Academic journal article Atlantic Economic Journal

The Economics of Conditional Heteroskedasticity: Evidence from Canadian and U.S. Stock and Futures Markets

Academic journal article Atlantic Economic Journal

The Economics of Conditional Heteroskedasticity: Evidence from Canadian and U.S. Stock and Futures Markets

Article excerpt


This paper investigates time variation and persistence in volatility for three index futures price series and each associated stock price index series. Time variation and persistence in the volatility of financial time series has been widely documented [Mandelbrot, 1963; Fama, 1965]. The autoregressive conditional heteroskedasticity (ARCH) and generalized autoregressive conditional heteroskedasticity (GARCH) processes pioneered by Engle [1982] and Bollerslev [1986] provide parsimonious models of the observed time-varying volatility for many financial time series [Bollerslev et al., 1992]. For example, Akgiray [1989] finds that a GARCH process provides a good fit to daily stock market returns data. Although persistence in the second moments of stock returns distribution is well documented, the economic explanation for GARCH is not established.

The observed dependence in conditional volatility could result from information arriving at the market in clusters or from how market participants react to new information when it reaches the market [Diebold, 1986; Diebold and Nerlove, 1989; Engle et al., 1990; Gallant et al., 1989]. If information arrives at the market discontinuously, serial correlation in conditional volatilities will be observed even if market participants immediately react to the news so that the news is efficiently impounded in market prices. Conversely, market participants may not immediately react to new information either because they have private information or because of market imperfections such as transactions costs. In either case, market prices may efficiently reflect all publicly available information even though volatility is persistent.

Several studies have investigated whether the time series properties of information arrival can explain the presence of ARCH. Lamoureux and Lastrapes [1990a] conclude that daily stock returns are generated by a mixture of distributions where the mixing variable is the rate of information arrival. Their results, however, may be biased due to a simultaneity problem [Bollerslev et al., 1992]. In addition, Laux and Ng [1993] find that the mixture of distributions hypotheses fails to explain all of the GARCH in data on foreign exchange futures contracts.

In a recent article, Errunza et al. [1994] examine the monthly returns behavior of 14 stock index series. ARCH is observed more often in emerging markets than in developed markets. Cross-sectional differences in how volatility evolves over time are attributed to differences in information arrival and transmission across markets. Sample markets with significant ARCH are characterized by concentration of ownership, no forward or futures trading, higher transactions costs, and large bid-ask spreads. Errunza et al. [1994] point out that these market features may affect the flow of information resulting in ARCH effects.

The purpose of this paper is to provide insight into the sources of time variation and persistence in volatility by presenting new evidence concerning the price behavior of three index futures contracts and associated stock price indexes (the New York Stock Exchange (NYSE) Composite index, Standard and Poor's (S&P) 500 index, and Toronto 35 index). To do so, the paper compares measures of persistence for each index futures contract and price index pair as well as across futures contracts and indexes. Transactions costs in futures markets are generally recognized to be lower than those in stock markets so that a market participant with information is more likely to transact in the futures market [Fleming et al., 1995; Schwert, 1990]. At the same time, futures and stock prices are highly correlated due to arbitrage forces. If persistence in volatility results from clustering in information arrival, measured persistence will be similar for each index futures contract and price index pair. However, if lower transactions costs in futures markets play a role, persistence will be lower in the futures markets. …

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