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34 pages, 3898 KiB  
Article
Particle Swarm Optimization Algorithm for Determining Global Optima of Investment Portfolio Weight Using Mean-Value-at-Risk Model in Banking Sector Stocks
by Moh. Alfi Amal, Herlina Napitupulu and Sukono
Mathematics 2024, 12(24), 3920; https://doi.org/10.3390/math12243920 - 12 Dec 2024
Viewed by 684
Abstract
Computational algorithms are systematically written instructions or steps used to solve logical and mathematical problems with computers. These algorithms are crucial to rapidly and efficiently analyzing complex data, especially in global optimization problems like portfolio investment optimization. Investment portfolios are created because investors [...] Read more.
Computational algorithms are systematically written instructions or steps used to solve logical and mathematical problems with computers. These algorithms are crucial to rapidly and efficiently analyzing complex data, especially in global optimization problems like portfolio investment optimization. Investment portfolios are created because investors seek high average returns from stocks and must also consider the risk of loss, which is measured using the value at risk (VaR). This study aims to develop a computational algorithm based on the metaheuristic particle swarm optimization (PSO) model, which can be used to solve global optimization problems in portfolio investment. The data used in the simulation of the developed computational algorithm consist of daily stock returns from the banking sector traded in the Indonesian capital market. The quantitative research methodology involves formulating an algorithm to solve the global optimization problem in portfolio investment with mathematical calculations and quantitative data analysis. The objective function is to maximize the mean-value-at-risk model for portfolio investment, with constraints on the capital allocation weights in each stock within the portfolio. The results of this study indicate that the adapted PSO algorithm successfully determines the optimal portfolio weight composition, calculates the expected return and VaR in the optimal portfolio, creates an efficient frontier surface graph, and establishes portfolio performance measures. Across 50 trials, the algorithm records an average expected return of 0.000737, a return standard deviation of 0.00934, a value at risk of 0.01463, and a Sharpe ratio of 0.0504. Further evaluation of the PSO algorithm’s performance shows high consistency in generating optimal portfolios with appropriate parameter selection. The novelty of this research lies in developing an accurate computational algorithm for determining the global optima of mean-value-at-risk portfolio investments, yielding precise, consistent results with relatively fast computation times. The contribution to users is an easy-to-use tool for computational analysis that can assist in decision-making for portfolio investment formation. Full article
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<p>The minimum of <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </semantics></math> is the maximum of <math display="inline"><semantics> <mrow> <mo>−</mo> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>BBCA stock closing price (blue line) and the trendline for the stock closing price (red dotted line).</p>
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<p>Chart of BBCA stock’s daily return.</p>
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<p>Distribution model assumption chart for daily returns of BBCA stock (<b>a</b>) and BBTN stock (<b>b</b>).</p>
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<p>Iteration plot for each value of <math display="inline"><semantics> <mrow> <mi>τ</mi> </mrow> </semantics></math>.</p>
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<p>Efficient frontier portfolio chart.</p>
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<p>Portfolio performance chart.</p>
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22 pages, 428 KiB  
Article
Estimation of Conditional Covariance Matrices for a Class of High-Dimensional Varying Coefficient Factor-Generalized Autoregressive Conditional Heteroscedasticity Model
by Yujiao Liu, Yuan Li and Xingfa Zhang
Symmetry 2024, 16(12), 1635; https://doi.org/10.3390/sym16121635 - 10 Dec 2024
Viewed by 563
Abstract
This paper explores a class of High-Dimensional Varying Coefficient Factor-GARCH (Generalized Autoregressive Conditional Heteroscedasticity) model, designed to capture dynamic relationships between variables and account for the heterogeneity of time series data. By exploiting the structure of the model, a mixed approach is proposed [...] Read more.
This paper explores a class of High-Dimensional Varying Coefficient Factor-GARCH (Generalized Autoregressive Conditional Heteroscedasticity) model, designed to capture dynamic relationships between variables and account for the heterogeneity of time series data. By exploiting the structure of the model, a mixed approach is proposed to estimate conditional covariance matrices. Furthermore, asymptotic properties for the estimators are established, providing a theoretical foundation for their consistency and efficiency. A simulation study is conducted to demonstrate the performance of estimators, and a real data example of portfolio allocation is presented to illustrate the practical application of the approach. Full article
(This article belongs to the Section Mathematics)
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<p>Annualized Sharpe ratios under the three-factor model (49 industrial portfolios).</p>
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<p>Annualized Sharpe ratios under the three-factor model (30 industrial portfolios).</p>
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<p>Annualized Sharpe ratios under the Carhart four-factor model.</p>
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16 pages, 570 KiB  
Article
Generative Bayesian Computation for Maximum Expected Utility
by Nick Polson, Fabrizio Ruggeri and Vadim Sokolov
Entropy 2024, 26(12), 1076; https://doi.org/10.3390/e26121076 - 10 Dec 2024
Viewed by 473
Abstract
Generative Bayesian Computation (GBC) methods are developed to provide an efficient computational solution for maximum expected utility (MEU). We propose a density-free generative method based on quantiles that naturally calculates expected utility as a marginal of posterior quantiles. Our approach uses a deep [...] Read more.
Generative Bayesian Computation (GBC) methods are developed to provide an efficient computational solution for maximum expected utility (MEU). We propose a density-free generative method based on quantiles that naturally calculates expected utility as a marginal of posterior quantiles. Our approach uses a deep quantile neural estimator to directly simulate distributional utilities. Generative methods only assume the ability to simulate from the model and parameters and as such are likelihood-free. A large training dataset is generated from parameters, data and a base distribution. Then, a supervised learning problem is solved as a non-parametric regression of generative utilities on outputs and base distribution. We propose the use of deep quantile neural networks. Our method has a number of computational advantages, primarily being density-free and an efficient estimator of expected utility. A link with the dual theory of expected utility and risk taking is also described. To illustrate our methodology, we solve an optimal portfolio allocation problem with Bayesian learning and power utility (also known as the fractional Kelly criterion). Finally, we conclude with directions for future research. Full article
(This article belongs to the Special Issue Deep Generative Modeling: Theory and Applications)
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<p>Density for prior, likelihood and posterior, distortion function, and 1 − <math display="inline"><semantics> <mo>Φ</mo> </semantics></math> for the prior and posterior of the normal-normal model.</p>
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<p>Left panel (<b>a</b>) shows plot of sorted values of <span class="html-italic">z</span> vs. sorted values of random draws from <math display="inline"><semantics> <mrow> <mo>−</mo> <mo form="prefix">exp</mo> <mo>(</mo> <mo>−</mo> <mi>ω</mi> <mo>*</mo> <mi>W</mi> <mo>)</mo> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>. Right panel (<b>b</b>) shows values of integral of <span class="html-italic">Z</span> with respect to <span class="html-italic">z</span> vs. the corresponding values of <math display="inline"><semantics> <mi>ω</mi> </semantics></math>. The integral was calculated using the trapezoid rule. The red vertical line corresponds to <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, which is the analytical optimum.</p>
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29 pages, 1079 KiB  
Article
Large Drawdowns and Long-Term Asset Management
by Eric Jondeau and Alexandre Pauli
J. Risk Financial Manag. 2024, 17(12), 552; https://doi.org/10.3390/jrfm17120552 - 10 Dec 2024
Viewed by 485
Abstract
Long-term investors are often hesitant to invest in assets or strategies prone to significant drawdowns, primarily due to the challenge of predicting these drawdowns. This study presents a multivariate Markov-switching model for small- and large-cap returns in the U.S. equity markets, demonstrating that [...] Read more.
Long-term investors are often hesitant to invest in assets or strategies prone to significant drawdowns, primarily due to the challenge of predicting these drawdowns. This study presents a multivariate Markov-switching model for small- and large-cap returns in the U.S. equity markets, demonstrating that three distinct regimes are necessary to capture the negative trends in expected returns during financial crises. Our findings indicate that this framework enhances the prediction of conditional drawdowns compared to standard alternative models of financial returns. Furthermore, out-of-sample analysis shows that investment strategies based on these predictions outperform those relying on models with one or two regimes. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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<p>Evolution of ADD, CDD, and MDD over non-overlapping subsamples. The figure displays the evolution in percentage of ADD, <math display="inline"><semantics> <mrow> <mn>20</mn> <mo>%</mo> </mrow> </semantics></math> CDD, and MDD over various non-overlapping subsamples (from one to four quarters) between 1926 and 2020. The straight line on right plots corresponds to <math display="inline"><semantics> <mrow> <mn>10</mn> <mo>%</mo> </mrow> </semantics></math> CED. The black lines correspond to the small caps, the red dashed lines to the large caps. CED is computed with 376, 188, and 94 observations for the one-quarter, two-quarter, and four-quarter horizons, respectively.</p>
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<p>Filtered Probability of Being in the Bear State. The figure displays the filtered probability <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mrow> <mi>d</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> of being in the low expected return regime (bear state), for the two-regime and three-regime models. The horizontal blue line corresponds to the stationary probability of being in the bear state <math display="inline"><semantics> <mrow> <msub> <mi>π</mi> <mrow> <mi>b</mi> <mo>,</mo> <mo>∞</mo> </mrow> </msub> <mo>=</mo> <mo form="prefix">Pr</mo> <mrow> <mo>[</mo> <msub> <mi>S</mi> <mrow> <mi>d</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>k</mi> <mi>b</mi> </msub> <mo>]</mo> </mrow> </mrow> </semantics></math>, where <math display="inline"><semantics> <msub> <mi>k</mi> <mi>b</mi> </msub> </semantics></math> denotes the bear state.</p>
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<p>Out-of-Sample Optimal Weights—Two-quarter Horizon (1990–2020). The figure displays the temporal evolution of the optimal weight of small caps for the <math display="inline"><semantics> <mrow> <mn>20</mn> <mo>%</mo> </mrow> </semantics></math> CDD, MDD, <math display="inline"><semantics> <mrow> <mn>10</mn> <mo>%</mo> </mrow> </semantics></math> CED, and MV portfolios over the two-quarter horizon, when predictions are based on the one-regime, two-regime, and three-regime models.</p>
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<p>Model Parameters: One-regime Models.</p>
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<p>Model Parameters: Two-regime Models.</p>
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<p>Model Parameters: Three-regime Models.</p>
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33 pages, 3721 KiB  
Article
Investment Portfolio Allocation and Insurance Solvency: New Evidence from Insurance Groups in the Era of Solvency II
by Thomas Poufinas and Evangelia Siopi
Risks 2024, 12(12), 191; https://doi.org/10.3390/risks12120191 - 29 Nov 2024
Viewed by 868
Abstract
This study examines the effect of the investment portfolio structure on insurers’ solvency, as measured by the Solvency Capital Requirement ratio. An empirical sample of 88 EU-based insurance groups was analyzed to provide robust evidence of the portfolio’s impact on the Solvency Capital [...] Read more.
This study examines the effect of the investment portfolio structure on insurers’ solvency, as measured by the Solvency Capital Requirement ratio. An empirical sample of 88 EU-based insurance groups was analyzed to provide robust evidence of the portfolio’s impact on the Solvency Capital Requirement ratio from 2016 to 2022. Linear regression and supervised machine learning models, particularly extra trees regression, were used to predict the solvency ratios, with the latter outperforming the former. The investigation was supplemented with panel data analysis. Firm-specific factors, including, unit-linked and index-linked liabilities, firm size, investments in property, collective undertakings, bonds and equities, and the ratio of government bonds to corporate bonds and country-specific factors, such as life and non-life market concentration, domestic bond market development, private debt development, household spending, banking concentration, non-performing loans, and CO2 emissions, were found to have an important effect on insurers’ solvency ratios. The novelty of this research lies in the investigation of the connection of solvency ratios with variables that prior studies have not yet explored, such as portfolio asset allocation, the life and non-life insurance market concentration, and unit-linked and index-linked products, via the employment of a battery of traditional and machine enhanced methods. Furthermore, it identifies the relation of solvency ratios with bond market development and investments in collective undertakings. Finally, it addresses the substantial solvency risks posed by the high banking sector concentration to insurers under Solvency II. Full article
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<p>Visualization of the decision trees of our dataset. Source: Authors’ estimates using Python. Code by <a href="#B101-risks-12-00191" class="html-bibr">Müller and Guido</a> (<a href="#B101-risks-12-00191" class="html-bibr">2017</a>), p. 78. Code for saving the .dot file in png and pdf from <a href="#B131-risks-12-00191" class="html-bibr">Stack Overflow</a> (<a href="#B131-risks-12-00191" class="html-bibr">2024</a>).</p>
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<p>Visualization of the random forests of our dataset. Source: Authors’ estimates using Python. Code by <a href="#B101-risks-12-00191" class="html-bibr">Müller and Guido</a> (<a href="#B101-risks-12-00191" class="html-bibr">2017</a>), p. 78. Code for saving the .dot file in png and pdf from <a href="#B131-risks-12-00191" class="html-bibr">Stack Overflow</a> (<a href="#B131-risks-12-00191" class="html-bibr">2024</a>).</p>
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<p>Visualization of the extra trees of our dataset. Source: Authors’ estimates using Python. Code by <a href="#B101-risks-12-00191" class="html-bibr">Müller and Guido</a> (<a href="#B101-risks-12-00191" class="html-bibr">2017</a>), p. 78. Code for saving the .dot file in png and pdf from <a href="#B131-risks-12-00191" class="html-bibr">Stack Overflow</a> (<a href="#B131-risks-12-00191" class="html-bibr">2024</a>).</p>
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<p>Comparison of the random forest and extra trees models. Source: Authors’ estimates using Python.</p>
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17 pages, 7514 KiB  
Article
Predicting Mutual Fund Stress Levels Utilizing SEBI’s Stress Test Parameters in MidCap and SmallCap Funds Using Deep Learning Models
by Suneel Maheshwari and Deepak Raghava Naik
Risks 2024, 12(11), 179; https://doi.org/10.3390/risks12110179 - 13 Nov 2024
Viewed by 940
Abstract
Abstract: The Association of Mutual Funds of India (AMFI), under the direction of the Securities and Exchange Board of India (SEBI), provided open access to various risk parameters with respect to MidCap and SmallCap funds for the first time from February 2024. Our [...] Read more.
Abstract: The Association of Mutual Funds of India (AMFI), under the direction of the Securities and Exchange Board of India (SEBI), provided open access to various risk parameters with respect to MidCap and SmallCap funds for the first time from February 2024. Our study utilizes AMFI datasets from February 2024 to September 2024 which consisted of 14 variables. Among these, the primary variable identified in grading mutual funds is the stress test parameter, expressed as number of days required to liquidate between 50% and 25% of the portfolio, respectively, on a pro-rata basis under stress conditions as a response variable. The objective of our paper is to build and test various neural network models which can help in predicting stress levels with the highest accuracy and specificity in MidCap and SmallCap mutual funds based on AMFI’s 14 parameters as predictors. The results suggest that the simpler neural network model architectures show higher accuracy. We used Artificial Neural Networks (ANN) over other machine learning methods due to its ability to analyze the impact of dynamic interrelationships among 14 variables on the dependent variable, independent of the statistical distribution of parameters considered. Predicting stress levels with the highest accuracy in MidCap and SmallCap mutual funds will benefit investors by reducing information asymmetry while allocating investments based on their risk tolerance. It will help policy makers in designing controls to protect smaller investors and provide warnings for funds with unusually high risk. Full article
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<p>Model 1 depicting ANN with one hidden layer and two nodes for February 2024.</p>
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<p>Model 2 presents ANN with one hidden layer and three nodes for February 2024.</p>
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<p>Model 3 depicts ANN with many nodes in the hidden layer for February 2024.</p>
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<p>Model 4 presents ANN with two hidden layer with two nodes each for February 2024.</p>
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<p>Model 5 presents ANN with two hidden layer with three nodes each for February 2024.</p>
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<p>Model 6 presents ANN with multiple nodes for two hidden layer for February 2024.</p>
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<p>Model −1 for February 2024, with estimates.</p>
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<p>Model −4 for February 2024, with estimates.</p>
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<p>Model −6 for February 2024, with estimates.</p>
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22 pages, 748 KiB  
Article
A Double Optimum New Solution Method Based on EVA and Knapsack
by Theofanis Petropoulos, Paris Patsis, Konstantinos Liapis and Evangelos Chytis
J. Risk Financial Manag. 2024, 17(11), 498; https://doi.org/10.3390/jrfm17110498 - 6 Nov 2024
Viewed by 626
Abstract
Optimizing resource allocation often requires a trade-off between multiple objectives. Since projects must be fully implemented or not at all, this issue is modeled as an integer programming problem, precisely a knapsack-type problem, where decision variables are binary (1 or 0). Projects may [...] Read more.
Optimizing resource allocation often requires a trade-off between multiple objectives. Since projects must be fully implemented or not at all, this issue is modeled as an integer programming problem, precisely a knapsack-type problem, where decision variables are binary (1 or 0). Projects may be complementary/supplementary and competitive/conflicting, meaning some are prerequisites for others, while some prevent others from being implemented. In this paper, a two-objective optimization model in the energy sector is developed, and the Non-dominated Sorting Genetic Algorithm III (NSGA III) is adopted to solve it because the NSGA-III method is capable of handling problems with non-linear characteristics as well as having multiple objectives. The objective is to maximize the overall portfolio’s EVA (Economic Value Added). EVA is different from traditional performance measures and is more appropriate because it incorporates the objectives of all stakeholders in a business. Furthermore, because each project generates different kilowatts, maximizing the total production of the portfolio is appropriate. Data from the Greek energy market show optimal solutions on the Pareto efficiency front ranging from (14.7%, 38,000) to (11.91%, 40,750). This paper offers a transparent resource allocation process for similar issues in other sectors. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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<p>Flow chart of process (Source: Author’s calculations).</p>
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<p>Pareto front (Source: Author’s calculations).</p>
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14 pages, 982 KiB  
Article
Online Investor Sentiment via Machine Learning
by Zongwu Cai and Pixiong Chen
Mathematics 2024, 12(20), 3192; https://doi.org/10.3390/math12203192 - 12 Oct 2024
Viewed by 756
Abstract
In this paper, we propose utilizing machine learning methods to determine the expected aggregated stock market risk premium based on online investor sentiment and employing the multifold forward-validation method to select the relevant hyperparameters. Our empirical studies provide strong evidence that some machine [...] Read more.
In this paper, we propose utilizing machine learning methods to determine the expected aggregated stock market risk premium based on online investor sentiment and employing the multifold forward-validation method to select the relevant hyperparameters. Our empirical studies provide strong evidence that some machine learning methods, such as extreme gradient boosting or random forest, show significant predictive ability in terms of their out-of-sample performances with high-dimensional investor sentiment proxies. They also outperform the traditional linear models, which shows a possible unobserved nonlinear relationship between online investor sentiment and risk premium. Moreover, this predictability based on online investor sentiment has a better economic value, so it improves portfolio performance for investors who need to decide the optimal asset allocation in terms of the certainty equivalent return gain and the Sharpe ratio. Full article
(This article belongs to the Special Issue Financial Econometrics and Machine Learning)
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<p>Feedforward neural network architecture.</p>
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<p>Recurrent neural network architecture.</p>
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<p>Random forest architecture.</p>
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<p>Extreme gradient boosting architecture.</p>
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24 pages, 566 KiB  
Article
Bitcoin Return Prediction: Is It Possible via Stock-to-Flow, Metcalfe’s Law, Technical Analysis, or Market Sentiment?
by Austin Shelton
J. Risk Financial Manag. 2024, 17(10), 443; https://doi.org/10.3390/jrfm17100443 - 1 Oct 2024
Viewed by 1486
Abstract
Popular methods to value Bitcoin include the stock-to-flow model, Metcalfe’s Law, technical analysis, and sentiment-related measures. Within this paper, I test whether such models and variables are predictive of Bitcoin’s returns. I find that the stock-to-flow model predictions and Metcalfe’s Law help to [...] Read more.
Popular methods to value Bitcoin include the stock-to-flow model, Metcalfe’s Law, technical analysis, and sentiment-related measures. Within this paper, I test whether such models and variables are predictive of Bitcoin’s returns. I find that the stock-to-flow model predictions and Metcalfe’s Law help to explain Bitcoin’s returns in-sample but have limited to no ability to predict Bitcoin’s returns out-of-sample. In contrast, Bitcoin market sentiment and technical analysis measures are generally unrelated to Bitcoin’s returns in-sample and are poor predictors of Bitcoin’s returns out-of-sample. Despite the poor performance of Bitcoin return predictors within out-of-sample regressions, I demonstrate that a very successful out-of-sample Bitcoin tactical allocation or “market timing” strategy is formed via blending out-of-sample univariate model predictions. This OOS-blended model trading strategy, which algorithmically allocates between Bitcoin and cash (USD), significantly outperforms buying-and-holding or “HODL”ing Bitcoin, boosting CAPM alpha by almost 1300 basis points while also increasing portfolio Sharpe Ratio and Sortino Ratio and dramatically reducing portfolio maximum drawdown relative to buying-and-holding Bitcoin. Full article
(This article belongs to the Special Issue Blockchain Technologies and Cryptocurrencies​)
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<p>Growth of USD 10,000 investment within the blended, univariate model trading strategy vs. BTC (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mo>∗</mo> </mrow> </msub> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mo> </mo> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>): The dollar value of two portfolios with initial investments of USD 10,000 on 1st June 2018 is plotted up through 29th February 2024. The portfolio in dotted blue is a buy-and-hold Bitcoin (BTC) portfolio. The portfolio in solid red is the “base” parameterization of the OOS blended, univariate model trading strategy as described in <a href="#sec2-jrfm-17-00443" class="html-sec">Section 2</a>. The steady-state allocation to Bitcoin within the “base” parameterization of the OOS blended, univariate model trading strategy, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mo>∗</mo> </mrow> </msub> </mrow> </semantics></math>, is 0.5. The leverage applied to this portfolio, <math display="inline"><semantics> <mrow> <mi>l</mi> </mrow> </semantics></math>, is 1. This portfolio holds, on average, allocations of 50% Bitcoin and 50% USD, with a minimum allocation of 0% to Bitcoin and s maximum allocation of 100% to Bitcoin. The OOS blended, univariate model trading strategy backtest assumes that trading costs and fees are 40 bp (0.4%) of the trade size; thus, the strategy’s portfolio returns in solid red are estimated net of trading costs and fees.</p>
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26 pages, 3867 KiB  
Article
A Unique Bifuzzy Manufacturing Service Composition Model Using an Extended Teaching-Learning-Based Optimization Algorithm
by Yushu Yang, Jie Lin and Zijuan Hu
Mathematics 2024, 12(18), 2947; https://doi.org/10.3390/math12182947 - 22 Sep 2024
Viewed by 850
Abstract
In today’s competitive and rapidly evolving manufacturing environment, optimizing the composition of manufacturing services is critical for effective supply chain deployment. Since the manufacturing environment involves many two-fold uncertainties, there are limited studies that have specifically tackled these two-fold uncertainties. Based on bifuzzy [...] Read more.
In today’s competitive and rapidly evolving manufacturing environment, optimizing the composition of manufacturing services is critical for effective supply chain deployment. Since the manufacturing environment involves many two-fold uncertainties, there are limited studies that have specifically tackled these two-fold uncertainties. Based on bifuzzy theory, we put forward a unique bifuzzy manufacturing service portfolio model. Through the application of the fuzzy variable to express quality of service (QoS) value of manufacturing services, this model also accounts for the preferences of manufacturing firms by allocating various weights to different sub-tasks. Next, we address the multi-objective optimization issue through the application of extended teaching-learning-based optimization (ETLBO) algorithm. The improvements of the ETLBO algorithm include utilizing the adaptive parameters and introducing a local search strategy combined with a genetic algorithm (GA). Finally, we conduct simulation experiments to show off the efficacy and efficiency of the suggested approach in comparison to six other benchmark algorithms. Full article
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<p>Framework for the model of manufacturing service portfolio under bifuzzy environment.</p>
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<p>The four fundamental structures of manufacturing service composition.</p>
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<p>The local search strategy combined with GA in ETLBO algorithm.</p>
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<p>The entire flow of the ETLBO algorithm.</p>
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<p>The evolutionary curves of fitness value among various algorithms.</p>
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<p>Comparison results of fitness with various initial population sizes between various algorithms.</p>
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<p>Comparison results of fitness with various numbers of candidate manufacturing services.</p>
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<p>Comparison results of fitness with various numbers of candidate manufacturing services.</p>
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<p>Comparison results of fitness with different numbers of sub-tasks between various algorithms.</p>
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<p>Comparison results of fitness with different numbers of sub-tasks between various algorithms.</p>
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<p>Comparison results of running time with various quantities of candidate manufacturing services.</p>
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<p>Comparison results of running time with various quantities of candidate manufacturing services.</p>
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<p>Comparison results of running time with different numbers of sub-tasks.</p>
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<p>Comparison results of running time with different numbers of sub-tasks.</p>
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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 1133
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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<p><math display="inline"><semantics> <msub> <mi mathvariant="script">G</mi> <mrow> <mi>eff</mi> </mrow> </msub> </semantics></math> as graph of <math display="inline"><semantics> <msub> <mi>γ</mi> <mrow> <mo>∣</mo> <mi>J</mi> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>ν</mi> <mrow> <mo>∣</mo> <mi>I</mi> </mrow> </msub> </semantics></math> (see (<a href="#B18-risks-12-00132" class="html-bibr">Maier-Paape et al. 2023</a>), fig. 2.2).</p>
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<p><math display="inline"><semantics> <msub> <mi mathvariant="script">G</mi> <mrow> <mi>eff</mi> </mrow> </msub> </semantics></math> examples for a risk function <math display="inline"><semantics> <mi mathvariant="fraktur">r</mi> </semantics></math> with non-negative values (see (<a href="#B18-risks-12-00132" class="html-bibr">Maier-Paape et al. 2023</a>), fig. 2.4).</p>
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<p>The efficient frontier <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="script">G</mi> <mrow> <mi>eff</mi> <mo>,</mo> <mo>*</mo> </mrow> <mrow> <mo>(</mo> <mn>2</mn> <mi>d</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi mathvariant="script">G</mi> <mrow> <mi>eff</mi> </mrow> <mrow> <mo>(</mo> <mn>2</mn> <mi>d</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <msup> <mi mathvariant="fraktur">r</mi> <mo>*</mo> </msup> <mo>,</mo> <msup> <mrow> <mi mathvariant="fraktur">u</mi> </mrow> <mo>*</mo> </msup> <mo>;</mo> <mspace width="0.166667em"/> <msup> <mi>A</mi> <mo>*</mo> </msup> <mo>)</mo> </mrow> <mo>⊂</mo> <msup> <mi mathvariant="double-struck">R</mi> <mn>3</mn> </msup> </mrow> </semantics></math> is build by three transparent “cord” facets.</p>
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32 pages, 3410 KiB  
Article
A Data Analytics and Machine Learning Approach to Develop a Technology Roadmap for Next-Generation Logistics Utilizing Underground Systems
by Seok Jin Youn, Yong-Jae Lee, Ha-Eun Han, Chang-Woo Lee, Donggyun Sohn and Chulung Lee
Sustainability 2024, 16(15), 6696; https://doi.org/10.3390/su16156696 - 5 Aug 2024
Cited by 2 | Viewed by 1406
Abstract
The increasing density of urban populations has spurred interest in utilizing underground space. Underground logistics systems (ULS) are gaining traction due to their effective utilization of this space to enhance urban spatial efficiency. However, research on technological advancements in related fields remains limited. [...] Read more.
The increasing density of urban populations has spurred interest in utilizing underground space. Underground logistics systems (ULS) are gaining traction due to their effective utilization of this space to enhance urban spatial efficiency. However, research on technological advancements in related fields remains limited. To address this gap, we applied a data-driven approach using patent data related to the ULS to develop a technology roadmap for the field. We employed Latent Dirichlet Allocation (LDA), a machine learning-based topic modeling technique, to categorize and identify six specific technology areas within the ULS domain. Subsequently, we conducted portfolio analytics to pinpoint technology areas with high technological value and to identify the major patent applicants in these areas. Finally, we assessed the technology market potential by mapping the technology life cycle for the identified high-value areas. Among the six technology areas identified, Topic 1 (Underground Material Handling System) and Topic 4 (Underground Transportation System) showed significant patent activity from companies and research institutions in China, the United States, South Korea, and Germany compared to other countries. These areas have the top 10 patent applicants, accounting for 20.8% and 13.6% of all patent applications, respectively. Additionally, technology life cycle analytics revealed a growth trajectory for these identified areas, indicating their rapid expansion and high innovation potential. This study provides a data-driven methodology to develop a technology roadmap that offers valuable insights for researchers, engineers, and policymakers in the ULS industry and supports informed decision-making regarding the field’s future direction. Full article
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<p>Research flow chart based on the analytics methodology.</p>
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<p>Example of Pentagon Visualization.</p>
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<p>DTM of the Technology Topic for Analytics.</p>
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<p>Technology Life Cycle Evaluation.</p>
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<p>Derive the Optimal Topic through Calculation of Perplexity.</p>
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<p>Visualizing Countries’ Patent Application Distribution.</p>
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<p>Result of Pentagon Visualization.</p>
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<p>Visualizing Topic 1’s Application Frequency Changes for the Top 10 Applicant Countries.</p>
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<p>Visualizing Topic 4’s Application Frequency Changes for the Top 10 Applicant Countries.</p>
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<p>TLC Analytics Results in Topics with High-Value Areas.</p>
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32 pages, 393 KiB  
Article
Crises and Contagion in Equity Portfolios
by Christos Floros, Dimitrios Vortelinos and Ioannis Chatziantoniou
Economies 2024, 12(7), 168; https://doi.org/10.3390/economies12070168 - 1 Jul 2024
Viewed by 1070
Abstract
We examine the international impact of recent financial crises on contagion dynamics within international equity portfolios. First, we highlight the importance of macroeconomics for portfolio weighting for each region, and then we examine contagion via a structural regime-switching model and a contagion test. [...] Read more.
We examine the international impact of recent financial crises on contagion dynamics within international equity portfolios. First, we highlight the importance of macroeconomics for portfolio weighting for each region, and then we examine contagion via a structural regime-switching model and a contagion test. We also examine sources of contagion using regime variables, crisis events, and macroeconomic variables. In particular, we study the Argentine debt crisis, the US financial crisis, and the EU sovereign debt crisis. The macroeconomic variables include changes in market capitalization, trade integration, GDP growth, inflation rate, and interest rate. We also employ two classifications, one relating to the portfolio weighting scheme and another one that considers implied global and regional betas. The empirical findings reveal the existence of financial contagion for all the crises that we investigate. Both methods produce similar results. Stronger contagion is evident for global rather than regional betas. Europe is the region with the highest level of contagion and the one mostly affected by the crises. As far as macroeconomic variables are concerned, they are very important in two ways. They statistically significantly explain contagion, while they also reveal contagion under various portfolio weighting schemes. Both methods suggest that the Argentinian crisis mainly contributes to contagion. The research implications suggest that asset allocation and portfolio management should consider both the global and the regional aspects of contagion as differences can occur. Full article
34 pages, 1965 KiB  
Article
Portfolio Optimization with Sector Return Prediction Models
by Wolfgang Bessler and Dominik Wolff
J. Risk Financial Manag. 2024, 17(6), 254; https://doi.org/10.3390/jrfm17060254 - 20 Jun 2024
Cited by 1 | Viewed by 2343
Abstract
We analyze return predictability for U.S. sectors based on fundamental, macroeconomic, and technical indicators and analyze whether return predictions improve tactical asset allocation decisions. We study the out-of-sample predictive power of individual variables for forecasting sector returns and analyze multivariate predictive regression models, [...] Read more.
We analyze return predictability for U.S. sectors based on fundamental, macroeconomic, and technical indicators and analyze whether return predictions improve tactical asset allocation decisions. We study the out-of-sample predictive power of individual variables for forecasting sector returns and analyze multivariate predictive regression models, including OLS, regularized regressions, principal component regressions, the three-pass regression filter, and forecast combinations. Using an out-of-sample Black–Litterman portfolio optimization framework and employing predicted returns as investors’ ‘views’, we evaluate the benefits of sector return forecasts for investors. We find that portfolio optimization with sector return prediction models significantly outperforms portfolios using historical averages as well as passive benchmark portfolios. Full article
(This article belongs to the Special Issue Portfolio Selection and Risk Analytics)
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Figure A1
<p>Distribution of returns. Notes: This figure shows the distribution of BL-optimized portfolio returns during the full period from January 1989 to December 2013 using the indicated return forecast models.</p>
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<p>Allocations over time. Notes: This figure shows the portfolio allocation of BL-optimized portfolios over the full period from January 1989 to December 2013 using the indicated return forecast models.</p>
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27 pages, 1929 KiB  
Article
Bayesian Learning in an Affine GARCH Model with Application to Portfolio Optimization
by Marcos Escobar-Anel, Max Speck and Rudi Zagst
Mathematics 2024, 12(11), 1611; https://doi.org/10.3390/math12111611 - 21 May 2024
Viewed by 1481
Abstract
This paper develops a methodology to accommodate uncertainty in a GARCH model with the goal of improving portfolio decisions via Bayesian learning. Given the abundant evidence of uncertainty in estimating expected returns, we focus our analyses on the single parameter driving expected returns. [...] Read more.
This paper develops a methodology to accommodate uncertainty in a GARCH model with the goal of improving portfolio decisions via Bayesian learning. Given the abundant evidence of uncertainty in estimating expected returns, we focus our analyses on the single parameter driving expected returns. After deriving an Uncertainty-Implied GARCH (UI-GARCH) model, we investigate how learning about uncertainty affects investments in a dynamic portfolio optimization problem. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize her expected utility from terminal wealth under an Affine GARCH(1,1) model. The corresponding stock evolution, and therefore, the wealth process, is treated as a Bayesian information model that learns about the expected return with each period. We explore the one- and two-period cases, demonstrating a significant impact of uncertainty on optimal allocation and wealth-equivalent losses, particularly in the case of a small sample size or large standard errors in the parameter estimation. These analyses are conducted under well-documented parametric choices. The methodology can be adapted to other GARCH models and applications beyond portfolio optimization. Full article
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<p>Standard error dependence on sample size.</p>
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<p>Histogram for <math display="inline"><semantics> <msub> <mi>π</mi> <mn>1</mn> </msub> </semantics></math> with C-H-J-2006 parameters of 100,000 scenarios. The portfolio weight without uncertainty (red line) is <math display="inline"><semantics> <mrow> <msub> <mi>π</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.5453</mn> </mrow> </semantics></math>. The mean (black line) is given by <math display="inline"><semantics> <mrow> <mn>0.5453</mn> </mrow> </semantics></math>.</p>
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<p>Histogram of 100,000 scenarios for <math display="inline"><semantics> <msub> <mi>π</mi> <mn>1</mn> </msub> </semantics></math> with C-H-J-2006 with annually scaled parameters (<b>left</b>) and an adjusted <math display="inline"><semantics> <msub> <mi>σ</mi> <mn>0</mn> </msub> </semantics></math> corresponding to a sample size of <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> (<b>right</b>). The portfolio weight without uncertainty (red line) is <math display="inline"><semantics> <mrow> <msub> <mi>π</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.5453</mn> </mrow> </semantics></math>. The mean (black line) is given by <math display="inline"><semantics> <mrow> <mn>0.5319</mn> </mrow> </semantics></math> (<b>left</b>) and <math display="inline"><semantics> <mrow> <mn>0.5436</mn> </mrow> </semantics></math> (<b>right</b>).</p>
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<p>Sensitivity of <math display="inline"><semantics> <msub> <mi>π</mi> <mn>0</mn> </msub> </semantics></math> and the mean of <math display="inline"><semantics> <msub> <mi>π</mi> <mn>1</mn> </msub> </semantics></math> with respect to variation in risk aversion <math display="inline"><semantics> <mi>γ</mi> </semantics></math> for daily C-H-J-2006 parameters (<b>left</b>) and annual C-H-J-2006 parameters (<b>right</b>) parameters.</p>
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<p>Sensitivity of <math display="inline"><semantics> <msub> <mi>π</mi> <mn>0</mn> </msub> </semantics></math> and the mean of <math display="inline"><semantics> <msub> <mi>π</mi> <mn>1</mn> </msub> </semantics></math> with respect to variation in <math display="inline"><semantics> <msub> <mi>σ</mi> <mn>0</mn> </msub> </semantics></math> for daily C-H-J-2006 parameters (<b>left</b>) and annual C-H-J-2006 parameters (<b>right</b>) parameters.</p>
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<p>Sensitivity of <math display="inline"><semantics> <msub> <mi>π</mi> <mn>1</mn> </msub> </semantics></math> with respect to variation in <math display="inline"><semantics> <msub> <mi>σ</mi> <mn>0</mn> </msub> </semantics></math> (<b>left</b>) resp. risk aversion <math display="inline"><semantics> <mi>γ</mi> </semantics></math> (<b>right</b>) simulated 100,000 times using C-H-J-2006 annual parameters.</p>
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<p>Annualized WEL in two-periods for daily C-H-J-2006 parameters (<b>left</b>) and annually scaled C-H-J-2006 parameters (<b>right</b>) depending on sample size.</p>
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<p>Annualized WEL in two-periods for daily C-H-J-2006 parameters (<b>left</b>) and annual C-H-J-2006 parameters (<b>right</b>) depending on sample size and risk aversion <math display="inline"><semantics> <mi>γ</mi> </semantics></math>.</p>
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<p>Sensitivity of <math display="inline"><semantics> <msub> <mi>π</mi> <mn>0</mn> </msub> </semantics></math> with respect to variation in <math display="inline"><semantics> <msub> <mi>z</mi> <mn>0</mn> </msub> </semantics></math> for daily C-H-J-2006 parameters (<b>left</b>) and annual C-H-J-2006 parameters (<b>right</b>) parameters.</p>
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<p>Front view on <a href="#mathematics-12-01611-f006" class="html-fig">Figure 6</a>: Sensitivity of <math display="inline"><semantics> <msub> <mi>π</mi> <mn>1</mn> </msub> </semantics></math> with respect to variation in <math display="inline"><semantics> <msub> <mi>σ</mi> <mn>0</mn> </msub> </semantics></math> (<b>left</b>) resp. risk aversion <math display="inline"><semantics> <mi>γ</mi> </semantics></math> (<b>right</b>) simulated 100 000 times using C-H-J-2006 annual parameters.</p>
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<p>Histogram for <math display="inline"><semantics> <msub> <mi>π</mi> <mn>1</mn> </msub> </semantics></math> with B-C-H-J-2018 parameters of 100,000 scenarios. The portfolio weight without uncertainty is shown in red.</p>
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<p>Histogram of 100,000 scenarios for <math display="inline"><semantics> <msub> <mi>π</mi> <mn>1</mn> </msub> </semantics></math> with B-C-H-J-2018 with annually scaled parameters (<b>left</b>) and to a sample size of <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> adjusted <math display="inline"><semantics> <msub> <mi>σ</mi> <mn>0</mn> </msub> </semantics></math> (<b>right</b>). The portfolio weight without uncertainty is shown in red.</p>
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<p>Sensitivity of <math display="inline"><semantics> <msub> <mi>π</mi> <mn>0</mn> </msub> </semantics></math> and the mean of <math display="inline"><semantics> <msub> <mi>π</mi> <mn>1</mn> </msub> </semantics></math> with respect to variation in <math display="inline"><semantics> <msub> <mi>σ</mi> <mn>0</mn> </msub> </semantics></math> for daily B-C-H-J-2018 parameters (<b>left</b>) and annual B-C-H-J-2018 parameters (<b>right</b>) parameters.</p>
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<p>Annualized WEL in two-periods for daily B-C-H-J-2018 parameters (<b>left</b>) and annual B-C-H-J-2018 parameters (<b>right</b>) depending on sample size and risk aversion <math display="inline"><semantics> <mi>γ</mi> </semantics></math>.</p>
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