Stock Correlation Calculator

Formula

The formula to calculate the stock correlation coefficient is:

\[ \text{Correlation} = \frac{n \sum(xy) - \sum x \sum y}{\sqrt{(n \sum x^2 - (\sum x)^2) (n \sum y^2 - (\sum y)^2)}} \]

Where:

\( \text{Correlation} \) is the stock correlation coefficient.
\( n \) is the number of data points.
\( \sum(xy) \) is the sum of the products of the x and y values.
\( \sum x \) is the sum of the x values.
\( \sum y \) is the sum of the y values.
\( \sum x^2 \) is the sum of the squared x values.
\( \sum y^2 \) is the sum of the squared y values.

Example

Let's say we have the following data points:

Number of Data Points (\( n \)): 5
Sum of Products of x and y values (\( \sum(xy) \)): 50
Sum of x values (\( \sum x \)): 15
Sum of y values (\( \sum y \)): 20
Sum of Squared x values (\( \sum x^2 \)): 55
Sum of Squared y values (\( \sum y^2 \)): 85

Using the formula:

\[ \text{Correlation} = \frac{5 \times 50 - 15 \times 20}{\sqrt{(5 \times 55 - 15^2) (5 \times 85 - 20^2)}} \]

We get:

\[ \text{Correlation} = \frac{250 - 300}{\sqrt{(275 - 225) (425 - 400)}} \]

\[ \text{Correlation} = \frac{-50}{\sqrt{50 \times 25}} = \frac{-50}{\sqrt{1250}} = \frac{-50}{35.36} \approx -1.414 \]

So, the stock correlation coefficient is approximately -1.414.

What is Stock Correlation?

Stock correlation is a statistical measure that indicates the relationship between the movements of two stocks in the financial market. It is expressed as a number between -1 and 1, where 1 indicates a perfect positive correlation (i.e., both stocks move in the same direction at the same time), -1 indicates a perfect negative correlation (i.e., the stocks move in opposite directions), and 0 indicates no correlation. This measure is crucial for investors and portfolio managers as it helps in diversifying a portfolio and reducing risk. For instance, by investing in stocks with a low or negative correlation, an investor can mitigate the impact of a poor performing stock, as its losses may be offset by the gains of the other less correlated or inversely correlated stock.