Volatility Targeting: Dynamic Approaches

In volatility targeting annualised rolling volatility is estimated using a lookback window or an exponentially weighted moving average . The recursive EWMA formula for variance is: $\sigma_t^2 = (1 - \alpha) \sigma_{t-1}^2 + \alpha r_t^2$ where $\alpha = \frac{2}{1+N}$ , and $N$ is the equivalent lookback window length. The non-recursive form, using $\lambda = 1 - \alpha$ , the variance is: $\sigma_t^2 = (1 - \lambda) \sum_{i=0}^\infty \lambda^i r_{t-i}^2$ The target annualized volatility is