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Stochastic Discount Factor Bounds with Conditioning Information

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  • Wayne E. Ferson
  • Andrew Siegel

Abstract

Hansen and Jagannathan (HJ, 1991) describe restrictions on the volatility of stochastic discount factors (SDFs) that price a given set of asset returns. This paper compares the sampling properties of different versions of HJ bounds that use conditioning information in the form of a given set of lagged instruments. HJ describe one way to use conditioning information. Their approach is to multiply the original returns by the lagged variables, and much of the asset pricing literature to date has followed this ihmultiplicativel. approach. We also study two versions of optimized HJ bounds with conditioning information. One is from Gallant, Hansen and Tauchen (1990) and the second is based on the unconditionally-efficient portfolios derived in Ferson and Siegel (2000). We document finite-sample biases in the HJ bounds, where the biased bounds reject asset-pricing models too often. We provide useful correction factors for the bias. We also evaluate the asymptotic standard errors for the HJ bounds, from Hansen, Heaton and Luttmer (1995).

Suggested Citation

  • Wayne E. Ferson & Andrew Siegel, 2002. "Stochastic Discount Factor Bounds with Conditioning Information," NBER Working Papers 8789, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:8789
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    Cited by:

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    2. Devraj Basu & Roel Oomen & Alexander Stremme, 2010. "International Dynamic Asset Allocation and Return Predictability," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 37(7-8), pages 1008-1025.
    3. Raymond Kan & Cesare Robotti, 2008. "The exact distribution of the Hansen-Jagannathan bound," FRB Atlanta Working Paper 2008-09, Federal Reserve Bank of Atlanta.
    4. Peñaranda, Francisco & Sentana, Enrique, 2016. "Duality in mean-variance frontiers with conditioning information," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 762-785.
    5. Driessen, Joost & Melenberg, Bertrand & Nijman, Theo, 2005. "Testing affine term structure models in case of transaction costs," Journal of Econometrics, Elsevier, vol. 126(1), pages 201-232, May.
    6. Jonathan Fletcher & Andrew Marshall, 2014. "Investor Heterogeneity and the Cross-section of U.K. Investment Trust Performance," Journal of Financial Services Research, Springer;Western Finance Association, vol. 45(1), pages 67-89, February.
    7. Wayne E. Ferson & Jerchern Lin, 2013. "Alpha and Performance Measurement: The Effects of Investor Disagreement and Heterogeneity," NBER Working Papers 19349, National Bureau of Economic Research, Inc.
    8. Abhyankar, Abhay & Basu, Devraj & Stremme, Alexander, 2007. "Portfolio efficiency and discount factor bounds with conditioning information: An empirical study," Journal of Banking & Finance, Elsevier, vol. 31(2), pages 419-437, February.
    9. Xu, Yuewu & Yao, Xiangkun, 2019. "Extending the Hansen–Jagannathan distance measure of model misspecification," Finance Research Letters, Elsevier, vol. 29(C), pages 384-392.
    10. Devraj Basu & Roel Oomen & Alexander Stremme, 2010. "International Dynamic Asset Allocation and Return Predictability," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 37(7‐8), pages 1008-1025, July.
    11. Liu, Yan, 2021. "Index option returns and generalized entropy bounds," Journal of Financial Economics, Elsevier, vol. 139(3), pages 1015-1036.
    12. Jonathan Fletcher & Patricia Ntozi‐Obwale, 2008. "Arbitrage Bounds and UK Unit Trust Performance," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 35(3‐4), pages 580-600, April.
    13. Carlo A. Favero & Fulvio Ortu & Andrea Tamoni & Haoxi Yang, 2020. "Implications of Return Predictability for Consumption Dynamics and Asset Pricing," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 527-541, July.
    14. Wayne E. Ferson & Andrew F. Siegel, 2006. "Testing Portfolio Efficiency with Conditioning Information," NBER Working Papers 12098, National Bureau of Economic Research, Inc.
    15. Favero, Carlo A. & Tamoni, Andrea & Ortu, Fulvio & Yang, Haoxi, 2016. "Implications of Return Predictability across Horizons for Asset Pricing Models," CEPR Discussion Papers 11645, C.E.P.R. Discussion Papers.
    16. Fletcher, Jonathan, 2019. "Model comparison tests of linear factor models in U.K. stock returns," Finance Research Letters, Elsevier, vol. 28(C), pages 281-291.
    17. Chrétien, Stéphane, 2012. "Bounds on the autocorrelation of admissible stochastic discount factors," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1943-1962.
    18. J. Sa‐Aadu & James Shilling & Ashish Tiwari, 2010. "On the Portfolio Properties of Real Estate in Good Times and Bad Times1," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 38(3), pages 529-565, September.
    19. Galvani, Valentina & Gubellini, Stefano, 2013. "Mean–variance dominant trading strategies," Finance Research Letters, Elsevier, vol. 10(3), pages 142-150.
    20. Fletcher, Jonathan & Kihanda, Joseph, 2005. "An examination of alternative CAPM-based models in UK stock returns," Journal of Banking & Finance, Elsevier, vol. 29(12), pages 2995-3014, December.
    21. Liu, Ludan, 2008. "It takes a model to beat a model: Volatility bounds," Journal of Empirical Finance, Elsevier, vol. 15(1), pages 80-110, January.
    22. Yuewu Xu, 2021. "A new measure of model misspecification with the no-arbitrage constraint: extending the second Hansen–Jagannathan distance," Review of Quantitative Finance and Accounting, Springer, vol. 56(3), pages 917-938, April.
    23. Dong‐Hyun Ahn & H. Henry Cao & Stéphane Chrétien, 2009. "Portfolio Performance Measurement: a No Arbitrage Bounds Approach," European Financial Management, European Financial Management Association, vol. 15(2), pages 298-339, March.
    24. Mikhail Chernov & Magnus Dahlquist & Lars Lochstoer, 2023. "Pricing Currency Risks," Journal of Finance, American Finance Association, vol. 78(2), pages 693-730, April.
    25. Wayne E. Ferson & Andrew F. Siegel & Pisun (Tracy) Xu, 2005. "Mimicking Portfolios with Conditioning Information," NBER Working Papers 11020, National Bureau of Economic Research, Inc.

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    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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