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

Author

Listed:
  • Tim Bollerslev

    () (Duke University and CREATES)

  • Daniela Osterrieder

    () (Aarhus University and CREATES)

  • Natalia Sizova

    () (Rice University)

  • George Tauchen

    () (Duke University and CREATES)

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.

Suggested Citation

  • Tim Bollerslev & Daniela Osterrieder & Natalia Sizova & George Tauchen, 2011. "Risk and Return: Long-Run Relationships, Fractional Cointegration, and Return Predictability," CREATES Research Papers 2011-51, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2011-51
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    References listed on IDEAS

    as
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    Keywords

    High-frequency data; realized volatility; options implied volatility; variance risk premium; fractional integration; long-memory; fractional cointegration; equilibrium asset pricing; return predictability.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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