3. Learn how Correlation has moved your Selected Stock, a basis for diversification

Sand Storm! 2010: Act III, Scene 3+; Correlation and Eigenstocks

At present, the remaining content of Act III consists of still images rather than animation. These focus upon the degree to which two or more time sequences or traces of log adjusted daily closing prices resemble one another. For example, two stocks which move up and down at the same times are said to be positively correlated. If one stock moves up when the other moves down, they are said to be anti-correlated. The measure is called the correlation coefficient, ranging from +100% for identical stocks to -100% for perfect opposites. To emphasize the day-to-day movements, we remove any linear trend. To uncover flock behavior, we build an "index" of all the stocks added together. To show significant behavior, all traces are normalized, that is, presented with the mean removed, and the result divided by the standard deviation.

The most interesting of these displays shows how we remove the influence of the flock, defined as all the stocks in the index, in the Correlation image. The result more closely tracks the underlying value specific to the Selected Stock, outside of the market behavior as a whole.

A closely related display uses one of the features of linear algebra, which decomposes the correlation matrix of all 2800-odd stocks in the "index" into perhaps a dozen least-similar sub-indices, something like a small collection of the most distinct tracking funds possible. Just as with the correlation image, removing these additional significant influences helps to clarify the uinique signal of the Selected Stock. These Eigenstocks also can influence the behavior of the Selected Stock, for example, as the components of a metals commodity fund may appear to influence the behavior of a mining company. As with all such correlation measures, there is no way to prove causality. If one goes up and another goes up, there need be no other common factor than that the luck of the draw finds similarity, or that both are subject to the same constraints. On the other hand, it does help to know if your portfolio contains a large number of stocks that move together, as discussed in the Diversify section on the Remarks page

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