Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-09T13:53:52.675Z Has data issue: false hasContentIssue false
  • English
  • Français

Simple Optimal Policy for Cash Management: The Average Balance Requirement Case

Published online by Cambridge University Press:  06 April 2009

R. G. Vickson
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper treats a problem of stochastic cash management under an average compensating-balance requirement. It develops a dynamic programming formulation of the problem in which the relevant state is a unidimensional quantity equivalent to the forecasted average balance at the end of the averaging period. Under usably broad conditions, it establishes the optimality of a transient policy of simple type, similar to the two-sided inventory type policy familiar from certain earlier studies of stationary cash balance problems having absolute balance requirements. The results apply to cases in which the transactions costs contain both fixed and proportional components. The paper discusses also a numerical example drawn from the literature of the cash balance problem and shows by simulation of the optimal (and simply modified forms of the optimal) policy, that good protection is afforded against negative balances, even though the model does not explicitly constrain the negative-balance probabilities.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 20 , Issue 3 , September 1985 , pp. 353 - 369
Copyright
Copyright © School of Business Administration, University of Washington 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Ambramowitz, A., and Stegun, I. A.. Handbook of Mathematical Functions. New York: Dover Publications, Inc. (1965).Google Scholar
[2]Baxter, N. D., and Shapiro, H. T.. “Compensating Balance Requirements: The Results of a Survey.” The Journal of Finance, Vol. 19 (09 1964), pp. 483–495.Google Scholar
[3]Campbell, T., and Brendsel, L.. “The Impact of Compensating Balance Requirements on the Cash Balances of Manufacturing Firms.” The Journal of Finance, Vol. 32 (03 1977), pp. 31–40.Google Scholar
[4]Constantinides, G. M., and Richard, F. S.. “Existence of Optimal Simple Policies for Discounted Cost Inventory and Cash Management in Continuous Time.” Operations Research, Vol. 26 (07–08 1978), pp. 620–636.CrossRefGoogle Scholar
[5]Davis, R. G., and Guttentag, J. M.. “Are Compensating Balances Irrational?” The Journal of Finance, Vol. 17 (03 1962), pp. 121–128.Google Scholar
[6]Elton, E. J., and Gruber, M.. Finance as a Dynamic Process. Englewood Cliffs, N.J.: Prentice-Hall, Inc. (1975).Google Scholar
[7]Eppen, G. D., and Fama, E. F.. “Solutions for Cash Balance and Simple Dynamic Portfolio Problems.” Journal of Business, Vol.41 (01 1968), pp. 94–112.CrossRefGoogle Scholar
[8]Eppen, G. D., and Fama, E. F. “Cash Balance and Simple Dynamic Portfolio Problems with Proportional Costs.” International Economic Review, Vol. 10 (06 1969), pp. 119–133.CrossRefGoogle Scholar
[9]Gibson, W. E. “Compensating Balance Requirements.” International Banking Review, Vol. 2 (03 1965), pp. 387–395.Google Scholar
[10]Girgis, N. M. “Optimal Cash Balance Levels.” Management Science, Vol. 15 (11 1968), pp. 130–140.CrossRefGoogle Scholar
[11]Hausman, W. M., and Sanchez-Bell, A.. “The Stochastic Cash Balance Problem with Average Compensating-Balance Requirements.” Management Science, Vol. 21 (04 1975), pp. 849–857.CrossRefGoogle Scholar
[12]Hellweg, D. “A Note on Compensating Balance Requirements.” The Journal of Finance, Vol. 16 (03 1961), pp. 80–84.CrossRefGoogle Scholar
[13]Homonoff, R., and Mullins, D.. Cash Management. Lexington, MA: Lexington Books, Inc. (1975).Google Scholar
[14]Karlin, S. “One Stage Inventory Models with Uncertainty.” In Studies in the Mathematical Theory of Inventory and Production, Arrow, K., Karlin, S., and Scarf, H., eds. Stanford, CA: Stanford University Press (1958).Google Scholar
[15]Karlin, S.Total Positivity, Volume 1. Stanford, CA: Stanford University Press (1968).Google Scholar
[16]“Pólya-Type Distributions, II.” Annals of Mathematical Statistics, Vol. 28 (06 1975), pp. 281–308.Google Scholar
[17]Kolodny, R., and Seeley, P.. “Optimal Borrowing Arrangements with Compensating Balance Requirements.” Southern Economic Journal, Vol. 44 (10 1977), pp. 313–322.CrossRefGoogle Scholar
[18]Lam, C. H., and Boudreaux, K. J.. “Compensating Balances, Rationality and Optimality.” Journal of Banking and Finance, Vol. 5 (12 1981), pp. 451–466.CrossRefGoogle Scholar
[19]Meinster, D. R. “The Demand for Compensating Balances.” Southern Economic Journal, Vol. 43 (04 1977), pp. 1538–1546.CrossRefGoogle Scholar
[20]Miller, M. H., and Orr, D.. “A Model for the Demand for Money by Firms.” The Quarterly Journal of Economics, Vol. 80 (08 1966), pp. 413–435.CrossRefGoogle Scholar
[21]Nadler, P. S. “Compensating Balances and the Prime at Twilight.” Harvard Business Review, Vol. 50 (01–02 1972), pp. 112–120.Google Scholar
[22]Neave, E. H. “The Stochastic Cash Balance Problem with Fixed Costs for Increases and Decreases.” Management Science, Vol. 16 (03 1970), pp. 472–490.CrossRefGoogle Scholar
[23]Orr., D.Cash Management and the Demand for Money. New York: Praeger Press, Inc. (1970).Google Scholar
[24]Ralston, A.A First Course in Numerical Analysis. New York: McGraw-Hill, Inc. (1965).Google Scholar
[25]Schoenberg, I. J. “On Totally Positive Functions, Laplace Integrals and Entire Functions.” Proceedings of the National Academy of Sciences, Vol. 33 (01 1947), pp. 11–17.CrossRefGoogle ScholarPubMed
[26]Schoenberg, I. J. “On Variation-Diminishing Operators of Convolution Type.” Proceedings of the National Academy of Sciences, Vol. 34 (04 1948), pp. 164–169.CrossRefGoogle ScholarPubMed
[27]Schoenberg, I. J. “On Pólya Frequency Functions, I: The Totally Positive Functions and Their Laplace Transforms.” Journal d'Analyse Mathématique, Vol. 1 (10 1951), pp. 331–374.CrossRefGoogle Scholar
[28]Schoenberg, I. J. “On Pólya Frequency Functions, II: Variation Diminishing Operators of Convolution Type.” Acta Scientiarum Mathematicarum, Szeged, Vol. 12 (05 1950), pp. 97–106.Google Scholar
[29]Wrightsman, D. “On the Rationality of Compensating Balance Requirements.” Southern Economic Journal, Vol. 39 (01 1973), pp. 427–430.CrossRefGoogle Scholar