Calculating daily volatility

Volatility is usually expressed as the annualized standard deviation of returns. Volatility is proportional to the square root of time. That means one can approximate a volatility over a smaller time period than one year by dividing the annual vol by the square root of the number of trading periods one is interested in.

So, to convert annual volatility to a daily vol, divide by 16, which is the square root of 256 — about the number of trading days in the year.

Back in the days when vol was 15-20% annually (way back in 2007), a daily vol was about 1%. These days, the VIX is closer to 80 which implies a daily return of +- 5%.

On Sept 15th, 2008, when Lehman was allowed to go bankrupt (“Lehman is not too big to fail” – Paulson), the VIX went up to 80 and has been in that region ever since. The Lehman bankruptcy has turned out to be a massive event in financial history.