How this number is made
This value at risk assumes the portfolio’s daily moves are a normal distribution with no drift. The figure is how far a loss can go and still be inside the confidence you picked. It is not the most you can lose. Expected shortfall is the average loss in the tail beyond that line, under the same normal assumption. Real books have fatter tails.
- Daily volatility is the standard deviation of one day’s percent move.
- Ten days uses the square-root-of-time rule. That rule fails when positions change or vol clusters.
Formula
VaR = value × daily volatility × Z × √days. Z is 1.64485 at 95% and 2.32635 at 99%. Expected shortfall uses the normal tail density divided by the tail probability.
Worked example
With the figures already in the form, value at risk is $52,015.
Questions
Is this historical VaR?
No. Historical VaR needs the actual daily P&L. This is the parametric shortcut.
Why can the real loss be larger?
Because 95% means one day in twenty is supposed to be worse, and markets are not normal. The shortfall row is the model’s average of those worse days, still under a normal curve.