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This paper examines the predictive power of idiosyncratic volatility in the context of daily stock market volatility dynamics. Specifically, the relative performance of various models of market volatility is considered with respect to whether idiosyncratic volatility is excluded or included as an explanatory variable in such models. Using high frequency data covering the thirty stocks within the Dow Jones Industrial Average (DJIA) index, the results indicate that the inclusion of idiosyncratic volatility leads to significant in-sample and out-of-sample improvements in the fit of all the volatility models considered. These results are shown to be relatively robust to the loss function adopted by the forecaster, with reasonable forecast accuracy improvements available to such forecasters.

The importance of measuring and forecasting risk in financial markets has motivated a vast body of literature on the dynamics of asset return volatility (see Poon and Granger, 2003, for a comprehensive review). All of the models proposed in this body of literature are, without exception, based on the highly time-dependent nature of volatility in each of the markets considered. However, they differentiate themselves from each other by innovating in terms of model specification, by using alternative definitions of volatility, or by enriching the informational content of the model (see Franses and McAleer, 2002, for an overview of the models used in the context of financial markets). It is to the latter tranche of the literature that this paper contributes. In particular, we introduce and examine volatility models of DJIA index returns that explicitly allow for intraday variation in the overall amount of private information flow in the relevant market. We demonstrate that improved forecasts of market volatility can be obtained by doing this. The information content of the volatility models proposed in the literature is ultimately based on one of three models, viz., the mixture of distributions model ( Andersen, 1996, Clark, 1973, Epps and Epps, 1976, Foster and Viswanathan, 1993, Foster and Viswanathan, 1995, Harris, 1987, Liesenfeld, 2001 and Tauchen and Pitts, 1983), the sequential information arrival model ( Copeland, 1976 and Jennings et al., 1981), or the no-arbitrage martingale model ( Ross, 1989). Despite differences in their underlying motivations, all of these models predict that the return volatility will be proportional to the (unobservable) rate of information arrival (i.e., information flow). Given this motivation, a number of studies have demonstrated that the performance of volatility models can be greatly improved by incorporating proxies for information flow in their specification. Perhaps most notably, the inclusion of contemporaneous trading volume within the specification of such models has been shown to lead to significant improvements in their fit to the data (see Karpoff, 1987, for an early survey, and Bessembinder and Seguin, 1993, Bollerslev and Jubinski, 1999, Lamoureux and Lastrapes, 1990 and Luu and Martens, 2003, for more recent examples). Despite these successes, trading volume may not be the most accurate measure of information flow. This is because trading volume may be driven by factors other than information flow; for example, trading may be liquidity motivated, and/or may be the result of divergent trader opinion. Indeed, many studies have found that lagged trading volume is not helpful in forecasting volatility (see, e.g., Brooks, 1998, Donaldson and Kamstra, 2005, Heimstra and Jones, 1994, Lamoureux and Lastrapes, 1994 and Richardson and Smith, 1994). For these reasons, an alternative measure of information flow is considered in the current paper. The noisiness of the trading volume measure of information flow has motivated a number of authors to propose alternative measures of information flow. Most notably, in the context of volatility models, a number of studies have used either firm-specific news headlines (see, e.g., Berry and Howe, 1993, Kalev et al., 2004 and Melvin and Yin, 2000; and Mitchell & Mulherin, 1994) or macroeconomic announcement data (see, e.g., Andersen and Bollerslev, 1998, Flannery and Protopapadakis, 2002 and Jones et al., 1998) as inputs into information flow measures. The disappointing performance of models based on these measures is often explained with reference to the nature of the information flow considered; specifically, these measures attempt to proxy public, as opposed to private, information flow. 1 Consequently, the large proportion of unexplained volatility is argued to be due to the effects of private information flow; see French and Roll (1986), Barclay, Litzenberger, and Warner (1990), and Jones, Kaul, and Lipson (1994), who find that return volatility is primarily driven by private information; and Darrat, Zhong, and Cheng (2005), who provide evidence in favour of this conjecture in the context of the relationship between return volatility and trading volume. Given this evidence, we consider a measure of private information flow, and examine its importance with regard to the dynamics of market return volatility. As private information is more common with respect to firms and industries than to the broad market, we use a measure of idiosyncratic volatility as our proxy for private information flow. This particular reasoning is commonly associated with Roll's (1988) conjectures that stocks with high (low) levels of idiosyncratic volatility are associated with either high (low) rates of ‘private information [flow]’ or an ‘occasional frenzy unrelated to concrete information’. Despite a large number of papers demonstrating the empirical validity of the former conjecture with ever richer cross-sectional (firm-specific) datasets ( Durnev et al., 2003, Durnev et al., 2004, Ferreira and Laux, 2007, Jin and Myers, 2006 and Morck et al., 2000), 2 few (if any) studies have examined the issue using aggregate intraday time series data. 3 This is somewhat surprising, given that if there is indeed a positive cross-sectional association between private information flow and idiosyncratic volatility, then this relationship should hold in aggregate (and over time), and hence we should expect to observe a positive time series relationship between aggregate idiosyncratic volatility and aggregate private information flow. Furthermore, given that return volatility is a positive function of private information flow (see, e.g., Ross, 1989), it follows that we should observe a positive relationship between aggregate return volatility (i.e., market volatility) and aggregate idiosyncratic volatility, with the former volatility dependent on the latter volatility. It is this hypothesised relationship that is examined in this paper. While many studies have used idiosyncratic volatility to explain cross-sectional variation in expected returns (see Chua et al., 2007 and Guo and Savickas, 2006, for recent examples), few have considered the explanatory power of idiosyncratic volatility with respect to future market volatility. Of the studies that have been conducted, all have examined the relationship between market and idiosyncratic volatility using low frequency data (see, e.g., Campbell et al., 2001 and Duffee, 2001). As an alternative to these papers, we choose to examine this relationship using high frequency intraday data. This is because it is at this frequency that the economic theory underlying this relationship is likely to hold. For instance, the relationship between return volatility and information flow can be based on Ross's (1989) no-arbitrage martingale model. In this model, disequilibrium is assumed to be short-lived, with its removal achieved via the process of arbitrage. Given the speed at which these arbitrageurs operate, it follows that the central prediction of this model (i.e., that return volatility is a positive function of information flow) should be observed when using high frequency data. This reasoning predicts a positive relationship between high frequency measures of idiosyncratic volatility and private information flow, and hence between high frequency measures of market and idiosyncratic volatility. Given the importance of appropriate market volatility forecasting in areas such as risk management and option pricing, the relationship between market and idiosyncratic volatility is examined in a forecasting context. Specifically, we investigate whether the inclusion of idiosyncratic volatility in market volatility models leads to improved forecasts of daily market volatility. To anticipate some of the results, we find that market volatility is positively associated with idiosyncratic volatility. Moreover, market volatility forecasts produced by models that incorporate idiosyncratic volatility are more accurate than the forecasts produced by existing (and competing) volatility models. In addition, these results are found to be relatively robust to variation in the loss function employed, and are shown to provide non-trivial utility improvements to forecasters. The rest of this paper is organised as follows. The next section provides definitions of idiosyncratic and market volatility, and is followed by a section that contains the modelling framework used to incorporate idiosyncratic volatility into the dynamics of market volatility. Section 4 contains results pertaining to various aspects of the estimated volatility models considered, and the final section concludes.

The dynamics of market volatility appear to be functionally dependent on past idiosyncratic volatility. Utilising this dependence in the daily DJIA index market leads to significant improvements in the quality of the in-sample fit of market volatility models, and the quality of market volatility forecasts. These quality improvements are particularly pronounced when the strong dependencies within the data are appropriately modelled. Furthermore, the benefits of using idiosyncratic volatility as an explanatory variable withinmarket volatility models is demonstrated under a number of different market volatility models, and under realistic loss function assumptions. Regarding the latter set of assumptions, non-trivial improvements in mean loss are available to those forecasters who incorporate idiosyncratic volatility within the specification of their volatility model — a finding that is largely unaffected by the assumption that under-prediction of volatility is penalisedmore heavily than over-prediction. In the context of the original motivation for this paper, these results lend support to the former of Roll's (1988) conjectures, that idiosyncratic volatility is (positively) associated with private information flow rather than irrational behaviour on the part of investors. That said, we cannot rule out the possibility that the results obtained in this paper are due to inefficiencies inherent in the DJIA index market.