Student Question
“I don’t understand the difference between Covariance and Correlation. The book implies that Covariance and Correlation are the same things.” – Syed.
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Here’s how to compute the covariance coefficient:
| Return | |||||
| Year | X | Y | (Xj – X̄) | (Yj – Ȳ) | Covariance Term |
| 2011 | -50% | -35% | -60% | -39% | 0.23 |
| 2012 | 33% | 33% | 23% | 29% | 0.07 |
| 2013 | 33% | 3% | 23% | -1% | 0.00 |
| 2014 | 16% | 14% | 6% | 10% | 0.01 |
| 2015 | 17% | 4% | 7% | 0% | 0.00 |
| Average Return: | 10% | 4% | Sum: | 0.30 | |
| Covariance: | 0.08 | ||||
The covariance can take on any value and therefore it is hard to interpret the number. We have no idea if this is highly correlated or not.
Correlation tells how strong the relation between X and Y is.
The most important property of the correlation coefficient is that its value is always between -1 and 1.
It is positively correlated if the correlation coefficient is positive and are highly correlated related if the correlation coefficient is closer to 1.
It is negatively correlated if the correlation coefficient is negative and are highly correlated if the correlation coefficient is closer to -1.
Here’s how to compute the correlation coefficient:
| Return | |||||
| Year | X | Y | (Xj – X̄) | (Yj – Ȳ) | Covariance Term |
| 2011 | -50% | -35% | -60% | -39% | 0.23 |
| 2012 | 33% | 33% | 23% | 29% | 0.07 |
| 2013 | 33% | 3% | 23% | -1% | 0.00 |
| 2014 | 16% | 14% | 6% | 10% | 0.01 |
| 2015 | 17% | 4% | 7% | 0% | 0.00 |
| Average Return: | 10% | 4% | Sum: | 0.30 | |
| Standard deviation: | 34% | 25% | Covariance: | 0.05 | |
P X, Y (Coefficient of Correlation) = 0.05/(34% x 25%)
P X, Y (Coefficient of Correlation) = 0.05/0.09
P X, Y (Coefficient of Correlation) = 0.5(9)
This means that X and Y are positively correlated.
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