Observability of market daily volatility

We study the price dynamics of 65 stocks from the Dow Jones Composite Average from 1973 to 2014. We show that it is possible to define a Daily Market Volatility σ(t)σ(t) which is directly observable from data. This quantity is usually indirectly defined by r(t)=σ(t)ω(t)r(t)=σ(t)ω(t) where the r(t)r(t) are the daily returns of the market index and the ω(t)ω(t) are i.i.d. random variables with vanishing average and unitary variance. The relation r(t)=σ(t)ω(t)r(t)=σ(t)ω(t) alone is unable to give an operative definition of the index volatility, which remains unobservable. On the contrary, we show that using the whole information available in the market, the index volatility can be operatively defined and detected.