“Volatility” is an important term used in the stock markets and by many
market professionals. Many investors use this term to manage their risk. “Volatility”,
in simpler terms, means the fluctuation in a stock’s or any other underlying’s
price, over a specific period of time. Volatility is divided in to two categories.
The first one is “Historical volatility” and the other one is “Implied
volatility”. “Historical volatility” is defined as the historical
fluctuation in a particular underlying’s price, whereas “Implied volatility”
is the estimation of volatility in an asset’s price. Generally, “Implied
volatility” finds extensive use in “Options”.
Understanding “Historical volatility” is important for many investors
as well as traders. For investors, this term is important, because it helps in estimating
or calculating their risk. Traders, generally use “Historical volatility”
to know how volatile a stock or an index will be in the future.
Before attempting to calculate “Historical volatility” of any particular
asset, one needs to keep in mind, the time frame in which the volatility is calculated.
According to the preferences of a trader or an investor, the time frames change.
More specifically, the time frame defined, is, in most cases, different for an investor
and a trader. An investor mostly looks out for the future volatility in an underlying
over a longer period of time, whereas a trader feels better with shorter time frames.
A time frame of around 30 days has around 21 trading days in it. Similarly, for
all the other time frames, the trading days would be less than the actual number.
So, this point also should be kept in mind, while calculating Historical volatility.
The calculation would be easy if we divide this whole process in to two parts. The
first one would include calculating periodic returns of a stock. The second one
is choosing the time frame, as specified above. Calculating periodic returns, in
turn, can be grouped in to calculating simple returns, and continuously compounded
returns. Most preferably, investors look out for the continuously compounded return
because this return has more accurate information associated with it, and will be
able to provide more accurate volatility in a stock.
As stated before, there are two types of returns, and these are ‘simple’
and ‘continuously compounded’. A ‘return’ is defined as
the movement of a share’s price in a specific period. So, a simple daily return
is the percentage change of a stock’s price from yesterday to today. Mathematically,
it can be shown as:
R = ( St - Sy ) / Sy
R = Simple daily return,
St = Today’s share price,
Sy = Yesterday’s share price.
On the other side, a continuously compounded return is the logarithm of the ‘ratio
between today’s share price and yesterday’s share price’. Mathematically,
R = Log ( St / Sy )
Now, with both, time frame and periodic returns available, it becomes easy to calculate
“Historical volatility”. Using the time period and continuously compounded
returns, variance is calculated by the following formula:
Here, s^2 = Variance,
n = Time period or number of days,
R = Average of daily returns.
Now, that the variance is known, we can calculate the standard deviation by taking
the square root of it. This standard deviation is called “Historical volatility”.