Historical value-at-risk

The second approach in calculating the value-at-risk metric doesn’t rely on an underlying model. Instead it’s based on historical data from which the risk metric can be constructed. The benefits of this approach are: no distributional assumptions, very intuitive, can be used for nonlinear contracts such as options. However, the downside is that data needs to be gathered and stored over time. Value at risk measures with another time horizon need other, or adjusted data. The most important downside is that historical value-at-risk measures change over time. During times of crises, they tend to increase, and may even lead to an endogenous market selling pressure. When, risk buffers are exceeded by a shock, many participants could start selling at the same time, leading to even further market declines.

Historical value-at-risk in practice

In practice, the historical value-at-risk (hvar) measure can be calculated as follows and shown in the provided excel file. As a first step, download sufficient data, for example 500 historical data points, at a choses frequency: daily, weekly, monthly. This is followed by calculating the stock returns. Then draw randomly with repetition returns out of the calculated stock returns. Take the x% of this sequence which equals your VaR. Multiplying this gives you the VaR in dollar amounts. On the next day, week,… drop the first observation from your dataset and include the new datapoint at the end of your dataset and repeat the previous exercise.

Summary

The historically simulated value-at-risk measure doesn’t require and underlying model the determine the risk metric. It is based on the data generated by the market. Its ease of use and applicability to any underlying instrument are its main strengths.

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