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Correlation Matrix is a square matrix of correlation coefficients for securities and factors. Correlation measures the co-movements between securities using an easily interpreted scale of -1 to +1, with endpoints indicating more similar co-movements. The figures can be generated using a single-variable linear regression. Alternatively in a multi-variable regression it is common to use factors to measure co-movements. The matrix is used to interpret portfolio risk or factor risk.
Synonym: correlation table
For context, think of an asset management firm which employs an asset allocation approach to investing client portfolios in index funds. Here, holdings represent asset classes, like domestic and international stocks, bonds of different types, commodities and cash. In this instance the covariance matrix demonstrates the historical co-movement of assets.
Calculations typically use a long-term history (5 or more years) with monthly data as observations. While correlations change, the correlation matrix is a great tool for communicating the benefit of diversification to low or negatively correlated asset classes.
Kay: Ann, will you do me a favor and cook up
a correlation matrix from this covariance matrix for me?
Ann: With standard deviation and covariance, don't you already have the ingredients?
This video can be accessed in a new window or App , at the YouTube Channel or from below.
Correlation Matrix definition for investment modeling (4:39)
The script includes two sections where we visualize and demonstrate the calculation of correlation.
We're sitting here in Excel, and this is a snippet from our boot camp course.
This is one depiction of the correlation matrix, generated using 60 monthly returns for four stocks, located on the Returns tab.
It is interpretable as the confusing scale from a covariance matrix is transformed to a scale of correlation that ranges from -1 to +1, by dividing covariance by the product of the standard deviations of each stock.
The first cell shows the relationship between Microsoft and itself, implying a perfect correlation score of 1. Then in the next cell down we're taking the correlation of Microsoft with eBay and generating a correlation coefficient of about 0.25, which is weak, and implies that Microsoft and eBay, are diversifying securities. Others, like the small negative figure of 0.04, between eBay and Abbott Labs, would be even more diversifying.
This matrix is used for interpretation, whereas the covariance matrix is used in software for risk analysis and portfolio optimization. It is also common to remove the repeated terms, so it is more visually appealing.
There is a link to the correlation video at the end if you'd like to brush up. Let's solidify this all with the creation of the matrix, and head there now.
We'll build a correlation matrix for four stocks manually in Excel, knowing that third-party model providers scale to thousands of stocks using statistical programming.
There are three types of correlation matrices: historical, single-index and multi-factor. We are using the easiest one here called historical.
Set up a table like this with matching rows and column labels for holding the co-movements between each stock.
In the first cell, use the function
=CORREL, then open parenthesis, select
the first array, comma, second array, closed parenthesis and Enter.
That's the correlation of Microsoft versus Microsoft.
Next, in the next row, we do the same thing but use the returns on Microsoft, then eBay and come up with a correlation of 0.2564 for the pair of stocks. Continue with the rest of the pairs from there.
Click box for answer.
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