Q: If the standard deviation is zero does that mean it's risk free?

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In terms of stock analysis, volatility.

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.

"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.

I've written before about the Sharpe Ratio, a measure of risk-adjusted returns for an asset or portfolio. The Sharpe ratio functions by dividing the difference between the returns of that asset or portfolio and the risk-free rate of return by the standard deviation of the returns from their mean. So it gives you an idea of the level of risk assumed to earn each marginal unit of return. The problem with using the Sharpe Ratio is that it assumes that all deviations from the mean are risky, and therefore bad. But often those deviations are upward movements. Why should an investment strategy by graded so sharply by the Sharpe Ratio for good performance? In the real world, investors don't usually mind upside deviations from the mean. Why would they? These were the questions on the mind of Frank Sortino when he developed what has been dubbed the Sortino Ratio. The ratio that bears his name is a modification of the Sharpe Ratio that only takes into account negative deviations and counts them as risk. To me, it always made a lot more sense not to include upside volatility from the equation because I rather like to see some upside volatility in my portfolios. With the Sortino Ratio only downside volatility is used as the denominator in the equation. So the way you calculate it is to divide the difference between the expected rate of return and the risk-free rate by the standard deviation of negative asset returns. (It can be a bit tricky the first time you try to do it. The positive deviations are set to values of zero during the standard deviation calculation in order to calculate downside deviation.) By using the Sortino Ratio instead of the Sharpe Ratio you’re not penalizing the investment manager or strategy for any upside volatility in the portfolio. And doesn’t that make a whole lot more sense?

For a two-asset portfolio, the risk of the portfolio, σp, is: 2222p1122112212222p11221212121212σ=wσ+wσ+2wσwσρorσ=wσ+wσ+2wwcovcov since ρ=σσ where σi is the standard deviation of asset i's returns, ρ12 is the correlation between the returns of asset 1 and 2, and cov12 is the covariance between the returns of asset 1 and 2. Problem What is the portfolio standard deviation for a two-asset portfolio comprised of the following two assets if the correlation of their returns is 0.5? Asset A Asset B Expected return 10% 20% Standard deviation of expected returns 5% 20% Amount invested $40,000 $60,000

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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 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 or volatility (square root of the variance) of returns.

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.

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 risk-adjusted return is a measure of how much risk a fund or portfolio takes on to earn its returns, usually expressed as a number or a rating. This is often represented by the Sharpe Ratio. The more return per unit of risk, the better. The Sharpe Ratio is calculated as the difference between the mean portfolio return and the risk free rate (numerator) divided by the standard deviation of portfolio returns (denominator).