Risk Assessment and Asset Allocation with Gross Exposure Constraints for Vast Portfolios

Mathematical Finance ColloquiumWhen: Friday, September 4, 2009, 3:30 PMWhere: KAP 414Title: "Risk Assessment and Asset Allocation with Gross Exposure Constraints for Vast Portfolios"Speaker: Jianqing Fan Frederick L. Moore Professor of Finance, and the Director of Committee of Statistical Studies in the Department of Operation Research and Financial Engineering of Princeton UniversityABSTRACT: Markowitz (1952, 1959) laid down the ground-breaking work on the
mean-variance analysis. Under his framework, the theoretical optimal allocation
vector can be very different from the estimated one for large portfolios due to the
intrinsic difficulty of estimating a vast covariance matrix and return vector. This
can result in adverse performance in portfolio selected based on empirical data
due to the accumulation of estimation errors. We address this problem by
introducing the gross-exposure constrained mean-variance portfolio selection.
We show that with gross-exposure constraint the empirically selected optimal
portfolios based on estimated covariance matrices have similar performance
to the theoretical optimal portfolios and there is no error accumulation effect
from estimation of vast covariance matrices. This gives theoretical justification
to the empirical results in Jagannathan and Ma (2003). We also show that the
no-short-sale portfolio is not diversified enough and can be improved by
allowing some short positions. As the constraint on short sales relaxes, the
number of selected assets gradually increases and finally reaches the total
number of stocks when tracking portfolios or selecting assets. This achieves
the optimal sparse portfolio selection, which has close performance to the
theoretical optimal one. Among 1000 stocks, for example, we are able to identify
all optimal subsets of portfolios of different sizes, their associated allocation
vectors, and their estimated risks. The utility of our new approach is illustrated
by simulation and empirical studies on the 100 Fama-French industrial portfolios
and the 600 stocks randomly selected from Russell 3000.

Location: Kaprielian Hall (KAP) - 414

Audiences: Everyone Is Invited

Contact: Georgia Lum