Portfolio Analysis

SA16.1 Problems of Optimization of an Investment Portfolio

• Efim M. Bronshtein; Ufa State Aviation Technical University, K.Marx Str. 12, Ufa, Bashkortostan, 450000 , Russia; brem@soros.basheda.ru
• Semjon I. Spivak; Bashkir State University, Frunze Str. 32, Ufa, Bashkortostan, 450074 , Russia; spivak@bsu.bashedu.ru

Formulations of problems of formation of optimal investment portfolio are shown at various definitions of risk of the projects. The interest rates are assumed to be stochastic. Different approaches are applied such as Markov claims, time-depending probabilities of refusals of investments and indexes of a condition.

SA16.2 Index Fund with Mean Square Tracking

• Yoshio Tabata; Osaka University, Grad. School of Econ., Toyonaka, Osaka, 560 , Japan; tabata@econ.osaka-u.ac.jp

Some properties of index fund designing problems are shown in discrete time and continuous time. The main property is that if the benchmark is (not) on the efficient frontier, then the index fund with minimum tracking error is (not) on the efficient frontier. More interesting results will be provided.

SA16.3 A Dynamic Asset Allocation Model with Downside Risk Control

• Yonggan Zhao; University of British Columbia, Fac. of Commerce, #419 2053 Main Mall, Vancouver, BC, V6T 1Z2 , Canada; zhao@phdlab.commerce.ubc.ca
• William T. Ziemba; University of British Columbia, Fac. of Commerce, 2053 Main Mall, Vancouver, BC, V6T 1Z2 , Canada; ziemba@interchange.ubc.ca

Assuming lognormality for prices, the strategy that gauges the dynamic portfolio weight by the risk neutral excess rate of return is determined by a stochastic differential equation. A constrained optimization model is established given investors' risk preference and asset price model. Under the risk measure, value at risk, the downside control method is superior to both buy and hold and fixed mix strategies.

SA16.4 Mean-Variance Portfolio Selection with Volatility Degeneracy Case

• Xun Li; Chinese University of Hong Kong, Dept. of SEEM, Shatin NT Hong Kong, , China; xli@s.cuhk.edu.hk,, http://www.se.cuhk.edu.hk/~xli/
• Xunyu Zhou; Chinese University of Hong Kong, Dept. of SEEM, Shatin NT Hong Kong, , China; xyzhou@se.cuhk.edu.hk,, http://www.se.cuhk.edu.hk/~xyzhou/

The mean-variance portfolio selection model with volatility degeneracy is studied in a financial market containing 1 bond and m stocks whose prices are associated with a d dimensional Brownian motion process. The efficient frontier, along with the analytical efficient policies, is obtained via solving an auxiliary stochastic linear-quadratic problem.