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THE EFFECT OF ESTIMATION IN HIGH‐DIMENSIONAL PORTFOLIOS
Author(s) -
Gandy Axel,
Veraart Luitgard A. M.
Publication year - 2013
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2011.00505.x
Subject(s) - econometrics , estimation , constraint (computer aided design) , economics , bond , investment (military) , investment strategy , expected utility hypothesis , mathematics , financial economics , finance , market liquidity , geometry , management , politics , political science , law
We study the effect of estimated model parameters in investment strategies on expected log‐utility of terminal wealth. The market consists of a riskless bond and a potentially vast number of risky stocks modeled as geometric Brownian motions. The well‐known optimal Merton strategy depends on unknown parameters and thus cannot be used in practice. We consider the expected utility of several estimated strategies when the number of risky assets gets large. We suggest strategies which are less affected by estimation errors and demonstrate their performance in a real data example. Strategies in which the investment proportions satisfy an L 1 ‐constraint are less affected by estimation effects.