No, it doesn't mean it is risk free; it only means there is no variation.
In terms of stock analysis, volatility.
Standard deviation is commonly used in statistics to measure the dispersion or variability of a set of data points around the mean. It is frequently applied in fields such as finance to assess investment risk, in quality control to evaluate product consistency, and in research to interpret the reliability of experimental results. By understanding standard deviation, analysts can make informed decisions based on the degree of variability in their data.
In finance, risk of investments may be measured by calculating the variance and standard deviation of the distribution of returns on those investments. Variance measures how far in either direction the amount of the returns may deviate from the mean.
The standard deviation and beta measure different aspects of a stock's returns. Standard deviation quantifies the total volatility or risk of a stock's price movements, while beta measures the stock's sensitivity to market movements. It is possible for the standard deviation to be higher than beta, especially for stocks that have high volatility relative to the market but do not correlate strongly with market movements. Conversely, stocks with a low beta may have a high standard deviation if they experience large price swings independent of market trends.
"Risk probability" does not quite make sense, perhaps you mean just how to calculate risk. There are many formulas and methods, a lot of them highly complex mathematical models. Risk calculation is an important subset of portfolio theory. For the simplest cases, consider some of the following definitions: * the greatest dive that a stock took over a given historical time period. For example, if stock A dropped 30% maximum over past 5 years before rebounding, and stock B dropped 40% maximum over the same period - then by this metric you can see that stock B is riskier. * standard deviation of the returns over a historical time period. Take as your data set the prices a stock assumed over the last 5 years daily. You can calculate the standard deviation of this data set. The standard deviation is a measure of risk.
Risk premium = Company's risk (standard deviation of the historical stock returns of the market as a whole) - Risk-free rate of return (standard deviation of the historical treasury bonds' returns) - Inflation
It depends on the standard deviation and risk of the new stock.
Standard deviation is a measure of total risk, or both systematic and unsystematic risk. Unsystematic risk can be diversified away, systematic risk cannot and is measured as Beta.
http://www.hedgefund.net/pertraconline/statbody.cfmStandard Deviation -Standard Deviation measures the dispersal or uncertainty in a random variable (in this case, investment returns). It measures the degree of variation of returns around the mean (average) return. The higher the volatility of the investment returns, the higher the standard deviation will be. For this reason, standard deviation is often used as a measure of investment risk. Where R I = Return for period I Where M R = Mean of return set R Where N = Number of Periods N M R = ( S R I ) ¸ N I=1 N Standard Deviation = ( S ( R I - M R ) 2 ¸ (N - 1) ) ½ I = 1Annualized Standard DeviationAnnualized Standard Deviation = Monthly Standard Deviation ´ ( 12 ) ½ Annualized Standard Deviation *= Quarterly Standard Deviation ´ ( 4 ) ½ * Quarterly Data
The correlation between an asset's real rate of return and its risk (as measured by its standard deviation) is usually:
The purpose of obtaining the standard deviation is to measure the dispersion data has from the mean. Data sets can be widely dispersed, or narrowly dispersed. The standard deviation measures the degree of dispersion. Each standard deviation has a percentage probability that a single datum will fall within that distance from the mean. One standard deviation of a normal distribution contains 66.67% of all data in a particular data set. Therefore, any single datum in the data has a 66.67% chance of falling within one standard deviation from the mean. 95% of all data in the data set will fall within two standard deviations of the mean. So, how does this help us in the real world? Well, I will use the world of finance/investments to illustrate real world application. In finance, we use the standard deviation and variance to measure risk of a particular investment. Assume the mean is 15%. That would indicate that we expect to earn a 15% return on an investment. However, we never earn what we expect, so we use the standard deviation to measure the likelihood the expected return will fall away from that expected return (or mean). If the standard deviation is 2%, we have a 66.67% chance the return will actually be between 13% and 17%. We expect a 95% chance that the return on the investment will yield an 11% to 19% return. The larger the standard deviation, the greater the risk involved with a particular investment. That is a real world example of how we use the standard deviation to measure risk, and expected return on an investment.
In terms of stock analysis, volatility.
The standard deviation or volatility (square root of the variance) of returns.
The Sharpe Ratio is a financial benchmark used to judge how effectively an investment uses risk to get return. It's equal to (investment return - risk free return)/(standard deviation of investment returns). Standard deviation is used as a proxy for risk (but this inherently assumes that returns are normally distributed, which is not always the case). See the related link for an Excel spreadsheet that helps you calculate the Sharpe Ratio, and other limitations.
The Standard deviation is an absolute measure of risk while the coefficent of variation is a relative measure. The coefficent is more useful when using it in terms of more than one investment. The reason being that they have different returns on average which means the standard deviation may understate the actual risk or overstate depending.
Standard deviation is commonly used in statistics to measure the dispersion or variability of a set of data points around the mean. It is frequently applied in fields such as finance to assess investment risk, in quality control to evaluate product consistency, and in research to interpret the reliability of experimental results. By understanding standard deviation, analysts can make informed decisions based on the degree of variability in their data.
To calculate the standard deviation of a portfolio, you need to first determine the individual standard deviations of each asset in the portfolio, as well as the correlation between the assets. Then, you can use a formula that takes into account the weights of each asset in the portfolio to calculate the overall standard deviation. This helps measure the overall risk of the portfolio.