building on the ensemble vs. time theme, here is one way to visualize our insidious friend volatility drag.
Arithmetic vs. geometric returns of a few select companies over a 21 year period: 2005 through 2025.
| Ticker | Arithmetic avg. | Geometric (CAGR) | Volatility drag | Annual σ | $100 grows to | Down years |
|---|---|---|---|---|---|---|
| NVDA | 63.3% | 38.6% | 24.7 pts | 85.3% | $95,004 | 6 of 21 |
| MU | 43.6% | 16.1% | 27.5 pts | 101.7% | $2,315 | 8 of 21 |
| BAC | 8.1% | 0.8% | 7.3 pts | 38.3% | $117 | 9 of 21 |
| C | 2.5% | −6.5% | 9.0 pts | 38.8% | $24 | 9 of 21 |
| XOM | 7.0% | 4.2% | 2.9 pts | 26.1% | $236 | 8 of 21 |
Citigroup is perhaps the sharpest example: a loss of approximately 75% over the investment period, even when the arithmetic average shows a positive 2.5% return.
the vol drag shortcut breaks in the extremes
There is a rule of thumb to estimate volatility drag:
arithmetic mean − σ²/2 ≈ geometric mean
Not surprisingly, as with most approximations, it works well when volatility is in the 25-40% range, but it badly misses the mark when things get wild.
| Ticker | Actual drag | σ²/2 | Error |
|---|---|---|---|
| XOM | 2.9% | 3.4% | −0.6 pts |
| BAC | 7.3% | 7.4% | −0.0 pts |
| C | 9.0% | 7.5% | +1.4 pts |
| NVDA | 24.7% | 36.3% | −11.6 pts |
| MU | 27.5% | 51.7% | −24.2 pts |
Note: I used price returns for the calculations, not total returns. Using total returns would marginally increase the arithmetic mean returns but the variance would be unchanged. The vol drag would move very little. BAC and C returns would look meaningfully better but C's compound return would still be negative.