Economics at your fingertips  

Analytic solution to variance optimization with no short-selling

Imre Kondor, G\'abor Papp and Fabio Caccioli

Papers from

Abstract: A large portfolio of independent returns is optimized under the variance risk measure with a ban on short positions. The no-short selling constraint acts as an asymmetric $\ell_1$ regularizer, setting some of the portfolio weights to zero and keeping the out of sample estimator for the variance bounded, avoiding the divergence present in the non-regularized case. However, the susceptibility, i.e. the sensitivity of the optimal portfolio weights to changes in the returns, diverges at a critical value $r=2$. This means that a ban on short positions does not prevent the phase transition in the optimization problem, it merely shifts the critical point from its non-regularized value of $r=1$ to $2$. At $r=2$ the out of sample estimator for the portfolio variance stays finite and the estimated in-sample variance vanishes. We have performed numerical simulations to support the analytic results and found perfect agreement for $N/T

New Economics Papers: this item is included in nep-rmg
Date: 2016-12, Revised 2017-01
References: View references in EconPapers View complete reference list from CitEc
Citations View citations in EconPapers (1) Track citations by RSS feed

Downloads: (external link) Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Access Statistics for this paper

More papers in Papers from
Series data maintained by arXiv administrators ().

Page updated 2017-10-21
Handle: RePEc:arx:papers:1612.07067