Value at Risk

What VaR Misses

VaR can miss the severity of losses beyond the threshold.

highlighted = computed this step

Same VaR, different tail

A second distribution can keep VaR at alpha 95% equal to $200.00 while making the far-tail loss larger.

same VaRα=$200.00\text{same VaR}_{\alpha}=\$200.00

Tail shape is invisible to VaR

In that heavier-tail distribution, expected shortfall at the same alpha becomes $2,000.00, while VaR remains $200.00. VaR does not measure how bad losses are beyond the threshold.

tail severity can change while VaR stays fixed\text{tail severity can change while VaR stays fixed}

VaR limitation

VaR is not subadditive in general, so it can miss diversification effects. It is a model output under the stated distribution, not a forecast. This is descriptive, not investment advice.

VaR can miss tail shape\text{VaR can miss tail shape}