Title:
A Downside Risk Analysis based on Financial Index Tracking Models

Authors:
Lian Yu
and 
Xun Yu Zhou
and 
Shuzhong Zhang
Department of Systems Engineering and Engineering Management
The Chinese University of Hong Kong
Shatin, Hong Kong

Abstract:
This paper is mainly concerned with a single-stage financial index
tracking problem under the downside risk constraint where
short-selling is allowed. First, we formulate the portfolio
selection model with the downside probability constraint to track
the financial index. Due to the convexity of this problem, the
optimal portfolio is derived analytically by applying the
Karush-Kuhn-Tucker optimality conditions. Moreover, we extend the
risk measure to higher order moment of the downside and study the
corresponding portfolio optimization problem.