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The Hybrid Model and Related Approaches to Capital Market Equilibria

  • Günter Bamberg

Summary

Single period capital-asset-pricing models provide a number of implications on capital market equilibria. Familiar notions as, for instance, the market price of risk or the market portfolio can be derived from the equilibrium conditions without having explicit representations of the equilibrium prices. However, such explicit solutions are required to conduct other investigations successfully. The availability of explicit solutions facilitates the analysis of changes in the value of firms under a variety of circumstances. The paper concentrates on the chances to obtain explicit solutions. It makes precise in which sense the hybrid model, characterized by multivariate normally distributed returns and constant risk aversion of the investors, is the most convenient model of capital market equilibrium. Some applications are surveyed concerning taxes, heterogeneous expectations, short sales restrictions, and imperfect capital markets.

Keywords

Risk Aversion Hybrid Model Equilibrium Price Optimal Portfolio Risky Asset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Agnew, R.A. (1972): Conter-Examples to an Assertion Concerning the Normal Distribution and a New Stochastic Price Fluctuation Model, RES 38, 381–383Google Scholar
  2. Allais, M. (1953): L’extension des théories de l’équilibre économique général et du rendement social au cas du risque, Econometrica 19, 269–290CrossRefGoogle Scholar
  3. Allingham, M.G. (1972): Risk-Taking and Taxation, Zeitschrift für Nationalökonomie 32, 203–224CrossRefGoogle Scholar
  4. Arditti, F.D.; Levy, H. (1975): Portfolio Efficiency Analysis in Three Moments: The Multiperiod Case, JoF, 797-809Google Scholar
  5. Arrow, K.J. (1970): Essays in the Theory of. Risk-Bearing, Amsterdam-LondonGoogle Scholar
  6. Bamberg, G.; Firchau, V. (1981): Some Remarks on the Aggregation Theorem for Divergent Borrowing and Lending Rates, Methods of Operations Research 44, 465–475Google Scholar
  7. Bamberg, G.; Spremann, K. (1981a): Implications of Constant Risk Aversion, Zeitschrift für Operations Research 25, 205–224CrossRefGoogle Scholar
  8. Bamberg, G.; Spremann, K. (1981b): Financial Smoothing and Firm Values, Methods of Operations Research 44, 477–488Google Scholar
  9. Bamberg, G.; Spremann, K. (1983): The Impacts of Several Emission Policies in an Imperfect Capital Market, in: Göppl, H.; Henn, R. (Eds.): Proceedings of the 2. Symposium on Money, Banking, and Insurance, Karsruhe, 531–536Google Scholar
  10. Bamberg, G. (1984): The Impacts of Variance Reducing Strategies in Dyopolistic Capital Market, in: Bamberg, G.; Spremann, K. (Fds.): Risk and Capital, Berlin-Heidelberg-New York-Tokyo, 52-63Google Scholar
  11. Bamberg, G.; Spremann, K. (Eds.) (1984): Risk and Capital, Berlin-Heidelberg-New York-TokyoGoogle Scholar
  12. Baron, D.P. (1977): On the Utility Theoretic Foundations of Mean-Variance Analysis, JoF 32, 1683–1697CrossRefGoogle Scholar
  13. Bawa, V.S.; Lindenberg, E.B. (1977): Capital Market Equilibrium in a Mean-Lower Partial Moment Framework, JFE 5, 189–200CrossRefGoogle Scholar
  14. Bierwag, G.O. (1974): The Rationale of the Mean-Standard Deviation Analysis: Comment, AER 64, 431–433Google Scholar
  15. Borch, K. (1969): A Note on Uncertainty and Indifference Curves, RES 36, 1–4Google Scholar
  16. Borch, K. (1974): The Rationale of the Mean-Standard Deviation Analysis: Comment, AER 64, 428–430Google Scholar
  17. Brennan, M.J. (1970): Taxes, Market Valuation and Corporate Financial Policy, National Tax Journal 23, 417–427Google Scholar
  18. Brennan, M.J. (1979): The Pricing of Contingent Claims Discrete Time Models, JoF 24, 53–68CrossRefGoogle Scholar
  19. Brenner, M. (1983) (Ed.): Option Pricing. Theory and Applications, LexingtonGoogle Scholar
  20. Chamberlain, G. (1983): A Characterization of the Distributions that Imply Mean-Variance Utility Functions, Journal of Economic Theory 29, 185–201CrossRefGoogle Scholar
  21. Chipman, J.S. (1973): The Ordering of Portfolios in Terms of Mean and Variance, RES 40, 167–190Google Scholar
  22. Copeland, T.E.; Weston, J.F. (1983): Financial Theory and Corporate Policy (second ed.), Reading (Mass.)Google Scholar
  23. Denneberg, D. (1984): Elements of Finance under Risk. An Average Deviation Approach to Risk, Economi Appliquée 37, 165–199Google Scholar
  24. Drukarczyk. J. (1980): Finanzierungstheorie, MünchenGoogle Scholar
  25. Dyer, J.S.; Sarin, R.K. (1982): Relative Risk Aversion, Management Science 20, 875–886CrossRefGoogle Scholar
  26. Epps, T.W. (1981): Necessary and Sufficient Conditions for the Mean-Variance Portfolio Model with Constant Risk Aversion, JFQA 16, 169–176CrossRefGoogle Scholar
  27. Fama, E.F.; Miller, M.H. (1972): The Theory of Finance, Hindsdale (I11.)Google Scholar
  28. Fama, E.F. (1965): The Behavior of Stock Market Prices, Journal of Business 38, 34–105CrossRefGoogle Scholar
  29. Feldstein, M.S. (1969): Mean-Variance Analysis in the Theory of Liquidity Preference and Portfolio Selection, RES 36, 5–12Google Scholar
  30. Firchau, V. (1983): Informationsbewertung und Portfolioplanung, in: Göppl, H.; Henn, R. (Eds.): tProceedings of the 2. Symposium on Money, Banking, and Insurance, Karlsruhe, 551–555Google Scholar
  31. Firchau, V. (1984): Variable Information and Capital Market Equilibria, in: Bamberg, G.; Spremann, K. (Eds): Risk and Capital, Berlin-Heidelberg-New York-Tokyo, 52-63Google Scholar
  32. Geske, R. (1978): The Pricing of Options with Stochastic Dividend Yield, JoF 33, 617–625CrossRefGoogle Scholar
  33. Gonzales, N.; Litzenberger, R.; Rolfo, J. (1977): On Mean-Variance Models of Capital Structure and the Absurdity of their Predictions, JFQA 12, 165–179CrossRefGoogle Scholar
  34. Hakansson, N.H. (1972): Mean-Variance Analysis in a Finite World, JFQA 7, 1873–1880CrossRefGoogle Scholar
  35. Hogan, W.W.; Warren, J.M. (1974): Toward the Development of an Equilibrium Capital Market Model Based on Semivariance, JFQA 9, 1–11CrossRefGoogle Scholar
  36. Jahankhani, A. (1976): E-V and E-S Capital Asset Pricing Models: Some Empirical Tests, JFQA 11, 513–528CrossRefGoogle Scholar
  37. Jarrow, R. (1980): Heterogeneous Expectations, Restrictions on Short Sales, and Equilibrium Asset Prices, JoF 35, 1105–1113CrossRefGoogle Scholar
  38. Jean, W. (1971): The Extension of Portfolio Analysis to Three or More Parameters, JFQA 6, 505–515CrossRefGoogle Scholar
  39. Jean, W. (1973): More on Multidimensional Portfolio Analysis, JFQA 8, 475–490CrossRefGoogle Scholar
  40. John, F. (1982): Partial Differential Equations (4ed.), New York-Heidelberg-BerlinGoogle Scholar
  41. Kallberg, J.G.; Ziemba, W.T. (1981): Remarks on Optimal Portfolio Selection, Methods of Operations Research 44, 19–40Google Scholar
  42. Kallberg, J.G.; Ziemba, W.T. (1984): Mis-Specifications in Portfolio Selection Problems, in: Bamberg, G.; Spremann, K. (Eds.): Risk and Capital, Berlin-Heidelberg-New York-Tokyo, 74-87Google Scholar
  43. Kraus, A.; Litzenberger, R. (1976): Skewness Preference and the Valuation of Risky Assets, JoF 31, 1085–1100CrossRefGoogle Scholar
  44. Levy, H. (1974): The Rationale of the Mean-Standard Deviation Analysis: Comment, AER 64, 434–441Google Scholar
  45. Lintner, J. (1964): The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets, RES 47, 13–37Google Scholar
  46. Lintner, J. (1969): The Aggregation of Investor’s Diverse Judgements and Preferences in Purely Competitive Securities Markets, JFQA 4, 347–400CrossRefGoogle Scholar
  47. Lintner, J. (1970): The Market Price of Risk, Size of Market and Investor’s Risk Aversion, RES 52, 87–99Google Scholar
  48. Mao, J.C.T. (1970): Models of Capital Budgeting, E-V versus E-S, JFQA 5, 657–675CrossRefGoogle Scholar
  49. Markowitz, H.M. (1959): Portfolio Selection, New YorkGoogle Scholar
  50. Masse, P. (1953): Reflexions sur les Comportements Rationnels en Economie Aléatoire, Cahiers Seminaire d’Econométrie 2, 11–58Google Scholar
  51. Miller, E. (1977): Risk Uncertainty, and Divergence of Opinion, JoF 32, 1151–1168CrossRefGoogle Scholar
  52. Mosler, K.C. (1982): Entscheidungsregeln bei Risiko. Multivariate Stochastische Dominanz, Berlin-Heidelberg-New YorkGoogle Scholar
  53. Mossin, J. (1968): Taxation and Risk-Taking: An Expected Utility Approach, Economica 35, 74–82CrossRefGoogle Scholar
  54. Mossin, J. (1973): Theory of Financial Markets, Englewood CliffsGoogle Scholar
  55. Müller, S. (1985): Arbitrage Pricing of Contingent Claims, Berlin-Heidelberg-New York-TokyoGoogle Scholar
  56. Nantell, T.J.; Price, B. (1979): An Analytical Comparision of Variance and Semivariance Capital Market Theories, JFQA 14, 221–242CrossRefGoogle Scholar
  57. Nantell, T.J.; Price, K.; Price, B. (1982): Mean-Lower Partial Moment Asset Pricing Model: Some Empirical Evidence, JFQA 17, 763–783CrossRefGoogle Scholar
  58. Owen, J.; Rabinovich, R. (1983): On the Class of Elliptical Distributions and their Applications to the Theory of Portfolio Choice, JoF 38, 745–752CrossRefGoogle Scholar
  59. Peterson, D.; Peterson, P. (1982): The Effect of Changing Expectations upon Stock return, JFQA 17, 799–813CrossRefGoogle Scholar
  60. Porter, R.B.; Bey, R.P.; Lewis, D.C. (1975): The Development of a Mean-Semivariance Approach to Capital Budgeting, JFQA 10, 639–649CrossRefGoogle Scholar
  61. Pratt, J.W. (1964): Risk Aversion in the Small and in the Large, Econometrica 32, 122–136CrossRefGoogle Scholar
  62. Price, K.; Price, B.; Nantell, T.J. (1982): Variance and Lower Partial Moment Measures of Systemtic Risk: Some Analytical and Empirical Results, JoF 37, 843–885CrossRefGoogle Scholar
  63. Roll, R. (1970): The Behavior of Interest Rates: The Application of the Efficient Market Model to US Treasury Bills, New YorkGoogle Scholar
  64. Ross, S.A. (1978): Mutual Fund Separation in Financial Theory — The Separating Distributions, Journal of Economic Theory 17, 254–286CrossRefGoogle Scholar
  65. Rudolph, B. (1979): Kapitalkosten bei unsicheren Erwartungen, Berlin-Heidelberg-New YorkGoogle Scholar
  66. Rudolph, B. (1982): Portfeuille-und Aktienkursbildung bei monopolistischem Anlegerwettbewerb, ZfB 52, 471–490Google Scholar
  67. Saelzle, R. (1976): Investitionsentscheidungen und Kapitalmarktheorie, WiesbadenGoogle Scholar
  68. Samuelson, P.A. (1970): The Fundamental Approximation Theorem of Portfolio Analysis in Terms of Means, Variances and Higher Moments, RES 37, 537–542Google Scholar
  69. Sarnat, M. (1974): A Note on the Implications of Quadratic Utility for Portfolio Theory, JFQA 9, 687–689CrossRefGoogle Scholar
  70. Schneeweiß, H. (1967): Entscheidungskriterien bei Risko, Berlin-Heidelberg-New YorkGoogle Scholar
  71. Schneider, D. (1980): Investition und Finanzierung (5ed.), WiesbadenGoogle Scholar
  72. Sengupta, J.K. (1985): Optimal Decisions Under Uncertainty, Berlin-Heidelberg-New York-TokyoGoogle Scholar
  73. Sharpe, W.F. (1964): Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk, JoF 19, 425–442CrossRefGoogle Scholar
  74. Sharpe, W.F. (1981): Investments (2ed.), Englewood CliffsGoogle Scholar
  75. Simkowitz, M.A.; Beedles, W.L. (1978): Diversification in a Three-Moment World, JFQA 13, 927–941CrossRefGoogle Scholar
  76. Spremann, K. (1984): A Firm in Statu Nascendi-Initial and Final Shareholders, in: Bamberg, G.; Spremann, K. (Eds.): Risk and Capital, Berlin-Heidelberg-New York-Tokyo, 103-121Google Scholar
  77. Spremann, K.; Bamberg, G. (1982): Bilanzpolitik, Mehrperioden-Diversifikation und kapitaltheoretische Unternehmenswerte, ZfB 51, 1204–1222Google Scholar
  78. Spremann, K.; Bamberg, G. (1983a): Emissionslimitierung und Kursbildung in einem unvollkommenen Kapitalmarkt, ZfbF 35, 302–314Google Scholar
  79. Spremann, K.; Bamberg, G. (1983b): Local Consistency of Risk Preferences, Statistische Hefte 24, 73–83CrossRefGoogle Scholar
  80. Stiglitz, J.E. (1969): The Effect of Income, Wealth, and Capital Gains Taxation on Risk Taking, Quarterly Journal of Economics 83, 263–283CrossRefGoogle Scholar
  81. Swoboda, P. (1981): Betriebliche Finanzierung, Würzburg-WienGoogle Scholar
  82. Tobin, J. (1958): Liquidity Preference as Behavior Towards Risk, RES 25, 65–86Google Scholar
  83. Tobin, J. (1969): Comment on Borch and Feldstein, RES 36, 13–14Google Scholar
  84. Tsiang, S.C. (1972): The Rationale of the Mean-Standard Deviation Analysis, Skewness Preference, and the Demand for Money, AER 62, 354–371Google Scholar
  85. Tsiang, S.C. (1974): The Rationale on the Mean-Standard Deviation Analysis: Replay and Errata for Original Article, AER 64, 442–450Google Scholar
  86. Vickson, R.G. (1977): Stochastic Orderings from Partially Known Utility Functions, Math. Operations Research 2, 244–252CrossRefGoogle Scholar
  87. Wilhelm, J.E.W. (1983): Finanztitelmarkt und Unternehmensfinanzierung, Berlin-Heidelberg-New YorkGoogle Scholar
  88. Wilhelm, J.E.W. (1985): Arbitrage Theory, Berlin-Heidelberg-New YorkGoogle Scholar
  89. Williams, J.T. (1977a): Capital Asset Prices with Heterogeneous Beliefs, JFE 5, 219–239CrossRefGoogle Scholar
  90. Williams, J.T. (1977b): A Note on Indifference Curves in the Mean-Variance Model, JFQA 12, 121–126CrossRefGoogle Scholar
  91. Zachow, E.W.; Schmitz, N. (1977): Eine Axiomatisierung des erwarteten Nutzens, in: Henn, R.; Möschlin, O. (Eds.): Mathematical Economics and Game Theory (Essays in Honor of Oskar Morgenstern), Berlin-Heidelberg-New York, 250-264.Google Scholar

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© Springer-Verlag Berlin Heidelberg New York Tokyo 1986

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  • Günter Bamberg

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