Historical Simulation and Gaussian VaR: Strengths and Limitations

Summary

The document compares historical simulation and Gaussian, or parametric, Value at Risk. Historical simulation uses the empirical distribution of past returns and is straightforward to calculate without assuming a particular return distribution. It can be modified to emphasize recent observations or adjust weights according to volatility. Its central limitation is reliance on past experience, so it may miss unprecedented events. In a basic rolling-window version, a large observation dropping out can also cause an abrupt VaR change, a problem described as ghosting.

The parametric approach is also relatively accessible, though it requires more work than historical simulation and a covariance matrix for the portfolio. It assumes normally distributed returns and that delta sensitivities capture the relevant risk. Those assumptions can produce poor estimates for nonlinear positions such as options. The comparison lists tradeoffs rather than declaring a universally superior method; it gives no performance results or guidance on choosing a window, weighting scheme, or distributional alternative.

Key ideas

• Historical simulation estimates VaR from observed returns without imposing a parametric return distribution.
• Historical estimates can miss events absent from the sample and can jump when extreme observations leave a rolling window.
• Recent-return or volatility weighting can be added to historical simulation.
• Gaussian VaR assumes normal returns and relies on delta sensitivities to represent portfolio risk.
• The Gaussian approach can misstate nonlinear exposures, including option positions.

Tags

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


# 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?

## Answer by AfterWorkGuinness (score 3, accepted)

https://quant.stackexchange.com/a/21476

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.