A minimax portfolio selection strategy with equilibrium

A new minimax model on optimal portfolio selection with uncertainty of both randomness and estimation in inputs is established and the corresponding optimal portfolio is derived analytically. Based on this result, a sufficient condition for the existence and uniqueness of a nonnegative equilibrium price system under which the total demand and supply of each asset are equal is provided and an explicit formula for such a price system is obtained. Furthermore, some properties of the equilibrium are discussed.

[1]  V. K. Chopra,et al.  Massaging mean-variance inputs: returns from alternative global investment strategies in the 1980s , 1993 .

[2]  Arun J. Prakash,et al.  Portfolio selection and skewness: Evidence from international stock markets , 1997 .

[3]  H. Konno,et al.  Equilibrium relations in a capital asset market: A mean absolute deviation approach , 1994 .

[4]  K Fan,et al.  Minimax Theorems. , 1953, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Luca Luigi Ghezzi,et al.  A maxmin policy for bond management , 1999, Eur. J. Oper. Res..

[6]  Ron S. Dembo,et al.  Scenario optimization , 1991, Ann. Oper. Res..

[7]  Stephen A. Ross,et al.  THE CURRENT STATUS OF THE CAPITAL ASSET PRICING MODEL (CAPM) , 1978 .

[8]  P. Pardalos,et al.  On the use of optimization models for portfolio selection: A review and some computational results , 1994 .

[9]  Jati K. Sengupta,et al.  Portfolio decisions as games , 1989 .

[10]  Byung Ha Lim,et al.  A Minimax Portfolio Selection Rule with Linear Programming Solution , 1998 .

[11]  Kok Lay Teo,et al.  Portfolio Optimization Under a Minimax Rule , 2000 .

[12]  Yusif Simaan.  Estimation risk in portfolio selection: the mean variance model versus the mean absolute deviation model , 1997 .

[13]  W. Sharpe.  CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* , 1964 .

[14]  Michael J. Best,et al.  Positively Weighted Minimum-Variance Portfolios and the Structure of Asset Expected Returns , 1992, Journal of Financial and Quantitative Analysis.

[15]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[16]  J. Lintner.  THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS , 1965 .

[17]  M. Best,et al.  On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results , 1991 .

[18]  J. Ingersoll.  Theory of Financial Decision Making , 1987 .

[19]  Lars Tyge Nielsen.  Existence of equilibrium in CAPM , 1990 .

[20]  Richard Roll,et al.  A Critique of the Asset Pricing Theory''s Tests: Part I , 1977 .

[21]  J. Mossin.  EQUILIBRIUM IN A CAPITAL ASSET MARKET , 1966 .

[22]  Hiroshi Konno,et al.  EXISTENCE OF A NONNEGATIVE EQUILIBRIUM PRICE VECTOR IN THE MEAN‐VARIANCE CAPITAL MARKET , 1995 .

[23]  H. Konno,et al.  Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market , 1991 .

[24]  W. Ziemba,et al.  Worldwide asset and liability modeling , 1998 .

[25]  Kin Keung Lai,et al.  A model for portfolio selection with order of expected returns , 2000, Comput. Oper. Res..

[26]  K. Feldman.  Portfolio Selection, Efficient Diversification of Investments . By Harry M. Markowitz (Basil Blackwell, 1991) £25.00 , 1992 .

[27]  Chi-Fu Huang,et al.  Foundations for financial economics , 1988 .

[28]  M. Best,et al.  Sensitivity Analysis for Mean-Variance Portfolio Problems , 1991 .

[29]  James C. T. Mao,et al.  Models of Capital Budgeting, E-V VS E-S , 1970, Journal of Financial and Quantitative Analysis.

[30]  H. Konno.  Equilibrium Relation in the Mean-Absolute Deviation Capital Market , 1994 .

[31]  W. Ziemba,et al.  The Effect of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice , 1993 .