Volatility Targeting

Key idea

Volatility Targeting dynamically adjusts portfolio exposure to maintain a desired volatility level.

Instead of forecasting return:

it stabilizes risk.

Core question:

If market risk changes, how should leverage change?

Definition

Target volatility:

\[\sigma^*\]

Observed portfolio volatility:

\[\hat\sigma_t\]

Scaling factor:

\[k_t = \frac{\sigma^}{\hat\sigma_t}\]

Adjusted weights:

\[w_t = k_tw_0\]

Interpretation:

  • realized volatility rises → reduce exposure
  • realized volatility falls → increase exposure

Example

Portfolio:

  • target vol: $10%$
  • current vol: $20%$

Then:

\[k=\frac{10}{20}=0.5\]

New exposure:

\[50%\]

If current volatility drops to $5%$:

\[k=2\]

Exposure doubles.

Estimating Volatility

Common estimators:

Rolling estimate:

\[\hat\sigma_t = \sqrt{ 252 \cdot \operatorname{Var}(r) }\]

EWMA:

\[\sigma_t^2 = \lambda\sigma_{t-1}^2 + (1-\lambda)r_t^2\]

Typical:

\[\lambda=0.94\sim0.99\]

Relationship to Kelly

Continuous Kelly:

\[f^ = \frac{\mu}{\sigma^2}\]

Vol targeting implicitly stabilizes:

\[f\sigma \approx \text{constant}\]

Kelly determines optimal leverage.

Vol targeting determines realized leverage.

Benefits

Advantages:

  • smoother risk profile
  • drawdown reduction
  • leverage normalization

Potential drawbacks:

  • delayed response
  • whipsaw
  • turnover increase

Usage in Quantitative Equity

Volatility targeting appears in:

  • portfolio overlays
  • market timing
  • risk budgeting
  • factor allocation
  • CTA and multi-asset systems

A common production pipeline:

\[\text{Signal} \rightarrow \text{Portfolio} \rightarrow \text{Vol Target} \rightarrow \text{Execution}\]

Volatility targeting is one of the most widely deployed risk-control mechanisms.