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# Variance

## What is Variance?

Variance is defined as volatility around the mean. Variance is calculated after squaring the deviations from the mean to ensure that σ^2 is positive. The variance of a random variable indicates how widely spread its values are around the mean.

Because it has the same units as the random variable, the square root of the variance is frequently used to measure dispersion. It measures the squared deviation from the mean, and thus it is not sensitive to the direction of the difference relative to the mean.

## Example of Variance:

The variance is the second moment and is denoted by:

σ2=E(X)2-[E(X)]2= E[(X-μ)2]

Proof:

VarX= E[(X-E[X])2]
=E[X2-EXEX+EX2]
=E[X]2-EEXEX+E[X]2
=E[X]2-[E{X)]2

Let’s imagine the stock of Company ABC returns 10% in the first year, 20% in the second, and 15% in the third. These three returns have an average of 5%. For each following year, the variances between each return and the average are 5%, 15%, and 20%, respectively.

0.25 per cent, 2.25 per cent, and 4.00 per cent, respectively, are obtained by squaring these variances. We get a total of 6.5 per cent when we sum these squared variances. The variance is 2.1667 per cent when the sum of 6.5 per cent is divided by the number of returns in the data set, which in this case, is three.

## Why is calculating variance significant in the investment industry?

In the investment industry, variance is a crucial indicator. It assists investors in assessing the risk they take when purchasing a specific asset and determining if the purchase will be worthwhile.

Owais Siddiqui
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