No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns, Volume 18, Issue 8
It is sometimes argued that an increase in stock market volatility raises required stock returns, and thus lowers stock prices. This paper modifies the generalized autoregressive conditionally heteroskedastic (GARCH) model of returns to allow for this volatility feedback effect. The resulting model is asymmetric, because volatility feedback amplifies large negative stock returns and dampens large positive returns, making stock returns negatively skewed and increasing the potential for large crashes. The model also implies that volatility feedback is more important when volatility is high. In U.S. monthly and daily data in the period 1926-88, the asymmetric model fits the data better than the standard GARCH model, accounting for almost half the skewness and excess kurtosis of standard monthly GARCH residuals. Estimated volatility discounts on the stock market range from 1% in normal times to 13% after the stock market crash of October 1987 and 25% in the early 1930's. However volatility feedback has little effect on the unconditional variance of stock returns.
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1-month Treasury bill Autoregressive Conditional Heteroskedasticity Bollerslev Campbell and Shiller changing volatility coefficient conditional standard deviation conditionally normal crash of October daily data dashed line Engle excess kurtosis excess stock returns excess variance expected return Figures 2a future dividends GARCH process GARCH variance GARCH-M half-life Heteroskedasticity implied increases January 1926-December likelihood function Likelihood Ratio Tests log excess returns log stock price maximum maximum likelihood Mean Variance Skewness Model Mean Variance model Table 2a monthly and daily monthly data negatively skewed Number of observations observed return parameter estimates persistence of volatility postwar period Poterba and Summers predictive asymmetry quadratic right hand side Robert Engle Robert F Sample Period Schwert skewness and excess solid line Stambaugh 1987 standard errors standard GARCH model stock market crash top panel unconditional variance unexpected stock return variable variance of returns Variance Skewness Exc volatility discount volatility feedback VOLATILITY IN STOCK volatility is high zero