Understanding VaR (Value at Risk) Simply

VaR (Value at Risk) is "the maximum loss amount expected over a set period, within a set probability."

Sounds hard, right? Here's an example. If someone says "my portfolio's 95% confidence 1-month VaR is ₩1 million," it means this:

"Over the next month, in 95 out of 100 cases the loss will not exceed ₩1 million. But in 5 out of 100 cases (5%), it could lose more than ₩1 million."

So VaR always contains three things: ① the period (a day? a month?), ② the confidence level (95%? 99%?), and ③ the loss amount. A proper VaR requires all three.

There are broadly three ways to compute VaR, each with clear pros and cons.

① The parametric (variance-covariance) method: assumes returns follow a normal distribution (bell shape) and multiplies volatility by a confidence factor. A simple approximation is 'VaR ≈ investment × volatility × confidence factor.' For 95% you use a confidence factor (z-value) of about 1.65, and for 99% about 2.33. It's fast and simple, but it has the weakness of underestimating extreme losses because real markets have 'fatter tails' than a bell shape.

② Historical simulation: it assumes no distribution. It lines up past actual returns in order from worst, then takes the bottom 5% point as VaR. Intuitive, but it depends on the assumption that 'the past represents the future.'

③ Monte Carlo simulation: uses a computer to generate thousands to tens of thousands of hypothetical scenarios and estimate the loss distribution. It's the most flexible and powerful, but the calculation is complex and the result is greatly swayed by which model you use.

Interestingly, at the 95% level the three methods give similar results, but the more extreme you go (like 99%), the more the values diverge by method.

VaR was convenient, so banks and funds used it widely, but it has a fatal weakness: it tells you nothing about 'how severe it gets once the line is crossed.'

VaR only tells you 'there's a 5% chance the loss exceeds ₩1 million'—it stays silent on whether, when that 5% hits, you'll lose ₩2 million or ₩20 million. This is expressed as 'failing to capture tail risk.'

This weakness was laid bare during the 2008 global financial crisis. Many financial institutions' actual losses far exceeded the VaR estimates they had calculated. Numbers that fit well in normal times failed, at the very moment of crisis, to guard against losses that went far beyond the supposed safe zone.

One more thing: VaR can theoretically violate 'sub-additivity.' Simply put, this means cases can arise where diversifying across assets is miscalculated as if it increased risk.

Since VaR can't answer 'if the line is crossed, how much?', a metric emerged to fill that gap: Expected Shortfall (ES), also called Conditional VaR (CVaR).

ES calculates 'the average of the losses that crossed the VaR line.' If VaR tells you only the 'entrance' of the tail, ES looks 'inside' that tail. So it reflects extreme losses far more realistically.

Regulators recognized this difference too. In the Basel III bank capital rules, under the FRTB (Fundamental Review of the Trading Book), the previous '99% VaR' was replaced with '97.5% Expected Shortfall' when calculating market-risk capital. It was a choice to capture tail risk better.

To summarize, VaR is a good starting point for first understanding risk, but if you want to know 'the size of the crisis' too, you must look at complementary metrics like ES together.

In truth, an individual investor rarely needs to compute VaR themselves every day. But the 'way of thinking' VaR provides is truly useful.

First, the habit of making risk concrete in terms of 'probability and amount.' Rather than "it's just risky," you ask yourself "how much could I lose in a month and still endure?"

Second, never forgetting that with any risk metric, 'normal times' and 'crises' are different. Even if VaR's 95% region looks pretty, what's truly scary is the remaining 5%.

Third, that's why, in long-term investing, it matters to look at the 'maximum drawdown' and 'recovery period' together. When you see with your own eyes how much assets fell during real historical crises and how long recovery took, the numbers sink in. Running past crash periods yourself with the crisis simulator on this site ('The Return of Almost Everything,' which I operate personally) will give you a much better feel.