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

Tim Bollerslev (), Daniela Osterrieder (), Natalia Sizova () and George Tauchen ()
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Daniela Osterrieder: Aarhus University and CREATES, Postal: Department of Economics and Business, Bartholins Allé 10, 8000 Aarhus C, DENMARK
Natalia Sizova: Rice University, Postal: Department of Economic, Houston, TX 77251, USA

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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 that directly links the realized and expected volatilities to returns, 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. These results in turn suggest that much of the existing literature seeking to establish a risk-return tradeoff relationship between expected returns and expected volatilities may be misguided, and that the variance risk premium provides a much better proxy for the true economic uncertainty that is being rewarded by the market.

Keywords: High-frequency data; realized volatility; options implied volatility; variance risk premium; fractional integration; long-memory; fractional cointegration; equilibrium asset pricing; return predictability. (search for similar items in EconPapers)
JEL-codes: C22 C32 C51 C52 G12 G13 G14 (search for similar items in EconPapers)
Pages: 40
Date: 2011-12-21
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-mst and nep-rmg
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