How to calculate volatility?
Roger E. Ison
: How do I calculate the volatility of a stock? That is, I want to have a
: benchmark to separate the steadily rising/declining stocks in a period
: from the wildly fluctuating ones.
Volatility will NOT help you separate steadily rising or declining stocks
from wildly fluctuating ones! It only measures the probable or expected
magnitude of price movements over time, not their direction.
Mathematically, volatility or sigma is the standard deviation of
the logarithm of the daily rate of return on a stock. From a sequence of
daily prices p[1], p[2], ... p[n] we calculate each daily return as
r[n+1] = p[n+1]/p[n]. This is today's price divided by yesterday's price,
or the relative or percent change from one day to the next. Then take the
logs of the daily returns x[i] = log(r[i]) and compute sigma as the
standard deviation of x[i] using the usual statistical formula you can
find in any stats textbook.
The standard deviation measures the deviation of elements in a series from
the mean value of the series, but the deviations are SQUARED. So the sign
(the direction of each deviation) is lost in the squaring operation. Thus
a series of moves that are all "up" by a given proportion would have the
same sigma as a series of "down" moves by the same proportion, or an
arbitrary sequence uududduddd ... of up/down moves of the same proportion.
Only the magnitude of the daily moves counts, not the direction. You can't
use volatility to spot trends because direction information is thrown away.
If you want to know more about this, send me your postal address and I will
mail you a paper on the subject.
Roger Ison
Mantic Software Corporation
Jacob Galley
>Mathematically, volatility or sigma is the standard deviation of
>the logarithm of the daily rate of return on a stock. . . .
Can you explain how this is better than just taking the standard
deviation of the last n days' price? In Excel, I have been using
=STDEVP($C6:$E10)
where columns C thru E are the high, low and close for each day.
Jake.
--
Philosophers cannot purely and simply forget what psychology, sociology, ethno-
graphy, history and psychiatry have taught us about the conditioning of human
behavior. It would be a very romantic way of showing one's love for reason to
base its reign on the disavowal of acquired knowledge. <-- Merleau-Ponty
Guido Hoss
benchmark to separate the steadily rising/declining stocks in a period
from the wildly fluctuating ones.
Guido
Too tall28
Let me complicate your life: if you found a truly trending market place i.e.
one in which say prices increased by 1 percent everyday... the calculations so
lovingly described for taking the standard deviation of the rates of return
would return zero as an answer surely not what you are looking for..
Volatility aka standard deviation will not help distinguish trendiness.