2
$\begingroup$

I have a model predicting 1-day VaR.

How does 1-year VaR follow from it?

Shall I just multiply by 365 or another method?

$\endgroup$
  • $\begingroup$ Square root of time. $\endgroup$ – SmallChess Dec 3 '14 at 23:43
  • 1
    $\begingroup$ as @Richard pointed out, the scaling rule depends on the distribution. Value at Risk is a distribution quantile. The Quantile of a Normal Distribution with $\mu = 0$ scales with $\sqrt{T}$, in general it does not! $\endgroup$ – vanguard2k Dec 4 '14 at 14:14
4
$\begingroup$

It depends on the method by which you calculate VaR. Some models (t-distributuion, normal) lead to a form of VaR such that it is just scaled volatility: $$ VaR = c \sigma $$ with some proper $c$ (e.g. $q_{\alpha}$ in the case of normal, bit more complicated for the t-distribution). Then as $\sigma$ scales with square-root-of-time so does VaR.

If VaR is modelled with some expectaion of the form $$ VaR = -\mu+c \sigma $$ then $\mu$, the expectation, scales with time and volatility as above.

Furthermore: it depends on the setting but usually it is just nonsense to calculate an annual VaR from a daily one.

$\endgroup$
3
$\begingroup$

The standard approach is to multiply by the square root of the number of trading days in a year. If you assume there are 250 trading days in the year, you multiply by $\sqrt{250}$.

Investopedia is one source explaining this approach.

$\endgroup$
  • 1
    $\begingroup$ The link recommends to multiply the standard deviation by $\sqrt{250}$, what about the mean $\mu\cdot 250$? $\endgroup$ – emcor Dec 4 '14 at 8:40
1
$\begingroup$

The most commonly used approach is multiplication by the square-root of T, 19.1 in this case.

This assumes no autocorrelation, however (Markov process). Interest rates tend to show a mean reversion, so the number would be smaller than 19.1. Other cases could show the oppoite effect if there are positive feedbacks. In both of these cases, a simple time scaling is not possible and the model should be re-run for the new time horizon.

$\endgroup$
0
$\begingroup$

The most common approach is to multiply by sqrt of 250. This is the standard. Although very basic. A much better solution is to make your monte carlo simulation on a 1 year time period using scaled parameters over 1 year.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.