A Bank Asset and Liability Management Model

In managing its assets and liabilities in light of uncertainties in cash flows, cost of funds and return on investments, a bank must determine its optimal trade-off between risk, return and liquidity. In this paper we develop a multiperiod stochastic linear programming model ALM that includes the essential institutional, legal, financial, and bank-related policy considerations, and their uncertainties, yet is computationally tractable for realistically sized problems. A version of the model was developed for the Vancouver City Savings Credit Union for a 5-year planning period. The results indicate that ALM is theoretically and operationally superior to a corresponding deterministic linear programming model, and that the effort required for the implementation of ALM, and its computational requirements, are comparable to those of the deterministic model. Moreover, the qualitative and quantitative characteristics of the solutions are sensitive to the model's stochastic elements, such as the asymmetry of cash flow distributions. We also compare ALM with the stochastic decision tree SDT model developed by S. P. Bradley and D. B. Crane. ALM is computationally more tractable on realistically sized problems than SDT, and simulation results indicate that ALM generates superior policies.

[1]  Richard C. Grinold,et al.  Time Horizons in Energy Planning Models , 1980 .

[2]  A. Charnes,et al.  PLANNING FOR LIQUIDITY IN FINANCIAL INSTITUTIONS: THE CHANCE‐CONSTRAINED METHOD , 1966 .

[3]  Michael A. Goldberg,et al.  Bank Management and Portfolio Behavior. , 1975 .

[4]  William T. Ziemba,et al.  Short Term Financial Planning under Uncertainty , 1982 .

[5]  S. Bradley,et al.  A Dynamic Model for Bond Portfolio Management , 1972 .

[6]  R. Wets,et al.  Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse , 1986 .

[7]  E. Beale.  ON MINIMIZING A CONVEX FUNCTION SUBJECT TO LINEAR INEQUALITIES , 1955 .

[8]  Kalman J. Cohen,et al.  LINEAR PROGRAMMING AND OPTIMAL BANK ASSET MANAGEMENT DECISIONS , 1967 .

[9]  Albert Madansky.  New Methods in Mathematical Programming---Methods of Solution of Linear Programs Under Uncertainty , 1961 .

[10]  R. Wets.  Solving stochastic programs with simple recourse , 1983 .

[11]  Roger J.-B. Wets,et al.  Programming under uncertainty: The complete problem , 1966 .

[12]  A. Charnes,et al.  A Chance-Constrained Approach to Bank Dynamic Balance Sheet Management. , 1982 .

[13]  Roger Jean-Baptiste Robert Wets.  Programming under uncertainty , 1965 .

[14]  Richard Grinold,et al.  Finite horizon approximations of infinite horizon linear programs , 1977, Math. Program..

[15]  E. Fama,et al.  CASH BALANCE AND SIMPLE DYNAMIC PORTFOLIO PROBLEMS WITH PROPORTIONAL COSTS , 1969 .

[16]  Hans G. Daellenbach,et al.  Are Cash Management Optimization Models Worthwhile? , 1974, Journal of Financial and Quantitative Analysis.

[17]  Charles R Wolf,et al.  A Model for Selecting Commercial Bank Government Security Portfolios , 1969 .

[18]  Abraham Charnes,et al.  APPLICATION OF CHANCE-CONSTRAINED PROGRAMMING TO SOLUTION OF THE SO- CALLED 'SAVINGS AND LOAN ASSOCIATION' TYPE OF PROBLEM , 1965 .

[19]  H. Markowitz.  Portfolio Selection: Efficient Diversification of Investments , 1971 .

[20]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[21]  Abraham Charnes,et al.  INTERTEMPORAL BANK ASSET CHOICE WITH STOCHASTIC DEPENDENCE , 1968 .

[22]  E. Fama,et al.  Three Asset Cash Balance and Dynamic Portfolio Problems , 1971 .

[23]  Roger Ho.  Management of Bank Portfolios , 1977 .

[24]  John V. Soden,et al.  Admissible Decision Rules for the E-Model of Chance-Constrained Programming , 1971 .

[25]  Abraham Charnes,et al.  Inter-Temporal Analysis and Optimization of Bank Portfolios , 1961 .

[26]  Abraham I Brodt.  A multi-period portfolio theory model for commercial bank management , 1976 .

[27]  Lewis J. Spellman.  The Depository Firm and Industry: Theory, History and Regulation , 1982 .

[28]  Richard C. Grinold,et al.  Model Building Techniques for the Correction of End Effects in Multistage Convex Programs , 1983, Oper. Res..

[29]  John R. Birge,et al.  The value of the stochastic solution in stochastic linear programs with fixed recourse , 1982, Math. Program..

[30]  A. Madansky.  Inequalities for Stochastic Linear Programming Problems , 1960 .

[31]  Stephen P. Bradley,et al.  Management of Commercial Bank Government Security Portfolios: An Optimization Approach Under Uncertainty , 1973 .

[32]  Hans G. Daellenbach,et al.  The Optimal Bank Liquidity: A Multi-Period Stochastic Model , 1969 .

[33]  Gary D. Eppen,et al.  Solutions for Cash-Balance and Simple Dynamic-Portfolio Problems , 1968 .

[34]  Dwight B. Crane,et al.  A Stochastic Programming Model for Commercial Bank Bond Portfolio Management , 1971, Journal of Financial and Quantitative Analysis.

[35]  John R. Birge,et al.  Aggregation bounds in stochastic linear programming , 1985, Math. Program..