Not all hours of the trading day are created equal. Decades ago, researchers noticed that the market has a daily rhythm: it is loud and fast right after the open, it goes quiet and sleepy around midday, and it wakes up again into the close. This "U-shape" is one of the most reliable patterns in all of finance — and knowing it can make almost any strategy better.
Who found it, and where (the who / what / when)
Two classic studies anchor this. Lawrence Harris published "A transaction data study of weekly and intraday patterns in stock returns" in the Journal of Financial Economics in 1986. Around the same time, Wood, McInish, and Ord published a closely related study in the Journal of Finance in 1985. Both used detailed, minute-by-minute data — a big deal in the 1980s — to map how the market behaves through the day.
What they actually did (the how they studied it)
They took intraday transaction data and measured, for each part of the trading day, how much volume, price movement (volatility), and return occurred. Instead of looking at one number per day, they sliced the day into small time buckets — the first 30 minutes, the next, and so on — and averaged each bucket across many days to find the typical shape of a day.
What they found (the data points)
The result was a clear U-shape. Volume and volatility were highest near the open and near the close, and lowest in the middle of the day — the famous "lunchtime lull." Returns also clustered at the edges of the day. In plain terms: the market does most of its real work in the first and last hour, and often just drifts sideways at midday. This pattern showed up again and again, across stocks and later across futures and forex sessions too.
The "equation" is a shape, not a formula
There is nothing to memorize — just a picture. If you plotted average volatility on the up-and-down axis and time of day on the left-to-right axis, you would get a curve like a smile:
High at the open → low at midday → high into the close
The practical takeaway: a fixed-size stop means very different things at 9:35 AM (wild) versus 12:30 PM (calm). A move that is normal at the open would be a huge, rare move at lunch. Smart strategies adjust to the hour instead of treating every minute the same.
Why it should work (the why)
The rhythm comes from how people and institutions behave. At the open, all the overnight news, earnings, and orders that piled up while the market was closed get released at once — a burst of activity. At midday, traders take lunch, big desks wait, and little new information arrives, so things go quiet. Into the close, funds rebalance, day traders exit, and end-of-day orders hit, firing activity back up. It is the natural schedule of a working day, printed onto the chart.
Does it still hold — honestly?
Yes — the U-shape is one of the most durable patterns in markets, and it still shows up on modern futures and forex sessions. Two honest notes. First, it is a pattern in volatility and volume, not a money-making signal by itself — it tells you when edges and risks are concentrated, which you then combine with an actual entry rule. Second, forex trades nearly 24 hours, so instead of one U-shape it has several tied to the Tokyo, London, and New York sessions and their overlaps — you have to define "the open" for the market you trade. Used right, this is less a standalone strategy and more a filter that sharpens every other strategy.
Build and test it in TapeScript, step by step
- See the rhythm first. Type: "On 5-minute MNQ, open the Time and Context view and show me average volatility and average return by 30-minute bucket across the day." You want to see the U-shape with your own eyes.
- Turn it into a filter. Type: "Take my breakout strategy and only allow entries in the first 90 minutes and the last 60 minutes of the session — skip the midday lull."
- Classify and baseline both. Type: "Classify this and run the baseline backtest for the all-day version and the open-and-close-only version, side by side."
- Prove the session edge. Type: "Run a session breakdown — is my edge actually concentrated at the open and close, and is midday just adding losing trades?"
- Right-size stops by time. Type: "Test scaling my stop by the average volatility of the hour I am trading in — does a time-aware stop beat a fixed stop?"
- Confirm out of sample. Type: "Run walk-forward and Monte-Carlo, then spend the untouched holdout."
- For forex, define the session. Type: "Clone this onto EURUSD and test the London open and the New York open separately — where is the rhythm strongest?"
The bottom line
The market breathes on a daily schedule that has been documented since the 1980s: busy at the edges, sleepy in the middle. You do not have to guess when your edge lives — you can measure it. Cutting the dead midday hours, or sizing risk by the clock, is one of the cheapest, most reliable upgrades you can make to a strategy. TapeScript shows you the U-shape and lets you trade around it with honest numbers. Find your strategy's best hours →
Citation: Harris, L. (1986). "A transaction data study of weekly and intraday patterns in stock returns." Journal of Financial Economics, 16(1), 99–117. See also Wood, R., McInish, T., & Ord, J. (1985), "An Investigation of Transactions Data for NYSE Stocks," The Journal of Finance. Free versions on Google Scholar.