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 counterunituitivecounter-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


2 Answers 2


That's in finance what we call a puzzle. From their follow on paper (here), they rule out many different economic explanations for such a thing to happen:

We conclude that the puzzle of why high idiosyncratic volatility stocks have low returns is a global phenomenon. Further research must investigate if there are true economic sources of risk behind the idiosyncratic volatility phenomenon causing stocks with high volatility to have low expected returns.

Few follow-on papers have tried to rationalize that. One finding is from this paper by Herskovic et al. (here)

We show that firms' idiosyncratic volatility obeys a strong factor structure and that shocks to the common factor in idiosyncratic volatility (CIV) are priced. Stocks in the lowest CIV-beta quintile earn average returns 5.4% per year higher than those in the highest quintile. The CIV factor helps to explain a number of asset pricing anomalies. We provide new evidence linking the CIV factor to income risk faced by households. These three facts are consistent with an incomplete markets heterogeneous-agent model. In the model, CIV is a priced state variable because an increase in idiosyncratic firm volatility raises the average household's marginal utility. The calibrated model matches the high degree of comovement in idiosyncratic volatilities, the CIV-beta return spread, and several other asset price moments.

  • $\begingroup$ Alright thank you for your time, indeed I have read that paper. I understand there is not/ no clear current economic rational for the 'abysmally' low returns of stock with high idiosyncratic volatility. However what is still not clear to me is why high sensitivity or exposure to aggregate (systematic) risk leads them to have low returns (even though this explains only part of the negative return. ) $\endgroup$
    – incognito
    Commented Sep 17, 2019 at 18:49
  • $\begingroup$ My logic would go like this: the risk based CAPM argues that exposure to aggregate risk is priced, i.e. higher beta precede greater returns. Hence when stocks have high sensitivity to aggregate innovations in volatility these returns would therefore also be greater. However in this context sensitivity to aggregate market risk is interpreted differently? $\endgroup$
    – incognito
    Commented Sep 17, 2019 at 19:33
  • $\begingroup$ Could you elaborate? Specifically on what this means: " they find that stocks with high sensitivity to innovations in aggregate (systematic) volatility earn negative average stock returns due to the hedging demand for stocks with high systematic volatility loading" $\endgroup$
    – incognito
    Commented Oct 10, 2019 at 10:41
  • 1
    $\begingroup$ I guess it boils down to the fact that you are assuming that high exposure to aggregate (systematic) risk means high returns. We know that the CAPM empirically fails, so high beta does not mean high returns in a world where the CAPM is not the right model. $\endgroup$
    – phdstudent
    Commented Oct 10, 2019 at 10:46
  • $\begingroup$ Okay. I maybe see where I go wrong. So it would go like this: High hedging demand of stock with high systematic volatility loading causes the returns of these high volatility assets to be low (where from a risk based perspective you would expect there to be no hedging demand in the first place as these stock seem to add more risk). $\endgroup$
    – incognito
    Commented Oct 10, 2019 at 10:50

I think the best source for the possible explanations of this anomaly is Ang's book. In there, he says:

We are still searching for a comprehensive explanation for the risk anomaly. Inmy opinion, the true explanation is a combination of all of the explanations listed below, plus potentially others being developed.

  • Data mining. Bali and Cakici (2008) and Han and Lesmond (2011) pointed out that the original findings are sensitive to portfolio weighting schemes and illiquidity effects.
  • Leverage constraints. Investors that do not have access to leverage will simply hold stocks with high beta (to get some leverage presumably). This leads to higher prices and consequently lower returns.
  • Agency problems. Benchmark trackers and investors that are restricted from short selling do not participate in capturing this alpha.
  • Preferences. Some investors simply have preference for high beta, high volatility stocks. This may also drive the expected returns lower.

Overall, I think Chapter 10 of Ang's book is the place for more information.


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