Historical VaR

Historical value at risk (VaR), also known as historical simulation or the historical method, refers to a particular way of calculating VaR. In this approach we calculate VaR directly from past returns. For example, suppose we want to calculate the 1-day 95% VaR for an equity using 100 days of data. The 95th percentile corresponds to the least worst of the worst 5% of returns. In this case, because we are using 100 days of data, the VaR simply corresponds to the 5th worst day.

For an infinitely-lived security such as an equity, the historical approach could not be easier. For derivatives, such as equity options, or other instruments with finite life spans, such as bonds, it is slightly more complicated.

One advantage of historical VaR is that it is extremely simple to calculate. Another advantage is that it is easy to explain to non-risk professionals.

The historical approach is non-parametric. We have not made any assumptions about the distribution of historical returns.

One disadvantage of the historical simulation approach is that it can be very slow to react to changing market environments. The hybrid approach tries to address this problem with the addition of a decay factor.

For more information on VaR models, see our white paper, An Introduction to Value at Risk.

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