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Portfolio Theory, Financial Risk Analysis and Applications
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Portfolio Theory, Financial Risk Analysis and Applications

A special issue of Risks (ISSN 2227-9091).

Deadline for manuscript submissions: 10 January 2025 | Viewed by 9923

Special Issue Editors

Prof. Dr. Stanislaus Maier-Paape

E-Mail Website
Guest Editor
Institut für Mathematik, RWTH Aachen University, D-52062 Aachen, Germany
Interests: asset allocation; risk management; portfolio optimization and quantitative finance
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Qiji Zhu

E-Mail Website
Guest Editor
Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USA
Interests: financial mathematics and risk management
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Portfolio optimization and related financial risk analysis are central themes in financial mathematics. The pioneering work of Markowitz on optimal portfolio theory has had a profound impact on both financial theory and practice. Early portfolio theory focused on the trade-off between return as an indication of reward and risk measured by volatility.

Nevertheless, portfolio optimization has evolved over the years, with several recent contributions made under the general portfolio theory framework. A major focus has been on systematically handling multiple risks in asset allocation.

Accordingly, we welcome research submissions to this Special Issue concerning new developments in portfolio theory with an emphasis on multiple financial risks, risk diversification, and applications. Contributions may be theoretical, practical, or a combination of both.

We encourage applications supported by statistical approaches, with a preference for distinguishing between in-sample and out-of-sample results to evaluate predictive quality. Comparisons with standard benchmarks such as indices or equal-weight portfolios are also welcome.

We welcome high-quality paper submissions related, but not limited, to the following topics:

- Portfolio theory/optimization;
- Analysis of risk measures and multiple risks;
- Applied risk management;
- Asset allocation in theory and practice;
- Applications in finance and elsewhere;
- Combinations of the above.

Prof. Dr. Stanislaus Maier-Paape
Prof. Dr. Qiji Zhu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Risks is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • portfolio theory and optimization
  • applied finance
  • asset allocation
  • multiple risks
  • portfolio diversification

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Published Papers (6 papers)

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Research

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44 pages, 9032 KiB  
Article
Modifying Sequential Monte Carlo Optimisation for Index Tracking to Allow for Transaction Costs
by Leila Hamilton-Russell, Thomas Malan O’Callaghan, Dmitrii Savin and Erik Schlögl
Risks 2024, 12(10), 155; https://doi.org/10.3390/risks12100155 - 30 Sep 2024
Viewed by 662
Abstract
Managing a portfolio whose value closely tracks an index by trading only in a subset of the index constituents involves an NP-hard optimisation problem. In the prior literature, it has been suggested that this problem be solved using sequential Monte Carlo (SMC, also [...] Read more.
Managing a portfolio whose value closely tracks an index by trading only in a subset of the index constituents involves an NP-hard optimisation problem. In the prior literature, it has been suggested that this problem be solved using sequential Monte Carlo (SMC, also known as particle filter) methods. However, this literature does not take transaction costs into account, although transaction costs are the primary motivation for attempting to replicate the index by trading in a subset, rather than the full set of index constituents. This paper modifies the SMC approach to index tracking to allow for proportional transaction costs and implements this extended method on empirical data for a variety stock indices. In addition to providing a more practically useful tracking strategy by allowing for transaction costs, we find that including a penalty for transaction costs in the optimisation objective can actually lead to better tracking performance. Full article
(This article belongs to the Special Issue Portfolio Theory, Financial Risk Analysis and Applications)
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19 pages, 2226 KiB  
Article
Trading Option Portfolios Using Expected Profit and Expected Loss Metrics
by Johannes Hendrik Venter and Pieter Juriaan de Jongh
Risks 2024, 12(8), 130; https://doi.org/10.3390/risks12080130 - 16 Aug 2024
Viewed by 793
Abstract
When trading in the call and put contracts of option chains, the portfolios of strikes must be selected. The trader must also decide whether to take long or short positions at the selected strikes. Dynamic strategies for making these decisions are discussed in [...] Read more.
When trading in the call and put contracts of option chains, the portfolios of strikes must be selected. The trader must also decide whether to take long or short positions at the selected strikes. Dynamic strategies for making these decisions are discussed in this paper. On any day, the strategies estimate the drift and volatility parameters of the future probability distribution of the price of the underlying asset. From this distribution, the trader can further estimate the future expected profit and expected loss that may be experienced for any portfolio of strikes of the call and put contracts. Expected profit and expected loss are the reward and risk metrics of such portfolios. An optimal portfolio can then be selected by making the reward as high as possible under the risk tolerance set by the trader. Extensive back-testing applications to historical data of SPY option chains illustrate the effectiveness of these strategies, particularly when dealing with short-term expiry options and when acting as a seller of put and call options. Full article
(This article belongs to the Special Issue Portfolio Theory, Financial Risk Analysis and Applications)
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19 pages, 1046 KiB  
Article
Mean-Reverting Statistical Arbitrage Strategies in Crude Oil Markets
by Viviana Fanelli
Risks 2024, 12(7), 106; https://doi.org/10.3390/risks12070106 - 25 Jun 2024
Viewed by 3400
Abstract
In this paper, we introduce the concept of statistical arbitrage through the definition of a mean-reverting trading strategy that captures persistent anomalies in long-run relationships among assets. We model the statistical arbitrage proceeding in three steps: (1) to identify mispricings in the chosen [...] Read more.
In this paper, we introduce the concept of statistical arbitrage through the definition of a mean-reverting trading strategy that captures persistent anomalies in long-run relationships among assets. We model the statistical arbitrage proceeding in three steps: (1) to identify mispricings in the chosen market, (2) to test mean-reverting statistical arbitrage, and (3) to develop statistical arbitrage trading strategies. We empirically investigate the existence of statistical arbitrage opportunities in crude oil markets. In particular, we focus on long-term pricing relationships between the West Texas Intermediate crude oil futures and a so-called statistical portfolio, composed by other two crude oils, Brent and Dubai. Firstly, the cointegration regression is used to track the persistent pricing equilibrium between the West Texas Intermediate crude oil price and the statistical portfolio value, and to identify mispricings between the two. Secondly, we verify that mispricing dynamics revert back to equilibrium with a predictable behaviour, and we exploit this stylized fact by applying the trading rules commonly used in equity markets to the crude oil market. The trading performance is then measured by three specific profit indicators on out-of-sample data. Full article
(This article belongs to the Special Issue Portfolio Theory, Financial Risk Analysis and Applications)
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26 pages, 882 KiB  
Article
Exploring Entropy-Based Portfolio Strategies: Empirical Analysis and Cryptocurrency Impact
by Nicolò Giunta, Giuseppe Orlando, Alessandra Carleo and Jacopo Maria Ricci
Risks 2024, 12(5), 78; https://doi.org/10.3390/risks12050078 - 11 May 2024
Cited by 1 | Viewed by 1160
Abstract
This study addresses market concentration among major corporations, highlighting the utility of relative entropy for understanding diversification strategies. It introduces entropic value at risk (EVaR) as a coherent risk measure, which is an upper bound to the conditional value at risk (CVaR), and [...] Read more.
This study addresses market concentration among major corporations, highlighting the utility of relative entropy for understanding diversification strategies. It introduces entropic value at risk (EVaR) as a coherent risk measure, which is an upper bound to the conditional value at risk (CVaR), and explores its generalization, relativistic value at risk (RLVaR), rooted in Kaniadakis entropy. Through extensive empirical analysis on both developed (i.e., S&P 500 and Euro Stoxx 50) and developing markets (i.e., BIST 100 and Bovespa), the study evaluates entropy-based criteria in portfolio selection, investigates model behavior across different market types, and assesses the impact of cryptocurrency introduction on portfolio performance and diversification. The key finding indicates that entropy measures effectively identify optimal portfolios, particularly in scenarios of heightened risk and increased concentration, crucial for mitigating negative net performances during low returns or high turnover. Bitcoin is primarily used for diversification and performance enhancement in the BIST 100 index, while its allocation in other markets remains minimal or non-existent, confirming the extreme concentration observed in stock markets dominated by a few leading stocks. Full article
(This article belongs to the Special Issue Portfolio Theory, Financial Risk Analysis and Applications)
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20 pages, 1352 KiB  
Article
Quantum Computing Approach to Realistic ESG-Friendly Stock Portfolios
by Francesco Catalano, Laura Nasello and Daniel Guterding
Risks 2024, 12(4), 66; https://doi.org/10.3390/risks12040066 - 12 Apr 2024
Cited by 2 | Viewed by 2136
Abstract
Finding an optimal balance between risk and returns in investment portfolios is a central challenge in quantitative finance, often addressed through Markowitz portfolio theory (MPT). While traditional portfolio optimization is carried out in a continuous fashion, as if stocks could be bought in [...] Read more.
Finding an optimal balance between risk and returns in investment portfolios is a central challenge in quantitative finance, often addressed through Markowitz portfolio theory (MPT). While traditional portfolio optimization is carried out in a continuous fashion, as if stocks could be bought in fractional increments, practical implementations often resort to approximations, as fractional stocks are typically not tradeable. While these approximations are effective for large investment budgets, they deteriorate as budgets decrease. To alleviate this issue, a discrete Markowitz portfolio theory (DMPT) with finite budgets and integer stock weights can be formulated, but results in a non-polynomial (NP)-hard problem. Recent progress in quantum processing units (QPUs), including quantum annealers, makes solving DMPT problems feasible. Our study explores portfolio optimization on quantum annealers, establishing a mapping between continuous and discrete Markowitz portfolio theories. We find that correctly normalized discrete portfolios converge to continuous solutions as budgets increase. Our DMPT implementation provides efficient frontier solutions, outperforming traditional rounding methods, even for moderate budgets. Responding to the demand for environmentally and socially responsible investments, we enhance our discrete portfolio optimization with ESG (environmental, social, governance) ratings for EURO STOXX 50 index stocks. We introduce a utility function incorporating ESG ratings to balance risk, return and ESG friendliness, and discuss implications for ESG-aware investors. Full article
(This article belongs to the Special Issue Portfolio Theory, Financial Risk Analysis and Applications)
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Review

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24 pages, 9098 KiB  
Review
Quick Introduction into the General Framework of Portfolio Theory
by Philipp Kreins, Stanislaus Maier-Paape and Qiji Jim Zhu
Risks 2024, 12(8), 132; https://doi.org/10.3390/risks12080132 - 19 Aug 2024
Viewed by 931
Abstract
This survey offers a succinct overview of the General Framework of Portfolio Theory (GFPT), consolidating Markowitz portfolio theory, the growth optimal portfolio theory, and the theory of risk measures. Central to this framework is the use of convex analysis and duality, reflecting the [...] Read more.
This survey offers a succinct overview of the General Framework of Portfolio Theory (GFPT), consolidating Markowitz portfolio theory, the growth optimal portfolio theory, and the theory of risk measures. Central to this framework is the use of convex analysis and duality, reflecting the concavity of reward functions and the convexity of risk measures due to diversification effects. Furthermore, practical considerations, such as managing multiple risks in bank balance sheets, have expanded the theory to encompass vector risk analysis. The goal of this survey is to provide readers with a concise tour of the GFPT’s key concepts and practical applications without delving into excessive technicalities. Instead, it directs interested readers to the comprehensive monograph of Maier-Paape, Júdice, Platen, and Zhu (2023) for detailed proofs and further exploration. Full article
(This article belongs to the Special Issue Portfolio Theory, Financial Risk Analysis and Applications)
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