In the discussion above, we have often pointed to the use of numerical simulation techniques as a way to calculate quantiles or distributions that are not available in closed form. These techniques differ in terms of their underlying assumptions ranging from fully parametric to essentially non-parametric.
Bootstrapping, or Filtered Historical Simulation (FHS), assumes a parametric model for the second moment dynamics, and then bootstraps from the standardized returns to build up the required distribution. At the portfolio level this is easy to do. First calculate the standardized pseudo portfolio returns as,