On the equivalence of the static and dynamic asset allocation problems

Robert Kohn, Oana M. Papazoglu-Statescu

Research output: Contribution to journalArticle

Abstract

A classic dynamic asset allocation problem optimizes the expected final-time utility of wealth, for an individual who can invest in a risky stock and a risk-free bond, trading continuously in time. Recently, several authors considered the corresponding static asset allocation problem in which the individual cannot trade but can invest in options as well as the underlying. The optimal static strategy can never do better than the optimal dynamic one. Surprisingly, however, for some market models the two approaches are equivalent. When this happens the static strategy is clearly preferable, since it avoids any impact of market frictions. This paper examines the question: when, exactly, are the static and dynamic approaches equivalent? We give an easily tested necessary and sufficient condition, and many non-trivial examples. Our analysis assumes that the stock follows a scalar diffusion process, and uses the completeness of the resulting market model. A simple special case is when the drift and volatility depend only on time; then the two approaches are equivalent precisely if (μ(t) - r)/σ2(t) is constant. This is not the Sharpe ratio or the market price of risk, but rather a nondimensional ratio of excess return to squared volatility that arises naturally in portfolio optimization problems.

Original languageEnglish (US)
Pages (from-to)173-183
Number of pages11
JournalQuantitative Finance
Volume6
Issue number2
DOIs
StatePublished - Apr 1 2006

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Allocation problem
Dynamic asset allocation
Equivalence
Market model
Sharpe ratio
Portfolio optimization
Completeness
Diffusion process
Excess returns
Market frictions
Market price of risk
Asset allocation
Wealth
Optimization problem

Keywords

  • Asset allocation
  • Portfolio optimization

ASJC Scopus subject areas

  • Economics, Econometrics and Finance(all)

Cite this

On the equivalence of the static and dynamic asset allocation problems. / Kohn, Robert; Papazoglu-Statescu, Oana M.

In: Quantitative Finance, Vol. 6, No. 2, 01.04.2006, p. 173-183.

Research output: Contribution to journalArticle

Kohn, Robert ; Papazoglu-Statescu, Oana M. / On the equivalence of the static and dynamic asset allocation problems. In: Quantitative Finance. 2006 ; Vol. 6, No. 2. pp. 173-183.
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