Volatility most frequently refers to the standard
deviation of the change in value of a financial
instrument with a specific time horizon. It is
often used to quantify the risk of the instrument
over that time period. Volatility is typically
expressed in annualized terms, and it may either
be an absolute number ($5) or a fraction of the
initial value (5%).
For a financial instrument, the volatility increases
by the square-root of time as time increases.
Conceptually, this is because there is an increasing
probability that the instrument's price will be
farther away from the initial price as time increases.
Historical volatility is the
standard deviation of a financial instrument based
on historical returns. This phrase is used particularly
when it is wished to distinguish between the actual
volatility of an instrument in the past, and the
current volatility implied by the market.
Volatility of returns of a fund is measured by
standard deviation which is a measure of total
risk of a fund. Volatility indicates the tendency
of the funds NAV (Net Asset Value) to rise and
fall in a short period. It measures the extent
to which the NAV fluctuates as compared to the
average returns during a period.
A fund that has a consistent four year return
of 3 %, for example, would have a mean , or average,
of 3 %. The standard deviation for this fund would
then be zero because the fund’s return in
any given year does not differ from its four year
mean of 3 %. On the other hand, a fund that in
each of the last four years returned -5%, 17%,
2% and 30% will have a mean return of 11%.The
fund will also exhibit a high standard deviation
because each year the return of the fund differs
from mean return. This fund is therefore more
risky because it fluctuates widely between negative
and positive returns within a short period.
A higher standard Deviation means that the returns
of the fund have been more volatile than a fund
having low standard deviation. In other words
high standard deviation means high risk.