Hyperfinite Asset Pricing Theory
We present a model of a financial market which unifies the capital-asset-pricing model (CAPM) of Sharpe-Lintner, and the arbitrage pricing theory (APT) of Ross. The model is based on a recent theory of hyperfinite processes, and it uncovers asset pricing phenomena which cannot be treated by classical methods, and whose asymptotic counterparts are not already, or even readily, apparent in the setting of a large but finite number of assets. In the model, an asset's unexpected return can be decomposed into a systematic and an unsystematic part, as in the APT, and the systematic part further decomposed leads to a pricing formula expressed in terms of a beta that is based on a specific index portfolio identifying essential risk, and constructed from factors and factor loadings that are endogenously extracted from the process of asset returns. Furthermore, the valuation formulas of the two individual theories imply, and are implied by, the pervasive economic principle of no arbitrage. Explicit formulas for the characterization, as well as conditions for the existence, of important portfolios are furnished. The hyperfinite factor model possesses an optimality property which justifies the use of a relatively small number of factors to describe the relevant correlational structures. The asymptotic implementability of the idealized limit model is illustrated by an interpretation of selected results for the large but finite setting.
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- Hal Varian, 1993. "A Portfolio of Nobel Laureates: Markowitz, Miller and Sharpe," Journal of Economic Perspectives, American Economic Association, vol. 7(1), pages 159-169, Winter.
- Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-23, September.
- Reisman, Haim, 1988. "A General Approach to the Arbitrage Pricing Theory (APT)," Econometrica, Econometric Society, vol. 56(2), pages 473-76, March.
- C. Gilles & S.F. Leroy, 1989.
"On the Arbitrage Pricing Theory,"
Carleton Economic Papers
89-09, Carleton University, Department of Economics, revised Jul 1991.
- Huberman, Gur, 1982. "A simple approach to arbitrage pricing theory," Journal of Economic Theory, Elsevier, vol. 28(1), pages 183-191, October.
- Chamberlain, Gary & Rothschild, Michael, 1983.
"Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets,"
Econometric Society, vol. 51(5), pages 1281-304, September.
- Gary Chamberlain & Michael Rothschild, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," NBER Working Papers 0996, National Bureau of Economic Research, Inc.
- Chamberlain, Gary & Rothschild, Michael, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Scholarly Articles 3230355, Harvard University Department of Economics.
- James Tobin, 1956. "Liquidity Preference as Behavior Towards Risk," Cowles Foundation Discussion Papers 14, Cowles Foundation for Research in Economics, Yale University.
- Michael Rothschild, 1985. "Asset Pricing Theories," NBER Technical Working Papers 0044, National Bureau of Economic Research, Inc.
- Admati, Anat R. & Pfleiderer, Paul, 1985. "Interpreting the factor risk premia in the arbitrage pricing theory," Journal of Economic Theory, Elsevier, vol. 35(1), pages 191-195, February.
- Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
- Ingersoll, Jonathan E, Jr, 1984. " Some Results in the Theory of Arbitrage Pricing," Journal of Finance, American Finance Association, vol. 39(4), pages 1021-39, September.
- Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," Review of Economic Studies, Oxford University Press, vol. 37(4), pages 537-542.
- Samuelson, Paul A., 1967. "General Proof that Diversification Pays," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(01), pages 1-13, March.
- Brown, Stephen J, 1989. " The Number of Factors in Security Returns," Journal of Finance, American Finance Association, vol. 44(5), pages 1247-62, December.
- Harald Uhlig, 1996.
"A law of large numbers for large economies (*),"
Springer, vol. 8(1), pages 41-50.
- Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
- Gur Huberman & Zhenyu Wang, 2005. "Arbitrage pricing theory," Staff Reports 216, Federal Reserve Bank of New York.
- Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
- Anderson, Robert M., 1991. "Non-standard analysis with applications to economics," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 39, pages 2145-2208 Elsevier.
- Michael C. Jensen, 1972. "Capital Markets: Theory and Evidence," Bell Journal of Economics, The RAND Corporation, vol. 3(2), pages 357-398, Autumn.
- Edward J. Green, 1994. "Individual Level Randomness in a Nonatomic Population," GE, Growth, Math methods 9402001, EconWPA.
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