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Optimal Dynamic Trading with Leverage Constraints

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  • Sanford J. Grossman
  • Jean-Juc Vila

Abstract

We solve for the optimal dynamic trading strategy of an investor who faces two constraints. The first constraint is a limitation on his ability to borrow for the purpose of investing in a risky asset, i.e., the market value of his investments in the risky asset X, must be less than an exogenously given function of his wealth X(W). The second constraint is the requirement that the investor’s wealth be non-negative at all times, i.e., Wt>O. We assume that the investor has constant relative risk aversion A, and the value of the risky asset follows a diffusion with drift m+r (where r is the risk free rate) and per unit time variance s2. In the absence of the constraints, X &Mac186; (m/s2)*W/A. We prove that in the presence of the above constraints the optimal investment is X &Mac186; Min[(m/s2)*W/a, X(W)]. The coefficient a is not in general equal to A, and represents the extent to which the investor alters his strategy even when the constraints are not binding because of the possibility that the constraints will become binding in the future.

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Bibliographic Info

Paper provided by Wharton School Rodney L. White Center for Financial Research in its series Rodney L. White Center for Financial Research Working Papers with number 36-89.

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Handle: RePEc:fth:pennfi:36-89

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Cited by:
  1. Vladislav Kargin, 2003. "Optimal Convergence Trading," Papers math/0302104, arXiv.org, revised Aug 2003.
  2. Leonid Kogan & Raman Uppal, . "Risk Aversion and Optimal Portfolio Policies in Partial and General Equilibrium Economies," Rodney L. White Center for Financial Research Working Papers 13-00, Wharton School Rodney L. White Center for Financial Research.
  3. Fang Cai, 2003. "Was there front running during the LTCM crisis," International Finance Discussion Papers 758, Board of Governors of the Federal Reserve System (U.S.).
  4. Paul Willen & Felix Kubler, 2006. "Collateralized Borrowing and Life-Cycle Portfolio Choice," NBER Working Papers 12309, National Bureau of Economic Research, Inc.
  5. Tobias Adrian & Michael J. Fleming, 2005. "What financing data reveal about dealer leverage," Current Issues in Economics and Finance, Federal Reserve Bank of New York, vol. 11(Mar).

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