You pick a direction, then you pick an option strategy based on risk tolerance, available capital, and volatility ("vol"). But here's
the rub—vol is almost always expressed
as an annual number, and it measures the
potential percentage returns of the stock’s
price. If someone tells you the Nasdaq 100
Index (NDX) has a 19% vol, it means that
in one year’s time, the NDX’s value will
theoretically be within +19% and -19% of
its current price 68% of the time. If NDX
is trading for 7,300, that’s between 5,913
and 8,687. But what if you want to estimate
where NDX might be in a day, or a week?
THE FINER POIN TS
First, you need to convert that annual vol
number into a different period of time, say,
one day. To do that, multiply it by the square
root of time. That’s all. And for most articles
on vol, that would be the end. But here we’re
going to give you a deeper dive.
Why use the square root of time? First,
think about how a stock’s price moves up
and down. The percentage returns are positive and negative, too. So if you took the
average of those positive and negative stock
returns, the result could be close to zero.
That would suggest the stock’s vol was low,
even though it was moving up and down
every day. For example, say a stock goes up
+10% one day and down -10% the next. The
average return is zero, but that’s huge vol.
To solve this problem, you square the stock
price’s returns to make them all positive, and
then average those squared returns to get
what’s known as variance. But who thinks
in terms of squared numbers? So, you take
the square root of that variance to get it back
into something usable. The square root of
variance returns is the standard deviation of
those returns, which is what traders refer to
Stock return variance is linearly related to
time. You double time, for example, and variance doubles. Because you take the square
root of variance to calculate vol, it’s related to
the square root of time. You double time, and
vol increases by the square root of 2. And oh,
that 68% thing? That’s Chebyshev’s inequality theorem. Theoretically, data will fall
between +1 and -1 standard deviations 68% of
the time, + 2 and - 2 standard deviations 95%
IN THE MONEY
Annual Vol Is Nice.
What About Tomorrow?
BIG IDEA: THE TROUBLE WITH VOLATILITY DATA IS
IT’S FOCUSED ON THE LONG TERM. WHAT'S A TRADER
TO DO? CONVERT IT TO THE SHORT TERM.