We examine the pricing of aggregate volatility risk in the cross-section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. In addition, we find that stocks with high idiosyncratic volatility relative to the Fama and French (1993) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book-to-market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility.

The Cross-Section of Volatility and Expected Returns

We examine the pricing of aggregate volatility risk in the cross-section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. Stocks with high idiosyncratic volatility relative to the Fama and French (1993, Journal of Financial Economics 25, 2349) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book-to-market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility. IT IS WELL KNOWN THAT THE VOLATILITY OF STOCK RETURNS varies over time. While considerable research has examined the time-series relation between the volatility of the market and the expected return on the market (see, among others, Campbell and Hentschel (1992) and Glosten, Jagannathan, and Runkle (1993)), the question of how aggregate volatility affects the cross-section of expected stock returns has received less attention. Time-varying market volatility induces changes in the investment opportunity set by changing the expectation of future market returns, or by changing the risk-return trade-off. If the volatility of the market return is a systematic risk factor, the arbitrage pricing theory or a factor model predicts that aggregate volatility should also be priced in the cross-section of stocks. Hence, stocks with different sensitivities to innovations in aggregate volatility should have different expected returns. The first goal of this paper is to provide a systematic investigation of how the stochastic volatility of the market is priced in the cross-section of expected stock returns. We want to both determine whether the volatility of the market

https://www0.gsb.columbia.edu/faculty/rhodrick/crosssection.pdf

Financial market volatility is an important input for investment, option pricing, and financial market regulation. The emphasis of this review article is on forecasting instead of modelling; it compares the volatility forecasting findings in 93 papers published and written in the last two decades. Provided in this paper as well are volatility definitions, insights into problematic issues of forecast evaluation, data frequency, extreme values and the measurement of "actual" volatility. We compare volatility forecasting performance of two main approaches; historical volatility models and volatility implied from options. Forecasting results are compared across different asset classes and geographical regions.

/pdf/forecasting-volatility-in-financial-markets-a-review-4c8zo5z26d.pdf

Forecasting Volatility in Financial Markets: A Review

Features of Financial Returns Modelling Price Volatility Forecasting Standard Deviations The Accuracy of Autocorrelation Estimates Testing the Random Walk Hypothesis Forecasting Trends in Prices Evidence Against the Efficiency of Futures Markets Valuing Options Appendix: A Computer Program for Modelling Financial Time Series.

Modelling Financial Time Series

Britten-Jones and Neuberger (2000) derived a model-free implied volatility under the diffusion assumption. In this article, we extend their model-free implied volatility to asset price processes with jumps and develop a simple method for implementing it using observed option prices. In addition, we perform a direct test of the informational efficiency of the option market using the model-free implied volatility. Our results from the Standard & Poor’s 500 index (SPX) options suggest that the model-free implied volatility subsumes all information contained in the Black-Scholes (B-S) implied volatility and past realized volatility and is a more efficient forecast for future realized volatility.

The Model-Free Implied Volatility and Its Information Content

The information content of implied volatilities and intra-day returns is compared, in the context of forecasting index volatility over horizons from one to twenty days. Forecasts of two measures of realised volatility are obtained after estimating ARCH models using daily index returns, daily observations of the VIX index of implied volatility and sums of squares of five minute index returns. The in-sample estimates show that all relevant information is provided by the VIX index and hence there is no incremental information in high-frequency index returns. For out-of-sample forecasting, the VIX index and information from five minute returns provide forecasts that have similar accuracy.

https://papers.ssrn.com/sol3/Delivery.cfm/991008211.pdf?abstractid=182128&mirid=5&type=2

Forecasting S&P 100 Volatility: The Incremental Information Content of Implied Volatilities and High Frequency Index Returns

http://www.smartquant.com/references/Volatility/vol21.pdf

Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high frequency index returns

Theoretical models that relate volatility to the quantity of information are extended to a multi-asset setting and it is deduced that stock returns may or may not have incremental information when modelling index volatility, depending on the sources of information that move stock prices. The first empirical study that can help resolve this theoretical uncertainty is presented. A detailed analysis of the daily volatility of the S&P 100 index from 1984 to 1998 shows there is some incremental volatility information in the returns from the 100 shares that define the index. This evidence is obtained from ARCH models that incorporate leverage effects, dummy variables for the 1987 crash and aggregate measures of stock return volatility. Significant differences between estimated volatilities are found for various stock measures and sub-periods.

Modelling S&P 100 volatility: the information content of stock returns

Forecasting S&P 100 Volatility: The Incremental Information Content of Implied Volatilities and High-Frequency Index Returns , Ser-Huang Poon, Stephen J Taylor

The volatility process of the S&P 100 index and all its constituent stocks are compared after estimating ARCH models from ten years of daily returns, from 1983 to 1992. The leverage effect of Black (1976) is estimated from an extension of the asymmetric volatility model of Glosten et al (1993) that isolates the effects of the crash in October 1987. The index and the majority of stocks have a greater volatility response to negative returns than to positive returns and the asymmetry is higher for the index than for most stocks. Conclusions about volatility asymmetry and persistence change when the crash is considered to be an extraordinary event.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID87568_code010910110.pdf?abstractid=87568

Bevan J. Blair

Papers

Forecasting S&P 100 Volatility: The Incremental Information Content of Implied Volatilities and High Frequency Index Returns

Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high frequency index returns

Modelling S&P 100 volatility: the information content of stock returns

Forecasting S&P 100 Volatility: The Incremental Information Content of Implied Volatilities and High-Frequency Index Returns , Ser-Huang Poon, Stephen J Taylor

Asymmetric and Crash Effects in Stock Volatility for the S&P 100 Index and its Constituents