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

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?

• Have you tried searching for this? There is a lot of info out there. Oct 27, 2015 at 19:11
• I have, but didn't find anything really relevant. Oct 27, 2015 at 19:13

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.
• which one is used the most? monte carlo? Oct 27, 2015 at 19:29
• No idea sorry. If I had to make an educated guess, historical as it is the least data and process intensive. Oct 27, 2015 at 19:32
• Thanks anyway! Maybe some praticioner will input something Oct 27, 2015 at 20:05
• But guys: in usual Monte Carlo approaches: what do you do? Estimate a covariance from historical data and sample Gaussians. There are more sophisticated approaches but in the basic case: what is the difference? Oct 28, 2015 at 9:13
• Monte Carlo simulation is quite different. Here are a couple of posts on the topic: quant.stackexchange.com/questions/17910/… and quant.stackexchange.com/questions/12592/… Oct 28, 2015 at 16:37