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Asset Pricing In Multiperiod Securities Markets


  • Chamberlain, Gary


The paper provides an intertemporal version of the capital asset pricing model (CAPM) of Sharpe and Lintner. Although we allow for general changes in the investment opportunity set and for general risk-averse preferences, there are conditions under which two mutual funds are sufficient to generate all optimal portfolios. In particular, we require that the Riesz claim, which represents the date O pricing functional for the marketed claims, should lie in a scalar Brownian information set. Then we obtain an instantaneous counterpart to the CAPM pricing formula: a linear relationship between the conditional mean returns on the securities and conditional covariances with the return on the market portfolio. Our use of option pricing techniques requires continuous trading but does not require continuous consumption. In addition, we consider a large economy with a factor structure, as in Ross' arbitrage pricing theory. The dividends are assumed to have an approximate factor structure, with the factor components lying in the information set generated by an N-dimensional Brownian motion, and with the covariance matrices of the idiosyncratic components having uniformly bounded eigenvalues. We obtain an N-factor version of the pricing formula and relate the factors to the gains processes {price change plus accumulated dividends) for well-diversified portfolios. An approximate factor structure for dividends implies an approximate factor structure for the gains processes of the securities. Furthermore, the assumption_that per.capita supply is well diversified can motivate our condition that the Riesz claim lies in an N-dimensional Brownian information set.

Suggested Citation

  • Chamberlain, Gary, 1985. "Asset Pricing In Multiperiod Securities Markets," SSRI Workshop Series 292599, University of Wisconsin-Madison, Social Systems Research Institute.
  • Handle: RePEc:ags:uwssri:292599
    DOI: 10.22004/ag.econ.292599

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    Cited by:

    1. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
    2. Bruno Feunou & Jean-Sébastien Fontaine & Abderrahim Taamouti & Roméo Tédongap, 2014. "Risk Premium, Variance Premium, and the Maturity Structure of Uncertainty," Review of Finance, European Finance Association, vol. 18(1), pages 219-269.
    3. Didrik Flåm, Sjur, 2012. "Coupled projects, core imputations, and the CAPM," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 170-176.
    4. Elvio Accinelli, 2004. "Inversión Bajo Incertidumbre," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 3(1), pages 21-44, Marzo 200.
    5. repec:dau:papers:123456789/5374 is not listed on IDEAS
    6. Nawalkha, Sanjay K., 1997. "A multibeta representation theorem for linear asset pricing theories," Journal of Financial Economics, Elsevier, vol. 46(3), pages 357-381, December.
    7. Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(2), pages 231-247, August.
    8. Pelger, Markus, 2019. "Large-dimensional factor modeling based on high-frequency observations," Journal of Econometrics, Elsevier, vol. 208(1), pages 23-42.
    9. Markus Pelger, 2020. "Understanding Systematic Risk: A High‐Frequency Approach," Journal of Finance, American Finance Association, vol. 75(4), pages 2179-2220, August.
    10. Björk, Tomas & Näslund, Bertil, 1996. "Diversified Portfolios in Continuous Time," SSE/EFI Working Paper Series in Economics and Finance 122, Stockholm School of Economics.
    11. Toru Igarashi, 2019. "An Analytic Market Condition for Mutual Fund Separation: Demand for the Non-Sharpe Ratio Maximizing Portfolio," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(2), pages 169-185, June.
    12. Elisabeth Leoff & Leonie Ruderer & Jörn Sass, 2022. "Signal-to-noise matrix and model reduction in continuous-time hidden Markov models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 327-359, April.
    13. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.

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