The Rule of 72 (and Where It Breaks)
An 8% average return at rising volatility: compound rate and doubling timeranking ·
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Rule of 72 against the exact doubling time, by annual returnranking ·
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Average return against compound return, five price histories, 2015 through 2024ranking ·
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Years to double: the Rule of 72 on the average against the compounded pathtable ·
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An 8% average return at rising volatility: compound rate and doubling time
An 8% average return at rising volatility: compound rate and doubling time
| annual_volatility | compound_return_pct | doubling_years |
|---|---|---|
| 0% | 8 | 9 |
| 5% | 7.88 | 9.1 |
| 10% | 7.5 | 9.6 |
| 15% | 6.88 | 10.4 |
| 20% | 6 | 11.9 |
| 25% | 4.88 | 14.6 |
| 30% | 3.5 | 20.1 |
| 35% | 1.88 | 37.3 |
the exact SQL behind every number
SELECT
concat(toString(vol_pct), '%') AS annual_volatility,
round(compound * 100, 2) AS compound_return_pct,
round(log(2) / log(1 + compound), 1) AS doubling_years
FROM
(
SELECT
vol_pct,
0.08 - 0.5 * pow(vol_pct / 100.0, 2) AS compound
FROM
(
SELECT arrayJoin([0, 5, 10, 15, 20, 25, 30, 35]) AS vol_pct
)
)
ORDER BY vol_pct ASC
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