Empirical Evidence

As the studies of the time series properties of prices have proliferated, the evidence can be classified into two classes - studies that focus on short-term (intraday, daily and weekly price movements) price behavior and research that examines long-term (annual and five-year returns) price movements.  Since the findings are contradictory, we will present them separately. We will also present evidence on seasonal patterns in stock prices that seem to persist not only over many periods but across most markets.

a. Short Term Price Patterns

            The notion that today's price change conveys information about tomorrow's price change is deep rooted in most investors' psyches. In its more sophisticated formats, the notion that there are patterns in price movements over short periods of time forms the basis for much of charting. All to often, these patterns are backed up anecdotal evidence, with the successful experiences on one or a few stocks extrapolated to form rules about all stocks and assets. Even in a market that follows a perfect random walk, you will see price patterns on some stocks that seem to defy probability. The entire market may go up ten days in a row, or down, for no other reason than pure chance. Given that this is often true, how do we test to see if there are significant price patterns?  We will consider two ways in which researchers have examined this question in this section.

a. Serial correlation

            If today is a big up day for a stock, what does this tell us about tomorrow? There are three different points of view. The first is that the momentum from today will carry into tomorrow, and that tomorrow is more likely to be an up day than a down day. The second is that there will be the proverbial profit taking as investors cash in their profits and that the resulting correction will make it more likely that tomorrow will be a down day. The third is that each day we begin anew, with new information and new worries, and that what happened today has no implications for what will happen tomorrow.

Statistically, the serial correlation measures the relationship between price changes in consecutive time periods, whether hourly, daily or weekly, and is a measure of how much the price change in any period depends upon the price change over the previous time period. A serial correlation of zero would therefore imply that price changes in consecutive time periods are uncorrelated with each other, and can thus be viewed as a rejection of the hypothesis that investors can learn about future price changes from past ones. A serial correlation that is positive, and statistically significant, could be viewed as evidence of price momentum in markets, and would suggest that returns in a period are more likely to be positive (negative) if the prior period's returns were positive (negative). A serial correlation which is negative, and statistically significant, could be evidence of price reversals, and would be consistent with a market where positive returns are more likely to follow negative returns and vice versa.

            From the viewpoint of investment strategy, serial correlations can sometimes be exploited to earn excess returns. A positive serial correlation would be exploited by a strategy of buying after periods with positive returns and selling after periods with negative returns. A negative serial correlation would suggest a strategy of buying after periods with negative returns and selling after periods with positive returns. Since these strategies generate transactions costs, the correlations have to be large enough to allow investors to generate profits to cover these costs. It is therefore entirely possible that there be serial correlation in returns, without any opportunity to earn excess returns for most investors.

            The earliest studies[1] of serial correlation all looked at large U.S. stocks and concluded that the serial correlation in stock prices was small. One of the first by Fama in 1965, for instance, found that 8 of the 30 stocks listed in the Dow had negative serial correlations and that most of the serial correlations were less than 0.05. Other studies confirm these findings – of very low correlation, positive or negative - not only for smaller stocks in the United States, but also for other markets. For instance, Jennergren and Korsvold (1974) report low serial correlations for the Swedish equity market and Cootner (1961) concludes that serial correlations are low in commodity markets as well. While there may be statistical significance associated with some of these correlations, it is unlikely that there is enough correlation in short-period returns to generate excess returns, after you adjust for transactions costs.

            The serial correlation in short period returns is affected by market liquidity and the presence of a bid-ask spread. Not all stocks in an index are liquid, and, in some cases, stocks may not trade during a period. When the stock trades in a subsequent period, the resulting price changes can create positive serial correlation. To see why, assume that the market is up strongly on day 1, but that three stocks in the index do not trade on that day. On day 2, if these stocks are traded, they are likely to go up to reflect the increase in the market the previous day. The net result is that you should expect to see positive serial correlation in daily or hourly returns in illiquid market indices. The bid-ask spread creates a bias in the opposite direction, if transactions prices are used to compute returns, since prices have a equal chance of ending up at the bid or the ask price. The bounce that this induces in prices will result in negative serial correlations in returns.[2] For very short return intervals, this bias induced in serial correlations might dominate and create the mistaken view that price changes in consecutive time periods are negatively correlated.

            There are some recent studies that find evidence of serial correlation in returns over short time periods, but the correlation is different for high volume and low volume stocks. With high volume stocks, stock prices are more likely to reverse themselves over short periods, i.e., have negative serial correlation. With low volume stocks, stock prices are more likely to continue to move in the same direction – i.e., have positive serial correlation.[3]

b. Runs Tests

            Once in a while a stock has an extended run where stock prices go up several days in a row or down several days in a row. While this, by itself, is completely compatible with a random walk, you can examine a stock’s history to see if these runs happen more frequently or less frequently than they should. A runs test is based upon a count of the number of runs, i.e., sequences of price increases or decreases, in price changes over time. Thus, the following time series of price changes, where U is an increase and D is a decrease would result in the following runs -


There were 18 runs in this price series of 33 periods. The actual number of runs in the price series is compared against the number that can be expected[4] in a series of this length, assuming that price changes are random. If the actual number of runs is greater than the expected number, there is evidence of negative correlation in price changes. If it is lower, there is evidence of positive correlation. A study of price changes in the Dow 30 stocks, assuming daily, four-day, nine-day and sixteen day return intervals provided the following results -

                                                            DIFFERENCING INTERVAL

                                  Daily                 Four-day              Nine-day              Sixteen-day

Actual runs                735.1                 175.7                   74.6                      41.6

Expected runs            759.8                 175.8                   75.3                      41.7

The actual number of runs in four day returns (175.8) is almost exactly what you would expect in a random process. Tthere is slight evidence of positive correlation in daily returns but no evidence of deviations from normality for longer return intervals.

            Again, while the evidence is dated, it serves to illustrate the point that long strings of positive and negative changes are, by themselves, insufficient evidence that markets are not random, since such behavior is consistent with price changes following a random walk. It is the recurrence of these strings that can be viewed as evidence against randomness in price behavior.

b. Long Term Price Patterns

            While most of the earlier studies of price behavior focused on shorter return intervals, more attention has been paid to price movements over longer periods (six months to five-year) in recent years. Here, there is an interesting dichotomy in the results. When long term is defined as months rather than years, there seems to be a tendency towards positive serial correlation. Jegadeesh and Titman present evidence of what they call “price momentum” in stock prices over time periods of up to eight months – stocks that have gone up in the last six months tend to continue to go up whereas stocks that have gone down in the last six months tend to continue to go down. The momentum effect is just as strong in the European markets, though it seems to be weaker in emerging markets.[5] What may cause this momentum? One potential explanation is that mutual funds are more likely to buy past winners and dump past losers, thus generating price continuity.[6]

However, when long term is defined in terms of years, there is substantial negative correlation in returns, suggesting that markets reverse themselves over very long periods. Fama and French examined five-year returns on stocks from 1941 to 1985 and present evidence of this phenomenon. They found that serial correlation is more negative in five-year returns than in one-year returns, and is much more negative for smaller stocks rather than larger stocks. Figure 7.2 summarizes one-year and five-years serial correlation by size class for stocks on the New York Stock Exchange.

Source: Fama and French (1988)

This phenomenon has also been examined in other markets, and the findings have been similar. There is evidence that returns reverse themselves over long time period.

            Given the findings of little or no correlation in the short term and substantial correlation in the long term, it is interesting that so many technical analysts focus on predicting intraday or daily prices. The bigger payoff seems to be in looking at price patterns over much longer periods, though there are caveats we will present in the next chapter on these long term strategies.

c. Seasonal and Temporal Patterns in Prices

            One of the most puzzling phenomena in asset prices is the existence of seasonal and temporal patterns in stock prices that seem to cut across all types of asset markets. As we will see in this section, stock prices seem to go down more on Mondays than on any other day of the week and do better in January than in any other month of the year. What is so surprising about this phenomenon, you might ask? It is very difficult to justify the existence of patterns such as these in a rational market – after all, if investors know that stocks do better in January than in any other month, they should start buying the stock in December and shift the positive returns over the course of the year. Similarly, if investors know that stocks are likely to be marked down on Monday, they are likely to begin marking them down on Friday and hence shift the negative returns over the course of the week.

The January Effect

            Studies of returns in the United States and other major financial markets consistently reveal strong differences in return behavior across the months of the year. Figure 7.3 reports average returns by month of the year from 1927 to 2001.

Source: Raw data from French

Returns in January are significantly higher than returns in any other month of the year. This phenomenon is called the year-end or January effect, and it can be traced to the first two weeks in January.

            The January effect is much more pronounced for small firms than for larger firms, and roughly half of the small firm premium, which is the additional return earned by small firms relative to large firms, is earned in the first few days of January. Figure 7.4 graphs returns in January by size and risk class for data from 1935 to 1986.[7]

Source: Chopra and Ritter

Note that the January effect is most pronounced for the smallest, riskiest firms in the market and least pronounced for larger, safer firms.

A number of explanations have been advanced for the January effect, but few hold up to serious scrutiny. One is that there is tax loss selling by investors at the end of the year on stocks which have gone down to capture the capital gain, driving prices down, presumably below true value, in December, and a buying back of the same stocks[8] in January, resulting in the high returns. The fact that the January effect is accentuated for stocks that have done worse over the prior year is offered as evidence for this explanation. There are several pieces of evidence that contradict it, though. First, there are countries, like Australia, which have a different tax year, but continue to have a January effect. Second, the January effect is no greater, on average, in years following bad years for the stock market, than in other years.

            A second rationale is that the January effect is related to institutional trading behavior around the turn of the years. It has been noted, for instance, that ratio of buys to sells for institutions drops significantly below average in the days before the turn of the year and picks to above average in the months that follow.[9] It is argued that the absence of institutional buying pushes down prices in the days before the turn of the year and pushes up prices in the days after.  Again, while this may be true, it is not clear why other investors do not step in and take advantage of these quirks in institutional behavior.

            The universality of the January effect is illustrated in Figure 7.5 where we examine returns in January versus the other months of the year in several major financial markets, and finds strong evidence of a January effect in every market.[10]

In fact, researchers have unearthed evidence of a January effect in bond and commodity markets as well.

The Weekend Effect

            Are stock returns consistently higher on some days of the week than others? A surprising feature of stock returns is the existence of what is called the weekend effect, another return phenomenon that has persisted over extraordinary long periods and over a number of international markets. It refers to the differences in returns between Mondays and other days of the week. The significance of the return difference is brought out in Figure 7.6, which graphs returns by days of the week from 1927 to 2001.

The returns on Mondays are significantly negative, whereas the returns on every day of the week are not.  In addition, returns on Mondays are negative more often than returns on any other trading day. There are a number of other findings on the Monday effect that researchers have fleshed out.

            There are some who have argued that the weekend effect is the result of bad news being revealed after the close of trading on Friday and during the weekend. They point to the fact that more negative earnings reports are revealed after close of trading on Friday. Even if this were a widespread phenomenon, the return behavior would be inconsistent with a rational market, since rational investors would build in the expectation of the bad news over the weekend into the price before the weekend, leading to an elimination of the weekend effect.

            The weekend effect is strong in most major international markets, as shown in Figure 7.7.

The returns on Monday are lower than returns on other days of the week for every international market examined. The presence of a strong weekend effect in Japan, which allowed Saturday trading for a portion of the period studies here indicates that there might be a more direct reason for negative returns on Mondays than bad information over the weekend.

            As a final note, the negative returns on Mondays cannot be just attributed to the absence of trading over the weekend. The returns on days following trading holidays, in general, are characterized by abnormally positive, not negative, returns. Figure 7.8 summarizes returns on trading days following major holidays and confirms this pattern.

In fact, the returns on the first trading day after a holiday tend to be much more positive than returns on other trading days.[12]

d. Volume Patters

            While the random walk hypothesis is silent about the relationship between trading volume and prices, it does assume that all available information is incorporated in the current price. Since trading volume is part of publicly available information, there should therefore be no information value to knowing how many shares were traded yesterday or the day before.

            As with prices, there is evidence that trading volume carries information about future stock price changes. Datar, Naik and Radcliffe (1998) show that low volume stocks earn higher returns than high volume stocks, though they attribute the differential return to a liquidity premium on the former.  A more surprising result comes from Lee and Swaminathan (1998) who look at the interrelationship between price and trading volume. In particular, they examine the price momentum effect that was documented by Jegadeesh and Titman – that stocks that go up are more likely to keep going up and stocks that go down are more likely to keep dropping in the months after - and show that it is much more pronounced for high volume stocks. Figure 7.9 classifies stocks based upon how well or badly they have done in the last six months (winners, average and loser stocks) and their trading volume (low, average and high) and looks at returns on these stocks in the following six months.

Note that the price momentum effect is strongest for stocks with high trading volume. In other words, a price increase or decrease that is accompanied by strong volume is more likely to continue into the next period. Stickel and Verecchia confirm this result with shorter period returns – they conclude that increases in stock prices that are accompanied by high trading volume are more likely to carry over into the next trading day.

            In summary, the level of trading volume in a stock, changes in volume and volume accompanied by price changes all seem to provide information that investors can use to pick stocks. It is not surprising that trading volume is an integral part of technical analysis.


[1] Alexander (1964), Cootner (1962)and Fama (1965) all estimated serial correlation in stock prices. Given the difficulty of obtaining data, they worked with small samples over short periods.

[2] Roll (1984) provides a simple measure of this relationship,

            Bid-Ask Spread = -√2 (Serial Covariance in returns)

where the serial covariance in returns measures the covariance between return changes in consecutive time periods.

[3] See “Volume and Autocovariances in Short-Horizon Individual Security Returns”, Conrad, Hameed and Niden, in Journal of Finance, 1994.

[4] There are statistical tables that summarize the expected number of runs, assuming randomness, in a series of any length.

[5] Rouwenhorst (1997) studied 12 European markets and finds evidence of momentum in each market. In 1999, he presented evidence of momentum in emerging markets. Another paper by Bekaert, Erb, Harvey and Viskanta (1997) finds that momentum investing is not consistently profitable in emerging markets.

[6] Grinblatt, Titman and Wermers (1995) present evidence that is consistent with this explanation.

[7] This finding is from Haugen, R. and J. Lakonishok, The Incredible January Effect, Dow-Jones Irwin.

[8] It is to prevent this type of trading that the internal revenue service has a “wash sale rule” that prevent you from Since wash sales rules would prevent an investor from selling and buying back the same stock within 45 days. To get around this rule,, there has to be some substitution among the stocks. Thus investor 1 sells stock A and investor 2 sells stock B, but when it comes time to buy back the stock, investor 1 buys stock B and investor 2 buys stock A.

[9] Instiitutional buying drops off in the last 10 days of the calendar year, and picks up again in tehthe first 10 days of tehthe next calendar year.

[10] This is also from Haugen, R. and j. Lakonishok, The Incredible January Effect, Dow Jones Irwin.

[11] See “The Individual Investor and the Weekend Effect”, Abraham and Ikenberry, Journal of Financial and Quantitative Analysis.