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# Volatility

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Volatility is 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 (100$+- 5$) or a fraction of the initial value (100$+- 5%). For a financial instrument whose return 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. Mathematically, this is a direct result of applying Itô's lemma to the random process. 'Historical volatility' 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. ## Defined The annualized volatility σ is proportional to standard deviation σSD of the instrument's returns by the square-root of time period of the returns : $\sigma = {\sigma_{SD}\over\sqrt{P}}$, where P is time period in years of returns. The generalized volatility σT for time horizon T is expressed as: $\sigma_T = \sigma \sqrt{T}$. 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 $\sigma = {0.01 \over \sqrt{1/252}} = 0.1587$. The monthly volatility (i.e., T = 1 / 12 of a year) would be $\sigma_{month} = 0.1587 \sqrt{1/12} = 0.0458$. ## External links ## See also 03-10-2013 05:06:04 The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details Science kits, science lessons, science toys, maths toys, hobby kits, science games and books - these are some of many products that can help give your kid an edge in their science fair projects, and develop a tremendous interest in the study of science. When shopping for a science kit or other supplies, make sure that you carefully review the features and quality of the products. Compare prices by going to several online stores. Read product reviews online or refer to magazines. Start by looking for your science kit review or science toy review. Compare prices but remember, Price$ is not everything. Quality does matter.
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