Certainly, a stock may generate a rate of return above its expected value. The expected rates of return and the variance provide the information about the natures of the probability distribution of a single stock or a portfolio of stocks indicating nothing about the returns on securities interrelated. Thus, the ex ante standard deviation is considered as a weighted average of the potential deviations from the expected returns and a reasonable measure of risk. In case of our example of probability distribution of possible return, the variance of the population by using ex ante data is computed as follows: The variance of expected rates of return by using ax ante data could be found as follows: Standard deviation is the positive square root of the variance. In the case of the example of historical data the computation of the variance would be as follows: The following is the formula for calculating the variance of historical returns (using ex-post data):ĭividing by N-1 gives us an unbiased estimate for the variance when the sample is relatively a small size.

However, the variance is simply the standard deviation squared (or the standard deviation is the root of the variance). Variance is directly related to the standard deviation and is of considerable importance in finance. The standard deviation of the rates of return is simply the square root of the variance of the rates of return which tells us about the potential for deviation of the return from its expected values. The standard deviation is derived so that a high standard deviation represents a large dispersion of return and is high risk a low deviation is a small dispersion and represents a low risk. It is a statistical concept and is widely used to measure risk from holding a single asset.

Standard deviation is a measure of the dispersion of forecast returns when such returns approximate a normal probability distribution.

Calculation of the expected return of the probability distribution is essential to calculate the variance and standard deviation. Variance and standard deviationof the estimated distribution of expected returns are, however, two possible measures of uncertainty. Statistical measures allow an investor to compare the return and risk measures for alternative investments directly. Here, We discussed Beta and its Characteristics. Co-variance of returns with the market portfolio called beta (b i) which is calculated as:

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