STRASMORE/EXPLORE 2,170 QUERIES

Variance ratio by block length: does SPY variance scale like independent draws?

Answered against 22 years of US equities and 12 years of US options data and published with the query that produced it. This result is stored as of 2026-08-14, from Bootstrapping Backtest Confidence Bands.

as of ranking 7×3read in context →
Variance ratio by block length: does SPY variance scale like independent draws? — 7 rows by 3 columns, computed from US exchange, SIP and OPRA data.
block_lengthblock_countvariance_ratio
2 sessions25150.844
3 sessions16760.918
5 sessions10050.809
10 sessions5020.848
21 sessions2380.646
42 sessions1180.632
63 sessions780.584
Rows × columns
7 × 3
Computed
Completeness
No missing values
Source
US exchange, SIP and OPRA market data
Licence
Strasmore terms · free, no signup
Formats
JSON · CSV · the SQL below

What each column holds

Column definitions for Variance ratio by block length: does SPY variance scale like independent draws?, derived from the stored result.
ColumnTypeRangeNotes
block_length text 7 distinct values (10 sessions, 2 sessions, 21 sessions…)
block_count number 78 to 2,515 count
variance_ratio number 0.584 to 0.918 ratio or rate

Computed from Strasmore's warehouse of US exchange, SIP and OPRA market data. Equity prices are delayed; options greeks and implied volatility are end-of-day. This result is stored, not recomputed on load — it is exactly the numbers that were returned on , and the query below is what returned them.

the exact SQL behind every number
WITH daily AS
(
    SELECT
        date,
        toFloat64(close) / nullIf(lagInFrame(toFloat64(close), 1)
            OVER (ORDER BY date ROWS BETWEEN 1 PRECEDING AND CURRENT ROW), 0) - 1 AS ret
    FROM global_markets.stocks_daily_aggs
    WHERE ticker = 'SPY'
      AND date >= '2005-12-01'
      AND date <  '2026-01-01'
),
indexed AS
(
    SELECT
        ret,
        row_number() OVER (ORDER BY date) AS i
    FROM daily
    WHERE date >= '2006-01-01'
      AND ret IS NOT NULL
),
base AS
(
    SELECT varSamp(ret) AS var_1d FROM indexed
),
blocks AS
(
    SELECT
        k,
        intDiv(i, k)  AS blk,
        count()       AS n,
        sum(ret)      AS block_ret
    FROM indexed
    CROSS JOIN (SELECT arrayJoin([2, 3, 5, 10, 21, 42, 63]) AS k) AS ks
    GROUP BY k, blk
    HAVING n = k
)
SELECT
    concat(toString(k), ' sessions')                          AS block_length,
    count()                                                   AS block_count,
    round(varSamp(block_ret) / (k * any(var_1d)), 3)          AS variance_ratio
FROM blocks
CROSS JOIN base
GROUP BY k
ORDER BY k

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