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At various informational websites about option trading, it is often mentioned that in order to compare different underlyings in an apples-to-apples comparison, it is useful to beta-weight the deltas. This way, deltas of various underlyings can all be “normalized” into the index deltas.

As far as I understand, beta of an underlying with regards to an index is a measure of correlation. At Beta=1 the underlying is expected to be as volatile as the index as well as move (more or less) together with the index. At Beta=-1 the underlying is expected to move inversely to the index as well as be as-volatile as the index.

My question is what happens for underlyings that have a beta very close to zero. These still have their own volatility, as well as their own directional change. Even though it is not correlated with the index in the measured period.

When hedging, using beta-weighted-deltas allows for positions on the index to hedge the various underlyings. But only the part that is away from 1.0? How to aggregate all the left overs?

When building a portfolio that tries to hedge directional risk. Where do these “glass-half-empty” betas play a role?

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"At Beta=1 the underlying is expected to be as volatile as the index as well as move (more or less) together with the index." is not right.

Beta has nothing to do with volatility, at-least from a mathematical point of view. Mathematically, two assets can have same betas but remarkably different volatilities.

A low beta index cannot contribute to the hedge in terms of hedging the index, but can still be useful if it's idiosyncratic moves are uncorrelated to the portfolio we have already built (independent things averaged reduce variance, central limit theorem).

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  • $\begingroup$ So if I understand this correctly, using the index to hedge a low-beta underlying will hedge "only" the market risk, but not the other risks involved with that underlying. And the underlying can have various other factors/risks that contribute to its volatility. $\endgroup$ Aug 28, 2023 at 23:08
  • $\begingroup$ I am using the covariance(underlying returns, index returns)/variance(index returns) formula to calculate beta. And I would love to learn more on how variance does not reflect volatility. $\endgroup$ Aug 28, 2023 at 23:10
  • $\begingroup$ Beta is not variance. Good luck on your journey! $\endgroup$
    – Arshdeep
    Aug 29, 2023 at 12:24

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