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What type of risk is measured by standard deviation?
In terms of stock analysis, volatility.
How is variance used to measure risk?
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.
How to calculate Risk probability?
"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.
The Sortino Ratio?
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?
How do you calculate risk on a two-asset portfolio?
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
