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Optimal hedging with the cointegrated vector autoregressive model


  • Lukasz Gatarek

    (Econometric Institute and Tinbergen Institute, Erasmus University Rotterdam)

  • Søren Johansen

    (Department of Economics, Copenhagen University)


We derive the optimal hedging ratios for a portfolio of assets driven by a Cointegrated Vector Autoregressive model (CVAR) with general cointegration rank. Our hedge is optimal in the sense of minimum variance portfolio. We consider a model that allows for the hedges to be cointegrated with the hedged asset and among themselves. We find that the minimum variance hedge for assets driven by the CVAR, depends strongly on the portfolio holding period. The hedge is defined as a function of correlation and cointegration parameters. For short holding periods the correlation impact is predominant. For long horizons, the hedge ratio should overweight the cointegration parameters rather then short-run correlation information. In the infinite horizon, the hedge ratios shall be equal to the cointegrating vector. The hedge ratios for any intermediate portfolio holding period should be based on the weighted average of correlation and cointegration parameters. The results are general and can be applied for any portfolio of assets that can be modeled by the CVAR of any rank and order.

Suggested Citation

  • Lukasz Gatarek & Søren Johansen, 2014. "Optimal hedging with the cointegrated vector autoregressive model," Discussion Papers 14-22, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:1422

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    More about this item


    hedging; cointegration; minimum variance portfolio.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions


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