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Ang, Xing and Zhang (2006) state that "stocks with high sensitivities to innovations in aggregate volatility have low average returns". I am familiar that this question has been asked before in similar words (see What is meant by innovations in volatility?), however the answer was not very satisfying.

To me it seems counter-intuitive that firms that have high sensitivity to market risk have lower average returns as argued from a risk based perspective. I understand that hedging demand of the particular stocks would lead them to have a negative stock premium however in market up-states, what I do not understand is: Why assets with high sensitivities to market volatility risk provide hedges against market downside risk?

If the stock 'produces' returns in the times when volatility is high (in market downturns) then it would make sense for investors to demand lower returns. However why do stocks with high sensitivity to volatility provide a hedge against volatility?

Hope to hear from you. Many thanks in advance

The paper in question: https://www.nber.org/papers/w10852.pdf

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