"A Separation Theorem of Active Management and Synthetic Enhanced Active Strategies"(in Japanese)

Takao Kobayashi () and Seiji Minami
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Seiji Minami: Resona Trust & Banking Co., Ltd.

No CIRJE-J-196, CIRJE J-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: We propose a Separation Theorem of Active Management. It asserts that in the so-called Enhanced Active Portfolio framework the efficient frontier is linear in the active return/active risk space, and one can separate the determination of optimal active portfolio weights from the determination of optimal leverage ratio. The risk preference of investors does not play any role in the former decision. The theorem holds under a fairly general set of conditions on portfolio restrictions. As such it enlightens to understand how the optimal overall portfolio is determined under realistic portfolio constraints, and how, given a specification of a tracking error, the optimal leverage ratio is determined. In Japan the enhanced prime brokerage structure, which enables the short-extension without borrowing on margin, is yet to come. An idea to overcome this institutional incompleteness is to use the futures contract to construct Synthetic Enhanced Active Strategies. A typical 130/30-enhanced active strategy is replaced by (1)100% long position in individual stocks, (2) (30+f)% long position in index futures, and (3)(30+f)% short position in individual stocks. We explain how this problem can be formulated as an optimal portfolio problem, and show that the synthetic strategy is very cost-effective as long as the required short-extension is not too large.

Pages: 43 pages
Date: 2008-06
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Persistent link: https://EconPapers.repec.org/RePEc:tky:jseres:2008cj196

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