Stocks in the Short Run

Abstract

The existing literature estimates stock-price volatility accumulated over the trading day. We focus on what happens to volatility within the trading day. Using transactions data from 2001 through 2009, we estimate the path of the quadratic variation process in 5-minute increments day by day for the 30 stocks of the DJIA and for an exchange-traded fund (the SPDR) that tracks the S&P 500. Using a Heston (1993) model, we estimate that 80% of the gap between the level of the volatility process and its asymptotic mean is eliminated within 5-minutes. Roughly two-thirds of daily realized volatility can be explained by a deterministic version of the Heston model that begins the trading day far above its equilibrium and converges to a constant. The remaining third reflects stochastic shocks to volatility arriving after trade begins. The asymptotic mean of the SPDR behaves much like the closing value of the VIX, a volatility index based on the S&P 500 stock index. When standardized by our 5-minute volatility estimates, 5-minute log returns are approximately normally distributed.

Keywords: discrete observation, intraday volatility estimation, quadratic variation, realized volatility, Heston, DJIA, SPDR, VIX

JEL Classification: G12, C58