THE EFFECT OF ESTIMATION IN HIGH-DIMENSIONAL PORTFOLIOS
Article first published online: 3 FEB 2012
© 2012 Wiley Periodicals, Inc.
Volume 23, Issue 3, pages 531–559, July 2013
How to Cite
Gandy, A. and Veraart, . L. A. M. (2013), THE EFFECT OF ESTIMATION IN HIGH-DIMENSIONAL PORTFOLIOS. Mathematical Finance, 23: 531–559. doi: 10.1111/j.1467-9965.2011.00505.x
- Issue published online: 8 JUN 2013
- Article first published online: 3 FEB 2012
- Manuscript received December 2009; final revision received May 2011.
- optimal investment;
- continuous time;
- estimation effects;
- vast portfolios
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 L1-constraint are less affected by estimation effects.