trading days per year is 256, because its square root is a round number: 16.
The formula is
For example, a $100 stock that has an at-the-money (ATM) call trading at
a 32 percent volatility implies that there is about a 68 percent chance that
the underlying stock will be between $68 and $132 in one year’s time—
that’s $100 ± ($100 × 0.32). The estimation for the market’s expectation for
the volatility of the stock for one day in terms of standard deviation as a
percentage of the price of the underlying is computed as follows:
In one day’s time, based on an IV of 32 percent, there is a 68 percent
chance of the stock’s being within 2 percent of the stock price—that’s
between $98 and $102.
There may be times when it is helpful for traders to have a volatility
estimation for a period of time longer than one day—a week or a month, for
example. This can be accomplished by multiplying the one-day volatility by
the square root of the number of trading days in the relevant period. The
equation is as follows:
If the period in question is one month and there are 22 business days
remaining in that month, the same $100 stock with the ATM call trading at a
32 percent implied volatility would have a one-month volatility of 9.38
percent.
Based on this calculation for one month, it can be estimated that there is a
68 percent chance of the stock’s closing between $90.62 and $109.38 based
on an IV of 32 percent.