What are the pros and cons of historial and Gaussian approaches to VaR?

Question

What is the difference between historical and Gaussian method of VaR estimation?

I know how they are calculated, but what are the pros and cons of each?

Answer 1

Historical Simulation

Pros:

• Easy to calculate
• Doesn't make assumptions about distribution of returns (uses empirical distribution)
• Can add some enhancements onto it such as giving a higher weighting to more recent returns (prevents ghosting mentioned below) or a weighting by volatility where more volatile returns get a higher weight.

Cons:

• Assumes the past will repeat itself, doesn't consider events that it has not seen before
• If you use the most basic historical simulation approach, as your historical window shifts, large losses or returns at the edge of the window will no longer be in your data-set and can cause a significant jump in the Var (this is called ghosting) which in very undesirable

Guassian/Parametric/Delta Normal/Variance-Covariance (has many names)

Pros:

• Relatively easy to calculate (more work than historical, but less compared to monte carlo)

Cons:

• Assumes returns are normally distributed, which is often incorrect
• Assumes delta sensitivity accounts for all the risk
• Very inaccurate for non-linear positions like options (because of above point re delta)
• Need to compute an NxN covariance matrix for the portfolio.