Historical VaR

Historical VaR

Value at Risk (VaR) answers: "What is the most I can lose over a given period at a given confidence level?"

The historical simulation approach uses actual past returns — no distributional assumptions needed. You simply sort your return series and read off the appropriate percentile.

Algorithm

Given a list of returns and a confidence level c:

1. Sort returns in ascending order
2. Compute the index: idx = int((1 - c) * n)
3. The VaR is the negative of the return at that index (so VaR is expressed as a positive loss)

For 95% confidence on 7 observations, idx = int(0.05 * 7) = 0, so we take the worst return.

Formula

VaR = -sorted_returns[int((1 - confidence) * n)]

Example

Returns: [-0.05, -0.03, -0.01, 0.01, 0.02, 0.03, 0.04]
Sorted (already sorted), 95% confidence:
idx = 0 → worst return = -0.05 → VaR = 0.05 (5%)