Estimate VaR using a historical simulation approach.

Estimating VaR with a historical simulation approach is by far the simplest and most straightforward VaR method. To make this calculation, you simply order return observations from largest to smallest. The observation that follows the threshold loss level denotes the VaR limit. We are essentially searching for the observation that separates the tail from the body of the distribution.

More generally, the observation that determines VaR for n observations at the $$(1 – \alpha)$$ confidence level would be: $$(\alpha * n)$$. Recall that the confidence level, $$(1 – \alpha)$$ , is typically a large value (e.g., 95% ) whereas the significance level, usually denoted as $$\alpha$$ , is much smaller (e.g., 5%).

To illustrate this VaR method, assume you have gathered 1,000 monthly returns for security and produced the distribution. You decide that you want to compute the monthly VaR for this security at a confidence level of 99%. At a 99% confidence level, the lower tail displays the lowest 1% of the underlying distributions returns. For this distribution, the value associated with a 99% confidence level is a return of -4%.

Figure 1

 Ranks Daily Return 1 7% 2 2.56% 3 2% 4 1.88% … … 96 1.02% 97 -0.9% 98 -2.7% 99 -3.5% 100 -4%