Risk and Return: Long-Run Relationships, Fractional Cointegration, and Return Predictability

• Activity Number: 514
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Natalia Sizova*+
• Companies: Rice University
• Keywords: high-frequency data ; return predictability ; variance risk premium ; long-memory ; fractional cointegration ; realized volatility

Abstract

The dynamic dependencies in financial market volatility are generally well described by a long-memory fractionally integrated process. At the same time, the volatility risk premium, defined as the difference between the ex-post realized volatility and the market's ex-ante expectation thereof, tends to be much less persistent and well described by a short-memory process. Using newly available intraday data for the S&P 500 and the VIX volatility index, coupled with frequency domain inference procedures that allow us to focus on specific parts of the spectra, we show that the existing empirical evidence based on daily and coarser sampled data carries over to the high-frequency setting. Guided by these empirical findings, we formulate and estimate a fractionally cointegrated VAR model for the two high-frequency volatility series and the corresponding high-frequency S&P 500 returns. Consistent with the implications from a stylized equilibrium model, we show that the equilibrium variance risk premium estimated with the intraday data within the fractionally cointegrated system results in non-trivial return predictability over longer interdaily and monthly horizons.