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Duality in Mean-Variance Frontiers with Conditioning Information

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  • Peñaranda, Francisco
  • Sentana, Enrique

Abstract

Portfolio and stochastic discount factor (SDF) frontiers are usually regarded as dual objects, and researchers sometimes use one to answer questions about the other. However, the introduction of conditioning information and active portfolio strategies alters this relationship. For instance, the unconditional portfolio frontier in Hansen and Richard (1987) is not dual to the unconditional SDF frontier in Gallant, Hansen and Tauchen (1990). We characterise the dual objects to those frontiers, and relate them to the frontiers generated with managed portfolios, which are commonly used in empirical work. We also study the implications of a safe asset and other special cases.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 6566.

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Date of creation: Nov 2007
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Handle: RePEc:cpr:ceprdp:6566

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Keywords: Asset Pricing; Dynamic Portfolio Strategies; Representing portfolios; Stochastic Discount Factors;

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References

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  1. Francisco Peñaranda & Enrique Sentana, 2004. "Spanning Tests In Return And Stochastic Discount Factor Mean-Variance Frontiers: A Unifying Approach," Working Papers wp2004_0410, CEMFI.
  2. Wayne E. Ferson & Andrew F. Siegel, 2003. "Stochastic Discount Factor Bounds with Conditioning Information," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 567-595.
  3. Wayne E. Ferson, 2001. "The Efficient Use of Conditioning Information in Portfolios," Journal of Finance, American Finance Association, vol. 56(3), pages 967-982, 06.
  4. Geert Bekaert & Robert J. Hodrick, 1991. "Characterizing Predictable Components in Excess Returns on Equity and Foreign Exchange Markets," NBER Working Papers 3790, National Bureau of Economic Research, Inc.
  5. Lars Peter Hansen & Ravi Jagannathan, 1990. "Implications of security market data for models of dynamic economies," Discussion Paper / Institute for Empirical Macroeconomics 29, Federal Reserve Bank of Minneapolis.
  6. Gallant, A. Ronald & Hansen, Lars Peter & Tauchen, George, 1990. "Using conditional moments of asset payoffs to infer the volatility of intertemporal marginal rates of substitution," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 141-179.
  7. 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.
  8. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-304, September.
  9. Nijman, T.E. & Roon, F.A. de, 2001. "Testing for mean-variance spanning: A survey," Open Access publications from Tilburg University urn:nbn:nl:ui:12-87531, Tilburg University.
  10. Geert Bekaert, 2004. "Conditioning Information and Variance Bounds on Pricing Kernels," Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 339-378.
  11. Wayne E. Ferson & Andrew F. Siegel, 2006. "Testing Portfolio Efficiency with Conditioning Information," NBER Working Papers 12098, National Bureau of Economic Research, Inc.
  12. Bekaert, Geert & Urias, Michael S, 1996. " Diversification, Integration and Emerging Market Closed-End Funds," Journal of Finance, American Finance Association, vol. 51(3), pages 835-69, July.
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Cited by:
  1. David Martinez-Miera & Rafael Repullo, 2010. "Does Competition Reduce the Risk of Bank Failure?," Review of Financial Studies, Society for Financial Studies, vol. 23(10), pages 3638-3664, October.
  2. Francisco Peñaranda, 2009. "Understanding Portfolio Efficiency with Conditioning Information," FMG Discussion Papers dp626, Financial Markets Group.

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