Low Volatility Optimal Portfolio Selection: Financial Experiments with Mixture Designs
65 / 31
Authors
-
Ravindra Khattree
Department of Mathematics and Statistics and Institute for Data Science Oakland University, Rochester, MI 48309
-
Md Shakhawat Alam
Department of Mathematics and Statistics and Institute for Data Science Oakland University, Rochester, MI 48309
Keywords:
Financial Experiments; Mixture designs; Portfolio optimization; Space-filling Designs. AMS Subject Classifications: 62K20, 62K99, 62P05Abstract
This article assesses the performance of various stock market portfolios using a space-filling mixture design and a model for the logratios in the
portfolio allocation. Traditional portfolio analysis relies on historical correlations between various returns and adopts various optimization models.
However, these methods rely excessively on the assumptions made and often tend to ignore the statistical variability in their optimization procedures.
As a result, they may not perform well when implemented on independent future data. Additionally, the constraints and bounds imposed play a
crucial role in determining the feasible region and hence the optimal value therein. By integrating a systematic simplex design approach for exploring
component mixtures in our portfolio and applying a logratio transformation, we offer a robust framework for analyzing the portfolios and exploring
how various portfolios perform relative to each other. An advantage of our method is that we are able to estimate the standard error for each portfolio,
and this allows us to incorporate the consideration of volatilities into our decision making. Using publicly available stock market data, we demonstrate
the effectiveness of our approach.
Downloads
References
J. Aitchison. The statistical analysis of compositional data. Journal of
the Royal Statistical Society: Series B (Methodological), 44(2),
139-160, 1982.
G.-Y. Ban, N. ElKaroui, and A.E. Lim. Machine learning and portfolio
optimization. Management Science, 64(3), 1136-1154, 2018.
L. Cheng, M. Shadabfar, and A. Sioofy Khoojine. A state-of-the-art
review of probabilistic portfolio management for future stock
markets. Mathematics, 11(5), 2023.
J.A. Cornell. Experiments with mixtures: Designs, models, and the
analysis of mixture data. Wiley- Interscience, New York, 1983.
A. Fernández and S. Gómez. Portfolio selection using neural networks.
Computers & Operations Research, 34(4), 1177-1191, 2007.
C. Gomes, M. Claeys-Bruno, and M. Sergent. Space-filling designs for
mixtures. Chemometrics and Intelligent Laboratory Systems, 174,
111-127, 2018.
M. Greenacre. Compositional data analysis. Annual Review of Statistics
and its Application, 8(1), 271-299, 2021
M. Greenacre, E. Grunsky, J. Bacon-Shone, I. Erb, and T. Quinn.
Aitchison’s compositional data analysis 40 years on: A reappraisal.
Statistical Science, 38(3), 386-410, 2023.
A. Gunjan and S. Bhattacharyya. A brief review of portfolio
optimization techniques. Artificial Intelligence Review, 56(5),
3847-3886, 2023.
V. R. Joseph. Space-filling designs for computer experiments: A review.
Quality Engineering, 28(1), 28-35, 2016.
R. Khattree and D.N. Naik. Applied multivariate statistics with SAS
software. SAS Press and John Wiley & Sons, 1999.
B. Kocuk and G. Cornuéjols. Incorporating Black–Litterman views
in portfolio construction when stock returns are a mixture of
normals. Omega, 91, 102008, 2020.
R. L. Manogna and N. Kulkarni. Portfolio optimization model for stock
price prediction using machine learning. Journal of Statistical
Theory and Applications, 24, 1091-1108, 2025.
H.M. Markowitz. Portfolio Selection: Efficient Diversification of
Investments. Yale University Press, New Haven, CT, 2008.
H.M. Markowitz and G.P. Todd. Mean-Variance Analysisin Portfolio
Choice and Capital Markets. John Wiley & Sons, New York, NY,
2000
A. Monticeli, P. Balestrassi, A. Souza, E. Carvalho, L. da Silva, and P.
Mappa. Mixture design of experiments as strategy for portfolio
optimization. Acta Scientiarum. Technology, 45, e63500,2023.
S. Nathaphan and P. Chunhachinda. Estimation risk modeling in optimal
portfolio selection: An empirical study from emerging markets.
Economics research international, 2010(1), 340181, 2010.
G.F. Piepel, B.A. Stanfill, S.K. Cooley, B. Jones, J.O. Kroll, and
J.D. Vienna. Developing a space-filling mixture experiment
design when the components are subject to linear and nonlinear
constraints. Quality Engineering, 31(3), 463-472, 2019.
C. Shenoy and P.P. Shenoy. Bayesian network models of portfolio risk
and return. Management Science, 46(3), 425-441, 2000
Downloads
Submitted
Published
Issue
Section
How to Cite
