There’s more to “buy low, sell high” than just buying low and selling high. Twitchy markets spew endless, jittery streams of temporary highs and retreating lows. Which low is the “buy” low? When is the “sell” high? A sellers’ high today may be humdrum in a week. Noontime buyers’ rock-bottom low might not impress an hour later. Given these fluctuations in stock prices and the recalibration of highs and lows, traders probe the peaks and valleys in search of patterns and values. New research by Robert Korajczyk (Professor of Finance at the Kellogg School of Management), Kellogg alumnus Ronnie Sadka (Professor of Finance at Boston College), and Steven L. Heston (Professor of Finance at the University of Maryland) reveals surprising patterns that can help predict daily peaks in stock price. This work was deemed so influential in the field of quantitative investment that it was awarded the 2009 Crowell Prize by PanAgora Asset Management.

The backbone of this project was an exhaustive analysis of real stock transactions. “We looked at every single trade in every stock on the New York Stock Exchange from 2001 to 2005, aggregated up into half-hour intervals,” said Korajczyk. “This is publicly available data, but it’s voluminous.”

When Thirteen is NOT an Unlucky Number

Managers of large funds, busy with research, client meetings, compliance, and reporting, are likely to go to great lengths to simplify and streamline their daily processes for adjusting portfolios.

Each 9:30 AM to 4:00 PM trading day was broken into thirteen half-hour intervals. The researchers studied more than 16,000 such intervals in total, spanning from January 2001 through December 2005. For each of the roughly 1,700 stocks, the group measured the return across each interval. They then compared stocks’ returns at each interval to returns at previous intervals. A clear pattern emerged. Earlier returns preceding in multiples of exactly thirteen intervals (e.g., 13, 26, 39, 52, etc.) showed significant correlation to the return over the current interval.

In other words, knowledge that a stock’s return was high between 3:00 and 3:30 yesterday afternoon predicts that its return will be high between 3:00 and 3:30 today, tomorrow, the next day, etc. So buyers could realize a premium by buying that stock on the cheaper side before 3:00, and sellers could wait until the value topped out between 3:00 and 3:30 to execute sales. Moreover, though the strength of the prediction diminishes from one day to the next, this predictive pattern persists every day for up to forty trading days, spanning roughly two months.

Timing Trades to Intra-Day Fluctuations

But for those who think this might be their ticket to a day-trading fortune, Korajczyk warns, “This isn’t useful to retail investors given the small fluctuations in returns.” An investor who takes advantage of recent intra-day trends to time his or her daily buying and selling—rather than trading at the same set time each day—could save a cent for every $30 of stock price on average. At certain times of the day these average savings approach three cents for a $30 stock. Given the small magnitudes of these savings compared to the costs involved in executing trades, it would be difficult to profit by trading based solely on these intra-day fluctuations.

“But for large institutions looking to minimize trading costs, this could be helpful,” continued Korajczyk. “It’s like picking up pennies. If you pick up enough pennies, make enough trades, the tiny savings on each trade can add up.”

He continued, “This won’t help you identify which stock to buy or sell. But if you have some exogenous reason to decide to buy Apple, for example, then this can suggest the time of day at which it would likely be best to buy or sell.”

Searching for the Pattern Drivers

Having observed these patterns, the group naturally wanted to find what was driving them. The ultimate sources remain somewhat elusive. But the process of elimination allowed the group to infer what did not seem to be causes. For example, these patterns are not due simply to daily fluctuations in trading volume, nor to the size of the firm or whether or not it is included in the Standard and Poor’s 500 Index. Previous research by others had described similar patterns that occurred at certain times of the week or month, or at the end of the quarter. But none of those larger-scale patterns appeared to be driving this regular, daily fluctuation.

Noted Korajczyk, “We can’t say for certain why this occurs, but we can conjecture based on two strands of research literature. One, there is autocorrelation in fund flows to institutional money managers.” Autocorrelation is a measure of how a pattern is repeated over time. “If managers perform well,” explained Korajczyk, “they’re likely to get cash inflows, and this would persist as people look at performance today and decide to give money tomorrow. And typical money manager strategies don’t change much, so they tend to invest in and divest from the same sets of stocks from day-to-day.”

Managers of large funds, busy with research, client meetings, compliance, and reporting, are likely to go to great lengths to simplify and streamline their daily processes for adjusting portfolios. Thus they may opt to simply execute trades at the same time each day and often in roughly the same sets of stocks as were traded on previous days. And these trades are made with funds that tend to come in similar amounts and from similar clients as on previous days. Patterns seemingly abound.

“I bought IBM at ten in the morning today. Then tomorrow, when I get fund flows, I’ll buy IBM at ten in the morning,” offered Korajczyk as an example.

He continued, “It can be optimal to trade in particular patterns, to minimize trading costs, to slice up your order and trickle it out over time. For example, if you’re risk averse, you may be worried that trading conditions might suddenly become unfavorable. In that case, research suggests that you should make initial trades very quickly, then slow down.”

Such standardized trading algorithms could introduce predictable patterns into trading activity. Said Korajczyk, “One of the co-authors used to work at a firm that managed several institutional accounts. And every day they would institute their trading algorithms at the same time in order to rebalance a different client’s portfolio.”

Patterns Driven By Investor Demands

When the dust had settled from all their analyses, the researchers concluded that these patterns likely arise as a result of investors’ demands for immediate trading activity at certain times of day, each day, every day. It appears that many investors, for example, demand immediate execution of trades, even if that means missing out on some slight advantage that might be predicted to arise only thirty minutes later.

“One of the biggest puzzles is why it appears that some people are leaving money on the table,” said Korajczyk. “If people understood it, you’d think they would take advantage. But that doesn’t seem to be the case. We find that people either aren’t fully aware, or they’re risk averse and there may be some perceived risk embedded in the periodicity.”

Companies do not typically alter their financial exposures hour-by-hour, so it seems unlikely that intra-day fluctuations in the value of their stock would be due to changes in perceived risk. But, observed Korajczyk, “If macroeconomic announcements are made at a particular time of day, you might avoid trading around that time of day.” Indeed, many organizations release economic news at regular times in the day, so might this influence daily fluctuation in stock price, with traders hesitant to hold stocks during the uncertain time leading up to the announcements? Further analyses, however, suggest that daily fluctuation in risk is not the driver of these daily stock price patterns.

“What if people now start taking advantage of this pattern?” asked Korajczyk. “You’d think that the pattern would be eliminated. For example, if everyone tried to time their trading in advance of a daily peak, the trading activity would shift in anticipation, thus changing the pattern.”

“In other words,” he concluded, “the patterns might be there just because no one knows they’re there.”