What is Variance and How to Calculate it?

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What is Variance and How to Calculate it?

Variance is a figure used in statistics to determine the average distance of a set of variables. This is done from an average value within that set. Variance provides insight regarding the spread of a set of data. The primary role it has in calculating standard deviation is where it is used.

You can use this in investing as well. The variance of returns that is a part of assets in a portfolio can be analyzed as a way to achieve the best asset allocation. There is obviously an equation to help you calculate it. So now, let’s take a look inside and figure out how to calculate it:

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What is Variance and How to Calculate it?

Understanding What it is

variance

You can calculate variance by taking the differences in the middle of each number inside the data set and mean. After that, you need to square the differences in order to turn them into positive. This needs to be followed up by making a division of the sum of squares. It has to be done by the number of values inside the data set.

So, here is the formula for variance:

Variance, σ2=ni=1n​(xi​−xˉ)

2​

In this:

xi= the ith data point

x = the mean of every data point

n= the number of data points

When it comes to asset allocation, variance is one of its key parameters. If you calculate the variance of asset returns, it will help investors with developing improved portfolios. It can be done by optimizing the return-volatility trade-off in every investment they make.

There are a few programs that you may use to calculate it. The best one is Excel and you may also use Rapid Tables.

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How Variance is Used

How Variance is Used

Variance is used to measure variability from the average. Variability is volatility and in the eyes of investors, volatility is a measure of risk. As such, variance statistic helps with determining the risks that investors assume when they purchase certain security.

If the variance is huge, it usually means that the numbers in the set are not close to the mean. They are also far from each other. On the other hand, if it is small then this indicates the opposite.

You can also end up with a negative variance. If the variance value is zero then it indicates that every value inside a set of numbers is identical. So, all of the variances that are not zero have positive numbers.

It may seem as if investors are the only individuals to use variance. However, there are actually individuals from other professions who use it as well. There are scientists, mathematicians, and data analysts, etc. who need to use variance to identify risks. In addition, these individuals may need to use it to determine information regarding the population for experiments or samples.

There are cases where you can use variance interchangeably with standard deviation. You can opt for standard deviation if the number is smaller. In fact, your work can get easier if you choose the standard deviation for this activity. On top of that, the chances of skewing having an impact reduce to quite an extent.


Advantage and Disadvantage of using Variance

Advantage and Disadvantage of using Variance

The use of variance allows statisticians to check how separate numbers are related to each other in data sets. They can use it in place of larger mathematical techniques. One of those techniques is to arrange numbers into quartiles.

There is a disadvantage to using variance. It can provide additional weight to outliers. These are numbers that are nowhere near the mean. So, if you square these numbers then it has a chance of skewing the data.

However, there is an advantage to using variance as well. It will treat each deviation from the mean in the same way without regard to their direction. There is no way for squared deviations to sum to zero. So, they cannot provide the appearance of no variability by any means in the data.

On the other hand, one of the biggest drawbacks of variance is that you cannot interpret it easily. When individuals use variance, they mostly utilize it for taking the square root of its value. It can certainly indicate the standard deviation from the data set.

You can use variance if you are looking to obtain information from a data set. No matter which profession you are from, this is quite useful. After all, you can use this information if you are looking to draw quick inferences.

It takes up a lot of time to plot all the numbers on a spread. Then you will need to determine the rough distance from the mean as well as every variable. As mentioned before, this is a time-consuming process that you can skip by choosing variance instead.

This is a measure that gives individuals the perfect opportunity to make estimations in statistics in a short time. They will only need a fast calculation which is sufficient for providing information regarding the range of samples.


Example

In order to understand the concept, let us take hypothetical investing into consideration. For instance, the returns for a stock are 12% in Year 1, 24% in Year 2, and in Year 3 it is -18%. Now, the average of these three returns will be 6%. So, the differences between all of these returns and averages are 6%, 18%, and -24% for every consecutive year.

If you square these deviations, it will yield 36%, 324%, and 576%. Now, if you make a summation of these squared deviations provides 936%. So, if you divide the sum of 936% by the number of returns inside the data set, you will get the variance. In this case, you will get the variance of 312%.

After that, you need to get the square root of the variance. Here, it is the standard deviation of 17.66% for the returns.


There is a fairly simple formula that you can use to calculate variance. It makes a lot of complex calculations easier and saves a lot of time. With that said, you can definitely use it to make fewer errors while calculating.

Reference:

https://www.investopedia.com/terms/v/variance.asp

https://www.indeed.com/career-advice/career-development/what-is-variance

https://sciencing.com/calculate-variance-4884715.html

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