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This study examines whether the implied volatility index can provide further information in forecasting volatility than historical volatility using GARCHfamily models. For this purpose, this researchhas been conducted to forecast volatility in two main markets the United States of America through its wildly used Standard and Poor’s 500 index and its correspondingvolatility index VIX and in Europe through its Euro Stoxx 50 and its correspondingvolatility index VSTOXX. To evaluate the in-sample content of information, the conditional variance equations of GARCH(1,1) and EGARCH (1,1) are supplemented by integrating implied volatility as an explanatory variable. The realized volatility has been generated from daily squared returns and was employed as a proxy for true volatility. To examine the out-of-sample forecast performance, one-day-ahead rolling forecasts have been generated, and Mincer–Zarnowitz regression and encompassing regression has been utilized. The predictive power of implied volatility has been assessed based on Mean Square Error (MSE). Findings suggest that the integration of implied volatility as an exogenous variable in the conditional variance of GARCHmodels enhancesthe fitness of modelsand decreasesvolatility persistency. Furthermore, the significance of the implied volatility coefficient suggests that implied volatility includes pertinent information in illuminating the variation of the conditional variance. Implied volatility is found to be a biased forecast of realized volatility. Empirical findings of encompassingregression testsimply that the implied volatility index does not surpass historical volatility in terms of forecasting future realized volatility.

Yes / A key prediction of the Capital Asset Pricing Model (CAPM) is that idiosyncratic risk is not priced by investors because in the absence of frictions it can be fully diversified away. In the presence of constraints on diversification, refinements of the CAPM conclude that the part of idiosyncratic risk that is not diversified should be priced. Recent empirical studies yielded mixed evidence with some studies finding positive correlation between idiosyncratic risk and stock returns, while other studies reported none or even negative correlation. We revisit the problem whether idiosyncratic risk is priced by the stock market and what are the probable causes for the mixed evidence produced by other studies, using monthly data for the US market covering the period from 1980 until 2013. We find that one-period volatility forecasts are not significantly correlated with stock returns. The mean-reverting unconditional volatility, however, is a robust predictor of returns. Consistent with economic theory, the size of the premium depends on the degree of 'knowledge' of the security among market participants. In particular, the premium for Nasdaq-traded stocks is higher than that for NYSE and Amex stocks. We also find stronger correlation between idiosyncratic risk and returns during recessions, which may suggest interaction of risk premium with decreased risk tolerance or other investment considerations like flight to safety or liquidity requirements. The difference between the correlations of the idiosyncratic volatility estimators used by other studies and the true risk metric the mean-reverting volatility is the likely cause for the mixed evidence produced by other studies. Our results are robust with respect to liquidity, momentum, return reversals, unadjusted price, liquidity, credit quality, omitted factors, and hold at daily frequency. / National Research Foundation of Korea (2016S1A2A2912265)