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Variance & Standard Deviation If we model a factor as a random variable with a specified probability distribution, then the variance of the factor is the expectation, or mean, of the squared deviation of the factor from its expected value or mean. Let X be the random variable. Let be the mean: =E[X], where E[X] denotes the expected value of X
The formula for the (sample) standard deviation (SD) is s = s P n i=1 (x i −x)2 n−1 Why divide by n−1? Not ? • Short answer: One cannot measure variability with only ONE observation (n = 1). We need at least 2. • Long answer: Dividing by n would underestimate the true (population) standard deviation. Dividing by n−1 instead of
5 Αυγ 2024 · Standard deviation is a statistic measuring the dispersion of a dataset relative to its mean. It is calculated as the square root of the variance. Learn how it's used.
In Finance, the risk-adjusted return for an investment is defined as the ratio of the mean to the standard deviation.
The standard deviation of the returns of the portfolio is a measure of the uncertainty in the expected returns. This uncertainty will depend upon the uncertainty in the performance of component securities, the weights of these securities, and how are these securities correlated.
What is the standard deviation? The standard deviation is a measure that indicates how much data scatter around the mean! of a small group of people. calculate the mean. We can get the mean simply by summing the heights of all individuals and dividing it by the number of individuals. deviates from the mean. the third 15 cm and so on.
Variance is calculated by subtracting the average return from each individual return, squaring that figure, summing the squares across all observations, and dividing the sum by the number of observations. The square root of the variance, called the standard deviation or the volatility, can be used to estimate risk.
