# Value at risk

> Value at risk estimates the one-month loss your portfolio stays above 95% of the time, read off your own history rather than a model of it.

> These figures are derived from a return series that the app currently flags as being reworked.
> Values and holdings are unaffected. See [about these numbers](/metrics/about-these-numbers).

Value at risk puts a number on a bad month. Gylder reports the loss your
portfolio has stayed above 95% of the time, over roughly one month.

Read the sentence carefully, because the framing is where most people go wrong.
A 95% value at risk of −9% does not mean you cannot lose more than 9%. It means
that in the worst 5% of months, you lose more than 9%, and this figure says
nothing whatsoever about how much more.

## How it is calculated

Gylder uses the historical method rather than a statistical model. It takes
your actual daily returns in the selected window, sorts them from worst to
best, and reads off the value at the 5th percentile. That daily figure is then
scaled to roughly one month:

```
value at risk (95%, 1 month) = 5th-percentile daily return × √21
```

The 21 is the approximate number of trading days in a month, and the square
root is the standard way of stretching a daily figure across a longer period.

The result is negative, because it is a loss. It needs at least a handful of
data points to mean anything; with too short a window Gylder shows nothing
rather than a confident wrong number.

## How to read it

It is a threshold, not a worst case. Three specific limitations follow, and all
three matter more than the number itself.

**It says nothing about the tail.** The 5% of months worse than this figure
could be slightly worse or catastrophically worse. Value at risk is silent on
exactly the outcomes that hurt most.

**It only knows what has already happened.** The historical method reads your
own past returns. If your window does not contain a crash, your value at risk
does not know crashes exist.

**The square-root scaling assumes independence.** Stretching a daily figure to
a month with √21 assumes each day is unrelated to the last. Real markets have
bad weeks, not just bad days, so this tends to understate the risk in exactly
the conditions where it would be most useful.

Gylder does not tell you what an acceptable value at risk is.

## Where it fits

Value at risk is a forward looking estimate built from history.
[Maximum drawdown](/metrics/max-drawdown) is the opposite: a record of the
worst thing that actually happened, with no estimation involved. Reading them
together is more informative than either alone, because a drawdown far worse
than the value at risk suggests your window contains an event the percentile
has smoothed away.