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مدیر وبلاگ : mehdi doostkamian
What Is Covariance?
In the stock market, a strong emphasis is placed on reducing the risk amount taken on for the same amount of return. When constructing a portfolio, an analyst will select stocks that will work well together. This usually means that these stocks do not move in the same direction.
From here, we need to calculate the average return for each stock:
For ABC it would be (1.1 + 1.7 + 2.1 + 1.4 + 0.2) / 5 = 1.30
For XYZ it would be (3 + 4.2 + 4.9 + 4.1 + 2.5) / 5 = 3.74
Now, it is a matter of taking the differences between ABC's return and ABC's average return, and multiplying it by the difference between XYZ's return and XYZ's average return. The last step is to divide the result by the sample size and subtract one. If it was the entire population, you could just divide by the population size.
This can be represented by the following equation:
Using our example on ABC and XYZ above, the covariance is calculated as:
= [(1.1 - 1.30) x (3 - 3.74)] + [(1.7 - 1.30) x (4.2 - 3.74)] + [(2.1 - 1.30) x (4.9 - 3.74)] + …
In this situation we are using a sample, so we divide by the sample size (five) minus one.
You can see that the covariance between the two stock returns is 0.665. Because this number is positive, it means the stocks move in the same direction. When ABC had a high return, XYZ also had a high return.
Using Microsoft Excel
= COVARIANCE.S() for a sample
You will need to set up the two lists of returns in vertical columns, just like in Table 1. Then, when prompted, select each column. In Excel, each list is called an "array," and two arrays ishould be nside the brackets, separated by a comma.
Uses of Covariance
where cov (X,Y) = covariance between X and Y
σX = standard deviation of X
σY = standard deviation of Y
The equation above reveals that the correlation between two variables is simply the covariance between both variables divided by the product of the standard deviation of the variables X and Y. While both measures reveal whether two variables are positively or inversely related, the correlation provides additional information by telling you the degree to which both variables move together. The correlation will always have a measurement value between -1 and 1, and 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, the covariance just tells you that two variables change the same way, while correlation reveals how a change in one variable effects a change in the other.
The covariance can also be used to find the standard deviation of a multi-stock portfolio. The standard deviation is the accepted calculation for risk, and this is extremely important when selecting stocks. Typically, you would want to select stocks that move in opposite directions. If the chosen stocks move in opposite directions, then the risk might be lower given the same amount or potential return.
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