On the Hansen-Jagannathan distance with a no-arbitrage constraint

Arbeitspapier

We provide an in-depth analysis of the theoretical and statistical properties of the Hansen-Jagannathan (HJ) distance that incorporates a no-arbitrage constraint. We show that for stochastic discount factors (SDF) that are spanned by the returns on the test assets, testing the equality of HJ distances with no-arbitrage constraints is the same as testing the equality of HJ distances without no-arbitrage constraints. A discrepancy can exist only when at least one SDF is a function of factors that are poorly mimicked by the returns on the test assets. Under a joint normality assumption on the SDF and the returns, we derive explicit solutions for the HJ distance with a no-arbitrage constraint, the associated Lagrange multipliers, and the SDF parameters in the case of linear SDFs. This solution allows us to show that nontrivial differences between HJ distances with and without no-arbitrage constraints can arise only when the volatility of the unspanned component of an SDF is large and the Sharpe ratio of the tangency portfolio of the test assets is very high. Finally, we present the appropriate limiting theory for estimation, testing, and comparison of SDFs using the HJ distance with a no-arbitrage constraint.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: Working Paper ; No. 2010-4

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Asset Pricing; Trading Volume; Bond Interest Rates ; Hypothesis Testing: General ; Estimation: General
• Thema: Hansen-Jagannathan distance ; no-arbitrage constraint ; stochastic discount factor ; specification tests ; model selection tests

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Gospodinov, Nikolay ; Kan, Raymond ; Robotti, Cesare
• Ereignis: Veröffentlichung
• (wer): Federal Reserve Bank of Atlanta
• (wo): Atlanta, GA
• (wann): 2010

Weitere Informationen

• Handle: http://hdl.handle.net/10419/70698
• Letzte Aktualisierung: 10.03.2025, 11:42 MEZ