Happy Equations

Note: For visitors of your site, this entry is only displayed for users with the preselected language English/English (en)

I was asked about VaR of a 20 years fixed-income or fund. VaR is an estimate about potential profit or loss in a short term, says 1, 5, or 10 days. How about VaR for a 20 years maturity government bond? Or for someone want to evaluate his long-term investment?

We know VaR is getting larger as the term longer:

n days VaR = 1 day VaR * sqrt(n)

if 1 day VaR is v
5 days VaR is v * sqrt(5) = 2.236v
10 days VaR is v * sqrt(10) = 3.162v

if you evaluate longer term
365 days VaR is 19.105v
3650 days VaR is 60.415v
7300 days VaR is 85.440v

Wow, the potential profit or loss might be very high.

By definition is true, of course, but we know it is not in practice. Why?

Because long term volatility is hard to estimate and the rule of square n is not a good way to calculate even short term VaR.

I clawed the webs and found only one paper about long term VaR model.
See Long-Term Value at Risk. By. Kevin Dowd, David Blake, and Andrew Cairns