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Pricing kernels and dynamic portfolios

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  • HENROTTE, Philippe

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    Abstract

    We investigate the structure of the pricing kernels in a general dynamic investment setting by making use of their duality with the self financing portfolios. We generalize the variance bound on the intertemporal marginal rate of substitution introduced in Hansen and Jagannathan (1991) along two dimensions, first by looking at the variance of the pricing kernels over several trading periods, and second by studying the restrictions imposed by the market prices of a set of securities. The variance bound is the square of the optimal Sharpe ratio which can be achieved through a dynamic self financing strategy. This Sharpe ratio may be further enhanced by investing dynamically in some additional securities. We exhibit the kernel which yields the smallest possible increase in optimal dynamic Sharpe ratio while agreeing with the current market quotes of the additional instruments.

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    Bibliographic Info

    Paper provided by HEC Paris in its series Les Cahiers de Recherche with number 768.

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    Length: 61 pages
    Date of creation: 16 Aug 2002
    Date of revision:
    Handle: RePEc:ebg:heccah:0768

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    Postal: HEC Paris, 78351 Jouy-en-Josas cedex, France
    Web page: http://www.hec.fr/
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    Related research

    Keywords: pricing kernel; Sharpe ratio; self financing portfolio; variance-optimal hedging;

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    1. HENROTTE, Philippe, 2001. "Dynamic mean-variance analysis," Les Cahiers de Recherche 729, HEC Paris.
    2. 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.
    3. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    4. Longarela, Iñaki R., 2001. "An Extension of Good-Deal Asset Price Bounds," Working Paper Series in Economics and Finance 0448, Stockholm School of Economics, revised 19 Oct 2001.
    5. Lars Peter Hansen & Ravi Jagannathan, 1994. "Assessing Specification Errors in Stochastic Discount Factor Models," NBER Technical Working Papers 0153, National Bureau of Economic Research, Inc.
    6. Cern›, Ales, 2002. "Generalized Sharpe Ratios and Asset Pricing in Incomplete Markets," Royal Economic Society Annual Conference 2002 41, Royal Economic Society.
    7. 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.
    8. Theil, Henri, 1983. "Linear algebra and matrix methods in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 1, pages 3-65 Elsevier.
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