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 whose price follows a Gaussian Random Walk , or Wiener Process , 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.
More broadly, volatility refers to the degree of (typically short-term) unpredictable change over time of a certain variable. It may be measured via the standard deviation of a sample, as mentioned above.
However, price changes actually do not follow Gaussian distributions. Better distributions used to describe them actually have "fat tails" although their variance remains finite. Therefore, other metrics may be used to describe the degree of spread of the variable. As such, volatility reflects the degree of Risk faced by someone with exposure to that variable.
is the volatility 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 is often viewed as a negative in that it represents uncertainty and Risk . However, volatility can be good in that if one Shorts on the peaks, and buys on the lows one can make money, with greater money coming with greater volatility. The possibility for money to be made via volatile markets is how short term market players like Day Traders hope to make money, and is in contrast to the long term Investment view of Buy And Hold .
It is also possible to trade volatility directly, through the use of derivative securities such as Options . See Volatility Arbitrage .
Volatility does not imply direction. (This is due to the fact that all changes are squared.) An instrument that is more volatile is likely to increase or decrease in value more than one that is less volatile.
For example, a checking account has low volatility. It won't lose 50% in a year. But then, it won't gain 50% in a year, either.
It's common knowledge that types of assets experience periods of high and low volatility. That is, during some periods prices go up and down quickly, while during other times, they can seem to move almost not at all for a long time.
Periods when prices fall quickly (a crash) are often followed by prices going down even more, or going up by an unusual amount. Also, a time when prices rise quickly (a bubble) may often be followed by prices going up even more, or going down by an unusual amount.
The converse is, 'doldrums' can last for a long time as well.
Most typically, extreme movements do not appear 'out of nowhere'; they're presaged by larger movements than usual.
This is termed Autoregressive Conditional Heteroskedasticity .
Of course, whether such large movements have the same direction, or the opposite, is more difficult to say. And an increase in volatility does not always presage a further increase--the volatility may simply go back down again.
The annualized volatility is proportional to standard deviation of the instrument's returns by the square-root of time period of the returns :
,
where is time period in years of returns. The generalized volatility for time horizon is expressed as:
.
For example, if the daily returns of a stock have a standard deviation of 0.01 and there are 252 trading days in a year, then the time period of returns is 1/252 and annualized volatility is
.
The monthly volatility (i.e., of a year) would be
.
Note that the formula used to annualize returns is not deterministic, but is an extrapolation valid for a random walk process whose steps have finite variance. Generally, the relation between volatility in different time scales is more complicated, involving the Lévy stability exponent :
.
If you get the Wiener process scaling relation, but some people believe for financial activities such as stocks, indexes and so on. This was discovered by Benoît Mandelbrot , who looked at cotton prices and found that they followed a Lévy Alpha-stable Distribution with α = 1.7. (See New Scientist, 19 April, 1997 .) Mandelbrot's conclusion is, however, not accepted by mainstream financial econometricians.
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