Bias statistic, volatility regime adjustment क्या है?

The bias statistic of a portfolio’s risk forecasts over $T$ periods is the standard deviation of its standardised returns $r_t/\hat\sigma_{t-1}$; it is one for correct forecasts, within $1 \pm \sqrt{2/T}$ with probability about 95% for normal returns. The cross-sectional bias of day $t$ is $B_t^2 = \frac1K\sum_k f_{kt}^2/\hat\sigma_{k,t-1}^2$ over the factors. A volatility regime adjustment multiplies the covariance forecast by an exponentially weighted average $\lambda_t^2$ of recent $B_t^2$, raising all factor volatilities together when the day’s factor returns are large for their forecasts.