# How To Calculate Beta

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## How To Calculate Beta

The aim of this short video tutorial is to teach how to calculate beta by using a mathematical formula. So follow this tutorial and learn to calculate your stock's risk.

In this video, I'm going to teach you how to calculate beta. Now, what is beta? It's a measure of a correlation between a stock and a basis at stock. In this case, we are going to use the S&P 500.

So, if you were trying to calculate the returns of a stock compared to the S&P, you would use beta, and I'll show you how to calculate beta. So, let's call Y the return of the stock and we're going to set this equal to a+b(Beta)x. Now, X is the return of your S&P 500 and beta, this is what you're trying to calculate, is the correlation between y and x.

So, as x is very big, how about y? Does y also increase or does y decrease, so it's negatively correlated? That is what we're going to try and find out. The best way to do this is to pick up historical data. And to do that, you would create a chart or a list with your stock returns and your S&P returns.

And you would list your stock returns over one day so we could have 1st of January 11, 2nd of January 11, all the way down to the end of the year. We could work out that stock return on that day or the S&P return on that day and we could basically create the data here. Once you've got the data there, you can draw a scatter plot.

This is the axis which you always use your control on, which of course is the S&P and this is your stock return, and it would look something maybe like this. There is a positive correlation, so when the S&P has a good day, your stock has a good day and if it has a bad day, your stock has a bad day so it has a positive correlation. Once you have the scatter plot of the data, and you can do this on the computer, you would draw a line of best fit straight through the data, so this is the line of best fit or a line of correlation.

With this data, you can see exactly where this one crosses the y axis. This is Y intersect and this is your A value here. Exactly where it crosses this y axis is your A value and then, the gradient of this line is your beta.

So, in this case, we have a positive correlation with the S&P so we have a positive beta. If the line was to look like this, you would have a negative correlation, so if the S&P has a great day, your stock would do badly and vice versa. So once you have figured out the gradient of this line here, that gradient is beta and you can use a computer to calculate that or you can draw along here and up here and calculate this distance here (delta Y) and this distance here (delta X) and beta is equal to delta Y over delta X.

And that is how to calculate beta. .