To calculate the correlation coefficient (denoted by $r$) between Stock X and Stock Y, we use the formula:

$r = \frac{n\sum{XY} - \sum{X}\sum{Y}}{\sqrt{(n\sum{X^2} - (\sum{X})^2)(n\sum{Y^2} - (\sum{Y})^2)}}$

Where:

• $X$ and $Y$ are the individual data points for Stock X and Stock Y, respectively.
• $n$ is the number of data points.

Let’s break it down step by step for the given data points:

Data:

• Stock X: 16%, 22%, 11%
• Stock Y: 30%, 21%, 22%

I’ll calculate the correlation coefficient for you.The correlation coefficient between Stock X and Stock Y is approximately $-0.153$. This indicates a weak, negative relationship between the two stocks' returns.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How does a negative correlation affect investment strategies?
2. What other measures can assess the relationship between two stocks?
3. How does the correlation coefficient range from -1 to 1 affect interpretation?
4. What are the implications of a weak correlation like this one?
5. How can we calculate covariance between Stock X and Stock Y?

Tip: A correlation coefficient closer to 0 suggests little to no linear relationship between two variables.