Volatility Expectations and Returns

Abstract

We provide evidence that agents have slow-moving beliefs about stock market volatility that lead to initial underreaction to volatility shocks followed by delayed overreaction. These dynamics are mirrored in the VIX and variance risk premiums, which reflect investor expectations about volatility, and are also supported in both surveys and firm-level option prices. We embed these expectations into an asset pricing model and find that the model can account for a number of stylized facts about market returns and return volatility that are difficult to reconcile, including a weak or even negative risk-return trade-off.AGENTS' PERCEPTIONS OF RISK PLAY a critical role in asset pricing models. However, a long literature finds that the empirical risk-return trade-off is weak at best (Glosten, Jagannathan, and Runkle (1993)), despite this trade-off being strong in leading asset pricing models (Moreira and Muir (2017)). 1 This paper proposes a model in which a representative agent has biased, slow-moving expectations about volatility. We show that these expectations help explain a weak relation between risk and returns. We discipline expectations about volatility in the model in three ways: we microfound beliefs based on sticky and extrapolative expectations (which have been shown to be present in many other contexts), we use survey data to directly assess agents' expectations of

Beta and size equity premia following a high‐VIX threshold

“…The high beta and size premia are elevated for holding periods over 1–6 months, commencing 1 month after the threshold breach. This skip‐a‐month aspect of our analysis also contributes to the literature, by reinforcing Lochstoer and Muir's (2022) findings that it can take time for volatility shocks to be fully integrated into prices. Thus, a skip‐a‐month approach can better measure the intertemporal risk‐return relation.…”

“…Our main empirical investigation in the prior subsections skips the month $$t$$ between the expected volatility (measured at the end of month $$t-1$$) and subsequent returns (with a holding period commencing in month $$t+1$$). In Section 3, we argued that our skip‐a‐month empirical choice relies on evidence and arguments in Lochstoer and Muir (2022) that it can take time for volatility shocks to be fully integrated into prices.…”

“…Supportive of this premise, Lochstoer and Muir (2022) present evidence that agents are slow in updating their expectations about stock‐market volatility—agents initially underreact to volatility shocks and then update their volatility expectations next period even without additional news. Similarly, Bali et al (2014) find that the price response to liquidity shocks tends to be extended over several months, presumably due to market frictions.…”

“…We report on variants of the above regression where the set of explanatory variables includes either: (1) the linear risk-return term only (Panel A); (2) the high expected-volatility threshold term only (Panel B); or (3) both these terms (Panel C). In each panel, the first three rows report on beta premia and the next three on size premia, with the three rows representing 1-, 11 See Lochstoer andMuir (2022, p. 1056): "Given the initial underreaction (to volatility shocks), however, agents on average update positively about volatility next period even without additional news. This effect can push next period prices down further, and make it appear as though the initial increase in volatility is associated with a future decline in the observed equity risk premium in the short term."…”

“…Our skip‐a‐month empirical choice relies on evidence and arguments in Lochstoer and Muir (LM, 2022) that it can take time for volatility shocks to be fully integrated into prices. Empirically, the skip‐a‐month approach serves to provide cleaner temporal separation between two opposing effects associated with positive volatility shocks—the negative contemporaneous price reaction and the increase in the subsequent return expectation.…”