Historical VaR for Assets with Short Return Histories
Summary
The document explains why historical value at risk can be unreliable when an asset has only a short return history: the observed sample may not include the full range of plausible losses. It considers using sector returns as a proxy, but notes that averaging can mute extreme moves and that a sector index may omit asset-specific risk.
The response suggests fitting an extreme value theory model, such as a generalized Pareto distribution, to extrapolate beyond observed tail data. This can estimate risk levels that the empirical sample cannot directly show. The exchange does not provide implementation details, validation evidence, or a solution for recovering idiosyncratic risk from very limited observations. Tail extrapolation depends on model assumptions and does not create new empirical information; simulation is mentioned as a way to generate additional scenarios, though the questioner wishes to avoid it.
Key ideas
- Short return histories may not capture the full range of potential losses.
- Averaging asset returns into a sector index can dampen extreme observations.
- Sector proxies may fail to represent asset-specific risk.
- Extreme value theory can extrapolate tail risk beyond the observed sample.
- Tail estimates remain dependent on modeling assumptions and limited data.
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# Calculating HIstorical VaR with short time series # Calculating HIstorical VaR with short time series Intuitively, Historical VAR is an approach which assumes that in the past data, we have observed everything that can happen, so we consider the worst case(tail). However, when your equity/instrument has a short time series, this assumption breaks down. It is very unlikely that a time series of 100 days will consist of the whole range of likely returns. What is the best approach to overcome this in a simple manner (avoiding MC or complex parametric approaches)? My first thought was to build an index of returns from those equities with a complete time series on a sector by sector basis. Then, we can use the index VAR as a proxy. There are 2 problems I have encountered with this: - Using an index means you are averaging returns, which mean you squash the distribution and dampen the extreme values. - This approach assumes everything in the same sector moves together on average, and therefore doesn't contain any idiosyncratic risk. I cannot see how to add in this idiosyncratic risk with such a short time series & such short data. I have seen EVT mentioned in places. This could possible be suitable for equities which have a moderate Time series length(?), but the problem still holds for equities whose series is too short. Thanks ## Answer by salisboss (score 2, accepted) https://quant.stackexchange.com/a/30053 The best approach is awfully subjective but by characterizing your data set with EVT (e.g. Generalized Pareto Distribution) you could extrapolate into the tail which will give you more risk levels than your data empirically allows. It appears you want to create more data points out of the ether but that would require MC (which you don't want to do).
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