Our previous post explored the differences between CAPM Beta and Hamming distance. Think of Beta as a linear regression between two time-series and Hamming distance as the number of days when the direction of returns differed. The usefulness of the Euclidian distance for non-reverting timeseries is somewhere between the two.
Extending the previous example using HDFC and keeping everything else the same, here’s what the Euclidian distance measure looks like.
![](https://raw.githubusercontent.com/stockviz/blog/master/hamming-euclid/HDFC-euclid.png)
Higher the distance, the farther apart their curves and worse the index hedge. Here’s the equity curve that can help map returns to distance.
![](https://raw.githubusercontent.com/stockviz/blog/master/hamming-euclid/HDFC-equity.png)
Reproducing the Beta and Hamming Distance charts:
![](https://raw.githubusercontent.com/stockviz/blog/master/beta-hamming/HDFC-beta.png)
![](https://raw.githubusercontent.com/stockviz/blog/master/hamming-euclid/HDFC-hamming.png)
From a linear portfolio point-of-view, which of these series is more “predictable?” Is it possible to specify bands beyond which things “break?” And does using shorter look-backs help?
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