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Dynamic mean-variance analysis
Abstract: We analyse the conditional versions of two closely
connected mean-variance investment problems, the replication of a
contingent claim on the one hand and the selection of an efficient
portfolio on the other hand, in a general discrete time setting with
We exhibit a positive process h which summarizes
two pieces of economically meaningful information. As a function the states
of the world, it can be used as a correction lens for myopic investors, and
it reveals the gap between static and dynamic mean-variance investment
strategies. A short sighted investor who corrects the probability
distribution with the help of h acts optimally for long horizons.
describe the dynamic mean-variance efficient frontier conditioned on the
information available at a future date in the form of a two fund separation
theorem. The dynamic Sharpe ratio measures the distance from of an
investment strategy to the efficient frontier. We explain how optimal
dynamic Sharpe ratios aggregate through time and we study the time
consistency rules which efficient portfolios must follow. We investigate
the effect of a change of investment horizon, in particular we show that
myopia is optimal as soon as the process h is deterministic.
Keywords: self financing portfolio; efficient frontier; sharpe ratio; myopia; (follow links to similar papers)
JEL-Codes: C11; F30; G11; (follow links to similar papers)
74 pages, August 1, 2001
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