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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.

as of scalar 1×7read in context →
months linked
12
simple sum pct
19.83
geometric compound pct
20.79
direct twelve month pct
20.79
compounding gap points
0.96
sum of monthly log returns pct
18.89
twelve month log return pct
18.89
Rows × columns
1 × 7
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 Sum vs compound: twelve SPY monthly returns linked three ways, derived from the stored result.
ColumnTypeRangeNotes
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.

the exact SQL behind every number 
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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