Sum vs compound: twelve SPY monthly returns linked three ways
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 2026-07-26, from How Monthly Stock Returns Are Measured.
- Rows × columns
- 1 × 7
- 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 |
|---|---|---|---|
months_linked |
number | every row is 12 | |
simple_sum_pct |
number | every row is 19.83 | percent |
geometric_compound_pct |
number | every row is 20.79 | percent |
direct_twelve_month_pct |
number | every row is 20.79 | percent |
compounding_gap_points |
number | every row is 0.96 | |
sum_of_monthly_log_returns_pct |
number | every row is 18.89 | percent |
twelve_month_log_return_pct |
number | every row is 18.89 | percent |
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.
Run it yourself
This is the exact query behind the result above. Change a ticker, a date or a column and run it against the warehouse — no account, no key. The no-signup tier is smaller than the one this page was computed on; a query that reaches past it comes back saying which plan runs it.
WITH daily AS (
SELECT toDate(toTimeZone(window_start, 'America/New_York')) AS day,
argMaxIf(toFloat64(close), window_start,
toTimeZone(window_start, 'America/New_York') >= toDateTime(concat(toString(toDate(toTimeZone(window_start, 'America/New_York'))), ' 09:30:00'), 'America/New_York')
AND toTimeZone(window_start, 'America/New_York') < toDateTime(concat(toString(toDate(toTimeZone(window_start, 'America/New_York'))), ' 16:00:00'), 'America/New_York')) AS cl
FROM global_markets.delayed_stocks_minute_aggs
WHERE ticker = 'SPY'
AND window_start >= '2025-06-24 04:00:00'
AND window_start < '2026-07-01 08:00:00'
GROUP BY day
),
monthly AS (
SELECT toStartOfMonth(day) AS month_start,
argMax(cl, day) AS month_close
FROM daily
GROUP BY month_start
),
rets AS (
SELECT month_start,
100 * (month_close / lagInFrame(month_close) OVER (ORDER BY month_start) - 1) AS r
FROM monthly
),
ends AS (
SELECT argMin(month_close, month_start) AS base_close,
argMax(month_close, month_start) AS final_close
FROM monthly
)
SELECT count() AS months_linked,
round(sum(r), 2) AS simple_sum_pct,
round(100 * (exp(sum(log(1 + r / 100))) - 1), 2) AS geometric_compound_pct,
round(100 * (any(final_close) / any(base_close) - 1), 2) AS direct_twelve_month_pct,
round(100 * (exp(sum(log(1 + r / 100))) - 1) - sum(r), 2) AS compounding_gap_points,
round(sum(100 * log(1 + r / 100)), 2) AS sum_of_monthly_log_returns_pct,
round(100 * log(any(final_close) / any(base_close)), 2) AS twelve_month_log_return_pct
FROM rets CROSS JOIN ends
WHERE isFinite(r)
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