Value at Risk (VaR)

Value at Risk (VaR) answers a precise question: over a given period, with a given confidence, what is the most I should expect to lose under normal conditions?

Reading a VaR statement

A VaR always has three parts — a time horizon, a confidence level, and an amount. For example:

"The 1-day 95% VaR is US$2,000."

Read it as: on 95% of days, the loss should not exceed US$2,000. Equivalently, on about 1 day in 20 (the worst 5%), the loss is expected to be worse than US$2,000 — VaR does not say how much worse.

A simple estimate

If a US$100,000 portfolio has a daily standard deviation of about 1.2%, a rough 95% VaR uses the fact that the 5% tail sits about 1.65 standard deviations below the mean:

Daily standard deviation in dollars = 100,000 x 1.2% = 1,200
1-day 95% VaR = 1.65 x 1,200 = 1,980  (about US$2,000)

So on a typical day you would not expect to lose more than roughly US$2,000.

What VaR is good for

It gives a single, comparable number across very different positions, which is why banks and funds report it daily and risk limits are often written in VaR terms.

Its famous blind spot

VaR tells you the threshold of the bad tail but says nothing about how bad the tail gets beyond it. A 95% VaR is silent about the worst 5% of days — exactly the days that cause ruin. It also leans on the assumption that returns are well-behaved, which fails in crashes. This is precisely the gap the next lesson fills.