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Risks
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Portfolio Optimization and Risk Management: New Development and Applications
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Portfolio Optimization and Risk Management: New Development and Applications

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

Deadline for manuscript submissions: closed (30 April 2019) | Viewed by 27354

Special Issue Editors

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
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

Special Issue Information

Dear Colleagues,

Portfolio optimization and related risk analysis is one of the central themes in financial mathematics. Since the pioneering work of Markowitz, portfolio theory has had a great impact on both financial theory and applications. Early portfolio theory focused on the trade-off between mean as an indication for reward and variation as a risk measure.

The need in financial practice stimulated the development of more general reward and risk measures. Recently, new frameworks for portfolio theory have begun to emerge. For instance, practically important drawdown risk measures attracted more attention from both researchers and practitioners.

This Special Issue aims to stimulate discussions on new developments of the portfolio theory and their practical applications. We therefore welcome and encourage the submission of high quality papers related, but not limited to, the following topics:

  • New framework for portfolio optimization
  • Theory on trading strategies (multi-period portfolios)
  • Analysis of risk measures
  • Applied risk management
  • Asset allocation in theory and practice
  • Application in finance and elsewhere

Prof. Dr. Qiji (Jim) Zhu
Prof. Dr. Stanislaus Maier-Paape
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
  • applied finance
  • risk measures
  • asset allocation

Published Papers (7 papers)

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Research

15 pages, 457 KiB  
Article
Optimal Risk Budgeting under a Finite Investment Horizon
by Marcos López de Prado, Ralph Vince and Qiji Jim Zhu
Risks 2019, 7(3), 86; https://doi.org/10.3390/risks7030086 - 05 Aug 2019
Cited by 4 | Viewed by 4498
Abstract
The Growth-Optimal Portfolio (GOP) theory determines the path of bet sizes that maximize long-term wealth. This multi-horizon goal makes it more appealing among practitioners than myopic approaches, like Markowitz’s mean-variance or risk parity. The GOP literature typically considers risk-neutral investors with an infinite [...] Read more.
The Growth-Optimal Portfolio (GOP) theory determines the path of bet sizes that maximize long-term wealth. This multi-horizon goal makes it more appealing among practitioners than myopic approaches, like Markowitz’s mean-variance or risk parity. The GOP literature typically considers risk-neutral investors with an infinite investment horizon. In this paper, we compute the optimal bet sizes in the more realistic setting of risk-averse investors with finite investment horizons. We find that, under this more realistic setting, the optimal bet sizes are considerably smaller than previously suggested by the GOP literature. We also develop quantitative methods for determining the risk-adjusted growth allocations (or risk budgeting) for a given finite investment horizon. Full article
(This article belongs to the Special Issue Portfolio Optimization and Risk Management: New Development and Applications)
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20 pages, 3480 KiB  
Article
Market-Risk Optimization among the Developed and Emerging Markets with CVaR Measure and Copula Simulation
by Nader Trabelsi and Aviral Kumar Tiwari
Risks 2019, 7(3), 78; https://doi.org/10.3390/risks7030078 - 07 Jul 2019
Cited by 4 | Viewed by 3623
Abstract
In this paper, the generalized Pareto distribution (GPD) copula approach is utilized to solve the conditional value-at-risk (CVaR) portfolio problem. Particularly, this approach used (i) copula to model the complete linear and non-linear correlation dependence structure, (ii) Pareto tails to capture the estimates [...] Read more.
In this paper, the generalized Pareto distribution (GPD) copula approach is utilized to solve the conditional value-at-risk (CVaR) portfolio problem. Particularly, this approach used (i) copula to model the complete linear and non-linear correlation dependence structure, (ii) Pareto tails to capture the estimates of the parametric Pareto lower tail, the non-parametric kernel-smoothed interior and the parametric Pareto upper tail and (iii) Value-at-Risk (VaR) to quantify risk measure. The simulated sample covers the G7, BRICS (association of Brazil, Russia, India, China and South Africa) and 14 popular emerging stock-market returns for the period between 1997 and 2018. Our results suggest that the efficient frontier with the minimizing CVaR measure and simulated copula returns combined outperforms the risk/return of domestic portfolios, such as the US stock market. This result improves international diversification at the global level. We also show that the Gaussian and t-copula simulated returns give very similar but not identical results. Furthermore, the copula simulation provides more accurate market-risk estimates than historical simulation. Finally, the results support the notion that G7 countries can provide an important opportunity for diversification. These results are important to investors and policymakers. Full article
(This article belongs to the Special Issue Portfolio Optimization and Risk Management: New Development and Applications)
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31 pages, 607 KiB  
Article
A General Framework for Portfolio Theory. Part III: Multi-Period Markets and Modular Approach
by Stanislaus Maier-Paape, Andreas Platen and Qiji Jim Zhu
Risks 2019, 7(2), 60; https://doi.org/10.3390/risks7020060 - 01 Jun 2019
Viewed by 2623
Abstract
This is Part III of a series of papers which focus on a general framework for portfolio theory. Here, we extend a general framework for portfolio theory in a one-period financial market as introduced in Part I [Maier-Paape and Zhu, Risks 2018, 6(2), [...] Read more.
This is Part III of a series of papers which focus on a general framework for portfolio theory. Here, we extend a general framework for portfolio theory in a one-period financial market as introduced in Part I [Maier-Paape and Zhu, Risks 2018, 6(2), 53] to multi-period markets. This extension is reasonable for applications. More importantly, we take a new approach, the “modular portfolio theory”, which is built from the interaction among four related modules: (a) multi period market model; (b) trading strategies; (c) risk and utility functions (performance criteria); and (d) the optimization problem (efficient frontier and efficient portfolio). An important concept that allows dealing with the more general framework discussed here is a trading strategy generating function. This concept limits the discussion to a special class of manageable trading strategies, which is still wide enough to cover many frequently used trading strategies, for instance “constant weight” (fixed fraction). As application, we discuss the utility function of compounded return and the risk measure of relative log drawdowns. Full article
(This article belongs to the Special Issue Portfolio Optimization and Risk Management: New Development and Applications)
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14 pages, 6427 KiB  
Article
Statistical Inference for the Beta Coefficient
by Taras Bodnar, Arjun K. Gupta, Valdemar Vitlinskyi and Taras Zabolotskyy
Risks 2019, 7(2), 56; https://doi.org/10.3390/risks7020056 - 15 May 2019
Cited by 4 | Viewed by 4071
Abstract
The beta coefficient plays a crucial role in finance as a risk measure of a portfolio in comparison to the benchmark portfolio. In the paper, we investigate statistical properties of the sample estimator for the beta coefficient. Assuming that both the holding portfolio [...] Read more.
The beta coefficient plays a crucial role in finance as a risk measure of a portfolio in comparison to the benchmark portfolio. In the paper, we investigate statistical properties of the sample estimator for the beta coefficient. Assuming that both the holding portfolio and the benchmark portfolio consist of the same assets whose returns are multivariate normally distributed, we provide the finite sample and the asymptotic distributions of the sample estimator for the beta coefficient. These findings are used to derive a statistical test for the beta coefficient and to construct a confidence interval for the beta coefficient. Moreover, we show that the sample estimator is an unbiased estimator for the beta coefficient. The theoretical results are implemented in an empirical study. Full article
(This article belongs to the Special Issue Portfolio Optimization and Risk Management: New Development and Applications)
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30 pages, 3450 KiB  
Article
The Optimum Leverage Level of the Banking Sector
by Sagara Dewasurendra, Pedro Judice and Qiji Zhu
Risks 2019, 7(2), 51; https://doi.org/10.3390/risks7020051 - 01 May 2019
Cited by 6 | Viewed by 4247
Abstract
Banks make profits from the difference between short-term and long-term loan interest rates. To issue loans, banks raise funds from capital markets. Since the long-term loan rate is relatively stable, but short-term interest is usually variable, there is an interest rate risk. Therefore, [...] Read more.
Banks make profits from the difference between short-term and long-term loan interest rates. To issue loans, banks raise funds from capital markets. Since the long-term loan rate is relatively stable, but short-term interest is usually variable, there is an interest rate risk. Therefore, banks need information about the optimal leverage strategies based on the current economic situation. Recent studies on the economic crisis by many economists showed that the crisis was due to too much leveraging by “big banks”. This leveraging turns out to be close to Kelly’s optimal point. It is known that Kelly’s strategy does not address risk adequately. We used the return–drawdown ratio and inflection point of Kelly’s cumulative return curve in a finite investment horizon to derive more conservative leverage levels. Moreover, we carried out a sensitivity analysis to determine strategies during a period of interest rates increase, which is the most important and risky period to leverage. Thus, we brought theoretical results closer to practical applications. Furthermore, by using the sensitivity analysis method, banks can change the allocation sizes to loans with different maturities to mediate the risks corresponding to different monetary policy environments. This provides bank managers flexible tools in mitigating risk. Full article
(This article belongs to the Special Issue Portfolio Optimization and Risk Management: New Development and Applications)
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17 pages, 495 KiB  
Article
Peer-To-Peer Lending: Classification in the Loan Application Process
by Xinyuan Wei, Jun-ya Gotoh and Stan Uryasev
Risks 2018, 6(4), 129; https://doi.org/10.3390/risks6040129 - 09 Nov 2018
Cited by 5 | Viewed by 4622
Abstract
This paper studies the peer-to-peer lending and loan application processing of LendingClub. We tried to reproduce the existing loan application processing algorithm and find features used in this process. Loan application processing is considered a binary classification problem. We used the area under [...] Read more.
This paper studies the peer-to-peer lending and loan application processing of LendingClub. We tried to reproduce the existing loan application processing algorithm and find features used in this process. Loan application processing is considered a binary classification problem. We used the area under the ROC curve (AUC) for evaluation of algorithms. Features were transformed with splines for improving the performance of algorithms. We considered three classification algorithms: logistic regression, buffered AUC (bAUC) maximization, and AUC maximization.With only three features, Debt-to-Income Ratio, Employment Length, and Risk Score, we obtained an AUC close to 1. We have done both in-sample and out-of-sample evaluations. The codes for cross-validation and solving problems in a Portfolio Safeguard (PSG) format are in the Appendix. The calculation results with the data and codes are posted on the website and are available for downloading. Full article
(This article belongs to the Special Issue Portfolio Optimization and Risk Management: New Development and Applications)
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15 pages, 514 KiB  
Article
A Threshold Type Policy for Trading a Mean-Reverting Asset with Fixed Transaction Costs
by Phong Luu, Jingzhi Tie and Qing Zhang
Risks 2018, 6(4), 107; https://doi.org/10.3390/risks6040107 - 29 Sep 2018
Cited by 1 | Viewed by 2513
Abstract
A mean-reverting model is often used to capture asset price movements fluctuating around its equilibrium. A common strategy trading such mean-reverting asset is to buy low and sell high. However, determining these key levels in practice is extremely challenging. In this paper, we [...] Read more.
A mean-reverting model is often used to capture asset price movements fluctuating around its equilibrium. A common strategy trading such mean-reverting asset is to buy low and sell high. However, determining these key levels in practice is extremely challenging. In this paper, we study the optimal trading of such mean-reverting asset with a fixed transaction (commission and slippage) cost. In particular, we focus on a threshold type policy and develop a method that is easy to implement in practice. We formulate the optimal trading problem in terms of a sequence of optimal stopping times. We follow a dynamic programming approach and obtain the value functions by solving the associated HJB equations. The optimal threshold levels can be found by solving a set of quasi-algebraic equations. In addition, a verification theorem is provided together with sufficient conditions. Finally, a numerical example is given to illustrate our results. We note that a complete treatment of this problem was done recently by Leung and associates. Nevertheless, our work was done independently and focuses more on developing necessary optimality conditions. Full article
(This article belongs to the Special Issue Portfolio Optimization and Risk Management: New Development and Applications)
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