generated interest in the sources of capital market inefficiency (Lo and MacKinley, 1999). The expansion of time series analysis as a discipline permits one to analyse stock market prices in ways not heretofore explored. What is the predictability of the error term and is there predictability in daily stock market returns? Peculiar problems arise when daily patterns are present in stock price data. We know that stock prices possess patterns known as daily effects. For example, Kato’s (1990a) results suggested that there are patterns in stock returns in Japanese securities. He observed low Tuesday and high Wednesday returns within weekly prices. If a week did not have trading on a Friday, he would observe effects related to the Monday of the following week. The following Monday would have low returns indicating transference of the pattern that would occur on the Friday if trading had occurred which it did not. A second study by Kato (1990b) found considerable anomalies on the Tokyo Stock Exchange (TSE), which is an organized exchange similar to the ones in North America. Only a few studies focused on the investigation of time series components of equity prices and the predictability of these prices. Ray et al. (1997) investigated a sample of 15 firms and found both permanent and temporary systematic components in individual time series of stock market prices of firms over a lengthy period of time. Moorkejee and Yu (1999) investigated the seasonality in stock returns on the Shanghai and Shenzen stock markets. They documented the seasonal patterns existing on these exchanges and the effects these factors have on risk in investing in securities listed on these exchanges. In addition they showed that risk in
investing is related to the predictability of security prices. Rothlein and Jarrett (2002) investigated the existence of seasonality present in Japanese stock prices, which affect the prices of these securities. They documented the evidence of seasonality in the prices of 55 randomly selected Tokyo Stock Exchange firms over a lengthy period of 18 years (1975 through 1992). In addition, they indicated that the accuracy of forecasts or predictions of these firms’ prices are seriously decreased if one does not recognize the patterns in the time series. Last, Jarrett and Kyper (2005) indicated how patterns in monthly stock prices have predictable patterns. This study differs in that we examine the predictable patterns in the closing daily prices of stock prices. It goes further than the study of Caporale and Gil-Alana (2002) noted before, because it attempts to determine the patterns in daily prices of listed securities.
II. Predictive Model The predictive model for measuring the effects of changes in the day of the week on closing prices of a security is Y ¼ bo þ b1X1 þ b2 X2 þ b3X3 þ b4X4 þ b5X5 þ " where Y ¼ closing price of security X1 ¼ dummy variable for Tuesday (1 or 0 when not Tuesday) X2 ¼ dummy variable for Wednesday (1 or 0 when not Wednesday) X3 ¼ dummy variable for Thursday (1 or 0 when not Thursday) X4 ¼ dummy variable for Friday (1 or 0 when not Friday) X5 ¼ dummy variable for Tuesday after Monday holiday (1 or 0 when not a Tuesday following a Monday holiday) "¼ error term with mean of zero, bo ¼ intercept of model.
III. The Sample The sample includes monthly closing prices of 62 firms listed on organized exchanges in the United States (NYSE and NASDAQ). Although the selection was random, a heavier weighting for larger firms was given in order that we collect complete sets of time series data covering the study period from April 1992 to September 2002. The study period was
Capital market efficiency lengthy enough to minimize any effects of short-term economic fluctuations. Table 1 contains a list of the firms included in the sample.
IV. Analysis and Results Estimations of the aforementioned ordinary least squares models for closing prices for the individual firms sampled resulted in OLS equations containing autocorrelation. Hence, we fitted autoregressive equations of the first order with no intercept to the sampled time series. The results of these time series estimations appear in Table 2. Note the overall F-statistic was significant at a level of 0.0001 or less for all but one firm. In that case, the F-statistic for significance of overall regression was 0.0076, again a very small significance value. The adjusted coefficients of determination were also very large with most above the R2 value of 0.7000. That is, more than 70% of the total variation in closing prices was associated with the regression on the day of the week after correcting for autoregression of the error term.
633 Three other firms were above 0.6000 and three were in the range from 0.4500 to 0.5000. The coefficients for the days of the week are presented in Table 3 as measured by the regressions for the firms in the sample. They represent the weight given to the day of the week including a special Tuesday (referred to Tuesday following a Monday holiday. We should note first the signs of the coefficients. For Tuesdays, all the coefficients were significant at levels equal to 0.0001 or less. The same results occur for Wednesdays, Thursdays and Fridays. For Tuesday after a Monday holiday (TAH), the results vary a little. FDC (First Data Corporation) did not have a significant coefficient for five additional firms. The significance of the coefficients ranged from a low of 0.0002 to 0.03. All of these coefficients were thus significant at somewhat higher levels but still the risk level of rejecting a true null hypothesis (Type 1 Error) are very small. Regression results are always subject to the limitation on the sample study period and the elements (firms) under study. However, the compelling results
Table 1. Study sample Symbol
Firm
Symbol
Firm
abv adrx ahc aig ald amat bmy c cat cers cmcsk cohr cost csco cvs cvx cytc dj f fbf fdc fnm fox fre g ge hal has hb hd hlt
Companhia de Bebidas das Americas Andrx Corp. Amerada Hess Corp. American International Group Inc. Allied Capital Corp. Applied Materials Inc. Bristol-Myers Squibb Co. Citigroup Inc. Caterpillar Inc. Cerus Corp. Comcast Corp. Coherent Inc. Costco Wholesale Corp. Cisco Systems Inc. CVS Corp. ChevronTexaco Corp. CYTYC Corp. Dow Jones & Company Inc. Ford Motor Co. FleetBoston Financial Corp. First Data Corp. Fannie Mae. Fox Entertainment Group Inc. Freddie Mac. Gillette Co. General Electric Co. Halliburton Co. Hasbro Inc. Hillenbrand Industries Inc. Home Depot Inc. Hilton Hotels Corp.
hpq intc jdsu jnj jpm klac ko l lmt low mcd mdt medi msft mwd nok orcl pfe pmcs rdn sunw t tpth txu unh unp utx vz wmb wmt yhoo
Hewlett-Packard Co. Intel Corp. JDS Uniphase Corp. Johnson & Johnson Inc. JP Morgan Chase KLA Tencor Coca-Cola Co. Liberty Media Corp. Lockheed Martin Corp. Lowe’s Cos Inc. McDonald’s Corp. Medtronic Inc. Medimmune Inc. Microsoft Corp. Morgan Stanley Nokia Oyj. Oracle Corp. Pfizer Inc. PMC-Sierra Radian Group Sun Microsystems AT&T Corp. TriPath Imaging TXU Corp. United Health Group Union Pacific Corp. United Technologies Verizon Communications Williams Companies Wal-Mart Stores Yahoo
J. E. Jarrett and E. Kyper
634 Table 2. Regression results with F-statistics Symbol abv adrx ahc aig ald amat bmy c cat cers cmcsk cohr cost csco cvs cvx cytc dj f fbf fdc fnm fox fre g ge hal has hb hd hlt
Adj. R sq. 0.8045 0.7833 0.799 0.8057 0.7985 0.7611 0.8052 0.807 0.787 0.7993 0.8063 0.7295 0.8048 0.6361 0.7902 0.8052 0.782 0.8065 0.801 0.8092 0.7882 0.7891 0.7863 0.7868 0.8077 0.8007 0.7922 0.7885 0.787 0.8015 0.8031
Overall F
Overall P
247.89 217.86 239.44 249.73 238.83 192.12 249.03 251.93 222.68 239.90 250.70 162.78 248.36 105.87 26.98 249.04 216.20 251.05 242.51 255.40 224.34 225.46 221.75 222.42 252.97 242.01 229.68 224.64 222.68 243.32 245.73
Symbol hpq intc jdsu jnj jpm klac ko lmt low mcd mdt medi msft mwd nok orcl pfe pmcs rdn sunw t tpth txu unh unp utx vz wmb wmt yhoo
Adj. R sq. 0.7317 0.7124 0.4963 0.8059 0.7965 0.7693 0.8027 0.7986 0.7986 0.8088 0.8064 0.7551 0.7972 0.7781 0.739 0.7106 0.8083 0.4941 0.7974 0.6212 0.7838 0.7628 0.7926 0.7953 0.7985 0.8033 0.8021 0.7996 0.8083 0.4529
Overall F
Overall P
164.64 149.61 60.12 250.12 234.23 201.04 245.13 238.95 238.95 254.72 250.98 185.95 236.90 211.35 170.92 148.35 254.05 59.60 237.10 99.40 218.52 193.91 230.25 234.17 238.83 246.07 244.15 240.42 253.91 50.68
Note: Significant at 0.0001 or less.
indicate that there is a day of the week effect on the closing prices of securities. However, the notion that closing prices of securities follow random walks is in doubt based on the results of this study. We do not dispute that financial markets function well, and that competitive institutions in which consistent abnormal profits based on public or historical information are rare. V. Conclusions We document in this study that daily closing prices for a sufficiently large sample of firms contain properties and one with enough time, patience and understanding of the mathematics of the underlying processes that give rise to a time series can properly model that time series. The result would permit one to note that time series of closing prices may not be random and do have daily effects. Hence, in this study, we indicate substantially the existence of time series components in closing prices of a randomly selected set of firms traded on organized market
exchanges in the United States. The results corroborate results of previous studies of international markets and previous studies of markets in the United States where time series daily and monthly components are present in closing prices and indexes of prices of securities. When these properties in closing prices exist, it is possible to forecast the patterns, and thus investors can benefit from this information. Furthermore, the results indicate that the weak form of the efficient markets hypothesis is in question when one must make decisions concerning investing in stock market securities. The notion that daily variation is random or stochastic is in doubt and possibly one can predict daily patterns with some degree of accuracy. We suggest, for purposes of prediction that forecasters predict systematic time series components of closing prices. In addition, one cannot understate the importance of stock returns and portfolio risk. These factors coupled with recognition of systematic time series components in stock prices can make one a better forecaster for prices of individual securities.
Capital market efficiency
635
Table 3. Regression results t-tests of coefficients Symbol abv adrx ahc aig ald amat bmy c cat cers cmcsk cohr cost csco cvs cvx cytc dj f fbf fdc fnm fox fre g ge hal has hb hd hlt hpq intc jdsu jnj jpm klac ko l lmt low mcd mdt medi msft mwd nok orcl pfe pmcs rdn sunw t tpth txu unh unp utx vz wmb wmt yhoo
T
T ( p)
21.17704 67.81722 70.78315 85.90704 19.02185 26.22481 55.51704 50.99685 41.87574 57.95537 39.63833 43.53 37.48593 36.12296 48.07426 83.14111 19.75574 56.57037 25.9707 36.2913 28.41926 72.16438 23.98241 57.63629 29.73241 47.5763 39.1063 12.68352 46.37519 46.6287 10.74981 35.49815 38.38389 51.01389 47.82593 41.91225 44.25674 51.28222 16.72222 34.6813 34.6813 29.21222 48.84352 49.79519 64.08593 70.62656 32.73648 25.08704 41.7637 94.89778 34.75722 32.00537 23.57241 7.39907 37.67667 56.58741 49.94963 69.77556 48.43815 37.31815 50.90019 46.58333
W
W ( p)
21.23623 67.86164 70.44836 85.56557 18.89393 26.44213 55.90705 50.60131 41.77754 57.90197 39.53311 44.18115 37.52656 36.35328 48.44164 82.8241 19.59984 56.45541 25.78525 36.32328 28.22459 73.18443 23.94689 58.43361 29.88262 47.34525 39.04607 12.68836 46.10377 46.76541 10.76279 35.37951 38.60705 50.82443 47.77967 42.69333 45.10475 51.90361 16.70492 34.35984 34.35984 29.48426 49.01131 50.61656 63.18984 70.61393 33.10098 25.41426 41.78148 94.08836 34.63443 31.88459 23.29639 7.48475 37.55328 56.27033 49.76672 69.53279 47.9782 37.1782 51.19803 46.77869
Note: Significance level of 0.0001 or less.
Th
Th ( p)
21.20623 67.92918 70.75803 85.56541 18.99262 26.51197 55.68377 50.83475 42.01066 58.93049 39.7682 44.24885 37.69033 36.14623 48.11967 82.91984 19.7518 56.46 25.88164 36.57492 28.37098 73.50508 24.08918 58.84967 29.85623 47.49213 38.79623 12.65295 46.32984 46.63262 10.82459 35.3418 38.67623 50.44754 47.84738 42.88517 45.84754 51.65082 16.73836 34.5082 34.5082 29.30934 49.08426 49.94918 63.44541 70.88131 32.82016 25.69246 41.60689 93.30984 34.78705 31.53016 23.36934 7.50656 37.69836 56.45246 50.07344 69.86836 48.13754 36.93213 51.16443 46.12934
F
F ( p)
21.21131 68.32295 70.71459 85.51525 18.95066 26.1641 55.75787 50.75754 41.70393 58.46033 39.6277 43.66852 37.41246 36.21918 47.8523 82.92852 19.80639 56.54148 25.6723 36.39705 28.2282 73.5077 23.99721 58.74148 29.91705 47.37148 38.71475 12.64426 46.51902 46.34016 10.83033 35.23672 38.20115 51.02115 47.84213 42.79131 45.11656 51.68738 16.83705 34.46361 34.46361 29.41689 49.04 50.1486 63.18803 70.9277 32.91869 25.49213 41.65508 94.36344 34.71885 31.61459 23.25967 7.55705 37.75148 56.38754 49.84869 69.47754 48.08869 36.93705 50.84164 45.78426
TAH
TAH ( p)
21.87286 66.18714 73.21429 87.02571 19.42143 24.72143 59.31429 51.80714 43.87143 63.03714 40.28857 41.29143 39.36714 34.40714 50.83429 82.88143 19.88286 56.27714 25.11714 37.40857 0.08069 65.10366 23.17143 52.54053 31.7 46.46714 39.36286 12.52714 47.21714 46.33857 11.26857 32.60857 35.81429 44.11 48.80286 39.00825 37.59618 54.53429 15.91143 34.86857 34.86857 31.39 51.59857 49.36143 56.46571 73.39143 34.19571 26.49429 42.01571 80.58714 34.91571 28.78857 21.72 8.62 39.24143 57.02 50.92571 72.00571 47.57143 36.78857 51.71571 37.27429
0.0002
0.9879
0.011
0.0125
0.0007
0.03
636 References Balvers, R. J., Cosimano, T. F. and MacDonald, B. (1990) Predicting stock returns in an efficient market, Journal of Finance, 45, 1109–28. Black, A. and Fraser, P. (1995) UK stock returns: predictability and business conditions, The Manchester School Supplement, 63, 85–102. Breen, W., Glosten, L. R. and Jagannathan, R. (1990) Predictable variations in stock index returns, Journal of Finance, 44, 1177–89. Campbell, J. Y. (1987) Stock returns and the term structure, Journal of Financial Economics, 27, 373–99. Campbell, J. Y. and Lo, A. (1997) The Econometrics of Financial Markets, Princeton University Press, Princeton, NJ. Caporale, G. M. and Gil-Alana, L. A. (2002) Fractional integration and mean reversion in stock prices, Quarterly Review of Economics and Finance, 42, 599–609. Chancellor, E. (1999) Devil Take Hindmost: History of Financial Speculation, Farrar Straus and Giroux, New York. Clare, A. D., Psaradakis, Z. and Thomas, S. H. (1995) An analysis of seasonality in the UK equity market, Economic Journal, 105, 398–409. Clare, S. D., Thomas, S. H. and Wickens, M. R. (1994) Is the gilt-equity yield ratio useful for predicting UK stock return?, Economic Journal, 104, 303–15. Dickey, D. A. and Fuller, W. A. (1979) Distribution of the estimators for autoregressive time series with a unit root, Journal of the American Statistical Association, 74, 427–31. Fama, E. F. (1955) The behavior of stock market prices, Journal of Business, 38, 34–105. Fama, E. F. (1970) Efficient capital markets: a review of theory and empirical work, Journal of Finance, 38, 34–105. Fama, E. F. and French, K. R. (1989) Business conditions and expected returns on stocks and bonds, Journal of Financial Economics, 25, 23–49.
J. E. Jarrett and E. Kyper Francis, J. C. (1993) Management of Investments, McGraw-Hill, New York. Granger, C. W. J. (1992) Forecasting stock market prices: lessons for forecasters, International Journal of Forecasting, 8, 3–13. Jarrett, J. and Kyper, E. (2005) Evidence on the seasonality of stock market prices of firms traded on organized markets, Applied Economics Letters, 12, 537–43. Kato, K. (1990a) Weekly patterns in Japanese stock returns, Management Science, 36, 1031–43. Kato, K. (1990b) Being a winner in the Tokyo stock market, Journal of Portfolio Management, 16, 52–6. Lo, A.W. and Mackinlay, A. C. (1999) A Non-Random Walk Down Wall Street, Princeton University Press, Princeton, NJ. Moorkejee, R. and Yu, Q. (1999) Seasonality in returns on the Chinese stock markets: the case of Shanghai Shenzhen, Global Finance Journal, 10, 93–105. Pesaran, M. H. and Timmermann, A. (1994) Forecasting stock returns: An examination of stock market trading in the presence of transaction costs, Journal of Forecasting, 13(4), 335–67. Pesaran, M. H. and Timmermann, A. (1995) The robustness and economic significance of predictability of stock returns, Journal of Finance, 50, 1201–28. Pesaran, M. H. and Timmermann, A. (2000) A recursive modeling approach to predicting UK stock returns, The Economic Journal, 110, 159–91. Ray, B., Chen, S. and Jarrett, J. (1997) Identifying permanent and temporary components in Japanese stock prices, Financial Engineering and the Japanese Markets, 4, 233–56. Rothlein, C. J. and Jarrett, J. (2002) Seasonality in prices of Japanese common stock, International Journal of Business and Economics, 1, 21–31. Said, S. E. and Dickey, E. A. (1984) Testing for unit roots in autoregressive moving average models of unknown order, Biometrika, 71, 599–607. Schiller, R. (1989) Market Volatility, MIT Press, Cambridge, MA.
