A Study on the Mahalanobis Universal Portfolio With and Without Transaction Cost for (2K+1)- Bandwidth Toeplitz Matrices

Chi-Hau Kor, Sheong-Wei Phoon () and Wing-Son Loh
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Chi-Hau Kor: Universiti Tunku Abdul Rahman, Lee Kong Chian, Faculty of Engineering and Science
Sheong-Wei Phoon: Universiti Tunku Abdul Rahman, Lee Kong Chian, Faculty of Engineering and Science
Wing-Son Loh: Universiti Tunku Abdul Rahman, Lee Kong Chian, Faculty of Engineering and Science

A chapter in Proceedings of the 11th International Conference on Business, Accounting, Finance and Economics (BAFE 2023), 2023, pp 13-44 from Springer

Abstract: Abstract Investing is crucial for wealth accumulation, safeguarding against inflation, and meeting financial objectives. Choosing effective strategies can significantly influence outcomes. Central to this is the Mahalanobis universal portfolio (MUP), characterised by its tendency to yield positive returns over extended durations. This paper delves into its optimisation using $$(2k+1)$$ ( 2 k + 1 ) -bandwidth Toeplitz matrices associated with positive definite Toeplitz matrices. A novel aspect of our study is examining transaction costs’ impact on this portfolio, a territory not previously ventured into. Eight portfolios were formed and obtained from Yahoo! Finance, spanning January 2, 2015, to January 21, 2021, encompassing 1,500 trading days. This paper examines the influence of bandwidth, trading period length, and portfolio sizes on the cumulative wealth investors generate. Alternative investment strategies such as Buy-and-Hold (BH), Constant Rebalanced Portfolio (CRP), and Best Constant Rebalanced Portfolios (BCRP) are scrutinised to gauge their effectiveness in generating wealth. The findings demonstrate that the MUP facilitates notable wealth growth for investors, offering a principal increase and a balance of lower risk with higher returns than other strategies. By incorporating various metrics and transaction costs, the study provides valuable insights into the performance of investment strategies, enabling individuals to make informed decisions to maximise their returns.

Keywords: Universal portfolio; Toeplitz matrix; Transaction cost; Best Constant Rebalanced Portfolio (BCRP) (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:advbcp:978-94-6463-342-9_3

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DOI: 10.2991/978-94-6463-342-9_3

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