Beta vs. Hamming

The beta of a portfolio is often used to hedge it against the market. We did a brief intro in our post: A Gentle Introduction to Hedging. And previously, we discussed how the Hamming distance can unearth relationships by simplifying the data that we have. Here, we bring the two concepts together.


CAPM Beta is a glorified linear regression between two return streams. It is useful in the context of linear-payoff portfolios.

For example, a typical long-only fund can use its portfolio beta to measure sensitivity to the market and to hedge against it. A single-stock portfolio with only HDFC in it will exhibit varying beta wrt different markets.

If you are after a linear-payoff (long stocks or futures outright,) beta can be a useful metric to track.


Betas are useless if you are trying to hedge or analyze a portfolio with convex payoffs. Like, say, an options portfolio. Here, you care more about up/down days over an index. This is where Hamming distances are useful.

A Hamming distance of 70 over a 250-day return stream means that by flipping the direction of just a third of the sample, the up/down series will equalize.

In our HDFC-only single-stock portfolio example above, we see that its beta over NIFTY/BANK-NIFTY is vastly different whereas its Hamming distances closely track each other. This behavior can be used to construct trades that go beyond being long-only equity.

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