Return Kurtosis

Family: Risk

What it computes

Emits ReturnKurtosisTick ticks carrying mean_return, second_moment, fourth_moment, excess_kurtosis, n_intraday_bars off stock trade tape (5m bars).

Available on the live, historical, and replay drives.

Methodology

Welford (1962) standardised fourth central moment (excess kurtosis) of per-bar log returns K = m_4 / m_2² − 3 over a rolling window — Cont (2001) fat-tail stylised fact.

See the methodology overview for the citation index.

Inputs

Stock trade tape (5m bars).

Key outputs

Mean_return, second_moment, fourth_moment, excess_kurtosis, n_intraday_bars. The full field set is in the tick table below.

Output schema (ReturnKurtosisTick)

The field / type / description table below is regenerated from the ReturnKurtosisTick Rust source by docs-site/scripts/inject-doc-tables.ts on every npm run docs:build. Do not hand-edit between the sentinels.

Field	Type	Description
symbol	Arc<str>	Underlying symbol (interned).
date	i32	Trading-session date (YYYYMMDD) at emission time.
ms_of_day	i32	Milliseconds since midnight ET at emission time.
mean_return	f64	Rolling-window mean per-bar log return μ_1. NaN before four bars have sealed.
second_moment	f64	Rolling-window second central moment m_2. NaN before four bars have sealed.
fourth_moment	f64	Rolling-window fourth central moment m_4. NaN before four bars have sealed.
excess_kurtosis	f64	Excess kurtosis K = m_4 / m_2² − 3. NaN before four bars have sealed; −3 for the flat-distribution degenerate case.
n_intraday_bars	i32	Count of intraday bars currently inside the rolling window.

Configuration (ReturnKurtosisParams)

Regenerated from the ReturnKurtosisParams Rust source — see the note above.

Field	Type	Description
contracts	SecurityFilter	Contracts the subscription tracks. Stocks only — the analytic silently ignores option / index trades at the on_tick entry point.
conditions	ConditionPolicy	Trade-condition admission policy applied to every print.
venues	ExchangeFilter	Exchange / venue admission policy.
bar_interval_ms	i32	Per-bar cadence in milliseconds. Defaults to [DEFAULT_BAR_INTERVAL_MS] (300_000 ms / 5 min).
window_bars	i32	Rolling-window length in bars. Defaults to [DEFAULT_WINDOW_BARS] (78 — one US-equity session at the default 5-minute cadence).
min_emit_interval_ms	i32	Minimum interval between consecutive emissions per symbol, in milliseconds. Defaults to [DEFAULT_MIN_EMIT_INTERVAL_MS] (60_000 ms). Set to 0 to publish on every sealed bar.

Example

Python

import kairos_thetadata as kt

client = kt.Client.connect(kt.Credentials.from_env())

def on_event(row):
    print(row)

sub = client.live().return_kurtosis(["QQQ"]).on_event(on_event)
sub.wait(timeout_seconds=60.0)

TypeScript

import { Client, Credentials } from "kairos-thetadata";

const client = await Client.connect(Credentials.fromEnv());

await client
  .live()
  .returnKurtosis(["QQQ"])
  .onEvent((tick) => {
    console.log(tick);
  });

Rust

// Cargo.toml:
//   kairos = "0.1"

use kairos::{Client, ReturnKurtosisRow};

# fn run() -> Result<(), Box<dyn std::error::Error>> {
let client = Client::connect(("me@example.com", "secret"))?;

let sub = client
    .live()
    .return_kurtosis(["QQQ"])
    .on_event(|row: &ReturnKurtosisRow| println!("mean_return={} fourth_moment={}", row.mean_return, row.fourth_moment))?;
// ... later ...
sub.unsubscribe();
# Ok(())
# }