The Stochastic Discount Factor: Extending the Volatility Bound and a New Approach to Portfolio Selection with Higher-Order Moments
AbstractThe authors extend the well-known Hansen and Jagannathan (HJ) volatility bound. HJ characterize the lower bound on the volatility of any admissible stochastic discount factor (SDF) that prices correctly a set of primitive asset returns. The authors characterize this lower bound for any admissible SDF that prices correctly both primitive asset returns and quadratic payoffs of the same primitive assets. In particular, they aim at pricing derivatives whose payoffs are defined as non-linear functions of the underlying asset payoffs. The authors construct a new volatility surface frontier in a three-dimensional space by considering not only the expected asset payoffs and variances, but also asset skewness. The intuition behind the authors' portfolio selection is motivated by the duality between the HJ mean-variance frontier and the Markowitz mean-variance portfolio frontier. The authors' approach consists of minimizing the portfolio risk subject not only to portfolio cost and expected return, as usual, but also subject to an additional constraint that depends on the portfolio skewness. In this sense, the authors shed light on portfolio selection when asset returns exhibit skewness.
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Bibliographic InfoPaper provided by Bank of Canada in its series Working Papers with number 05-2.
Length: 48 pages
Date of creation: 2005
Date of revision:
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Financial markets; Market structure and pricing;
Find related papers by JEL classification:
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-02-13 (All new papers)
- NEP-BEC-2005-02-13 (Business Economics)
- NEP-FIN-2005-02-13 (Finance)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-69, July.
- DeRoon, Frans A. & Nijman, Theo E., 2001.
"Testing for mean-variance spanning: a survey,"
Journal of Empirical Finance,
Elsevier, vol. 8(2), pages 111-155, May.
- 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.
- Roon, F.A. de & Nijman, T.E., 1998. "Testing for mean-variance spanning: A survey," Discussion Paper 1998-132, Tilburg University, Center for Economic Research.
- Gordon, Stephen & St-Amour, Pascal, 1999.
"A Preference Regime Model of Bull and Bear Markets,"
Cahiers de recherche
9906, Université Laval - Département d'économique.
- Pascal St-Amour & Stephen Gordon, 2000. "A Preference Regime Model of Bull and Bear Markets," American Economic Review, American Economic Association, vol. 90(4), pages 1019-1033, September.
- Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, 06.
- Raymond Kan & Guofu Zhou, 2006. "A New Variance Bound on the Stochastic Discount Factor," The Journal of Business, University of Chicago Press, vol. 79(2), pages 941-962, March.
- Giovanni Barone Adesi & Patrick Gagliardini & Giovanni Urga, 2004. "Testing Asset Pricing Models With Coskewness," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 474-485, October.
- Peñaranda, Francisco & Sentana, Enrique, 2004.
"Spanning Tests in Return and Stochastic Discount Factor Mean Variance Frontiers: A Unifying Approach,"
CEPR Discussion Papers
4422, C.E.P.R. Discussion Papers.
- Peñaranda, Francisco & Sentana, Enrique, 2012. "Spanning tests in return and stochastic discount factor mean–variance frontiers: A unifying approach," Journal of Econometrics, Elsevier, vol. 170(2), pages 303-324.
- Francisco Peñaranda & Enrique Sentana, 2008. "Spanning tests in return and stochastic discount factor mean-variance frontiers: A unifying approach," Economics Working Papers 1101, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 2010.
- Enrique Sentana & Francisco Penaranda, 2004. "Spanning Tests in Return and Stochastic Discount Factor Mean-Variance Frontiers: A Unifying Approach," FMG Discussion Papers dp497, Financial Markets Group.
- Francisco Peñaranda & Enrique Sentana, 2004. "Spanning Tests In Return And Stochastic Discount Factor Mean-Variance Frontiers: A Unifying Approach," Working Papers wp2004_0410, CEMFI.
- Lars Peter Hansen & Ravi Jagannathan, 1990.
"Implications of Security Market Data for Models of Dynamic Economies,"
NBER Technical Working Papers
0089, National Bureau of Economic Research, Inc.
- 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 225-62, April.
- 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.
- Angelo Melino & Alan X. Yang, 2003.
"State Dependent Preferences Can Explain the Equity Premium Puzzle,"
Review of Economic Dynamics,
Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 806-830, October.
- Angelo Melino & Alan X. Yang, 2003. "State Dependent Preferences Can Explain the Equity Premium Puzzle," Working Papers melino-03-01, University of Toronto, Department of Economics.
- Robert F. Dittmar, 2002. "Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns," Journal of Finance, American Finance Association, vol. 57(1), pages 369-403, 02.
- Geert Bekaert & Jun Liu, 1999.
"Conditioning Information and Variance Bounds on Pricing Kernels,"
NBER Working Papers
6880, National Bureau of Economic Research, Inc.
- 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.
- Hansen, Lars Peter & Richard, Scott F, 1987. "The Role of Conditioning Information in Deducing Testable," Econometrica, Econometric Society, vol. 55(3), pages 587-613, May.
- Andrea Gamba & Francesco Rossi, 1998. "A three-moment based portfolio selection model," Decisions in Economics and Finance, Springer, vol. 21(1), pages 25-48, June.
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