Volatility Drag

Volatility drag (sometimes called volatility tax or variance drain) is the idea that volatility reduces compounded growth. Even with the same average return, the more volatile asset usually ends up with a lower CAGR over time.

A common rule of thumb (for small moves) is that expected log growth is roughly the arithmetic mean return minus half the variance:

$$g \approx \mu_s - \tfrac{1}{2}\sigma_s^2$$

So the “drag” term is:

$$\text{drag} \approx \tfrac{1}{2}\sigma_s^2$$

Where:

• $g$ is the expected log growth rate over the horizon,
• $\mu_s$ is the mean of simple returns,
• $\sigma_s$ is the standard deviation of simple returns.

In log-return notation, if $\ell_t = \ln(1 + r_t)$ and $\mu_{\ell} = \mathbb{E}[\ell_t]$, then $g = \mu_{\ell}$. For small moves, the “drag” is the gap between arithmetic and log means:

$$\mu_s - \mu_{\ell} \approx \tfrac{1}{2}\sigma_s^2$$

For small moves, simple-return and log-return volatility are close, so you may also see this written as $\mu_s - \mu_{\ell} \approx \tfrac{1}{2}\sigma_{\ell}^2$.

In annualized terms, if $\sigma_{ann}$ is annualized volatility (simple-return volatility), the rule of thumb becomes:

$$\text{drag}_{ann} \approx \tfrac{1}{2}\sigma_{ann}^2$$

How we use this at Gale Finance

On compare pages we show a rule-of-thumb volatility drag estimate in the “Audit this calculation” panel.

• Conceptually it’s about log growth (see log returns).
• Practically we estimate it from the page’s annualized volatility (computed from simple daily returns). For small daily moves, simple and log return volatility are close, so this is usually a reasonable intuition.

Important caveats

• It’s an approximation. It becomes less accurate for extremely volatile assets and big jumps.
• It doesn’t include “skill”. A high-volatility asset can still have a great CAGR if its average returns are high enough.
• Not a forecast. This is a descriptive rule of thumb for compounding, not a prediction.