What does Value at Risk NOT tell you?
This is the most important lesson in the course, and it is a lesson about a silence.
Return to the defining sentence: the 1-day 95% VaR is $200,000 — on 95 days in 100, the loss should stay under $200,000. Now ask the obvious follow-up:
On the other five days, how bad is it?
VaR does not answer. It cannot answer. It is a threshold, and by construction it says nothing about the region beyond the threshold. The distribution past the cutoff could be a gentle slope or a cliff, and the VaR number is identical either way.
Two portfolios, one VaR
Consider two portfolios, both with a 1-day 95% VaR of exactly $200,000.
Portfolio A is a diversified basket of large-cap equities. On its worst 5% of days it loses between $200,000 and roughly $450,000. The tail is a slope.
Portfolio B has sold deep out-of-the-money options. It collects small premiums almost every day, so 95% of the time it looks placid — better than A, in fact. But on the days the option strikes are breached, losses run to $5 million or more. The tail is a cliff.
Identical VaR. One portfolio has an ugly week; the other has an existential event. Any risk measure that reports these two as equivalent has failed at the only moment that matters.
This shape — many small gains, rare enormous losses — is common in real strategies: selling insurance-like exposures, carry trades, some yield-enhancement products. VaR is close to blind to all of them, and that blindness is structural, not a calibration problem.
Three more silences
It says nothing about the path. A 10-day VaR of $600,000 is silent on whether the loss arrives evenly or all at once on day three, when a margin call would force liquidation at the worst possible price.
It is not additive. Combine two portfolios and the VaR of the whole can, in some cases, exceed the sum of the parts' VaRs — which is nonsense as a description of diversification. Formally, VaR is not sub-additive, and therefore not a "coherent" risk measure in the technical sense. Practically, it means you cannot always trust the sum of desk-level VaRs.
It can be gamed. If a trader's limit is expressed in VaR, the way to take enormous risk while showing a small number is to concentrate exposure beyond the VaR cutoff — precisely where the measure stops looking. Any metric used as a constraint eventually gets optimised against.
The frame to keep
None of this makes VaR worthless. It remains a good answer to a narrow question: how big is a routine bad day, and is that number drifting? The failure is not the tool. The failure is treating "the risk number" as if it described the whole distribution.
The map is not the territory. VaR is a map with the edge of the world drawn at the 95th percentile, and no marking for what lies beyond it.
Try it now
- The same five years are below. Take your 95% cutoff from the previous lessons and isolate the sessions worse than it. Measure each one and write the list down in order.
- Look at the range of that list: how much worse than the cutoff does it get? The worst session in five years is usually several times the threshold — and VaR, by construction, said nothing about any of them beyond "worse than this".
- Average your beyond-the-cutoff list. Hold that number: it is the answer to VaR's silence, and it is the subject of the next lesson. Then write the sentence that both A and B above would print on a risk report, and one sentence naming what the report leaves out. Description, not judgement.
Unit done. Next: the measure that looks past the threshold.