When should I prefer historical simulation VaR over delta-normal VaR?

Historical simulation becomes more attractive when the portfolio cannot be summarized reliably with a small-move linear approximation.

That usually happens when:

• options or callable instruments make payoffs curved rather than linear
• current holdings are very different from the historical portfolio, so old portfolio returns are not directly relevant
• you can reprice the current portfolio under each historical factor move

Delta-normal VaR is fast because it compresses risk into exposures, volatility, and correlation. That works well for mostly linear books over short horizons. It works less well when gamma, optionality, or regime changes matter.

A useful mental rule is:

If the book is nonlinear and you can revalue it across historical shocks, historical simulation usually gives a more defensible first answer. If you also need scenarios beyond the observed sample, that is when Monte Carlo starts to dominate.