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Pca – how it really works

Tuesday, October 25, 2016 6:24
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(Before It's News)

I suppose that my previous post did not provide insights on how PCA really works. Here is another try at the subject, using a simple pair as an example.
Let's take SPY and IWM, which are highly correlated. If daily returns of IWM are plotted against daily returns of SPY, the relationship is highly linear (see left chart).
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Applying PCA on this data gives two principal component vectors, plotted in red (first) and green (second). These two vectors are orhogonal, with the first one pointing in the direction of highest variance. Transformed data is nothing more than the original data projected on the new coordinate axis formed by these two vectors. The transformed data is shown in the right chart. As you can clearly see, all  points are still there, but the dataset is rotated.
The second vector is in this case -0.78 SPY + 0.62 IWM which produces a market-neutral spread.  Of course the same result would be achieved by using the beta of IWM.
The fun thing about PCA is that it is useful in building three- and more legged spreads. The procedure is exactly the same as above, but the transformation is done in a higer dimensional space. 

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