Portfolio optimization problem with nonidentical variances of asset returns using statistical mechanical informatics
1Mori Arinori Center for Higher Education and Global Mobility, Hitotsubashi University, Tokyo, 1868601, Japan.
Physical Review. E
|January 14, 2017
Summary
This study analyzes portfolio optimization with varying asset return variances using statistical mechanical informatics. Replica analysis determined minimal investment risk and concentration, validated by numerical experiments.
Area of Science:
- Quantitative Finance
- Statistical Mechanics
- Informatics
Background:
- Traditional portfolio optimization often assumes identical asset return variances.
- Complex financial markets necessitate advanced analytical methods for accurate optimization.
Purpose of the Study:
- To analyze the portfolio optimization problem with non-identical asset return variances.
- To define and analytically determine characteristic quantities of optimal portfolios.
Main Methods:
- Utilized statistical mechanical informatics, specifically replica analysis.
- Defined minimal investment risk and investment concentration as key portfolio metrics.
- Employed analytical determination of asymptotical behaviors for these quantities.
Main Results:
- Derived analytical solutions for minimal investment risk and investment concentration.
- Demonstrated the asymptotic behavior of these optimal portfolio characteristics.
- Validated the replica analysis method through comparison with numerical experiments.
Conclusions:
- The replica analysis methodology effectively addresses portfolio optimization with heterogeneous asset return variances.
- The defined metrics and their derived behaviors offer valuable insights into optimal portfolio construction.
- The study validates a robust analytical approach for complex financial optimization problems.
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