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Analytical solution for the constrained Hansen-Jagannathan distance under multivariate ellipticity

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  • Nikolay Gospodinov
  • Raymond Kan
  • Cesare Robotti

Abstract

We provide an in-depth analysis of the theoretical properties of the Hansen-Jagannathan (HJ) distance that incorporates a no-arbitrage constraint. Under a multivariate elliptical distribution assumption, we present explicit expressions for the HJ-distance with a no-arbitrage constraint, the associated Lagrange multipliers, and the SDF parameters in the case of linear SDFs. This approach allows us to analyze the benefits and costs of using the HJ-distance with a no-arbitrage constraint to rank asset pricing models.

Suggested Citation

  • Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2012. "Analytical solution for the constrained Hansen-Jagannathan distance under multivariate ellipticity," FRB Atlanta Working Paper 2012-18, Federal Reserve Bank of Atlanta.
  • Handle: RePEc:fip:fedawp:2012-18
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    References listed on IDEAS

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    1. Mahmoud Hamada & Emiliano A. Valdez, 2008. "CAPM and Option Pricing With Elliptically Contoured Distributions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 387-409.
    2. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
    3. Raymond Kan & Cesare Robotti, 2009. "Model Comparison Using the Hansen-Jagannathan Distance," Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3449-3490, September.
    4. John Y. Campbell & John H. Cochrane, 2000. "Explaining the Poor Performance of Consumption-based Asset Pricing Models," Journal of Finance, American Finance Association, vol. 55(6), pages 2863-2878, December.
    5. Bansal, Ravi & Hsieh, David A & Viswanathan, S, 1993. " A New Approach to International Arbitrage Pricing," Journal of Finance, American Finance Association, vol. 48(5), pages 1719-1747, December.
    6. Raymond Kan & Cesare Robotti, 2008. "The exact distribution of the Hansen-Jagannathan bound," FRB Atlanta Working Paper 2008-09, Federal Reserve Bank of Atlanta.
    7. Hansen, Lars Peter & Heaton, John & Luttmer, Erzo G J, 1995. "Econometric Evaluation of Asset Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 237-274.
    8. Owen, Joel & Rabinovitch, Ramon, 1983. " On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-752, June.
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