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.