Estimating Value at Risk from Equally Likely Scenarios

Summary

The document describes a direct way to interpret a finite set of equally probable portfolio-return scenarios for Value at Risk. With 250 scenarios, sorting the outcomes from worst to best makes the 25th-worst outcome the 10% VaR under the convention described: one tenth of the scenarios are at or beyond that loss threshold.

For a confidence level whose quantile does not align with an observed scenario, such as 1% in this example, the response suggests approximating the distribution curve and interpolating, with cubic splines offered as one possible method. This is a practical description rather than a detailed statistical treatment. The result depends on scenarios being equally likely and on the chosen quantile convention and interpolation method; it does not address how scenarios are generated or whether they adequately capture tail risk.

Key ideas

• Sort scenario returns or losses from worst to best to locate an empirical VaR quantile.
• With 250 equally likely cases, the 25th-worst outcome corresponds to the stated 10% VaR convention.
• A 1% quantile may fall between observed scenarios in a sample of this size.
• Interpolation can estimate an unobserved quantile, though the selected curve-fitting method affects the estimate.
• The approach assumes equally probable scenarios and does not validate their coverage of extreme losses.

Tags

# Scenario generation for Value at risk: How to interpret the scenarios


# Scenario generation for Value at risk: How to interpret the scenarios












This is a a simple and rather pratical approach and not theoretical. Let's assumes I have generated 250 scenarios for a given fixed portfolio. Hence we assume that the asset returns can result in 250 returns and each of them are equally probable

How would you interpret the scenarios in terms of value at risk?. Say you want 10% VaR. Can you simply call the 25th worst scenario as your 10% VaR. What is my 1% var then?

## Answer by dismalscience (score 0, accepted)

https://quant.stackexchange.com/a/42768

Yes, your 25th-worst scenario of 250 cases would be your 10% VaR. For your 1% VaR, as it doesn’t rest directly on a known point, you’d choose some function (cubic splines are popular) to approximate the curve, and interpolate.

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