Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-15T06:29:09.405Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal Dynamic Trading with Leverage Constraints

Published online by Cambridge University Press:  06 April 2009

Sanford J. Grossman  and
Jean-Luc Vila
Get access Rights & Permissions [Opens in a new window]

Abstract

We solve for the optimal dynamic trading strategy of an investor who faces a leverage constraint, i.e., a limitation on his ability to borrow for the purpose of investing in a risky asset. We assume that the investor has constant relative risk aversion, and that the value of the risky asset follows a geometric Brownian motion. In the absence of the leverage constraint, the optimal strategy involves investing a fixed proportion of wealth in the risky asset. We prove that, in the presence of the leverage constraint, the optimal investment also involves investing a fixed proportion of wealth in the risky asset when the leverage constraint is not binding. However, the two proportions are different, reflecting the extent to which the investor alters his strategy even when the leverage constraint is not binding because of the possibility that the leverage constraint will become binding in the future.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 27 , Issue 2 , June 1992 , pp. 151 - 168
Copyright
Copyright © School of Business Administration, University of Washington 1992

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

Black, F., and Jones, R.. “Simplifying Portfolio Insurance.” Journal of Portfolio Management, 14 (Fall 1987), 48–51.CrossRefGoogle Scholar
Black, F., and Perold, A.. “Theory of Constant Proportion Portfolio Insurance.” Unpubl. manuscript, Harvard Business School (1987).Google Scholar
Brennan, M., and Solanki, R.. “Optimal Portfolio Insurance.” Journal of Financial and Quantitative Analysis, 14 (09 1981), 279–300.CrossRefGoogle Scholar
Dybvig, P. “Inefficient Dynamic Portfolio Strategies or How to Throw Away a Million Dollars in the Stock Market.” The Review of Financial Studies, 1 (Spring 1988), 67–88.CrossRefGoogle Scholar
Dybvig, P., and Huang, C.F.. “Non Negative Wealth, Absence of Arbitrage, and Feasible Consumption Plans.” The Review of Financial Studies, 1 (Winter 1988), 377–401.CrossRefGoogle Scholar
Fleming, W.; Grossman, S.; Vila, J-L; and Zariphopoulou, T.. “Optimal Portfolio Rebalancing with Transaction Costs.” Unpubl. manuscript, M.I.T. (1990).Google Scholar
Grossman, S. “An Analysis of the Implications for Stock and Futures Price Volatility of Program Trading and Dynamic Hedging Strategies.” Journal of Business, 61 (07 1988), 275–298.CrossRefGoogle Scholar
Grossman, S., and Vila, J.L.. “Portfolio Insurance and Complete Markets: A Note.” Journal of Business, 62 (11 1989), 473–476.CrossRefGoogle Scholar
Harrison, M., and Kreps, D.. “Martingales and Arbitrage in Multiperiod Securities Markets.” Journal of Economic Theory, 20 (06 1979), 381–408.CrossRefGoogle Scholar
Karatzas, I.; Lehoczky, J.; Sethi, S.; and Shreve, S.. “Explicit Solution of a General Consumption/Investment Problem.” Mathematics of Operations Research, 11 (05 1986), 261–294.CrossRefGoogle Scholar
Merton, R. “Optimal Consumption and Portfolio Rules in a Continuous Time Model.” Journal of Economic Theory, 3 (12 1971), 373–413.CrossRefGoogle Scholar
Perold, A. “Constant Proportion Portfolio Insurance.” Unpubl. manuscript, Harvard Business School, (1986).Google Scholar
Vila, J.L., and Zariphopoulou, T.. “Optimal Consumption and Portfolio Choice with Borrowing Constraints.” Unpubl. manuscript, M.I.T. (1990).Google Scholar