Relation between correlation and standard deviation
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The equation above reveals that the correlation between two variables is the covariance between both variables divided by the product of the standard deviation of the variables. While both measures reveal whether two variables are positively or inversely related, the correlation provides additional information by determining the degree to which both variables move together. The correlation will always have a measurement value between -1 and 1, and it adds a strength value on how the stocks move together.
If the correlation is 1, they move perfectly together, and if the correlation is -1, the stocks move perfectly in opposite directions. If the correlation is 0, then the two stocks move in random directions from each other. In short, covariance tells you that two variables change the same way while correlation reveals how a change in one variable affects a change in the other.
You also may use covariance to find the standard deviation of a multi-stock portfolio. The standard deviation is the accepted calculation for risk, which is extremely important when selecting stocks. Most investors would want to select stocks that move in opposite directions because the risk will be lower, although they'll provide the same amount of potential return.
Covariance is a common statistical calculation that can show how two stocks tend to move together. Because we can only use historical returns, there will never be complete certainty about the future. Also, covariance should not be used on its own. Instead, it should be used in conjunction with other calculations such as correlation or standard deviation.
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