Good Volatility, Bad Volatility, and the Cross Section of Stock Returns

Bollerslev, Tim; Li, Sophia Zhengzi; Zhao, Bingzhi

doi:10.1017/s0022109019000097

Cited by 134 publications

(106 citation statements)

References 66 publications

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“…However, neither of

S J_{t}

and

I V A_{t}

are significantly correlated with excess returns at intermediate and low frequencies. The significantly negative risk‐return relation for

S J_{t}

in the short run is in agreement with the results of Bollerslev et al (2019). The long‐run correlations between variance differences and returns are also depicted in Figure 1, where

V R P_{t}, V R P_{t}^{U}

, and

V R P_{t}^{D}

generally display strong comovements with returns.…”

Section: Resultssupporting

confidence: 92%

“…In addition, our simulation supports the empirical evidence of the inferior performances of the

S J_{t}

and

I V A_{t}

in predicting returns, especially for intermediate and long horizons after

h > 9

. The nature of the

S J_{t}

as a short‐lived return predictor is discussed in Bollerslev et al (2019), who show that the

S J_{t}

only predicts returns at weekly horizons and raise concerns regarding the role of

S J_{t}

as a priced risk factor.…”

Section: Simulationsupporting

confidence: 81%

“…The SJ proposed by Bollerslev et al (2019) is computed as the difference between the semivariances

R V_{t}^{U}

and

R V_{t}^{D}

, which eliminates the variation caused by the continuous part but retains the variation arising from jumps.

S J_{t} = R V_{t - 1}^{U} - R V_{t - 1}^{D}

Finally, we construct the IVA introduced by Huang and Li (2019).…”

Section: Measuring Variance Differencesmentioning

confidence: 99%

“…In addition, the SJ risk is found to contain information about future market returns that is independent of that captured by the

V R P

. With an alternative decomposition approach, Bollerslev, Li, and Zhao (2019) derive the SJ variation as the difference between the good and bad realized volatility and show that this difference significantly predicts the variation in future returns. Under the risk‐neutral measure, Huang and Li (2019) identify a significant relationship between future stock returns and implied variance asymmetry (IVA) defined as the difference between the upside and downside semi‐variances derived from out‐of‐the‐money (OTM) options.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Return predictability of variance differences: A fractionally cointegrated approach

Izzeldin

Yao

2020

Journal of Futures Markets

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This paper examines the fractional cointegration between downside (upside) components of realized and implied variances. A positive association is found between the strength of their cofractional relation and the return predictability of their differences. That association is established via the common longmemory component of the variances that are fractionally cointegrated, which represents the volatility-of-volatility factor that determines the variance premium. Our results indicate that market fears play a critical role not only in driving the long-run equilibrium relationship between implied-realized variances but also in understanding the return predictability. A simulation study further verifies these claims. K E Y W O R D S fractional cointegration, return predictability, variance risk premium J E L C L A S S I F I C A T I O N C14; C32; C51 | INTRODUCTIONNumerous empirical studies suggest that, unlike the variance, the variance risk premium (VRP) carries nontrivial predictive power for aggregate stock market returns over quarterly to annual horizons, where the degree of return predictability is greater than that afforded by more conventional predictors, see, Bollerslev, Tauchen, and Zhou (2009), Drechsler and Yaron (2010), Bollerslev, Marrone, Xu, and Zhou (2014), and Bali and Zhou (2016), among others. Those studies also provide strong evidence that much of the predictability implicit in the VRP may be attributed to its close relation with macroeconomic uncertainty and aggregate risk aversion.The VRP is formally defined as the wedge between option-implied and realized variances. It is measured as the difference between (the square of) the CBOE VIX index and the statistical expectation of the future return variation. In Bollerslev et al. (2009), Drechsler andYaron (2010) and Bollerslev, Sizova, and Tauchen (2012), the return predictability of the VRP is investigated using a self-contained general equilibrium model. This is in the spirit of the long-run risks (LRR) model pioneered by Bansal and Yaron (2004). Specifically, Bollerslev et al. (2009) andBollerslev et al. (2012) extend the LRR model by allowing the time-varying volatility-of-volatility (vol-of-vol) within the economy to be generated by its own stochastic process. They further show that the difference between the risk-neutral and the objective expectations of return variation isolates the vol-of-vol factor, which then serves as the sole source of the true VRP. The VRP, therefore, displays good predictive power for future returns in cases where the vol-of-vol plays a more dominant role in determining variation in the equity premium. A direct link between the VRP and the vol-of-vol is also demonstrated in a purely probabilistic model introduced by Barndorff-Nielsen and Veraart (2013). U D . The SJ and IVA are, respectively, measured as the difference between RV U and RV D and the difference between IV U and IV D . Using a semiparametric approach, we demonstrate the existence of a fractionally cointegrating relation in each pair of the semivariances...

show abstract

“…However, neither of

S J_{t}

and

I V A_{t}

are significantly correlated with excess returns at intermediate and low frequencies. The significantly negative risk‐return relation for

S J_{t}

in the short run is in agreement with the results of Bollerslev et al (2019). The long‐run correlations between variance differences and returns are also depicted in Figure 1, where

V R P_{t}, V R P_{t}^{U}

, and

V R P_{t}^{D}

generally display strong comovements with returns.…”

Section: Resultssupporting

confidence: 92%

“…In addition, our simulation supports the empirical evidence of the inferior performances of the

S J_{t}

and

I V A_{t}

in predicting returns, especially for intermediate and long horizons after

h > 9

. The nature of the

S J_{t}

as a short‐lived return predictor is discussed in Bollerslev et al (2019), who show that the

S J_{t}

only predicts returns at weekly horizons and raise concerns regarding the role of

S J_{t}

as a priced risk factor.…”

Section: Simulationsupporting

confidence: 81%

“…The SJ proposed by Bollerslev et al (2019) is computed as the difference between the semivariances

R V_{t}^{U}

and

R V_{t}^{D}

, which eliminates the variation caused by the continuous part but retains the variation arising from jumps.

S J_{t} = R V_{t - 1}^{U} - R V_{t - 1}^{D}

Finally, we construct the IVA introduced by Huang and Li (2019).…”

Section: Measuring Variance Differencesmentioning

confidence: 99%

“…In addition, the SJ risk is found to contain information about future market returns that is independent of that captured by the

V R P

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Return predictability of variance differences: A fractionally cointegrated approach

Izzeldin

Yao

2020

Journal of Futures Markets

View full text Add to dashboard Cite

show abstract

“…In addition, decomposition of volatility into short-run and long-run when determining asset premium was proven to be useful as well (Adrian and Rosenberg, 2008). Moreover, Bollerslev et al (2016) incorporated notion of downside risk into concept of volatility risk and showed that stocks with high negative realized semivariance yield higher returns. Farago and Tédongap (2017) examine downside volatility risk in their five-factor model and obtain model with negative prices of risk of volatility downside factor yielding low returns for assets that positively covary with innovations of market volatility during disappointing events.…”

Section: Extreme Volatility Riskmentioning

confidence: 99%

Tail Risks, Asset Prices, and Investment Horizons

Baruník

Nevrla

2018

SSRN Journal

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We examine how extreme market risks are priced in the cross-section of asset returns at various horizons. Based on the frequency decomposition of covariance between indicator functions, we define the quantile cross-spectral beta of an asset capturing tail-specific as well as horizon-, or frequency-specific risks. Further, we work with two notions of frequencyspecific extreme market risks. First, we define tail market risk that captures dependence between extremely low market as well as asset returns. Second, extreme market volatility risk is characterized by dependence between extremely high increments of market volatility and extremely low asset return. Empirical findings based on the datasets with long enough history, 30 Fama-French Industry portfolios, and 25 Fama-French portfolios sorted on size and book-to-market support our intuition. Results suggest that both frequency-specific tail market risk and extreme volatility risks are significantly priced and our five-factor model provides improvement over specifications considered by previous literature.1 In addition, it is interesting to note that equity and variance risk premium are also associated with compensation for jump tail risk (Bollerslev and Todorov, 2011). More general exploration of asymmetry of stock returns is provided by Ghysels et al. (2016), who propose a quantile-based measure of conditional asymmetry and show that stock returns from emerging markets are positively skewed. Conrad et al. (2013) use option price data and find a relation between stock returns and their skewness. Another notable approach uses high frequency data to define realized semivariance as a measure of downside risk (Barndorff-Nielsen et al., 2008). From a risk-measure standpoint, dealing with negative events, especially rare events, is highly discussed theme in both practice and academics. The most prominent example is Value-at-Risk (Adrian and Brunnermeier, 2016;Engle and Manganelli, 2004).

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Forecasting aggregate market volatility: The role of good and bad uncertainties

Liu

Wang

2020

Journal of Forecasting

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We decompose economic uncertainty into "good" and "bad" components according to the sign of innovations. Our results indicate that bad uncertainty provides stronger predictive content regarding future market volatility than good uncertainty. The asymmetric models with good and bad uncertainties forecast market volatility in a better way than the symmetric models with overall uncertainty. The combination for asymmetric uncertainty models significantly outperforms the benchmark of autoregression, as well as the combination for symmetric models. The revealed volatility predictability is further demonstrated to be economically significant in the framework of portfolio allocation.

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Good Volatility, Bad Volatility, and the Cross Section of Stock Returns

Cited by 134 publications

References 66 publications

Return predictability of variance differences: A fractionally cointegrated approach

Return predictability of variance differences: A fractionally cointegrated approach

Tail Risks, Asset Prices, and Investment Horizons

Forecasting aggregate market volatility: The role of good and bad uncertainties

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