The Kelly Capital Growth Investment Criterion:Theory and Practice: 3 (World Scientific Handbook in Financial Economics Series) by MacLean Leonard C & Edward O Thorp & William T Ziemba

The Kelly Capital Growth Investment Criterion:Theory and Practice: 3 (World Scientific Handbook in Financial Economics Series) by MacLean Leonard C & Edward O Thorp & William T Ziemba

Author:MacLean, Leonard C & Edward O Thorp & William T Ziemba [MacLean, Leonard C]
Language: eng
Format: epub
Publisher: World Scientific Publishing Co Pte Ltd
Published: 2011-02-10T00:00:00+00:00


7.1.2 Benchmark as a portfolio of traded assets only

We assume that the benchmark follows a constant proportion strategy invested in a combination of traded assets. Its dynamics is given by the equation

where v is a m-element allocation vector satisfying the budget equation

In this setting, Corollary 3 can be expressed as:

Corollary 4. (Fund Separation Theorem with a Constant Proportion Benchmark (I)). Given a time t and a state vector X(t), any portfolio can be expressed as a linear combination of investments into a “mutual fund”, an index fund and a “long-short hedge fund” with respective risky asset allocations



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