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# Intraday Patterns: Volume and Volatility Dynamics


# Intraday Patterns: Volume and Volatility Dynamics

**Chapter 3: Market Microstructure**

**Docker image**: `ml4t`

## Purpose

Quantify the intraday volume U-shape across high-, medium-, and low-liquidity
NASDAQ tickers using ITCH-derived trade data, and produce the comparative
30-minute-resolution figures that §3.1 and §3.3 reference.

## Learning Objectives

After completing this notebook, you will be able to:
- Resample tick-level trades into 30-minute volume bars and recognize the
  open/close hump versus midday lull.
- Compare intraday patterns across liquidity tiers (TSLA / mid-tier / illiquid)
  and quantify the open-vs-midday volume ratio.
- Connect the U-shape to feature engineering choices in Chapter 8 (time-of-day
  features, volume-normalized signals).

## Book reference

Section §3.1 (intraday-flow narrative) and Section §3.3 (stylized-facts
subsection on intraday U-shape).

## Prerequisites

- The canonical enriched-trade parquet at
  `03_market_microstructure/output/nasdaq_itch/trading_activity/trades.parquet` and the matching
  `trade_summary.parquet` (used for liquidity-tier symbol selection); both
  are produced by `05_itch_trading_activity`.

---

## 1. Setup

```python
"""Intraday Patterns — volume and volatility dynamics from NASDAQ ITCH data."""

import matplotlib.pyplot as plt
import numpy as np
import polars as pl

from data import load_nasdaq_itch
from utils.paths import display_path, get_output_dir, require_chapter_inputs
from utils.style import COLORS, show_with_alt
```

### Declared parameters

`MIN_TRADES_LOW` is the floor a ticker must clear to stand for the low-liquidity tier.
A ticker that printed a handful of trades all day produces a panel with two points on
it, which shows nothing about intraday shape; the floor picks the least active name
that still has one.

`PATTERN_TICKERS` is how many of the most actively traded tickers the aggregate
U-shape averages over. Averaging over a handful would let one name's day decide the
shape; averaging over everything would let thousands of barely traded ones bury it.

`PATTERN_FREQ` sets the bar width for that aggregate. Thirty minutes divides the
session into thirteen bars, which is fine enough to separate the open and the close
from the middle of the day and coarse enough that each bar holds real volume.

```python
MIN_TRADES_LOW = 500
PATTERN_TICKERS = 20
PATTERN_FREQ = "30m"
```

```python
NASDAQ_ITCH_OUTPUT = get_output_dir(3, "nasdaq_itch")
MESSAGE_DIR = load_nasdaq_itch(get_base_path=True)
TRADING_ACTIVITY_DIR = NASDAQ_ITCH_OUTPUT / "trading_activity"

print(f"Input directory (messages): {display_path(MESSAGE_DIR)}")
print(f"Input directory (trade summary): {display_path(TRADING_ACTIVITY_DIR)}")
```

## 2. Load Trade Data

Load outputs from `05_itch_trading_activity`:
- `trade_summary.parquet`: Aggregated stats by ticker (for symbol selection)
- `trades.parquet`: Canonical tick-level trades (for analysis)

`trades.parquet` is the table `05_itch_trading_activity` builds by attributing each
`E` and `C` execution back to a ticker, so reading it here means the two notebooks
cannot disagree about what a trade is.

```python
# Load trade summary and canonical trades from notebook 05
TRADE_SUMMARY_PATH = TRADING_ACTIVITY_DIR / "trade_summary.parquet"
TRADES_PATH = TRADING_ACTIVITY_DIR / "trades.parquet"

# Substituting well-known tickers for the ones this dataset actually traded would let
# the notebook finish with nothing to plot, so stop instead and say what is missing.
require_chapter_inputs(
    {
        MESSAGE_DIR: "01_itch_parser",
        TRADE_SUMMARY_PATH: "05_itch_trading_activity",
        TRADES_PATH: "05_itch_trading_activity",
    }
)

# Load trade summary for ticker selection
trade_summary = pl.read_parquet(TRADE_SUMMARY_PATH)
# Sort explicitly by value to ensure correct selection
trade_summary = trade_summary.sort("total_value", descending=True)
trade_col = next(
    (c for c in ("trade_count", "n_trades", "total_trades") if c in trade_summary.columns),
    None,
)
if trade_col is None:
    # No trade-count column: fall back to the top half by traded value.
    active_summary = trade_summary.head(len(trade_summary) // 2)
else:
    active_summary = trade_summary.filter(pl.col(trade_col) >= MIN_TRADES_LOW)
num_syms = len(active_summary)
high_sym = active_summary["ticker"][0]  # highest value, still traded
mid_sym = active_summary["ticker"][num_syms // 2]  # middle of active band
low_sym = active_summary["ticker"][-1]  # lowest value above min-activity floor
print(f"Loaded trade summary: {len(trade_summary)} tickers; {num_syms} above min-activity floor")

# Load canonical trades (single source of truth for trade extraction)
all_trades = pl.read_parquet(TRADES_PATH)
print(f"Loaded canonical trades: {len(all_trades):,} trades")
if "msg_type" in all_trades.columns:
    msg_breakdown = all_trades.group_by("msg_type").len().sort("msg_type")
    print("  Message type breakdown:")
    for row in msg_breakdown.iter_rows():
        print(f"    {row[0]}: {row[1]:>12,}")

print("\nSelected tickers for analysis:")
print(f"  High liquidity:   {high_sym}")
print(f"  Medium liquidity: {mid_sym}")
print(f"  Low liquidity:    {low_sym}")
```

## 3. Intraday Volume and Price by Liquidity Tier

We resample tick-level trades into intraday bars for one high-, one medium-,
and one low-liquidity ticker, and read the volume and price panels side by
side. The bar frequency widens for the illiquid name so its sparse prints
still form a legible shape.

```python
def intraday_resample(trades_df: pl.DataFrame, ticker: str, freq: str = "5m") -> pl.DataFrame:
    """
    Filter trades for a single ticker and resample to intraday bars.

    Args:
        trades_df: Canonical trades DataFrame from notebook 05 (trades.parquet)
        ticker: Stock symbol to filter
        freq: Bar frequency (e.g., "5m", "15m", "30m")

    Returns:
        DataFrame with columns: timestamp, shares, value, price, vwap, trade_count
    """
    if trades_df is None or len(trades_df) == 0:
        return pl.DataFrame()

    # Filter to ticker
    df = trades_df.filter(pl.col("ticker") == ticker)
    if len(df) == 0:
        return pl.DataFrame()

    # Ensure we have required columns (compute value if missing)
    required = ["timestamp", "shares", "price"]
    if not all(c in df.columns for c in required):
        return pl.DataFrame()

    if "value" not in df.columns:
        df = df.with_columns((pl.col("shares") * pl.col("price")).alias("value"))

    df = df.select(["timestamp", "shares", "price", "value"]).sort("timestamp")

    # Resample to bars using group_by_dynamic
    bars = df.group_by_dynamic("timestamp", every=freq).agg(
        [
            pl.col("shares").sum().alias("shares"),
            pl.col("value").sum().alias("value"),
            pl.col("price").last().alias("price"),
            pl.len().alias("trade_count"),
        ]
    )

    # Calculate VWAP
    bars = bars.with_columns(
        pl.when(pl.col("shares") > 0)
        .then(pl.col("value") / pl.col("shares"))
        .otherwise(None)
        .alias("vwap")
    )

    bars = bars.drop_nulls(subset=["price"])
    return bars
```

### Plot Intraday Bars
Resample trades for a ticker and visualize volume and price patterns side by side.

```python
def plot_intraday_bars(trades_df: pl.DataFrame, ticker: str, freq: str = "5m") -> None:
    """Resample trades for ticker and plot volume and price patterns."""
    bars = intraday_resample(trades_df, ticker, freq)
    if len(bars) == 0:
        print(f"No trade data found for {ticker}.")
        return

    # Convert to pandas for matplotlib
    bars_pd = bars.to_pandas()

    fig, axes = plt.subplots(2, 1, figsize=(12, 8), sharex=True)
    fig.suptitle(f"{ticker}: intraday trading in {freq} bars", fontsize=14)

    ax1 = axes[0]
    ax1.bar(
        bars_pd["timestamp"],
        bars_pd["shares"],
        alpha=0.7,
        color=COLORS["blue"],
        label="Shares traded",
    )
    ax1.set_ylabel("Shares traded")
    ax1.legend(loc="upper left")

    ax1_2 = ax1.twinx()
    ax1_2.plot(bars_pd["timestamp"], bars_pd["trade_count"], color=COLORS["amber"], label="Trades")
    ax1_2.set_ylabel("Number of trades")
    ax1_2.legend(loc="upper right")

    ax2 = axes[1]
    ax2.plot(
        bars_pd["timestamp"], bars_pd["price"], label="Last trade price", color=COLORS["slate"]
    )
    ax2.plot(
        bars_pd["timestamp"],
        bars_pd["vwap"],
        label="Volume-weighted average price",
        color=COLORS["copper"],
        linestyle="--",
    )
    ax2.set_ylabel("Price ($)")
    ax2.set_xlabel("Time (US/Eastern)")
    ax2.legend()

    show_with_alt(
        fig,
        f"Two stacked panels for {ticker} sharing a clock-time axis over one session. The upper panel is a bar chart of shares traded in each {freq} bar, with a line on a second vertical axis giving the number of trades in the same bar. The lower panel plots two price lines, the last trade price and the volume-weighted average price of the bar, the second dashed.",
    )
```

```python
print(f"High-Volume Ticker: {high_sym}")
plot_intraday_bars(all_trades, high_sym, freq="5m")
```

```python
print(f"Medium-Volume Ticker: {mid_sym}")
plot_intraday_bars(all_trades, mid_sym, freq="5m")
```

```python
print(f"Low-Volume Ticker: {low_sym}")
plot_intraday_bars(all_trades, low_sym, freq="15m")  # Longer bars for sparse data
```

## 4. The Intraday U-Shape

Averaging volume across the top-20 most active tickers reveals the
characteristic U-shape: trading concentrates at the open and the close and
thins out at midday.
- **High at open**: price discovery and overnight-information incorporation.
- **Low at midday**: the "lunch lull" of reduced institutional activity.
- **High at close**: portfolio rebalancing, index arbitrage, and MOC orders.

This regularity drives feature construction in Chapter 8: time-of-day
features encode it directly.

```python
def compute_intraday_pattern(
    trades_df: pl.DataFrame, tickers: list[str], freq: str = "30m"
) -> pl.DataFrame:
    """
    Compute average intraday patterns across multiple tickers.

    Args:
        trades_df: Canonical trades DataFrame from notebook 05
        tickers: List of stock symbols to analyze
        freq: Bar frequency (e.g., "30m")

    Returns:
        DataFrame with time_slot, vol_pct, trade_count, ticker
    """
    all_patterns = []

    for ticker in tickers:
        bars = intraday_resample(trades_df, ticker, freq)
        if len(bars) == 0:
            continue

        # Extract hour and compute relative metrics
        bars = bars.with_columns(
            pl.col("timestamp").dt.hour().alias("hour"),
            pl.col("timestamp").dt.minute().alias("minute"),
        )

        # Compute time-of-day slot (e.g., 9:30 -> 9.5)
        bars = bars.with_columns((pl.col("hour") + pl.col("minute") / 60).alias("time_slot"))

        # Each ticker's bars are expressed as shares of its own daily total, so that a
        # mega-cap and a mid-cap contribute equally to the average shape rather than in
        # proportion to their size.
        total_vol = bars["shares"].sum()
        if total_vol > 0:
            bars = bars.with_columns(
                (pl.col("shares") / total_vol).alias("vol_pct"),
                pl.lit(ticker).alias("ticker"),
            )
            all_patterns.append(bars.select(["time_slot", "vol_pct", "trade_count", "ticker"]))

    if not all_patterns:
        return pl.DataFrame()

    return pl.concat(all_patterns)
```

```python
top_tickers = trade_summary.head(PATTERN_TICKERS)["ticker"].to_list()
pattern_df = compute_intraday_pattern(all_trades, top_tickers, freq=PATTERN_FREQ)
assert not pattern_df.is_empty(), (
    f"None of the {len(top_tickers)} most active tickers produced intraday bars; the "
    f"trade table is empty or carries no usable timestamps."
)

hourly_pattern = (
    pattern_df.group_by("time_slot")
    .agg(
        pl.col("vol_pct").mean().alias("avg_vol_pct"),
        pl.col("vol_pct").std().alias("std_vol_pct"),
        pl.col("trade_count").mean().alias("avg_trades"),
    )
    .sort("time_slot")
    # Regular trading hours only: pre- and post-market bars are a different market with
    # its own participants, and mixing them in flattens the shape being measured.
    .filter((pl.col("time_slot") >= 9.5) & (pl.col("time_slot") <= 16))
)
```

```python
times = hourly_pattern["time_slot"].to_numpy()
vol_pct = hourly_pattern["avg_vol_pct"].to_numpy() * 100
vol_std = hourly_pattern["std_vol_pct"].to_numpy() * 100
trades = hourly_pattern["avg_trades"].to_numpy()

fig, axes = plt.subplots(1, 2, figsize=(14, 5))

axes[0].fill_between(
    times,
    vol_pct - vol_std,
    vol_pct + vol_std,
    alpha=0.3,
    color=COLORS["blue"],
    label="±1 standard deviation across tickers",
)
axes[0].plot(times, vol_pct, color=COLORS["blue"], linewidth=2, marker="o", label="Mean")
axes[0].set_xlabel("Time of day (US/Eastern, hours)")
axes[0].set_ylabel("Share of the ticker's daily volume (%)")
axes[0].set_title("Volume by time of day, averaged over the most active tickers")
axes[0].axhline(
    100 / len(times),
    color=COLORS["negative"],
    linestyle="--",
    label="Even across the session",
)
axes[0].legend()
axes[0].set_xlim(9.5, 16)

axes[1].bar(times, trades, width=0.4, alpha=0.7, color=COLORS["blue"])
axes[1].set_xlabel("Time of day (US/Eastern, hours)")
axes[1].set_ylabel(f"Mean trades per {PATTERN_FREQ} bar")
axes[1].set_title("Number of trades by time of day, the same tickers")
axes[1].set_xlim(9.5, 16)

show_with_alt(
    fig,
    "Two panels side by side, both against time of day from the 09:30 open to the 16:00 close. The left plots the mean share of a ticker's daily volume falling in each bar as a line with circular markers, inside a shaded band of one standard deviation across tickers, with a dashed horizontal line marking the level an even split across the session would give. The right is a bar chart of the mean number of trades in each bar over the same hours.",
)

# Name the bars by the clock, not by position: the number of bars follows from
# PATTERN_FREQ, so an index into the middle is not a fixed time of day.


def slot_label(slot: float) -> str:
    """Render a decimal hour such as 12.5 as a clock time."""
    hour, minute = divmod(round(slot * 60), 60)
    return f"{hour:02d}:{minute:02d}"


midday = int(np.argmin(np.abs(times - 12.5)))
print(f"Share of daily volume by {PATTERN_FREQ} bar, averaged over the selected tickers:")
print(f"  Opening bar   ({slot_label(times[0])}): {vol_pct[0]:.1f}%")
print(f"  Midday bar    ({slot_label(times[midday])}): {vol_pct[midday]:.1f}%")
print(f"  Closing bar   ({slot_label(times[-1])}): {vol_pct[-1]:.1f}%")
print(
    f"  Opening and closing bars against the midday bar: "
    f"{(vol_pct[0] + vol_pct[-1]) / (2 * vol_pct[midday]):.1f}x"
)
```

## Key Takeaways

1. **Volume is not spread evenly across a session.** The opening and closing bars carry
   a multiple of what a midday bar carries; the figure above draws the level an even
   split would give, and the printed ratio says by how much the ends exceed the middle.
   Any statistic computed per bar - a volatility, a spread, an average trade size - is
   estimated from very different sample sizes depending on when the bar falls.
2. **Normalise each ticker before averaging shapes.** Expressing every bar as a share
   of that ticker's own day is what makes the average a shape rather than a picture of
   whichever ticker traded most.
3. **Read the bar by the clock, not by its index.** The number of bars follows from the
   chosen frequency, so 'the middle one' is a different time of day at 15 minutes than
   at 30, and a label written against one is wrong for the other.
4. **Time of day is a feature.** Chapter 8 encodes it directly, and this is the shape
   it encodes.

### Known limitations

- One venue and one session. The U-shape is a well-established regularity, and one day
  of one venue illustrates it rather than establishing it.
- The three per-tier panels are one ticker each, chosen by traded value. They show what
  the shape looks like at different activity levels; they do not test whether it varies
  systematically with liquidity, which would need the whole cross-section.
- Regular trading hours only. Pre- and post-market bars are dropped rather than shown.

**Next**: `07_itch_stylized_facts` for bid-ask bounce and liquidity.

---

## Reference

Bouchaud, J.-P., Bonart, J., Donier, J., & Gould, M. (2018).
*Trades, Quotes and Prices: Financial Markets Under the Microscope*.
Cambridge University Press.
[https://doi.org/10.1017/9781009028943](https://doi.org/10.1017/9781009028943)
![notebook output](figures/p1_1.png)
![notebook output](figures/p1_2.png)
![notebook output](figures/p1_3.png)
![notebook output](figures/p1_4.png)