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For any fund that evolves randomly with time, volatility is defined as the standard deviation of a sequence of random variables, each of which is the return of the fund over some corresponding sequence of (equally sized) times. Thus, "annualized" volatility σ annually is the standard deviation of an instrument's yearly logarithmic returns. [2]
The MPT is a mean-variance theory, and it compares the expected (mean) return of a portfolio with the standard deviation of the same portfolio. The image shows expected return on the vertical axis, and the standard deviation on the horizontal axis (volatility). Volatility is described by standard deviation and it serves as a measure of risk. [7]
Under the assumption of normality of returns, an active risk of x per cent would mean that approximately 2/3 of the portfolio's active returns (one standard deviation from the mean) can be expected to fall between +x and -x per cent of the mean excess return and about 95% of the portfolio's active returns (two standard deviations from the mean) can be expected to fall between +2x and -2x per ...
σ M = standard deviation of the market portfolio σ P = standard deviation of portfolio (R M – I RF)/σ M is the slope of CML. (R M – I RF) is a measure of the risk premium, or the reward for holding risky portfolio instead of risk-free portfolio. σ M is the risk of the market portfolio. Therefore, the slope measures the reward per unit ...
The mean and the standard deviation of a set of data are descriptive statistics usually reported together. In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean. This is because the standard deviation from the mean is smaller than from any other point.
It is defined as the difference between the returns of the investment and the risk-free return, divided by the standard deviation of the investment returns. It represents the additional amount of return that an investor receives per unit of increase in risk. It was named after William F. Sharpe, [1] who developed it in 1966.
The standard deviation will delineate the normal fluctuations one can expect in that particular security above and below the mean, or average. However, since most investors would not consider fluctuations above the average return as "risk," some economists prefer other means of measuring it.
Standard deviation is a measure of volatility of the fund's performance over a period of time. The higher the figure the greater the variability of the fund's performance. The higher the figure the greater the variability of the fund's performance.