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.
| block_length | block_count | variance_ratio |
|---|---|---|
| 2 sessions | 2515 | 0.844 |
| 3 sessions | 1676 | 0.918 |
| 5 sessions | 1005 | 0.809 |
| 10 sessions | 502 | 0.848 |
| 21 sessions | 238 | 0.646 |
| 42 sessions | 118 | 0.632 |
| 63 sessions | 78 | 0.584 |
- Rows × columns
- 7 × 3
- Computed
- Completeness
- No missing values
- Source
- US exchange, SIP and OPRA market data
- Licence
- Strasmore terms · free, no signup
What each column holds
| Column | Type | Range | Notes |
|---|---|---|---|
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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