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.