Survey_CD_2003

Abstract

We simulate prices at 5-minute intervals and assume 24-hour trading with 250 trading days per year. For the purpose of sign prediction, we proceed by discarding the intra-day observations and take daily to be the highest frequency of interest. We calibrate the parameters to typical values estimated in the empirical literature. Our benchmark values are , , , and , which imply a daily mean of about 0.037%, a daily unconditional standard deviation of 0.77%, unconditional skewness of about -0.1, and unconditional excess kurtosis of about 1. The annualized mean reversion parameter 6 = 2 implies a daily persistence of about 1-2/250 = .992 in a standard GARCH(1,1) model. Notice also that the parameters satisfy the condition. We now present a simple empirical example, both to illustrate our ideas and methods and to provide some preliminary evidence as to their empirical relevance. As we have shown, a key ingredient in any successful equity sign forecast is a successful volatility forecast, which could be obtained either from an econometric volatility model (see Andersen, Bollerslev, Diebold and Labys, 2003, for a comparison of several) or from the marketplace via option-implied volatilities. Here we take the latter route, forecasting return signs using the VIX index of S&P 100 volatility, which is traded on the Chicago Board Options Exchange (CBOE), and which is widely viewed as a good indicator of market sentiment (an “investor fear gauge” in the colorful language of Whaley, 2000). It is calculated as a weighted average of the implied volatility from eight S&P 100 options (four calls and four puts nearest to the money), with the observed option quotes interpolated so as to obtain a synthetic volatility from an at-themoney option with a maturity of exactly thirty days.18 To match the maturity of the VIX, we forecast signs of 30-day returns. More precisely, let be the S&P 100 30-day excess return (relative to the 30-day return on a 3-month Treasury bill), and define the sign indicator sequence as . Logit models are traditionally estimated by the method of maximum likelihood (ML) under an iid assumption. However, the 29-day overlap in the daily cumulative 30-day returns introduces dependence, biasing the traditional ML standard errors. We therefore estimate the logit model using GMM instead.