Variance Framework Research Articles

Employing behavioural portfolio theory for sustainable investment: Examining drawdown risks and ESG factors

ABSTRACT This study uses behavioural portfolio theory (BPT) within the Markowitz Portfolio Theory framework to enhance portfolio management by focusing on sustainability and risk mitigation during market downturns. It selects portfolios to hedge against market lows using Conditional Drawdown at Risk (CDaR) and Expected Regret of Drawdown (ERoD). These measures help choose securities that perform well during a market decline. This study applies drawdown-based risk metrics to assist institutional investors and fiduciaries in making informed investment and fund management decisions. By merging BPT with Markowitz’s mean–variance framework, selected investments are maintained above a safety threshold, contributing to the portfolio’s overall quality and sustainability. Additionally, by incorporating an Environmental, Social, and Governance (ESG) preference function, the findings suggest that BPT built portfolios meet traditional performance standards and align with socially responsible investment principles, thereby offering higher utility and alignment with investor values focused on sustainable investing.

Elliptically-Contoured Tensor-variate Distributions with Application to Image Learning

Statistical analysis of tensor-valued data has largely used the tensor-variate normal (TVN) distribution that may be inadequate for data arising from distributions with heavier or lighter tails. We study a general family of elliptically contoured (EC) tensor-variate distributions and derive its characterizations, moments, marginal and conditional distributions. We describe procedures for maximum likelihood estimation from data that are (1) uncorrelated draws from an EC distribution, (2) from a scale mixture of the TVN distribution, and (3) from an underlying but unknown EC distribution, for which we extend Tyler’s robust estimator. A detailed simulation study highlights the benefits of choosing an EC distribution over the TVN for heavier-tailed data. We develop tensor-variate classification rules using discriminant analysis and EC errors and show that they better predict cats and dogs from images in the Animal Faces-HQ dataset than the TVN-based rules. A novel tensor-on-tensor regression and tensor-variate analysis of variance (TANOVA) framework under EC errors is also demonstrated to better characterize gender, age and ethnic origin than the usual TVN-based TANOVA in the celebrated Labeled Faces of the Wild dataset.

Volatile safe-haven asset: Evidence from Bitcoin

Despite high volatility, Bitcoin is known to offer diversification benefits through its relatively low correlation with stock markets. Unlike traditional safe-haven assets, Bitcoin prices strongly respond to time-varying correlations and diversification benefits. We find that a decrease (an increase) in correlation between Bitcoin and S&P500 index returns strongly predicts higher (lower) Bitcoin returns the next day. Under the classical mean–variance framework, we develop a stylized model of Bitcoin prices utilizing extreme disagreement among heterogeneous Bitcoin investors. When our model is calibrated to the observed predictability of Bitcoin returns, the model simultaneously explains the lack of predictability in traditional safe-haven assets such as gold and long-term treasuries.

Revisiting the modelling framework for the unresolved scalar variance

The unresolved scalar variance in large-eddy simulations of turbulent flows is a fundamental physical and modelling parameter. Despite its importance, relatively few algebraic models have been developed for this important variable with the most prominent models to date being the classic scale-similarity and gradient models. In this work a new generalized modelling framework based on reconstruction has been developed, which in contrast to classic modelling approaches allows the construction of base static variance models of arbitrary accuracy. It is demonstrated that higher-order reconstructions naturally lead to base static variance models of increased accuracy, and that the classic scale-similarity and gradient models are subsets of more general and higher-order models. The classic scale-similarity assumption for developing dynamic models is also revisited, and it is demonstrated that this can essentially be reinterpreted as a two-level reconstruction approach. Based on this result, a new general methodology is proposed that allows the construction of dynamic models for any given base static model, and a corresponding general reconstruction operator, algebraic or iterative. Consequently, improved static and dynamic models for the scalar variance are developed. The newly developed models are then thoroughly tested a priori using two high-fidelity direct numerical simulation databases corresponding to two substantially different flame and flow configurations, and are shown to outperform classic algebraic models for the variance.

The mean–variance (in)efficiency of duration‐based immunization

AbstractEmpirical studies report inconclusive assessment of duration‐based immunization, notably showing that more sophisticated strategies do not outperform immunization relying on Macaulay duration. This article provides a mean–variance framework to explain this puzzle. We characterize the efficient portfolio allocations for a stylized barbell strategy trading off reinvestment risk with discounting risk. We show, in a model‐free setting, that barbell allocations form a convex set in the mean–variance space, and the endpoints of the efficient frontier can switch as time passes, reversing the set of efficient allocations. Consequently, duration‐based immunization, which is not minimum variance, can exhibit temporary inefficiency. This result is numerically illustrated in a one‐factor Gaussian and a two‐factor non‐Gaussian model. Using yield curve scenarios resampled from U.S. data over the 1977–2020 period, we further corroborate our conclusions non‐parametrically, and find that duration‐based immunization is sometimes inefficient.

Trend Projections of Potential Evapotranspiration in Yangtze River Delta and the Uncertainty

Global warming may increase potential evapotranspiration (ETp), reducing the water resources in Yangzi River Delta. Therefore, it is important to investigate the trend of ETp there under the background of climate change. To this purpose, the systematic biases in temperature outputs of 24 global climate models (GCMs) under 3 shared socioeconomic pathways—representative concentration pathways (SSPs) emission scenarios (SSP1-2.6, SSP2-4.5, and SSP5-8.5)—are first corrected by using 8 bias correction methods. Then, the trend of ETp in Yangtze River Delta is projected by using 4 ETp calculation formulas (Blaney–Criddle, Hargreaves–Samani, Makkink, and Priestley–Taylor). The uncertainty of the projections is estimated and decomposed by using multi-way analysis of variance frameworks. The influence of uncertainty on the projected change signal is quantified by using the signal-to-noise ratio. The results show that all emission scenarios indicate robust increments of ETp. Specifically, relative to 1971~2000, ETp will increase by 0.14~0.17 mm d−1 (5.7~6.8%) during 2021~2050 and by 0.21~0.41 mm d−1 (8.5~16.7%) during 2061~2090, respectively. During 2021~2050, the uncertainty of ETp projections is dominantly contributed by the main effects of GCM (63%) and the ETp calculation formula (24%). During 2061~2090, it is mainly contributed by the main effect of GCM (36%), followed by the main effects of the emission scenario (34%) and the ETp calculation formula (18%). The ETp projections are generally reliable and robust during the two projection periods.

An Adaptive Neural Network Regression Method for Structure Identification

This article reports a study on a flexible neural network regression method within the functional analysis of variance framework that aims to adapt to the underlying structure of the target function. We develop a novel penalization scheme where a concept of node impurity is introduced in the neural network framework. The node impurity in neural networks represents the homogeneity of the effects of the inputs on the node. We first define the effect of individual input on node and in turn, measure the node impurity based on the effects of inputs on node. We adopt the sum of node impurities as a penalty function whose usage makes the connections from inputs to nodes sparse, which improves estimation accuracy by reducing unnecessary complexity and enables data-adaptive structure identification. Our method takes into account of a large parameter space of the networks ranging from a fully-connected structure to sparsely connected structures. Among possible node connection structures, an optimal model is selected based purely on observed data. Numerical studies based on simulated and real datasets show that the proposed method performs well in identifying the inherent structure of the regression function and produces good estimation accuracy. Supplementary materials for this article are available online.

Theoretical Foundations and Implications of Neural Ordinary Differential Equations (Nodes) For Real-Time Portfolio Optimization

This paper embarks on a comprehensive exploration of the theoretical landscape surrounding the integration of Neural Ordinary Differential Equations (NODEs) into the domain of real-time portfolio optimization. The study commences by establishing the background and motivation for this research, shedding light on the challenges encountered in real-time portfolio management and the potential transformative role NODEs can play in addressing these challenges. The theoretical framework unfolds in a structured manner, encompassing critical facets of portfolio optimization theory. It delves into classical portfolio optimization methodologies, including the mean- variance framework and continuous-time stochastic control techniques. This solid theoretical foundation provides the basis for understanding the nuances of optimizing portfolio weights, expected returns, and risk measures. The heart of the research lies in the integration of NODEs, an innovative fusion of deep learning and differential equations, into the fabric of portfolio optimization. NODEs, with their adaptability and ability to model continuous- time dynamics, emerge as a potent tool for real-time portfolio rebalancing and decision-making. The study provides an in-depth overview of NODEs, elucidating their architecture and their application in modeling financial time series data. This theoretical journey leads to the exploration of practical implications. The study highlights the potential benefits of incorporating NODEs into portfolio management, including improved risk management, enhanced returns, and the capacity for adaptive asset allocation strategies. However, it also addresses the limitations and challenges associated with this integration, such as data quality issues and computational requirements. In conclusion, this research presents a theoretical framework that bridges the gap between deep learning and continuous-time financial models, offering a promising avenue for real-time portfolio optimization. The insights derived from this study serve as a foundation for future research and practical applications in navigating the intricate landscape of financial markets.

Risk Budgeting portfolios: Existence and computation

AbstractModern portfolio theory has provided for decades the main framework for optimizing portfolios. Because of its sensitivity to small changes in input parameters, especially expected returns, the mean–variance framework proposed by Markowitz in 1952 has, however, been challenged by new construction methods that are purely based on risk. Among risk‐based methods, the most popular ones are Minimum Variance, Maximum Diversification, and Risk Budgeting (especially Equal Risk Contribution) portfolios. Despite some drawbacks, Risk Budgeting is particularly attracting because of its versatility: based on Euler's homogeneous function theorem, it can indeed be used with a wide range of risk measures. This paper presents mathematical results regarding the existence and the uniqueness of Risk Budgeting portfolios for a very wide spectrum of risk measures and shows that, for many of them, computing the weights of Risk Budgeting portfolios only requires a standard stochastic algorithm.

Using Cultural Variance Framework to Promote Vaccine Confidence among African Americans: A Qualitative Content Analysis of “We Can Do This” COVID-19 Vaccine Campaign

The study examines ways the cultural variance framework (CVF) enhances vaccine confidence messaging among African American healthcare consumers concerning coronavirus. The main emphasis lies in the “We Can Do This” campaign, which employs CVF to develop tailored social media, advertising, and televised commercials to actively involve African Americans and advocate for the advantages of the coronavirus vaccine. This qualitative study seeks to fill a gap in health communication literature by investigating how CVF, as a sub-feature of audience-centered messaging, engages with African Americans, encouraging their active engagement in vaccine participation. The findings reveal that contextual specificity, cultural identity, and characteristic features of the CVF play a significant role in fostering vaccine confidence among African Americans using culturally tailored messaging. The study explicates conceptual implications for future interventions prioritizing African Americans regarding health disparities.

Pricing decisions of risk averse logistic companies with carbon cap and trade under Stackelberg game.

With the implementation of the double carbon plan, this paper considers the delivery fees of two risk averse logistics companies under carbon cap and trade mechanism. We establish logistics company Stackelberg (MS) model and retailer Stackelberg (RS) model under mean variance (MV) framework, respectively. We obtain the optimal delivery fees and retail prices. We find out that the higher degree of risk aversion can lead to a lower delivery fee. We also show that a higher carbon trading price or a higher cross price sensitivity will increase delivery fees. Moreover, we indicate that the performances of logistics companies under MS scenario are higher than that RS scenario. In addition, we suggest that under the carbon cap and trade rules, in order to obtain higher profits, logistics companies should use fuel vehicle for transportation under certain conditions, and use electric vehicle in other cases.

Model averaging of machine learning algorithms for digital soil mapping: A minimum variance framework

In the digital soil mapping framework, machine learning (ML) algorithms are currently the most popular methods for the spatial prediction of soil properties. The fast developments of easy-to-use software implementations for a large panel of ML algorithms have encouraged comparison studies between algorithms, with the goal of ranking their performances and identifying the best ones among them. However, as no firm conclusions can be drawn about the best ML algorithm to be used in general, this suggests that combining a set of them could be a better approach. Numerous methods have been proposed to do so, most of them relying on a linear weighting of the individual algorithms. However, there are almost as many methods for linearly weighting ML algorithms as there are ML algorithms, thus leaving the problem unsolved. Moreover, these weighting methods are mostly used out-of-the-box, without paying a proper attention to the associated hypotheses. In this paper, we propose to address this issue by setting the problem in a more formal framework. Starting from classical hypotheses, it is shown how the benefit of averaging various ML algorithms can be estimated from their joint performances. Relying afterwards on the most commonly used linear weighting schemes, it is reminded that, as long as the performance metrics are based on mean square errors, the best averaging method is by essence the best linear (unbiased) predictor. Using a more general Bayesian framework, it is also shown that accounting for conditional biases when weighting ML algorithms is a key issue for obtaining improved predictions, and explicit formulas are proposed for that goal. Finally, these theoretical results are illustrated and discussed using a soil data set collected over an arid and semi-arid region in Iran where clay content, calcium carbonate equivalent, soil organic carbon and electrical conductivity were measured in topsoil samples.

A conditional decomposition of proper scores: quantifying the sources of information in a forecast

AbstractScoring rules condense all information regarding the performance of a probabilistic forecast into a single numerical value, providing a convenient framework with which to rank and compare competing prediction schemes objectively. Although scoring rules provide only a single measure of forecast accuracy, the expected score can be decomposed into components that each assess a distinct aspect of the forecast, such as its calibration or information content. Since these components could depend on several factors, it is useful to evaluate forecast performance under different circumstances; if a forecaster were able to identify situations in which their forecasts perform particularly poorly, then they could more easily develop their forecast strategy to account for these deficiencies. To help forecasters identify such situations, a novel decomposition of scores is introduced that quantifies conditional forecast biases, allowing for a more detailed examination of the sources of information in the forecast. From this, we claim that decompositions of proper scores provide a broad generalisation of the well‐known analysis of variance (ANOVA) framework. The new decomposition is applied to the Brier score, which is then used to evaluate forecasts that the daily maximum temperature will exceed a range of thresholds, issued by the Swiss Federal Office of Meteorology and Climatology (MeteoSwiss). We demonstrate how the additional information provided by this decomposition can be used to improve the performance of these forecasts, by identifying appropriate auxiliary information to include within statistical postprocessing methods.

Assessment of Machining of Hastelloy Using WEDM by a Multi-Objective Approach

Superalloys are a much-needed material for abundant engineering fields, such as nuclear-powered reactor components and aeronautics. Owing to their exceptional characteristics, such as higher thermal conductivity, they can be difficult to machine using conventional processes. Modern approaches to machining have evolved to utilize these materials. One of the techniques studied in this project is electrical discharge in a wire machine. This process can help to reduce the energy consumption during machining and negative impact on the environment. In addition, shortening the operation time of the machine can help to minimize its impact on the environment. The duration of the pulse and applied current are independent factors considered in this study. Material removal rate, surface roughness, dimensional deviation, and form/orientation tolerance errors are deemed as performance measures. The goal of this investigation is to reduce the time required to machine and improve the surface finish of components by implementing a Grey-based artificial neural network model. This method is useful in foretelling the conditions of the Wire Electro Discharge Machining (WEDM) process. This paper uses the Taguchi design and Analysis of Variance (ANOVA) framework to analyze the model’s variable inputs. The overall best coefficient of correlation (R = 0.9981) is fetched with an RMSE value of 0.0086. The material removal rate has been increased by decreasing the time taken for removal, which gives the possibility of consuming minimum energy. The finishing of the machined surface also improved. Moreover, this paper shows how to use an Artificial Neural Network (ANN) model with Grey Analysis. The results of the comparative analysis show that the values envisaged are closer with the actual values. The foretelling capacity of the evolved model is confirmed with the performance analysis of the developed model.

Controlling for false discoveries subsequently to large scale one-way ANOVA testing in proteomics: Practical considerations.

In discovery proteomics, as well as many other "omic" approaches, the possibility to test for the differential abundance of hundreds (or of thousands) of features simultaneously is appealing, despite requiring specific statistical safeguards, among which controlling for the false discovery rate (FDR) has become standard. Moreover, when more than two biological conditions or group treatments are considered, it has become customary to rely on the one-way analysis of variance (ANOVA) framework, where a first global differential abundance landscape provided by an omnibus test can be subsequently refined using various post-hoc tests (PHTs). However, the interactions between the FDR control procedures and the PHTs are complex, because both correspond to different types of multiple test corrections (MTCs). This article surveys various ways to orchestrate them in a data processing workflow and discusses their pros and cons.

Regularization methods for sparse ESG-valued multi-period portfolio optimization with return prediction using machine learning

In the context of global sustainable development, environmental, social, and governance (ESG) investment has become a frontier topic in the field of asset management. This paper focuses on ESG-valued multi-period portfolio selection problem which incorporates ESG factor into traditional portfolio optimization. Using ESG-valued returns instead of traditional returns, we propose an ESG-valued fused LASSO model to promote an optimal sparse multi-period portfolio strategy. The objective of the model is to minimize a combination of returns and risks with respect to ESG ratings based on classical Markowitz mean–variance framework. The sparsity of the portfolio at each period and the turnover across periods is achieved by the ℓ1 regularization approach. To improve the out-of-sample performance of the ESG-valued model, we introduce two machine learning methods, namely random forest and support vector regression, to predict the ESG-valued returns. We develop a symmetric alternating direction method of multipliers to solve the regularized optimization model. Additionally, some other sparsity-driven penalty functions are discussed which results in a general framework of multi-period portfolio optimization. Finally, numerical experiments on several real datasets from both in-sample and out-of-sample demonstrate the positive effect of ESG in multi-period portfolio optimization.

The Markowitz’s Mean–Variance Interpretation under the efficient market hypothesis in the context of critical recession periods

The validity of the Efficient Market Hypothesis (EMH) as an assumption for portfolio optimization in the Mean–Variance (MV) framework under large scale financial crises is tested for two of the most prominent periods of global economic instability of the first quarter of the 21’st century. Despite that emergent large scale correlations are detected for the considered critical periods, EMH appears to hold from an expected profit standpoint. In concordance with well established results regarding risk assessment under stable economic periods, we find that the risk of the MV portfolios turns out to be however sub optimal during crises. A spatio-temporal covariance prediction model is proposed and it is shown that by the application of this predictive model to the MV framework, the portfolio’s risk assessment can to some extent be alleviated.

Financial recommendations on Reddit, stock returns and cumulative prospect theory

This study investigates stock recommendations from the three largest finance subreddits on Reddit: wallstreetbets, investing and stocks. A simple strategy that buys recommended stocks weighted by the number of posts per day yields a portfolio with higher average returns at the expense of higher risks than the market for all holding periods, i.e., unfavorable Sharpe ratios. Furthermore, the strategy leads to positive (insignificant) short-term and negative (significant) long-term alphas when considering common risk factors. This is consistent with the idea of “meme stocks”, meaning that the recommended stocks are artificially inflated in the short term when they are recommended, and that the posts contain no information about long-term success. However, it is likely that Reddit users, especially on the subreddit wallstreetbets, have preferences for bets which are not captured by the mean–variance framework. Therefore, we draw on cumulative prospect theory (CPT). We find that the CPT-valuations of the Reddit portfolio exceed those of the market, which may explain the persistent attractiveness for investors to follow social media stock recommendations despite the unfavorable risk-return ratio.

TRADING AMBIGUITY: A TALE OF TWO HETEROGENEITIES

AbstractWe consider markets with heterogeneously ambiguous assets and heterogeneously ambiguity‐averse investors whose preferences are a parsimonious extension of the mean–variance framework. We study portfolio choice and trade upon arrival of public information, and show systematic departures from the predictions of standard theory, that occur in the direction of empirical regularities. In particular, our theory speaks to several phenomena in a unified fashion: the asset allocation puzzle, the observation that earnings announcements are followed by significant trading volume with small price change, and that increases in uncertainty are positively associated with increased trading activity and portfolio rebalancing toward safer assets.

An exact version of Life Table Response Experiment analysis, and the R package exactLTRE

Abstract Matrix population models are frequently built and used by ecologists to analyse demography and elucidate the processes driving population growth or decline. Life Table Response Experiments (LTREs) are comparative analyses that decompose the realized difference or variance in population growth rate () into contributions from the differences or variances in the vital rates (i.e. the matrix elements). Since their introduction, LTREs have been based on approximations and have not included biologically relevant interaction terms. We used the functional analysis of variance framework to derive an exact LTRE method, which calculates the exact response of to the difference or variance in a given vital rate, for all interactions among vital rates—including higher‐order interactions neglected by the classical methods. We used the publicly available COMADRE and COMPADRE databases to perform a meta‐analysis comparing the results of exact and classical LTRE methods. We analysed 186 and 1487 LTREs for animal and plant matrix population models, respectively. We found that the classical methods often had small errors, but that very high errors were possible. Overall error was related to the difference or variance in the matrices being analysed, consistent with the Taylor series basis of the classical method. Neglected interaction terms accounted for most of the errors in fixed design LTRE, highlighting the importance of two‐way interaction terms. For random design LTRE, errors in the contribution terms present in both classical and exact methods were comparable to errors due to neglected interaction terms. In most examples we analysed, evaluating exact contributions up to three‐way interaction terms was sufficient for interpreting 90% or more of the difference or variance in . Relative error, previously used to evaluate the accuracy of classical LTREs, is not a reliable metric of how closely the classical and exact methods agree. Error compensation between estimated contribution terms and neglected contribution terms can lead to low relative error despite faulty biological interpretation. Trade‐offs or negative covariances among matrix elements can lead to high relative error despite accurate biological interpretation. Exact LTRE provides reliable and accurate biological interpretation, and the R package exactLTRE makes the exact method accessible to ecologists.