Value at Risk (VaR)

Value at Risk, or VaR, is one of the most widely used risk numbers in finance, relied on by banks, regulators, and asset managers. It tries to package a portfolio's risk into a single figure. It is useful, but it hides blind spots that connect straight to the fat-tails warning of Unit 5. You need to understand both what it says and what it cannot see.

What VaR measures

VaR answers a specific question: what loss will not be exceeded over a given period, at a given confidence level? A one-day 95 percent VaR of 1 million dollars means that, under normal conditions, there is a 95 percent chance the portfolio will not lose more than 1 million dollars in a day. Equivalently, there is a 5 percent chance the loss will be worse than that. So VaR ties a loss threshold to a probability and a time horizon, which is what makes it feel so tidy.

Computing a simple VaR

The parametric method assumes returns are roughly normal and reads the threshold off the bell curve. For a normal distribution, the 95 percent one-tailed cutoff sits about 1.65 standard deviations into the loss tail. So the 95 percent VaR is roughly 1.65 times the portfolio's volatility, expressed in dollars.

The first blind spot: the tail is invisible

Here is the main flaw in VaR. It tells you a threshold losses are unlikely to exceed, but it says nothing about how bad the loss could be when it does exceed it. In the example, the 5 percent of days worse than 33,000 dollars could mean a 40,000 dollar loss or a 5 million dollar loss. VaR does not distinguish between them. It draws a line and gives the probability of crossing it, while staying completely silent about the size of the catastrophe on the other side. For a risk measure, being blind to the severity of the worst outcomes is a serious weakness.

VaR tells you how much you might lose on a normal bad day, and nothing about the rare day that can destroy you. The blind spot is exactly the catastrophe.

The second blind spot: false comfort from normality

The parametric VaR you just computed assumes normal returns, which runs straight into the central lesson of Unit 5: real returns have fat tails. By assuming a bell curve, parametric VaR underestimates the probability and size of extreme losses, producing a comforting but wrong picture. This is not hypothetical. Over-reliance on VaR and the false confidence it gave was widely blamed in the 2008 financial crisis, when losses the models deemed nearly impossible arrived with devastating force. A risk number that convinces its users catastrophe cannot happen can be worse than no number at all.

Expected Shortfall, and the honest takeaway

Recognizing VaR's blindness to tail severity, risk managers use a complement called Expected Shortfall, also known as Conditional VaR. Instead of just marking the threshold, it estimates the average loss in the worst cases beyond the VaR line, answering the question VaR ignores: when things go badly, how bad on average? It gives a fuller view of tail risk and increasingly supplements or replaces VaR. The honest takeaway: VaR is useful but dangerously incomplete. It describes a normal-conditions threshold, says nothing about the disaster beyond it, and in its normal-distribution form understates exactly the extreme events most capable of ruin. Use it with full awareness of these limits, alongside Expected Shortfall and the stress testing later in this unit.

VaR and its cousins describe risk in probabilities. The next lesson turns to the most visceral risk measure of all, the drawdown, and the unforgiving arithmetic of climbing out of a loss.