Real-Time Scaling

Scale covariance matrix based on recent realized volatility:

\[\text{scale\_factor} = \frac{\sigma_{recent}}{\sigma_{longterm}}\] \[\Sigma_{scaled} = \Sigma_{base} \times \text{scale\_factor}^2\]

Asymmetric Response

Respond faster to volatility increases than decreases:

Up moves: Short half-life (5-10 days)
Down moves: Long half-life (21-42 days)

This helps preserve risk control during sudden volatility spikes.

Python Implementation

class AdaptiveCovarianceScaler:
    """Scale covariance matrix based on recent volatility regime."""
    
    def __init__(self, fast_hl=5, slow_hl=42):
        self.fast_hl = fast_hl
        self.slow_hl = slow_hl
        
    def scale_covariance(self, cov_matrix, returns, lookback=252):
        """
        Scale covariance matrix based on volatility regime.
        
        Parameters
        ----------
        cov_matrix : np.ndarray
            Base covariance matrix
        returns : pd.DataFrame
            Recent returns data
        lookback : int
            Lookback period for long-term volatility
            
        Returns
        -------
        np.ndarray
            Scaled covariance matrix
        """
        # Calculate portfolio volatility
        recent_vol = returns.tail(self.fast_hl).std()
        longterm_vol = returns.tail(lookback).std()
        
        # Asymmetric scaling
        vol_ratio = recent_vol / longterm_vol
        
        if vol_ratio > 1:
            scale_factor = vol_ratio ** 2
        else:
            # Slower response to vol decreases
            scale_factor = 1 + (vol_ratio - 1) * (self.fast_hl / self.slow_hl)
            scale_factor = max(scale_factor, 0.5)  # Floor at 50%
        
        return cov_matrix * scale_factor

Benefits