Years to double: the Rule of 72 on the average against the compounded path

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
        ticker,
        date,
        toFloat64(max(close)) AS close_px
    FROM global_markets.stocks_daily_aggs
    WHERE ticker IN ('SPY', 'QQQ', 'MSFT', 'ARKK', 'AMD')
      AND date >= '2015-01-02'
      AND date <= '2024-12-31'
      AND close > 0
    GROUP BY ticker, date
),
rets AS
(
    SELECT
        ticker,
        close_px / nullIf(lagInFrame(close_px) OVER (PARTITION BY ticker ORDER BY date ASC), 0) - 1 AS r
    FROM daily
),
stats AS
(
    SELECT
        ticker,
        avg(r) * 252          AS arith_annual,
        avg(log(1 + r)) * 252 AS log_annual
    FROM rets
    WHERE r IS NOT NULL
      AND isFinite(r)
    GROUP BY ticker
)
SELECT
    ticker,
    round(72.0 / (arith_annual * 100), 2)                                       AS rule_of_72_years,
    round(log(2) / log_annual, 2)                                               AS compounded_years,
    round(log(2) / log_annual - 72.0 / (arith_annual * 100), 2)                 AS extra_years,
    round((log(2) / log_annual) / (72.0 / (arith_annual * 100)) * 100 - 100, 1) AS extra_time_pct
FROM stats
ORDER BY extra_years DESC