Individual Asset Returns Research Articles

Comparative Analysis on the Application of Markowitz Model and Index Model in Portfolios

This article presents a comparison between the Markowitz model and the index model, focusing on their applications in portfolio management. The Markowitz model, also known as the mean-variance model, revolutionized portfolio theory by introducing a quantitative method for balancing risk and return. This model constructs optimal portfolios that maximize expected return for a given level of risk or minimize risk for a given expected return, using a covariance matrix to assess relationships between asset returns. In contrast, index models popularized by William Sharpe offer a simplified approach focused on the relationship between individual asset returns and a common benchmark (usually a market portfolio). The article explores the theoretical foundations of the two models, highlighting their mathematical formulations and assumptions. It also discusses the computational methodologies involved in implementing these models and examines the challenges and advances in optimization techniques. It evaluates how these technological innovations have enhanced portfolio optimization, enabling the handling of larger datasets and more complex market dynamics. In addition to comparing these two models, the article delves deeper into the concepts of efficient frontier, inefficient frontier and minimum variance frontier. The efficient frontier is the portfolios that offer the highest expected return for target risk, while the inefficient frontier includes portfolios that do not offer the best return for the level of risk. Minimum variance frontier focuses on portfolios that minimize risk for target expected return, emphasizing the importance of risk management in investment decisions.

An Empirical Research on the Performance of Asset Pricing Models in the Chinese A-Share Market

Asset pricing remains a cornerstone of financial field, providing a framework to understand the anticipated returns of asset portfolios and individual assets. Its widespread application spans academic discourse and practical financial methodologies. This study conducts an empirical analysis of the Chinese A-share Market, utilizing transaction data from the A-share market spanning from 1994 to 2024. It examines the applicability of the traditional asset pricing models within the Chinese stock market. Through classic regression analyses of the CAPM, the Fama and French three-factor model (FF3), the Fama and French five-factor model (FF5), this study verifies that the FF5 provides a superior explanation of stock expectations for the A-share market during this period compared to other traditional asset pricing models. The conclusions of this study indicate that, among the CAPM, FF3, and FF5 models, the number of parameters taken into account by the model and its capacity to explain asset returns are positively correlated.

Optimal Impact Portfolios with General Dependence and Marginals

Using Induced Order Statistics to Construct Optimal Impact Portfolios with General Dependence and Marginals We develop a mathematical framework for constructing optimal impact portfolios and quantifying their financial performance by characterizing the returns of impact-ranked assets using induced order statistics and copulas. Our results apply to any joint distribution of impact factors and residual returns, making them broadly applicable to a wide range of contexts. We develop significant extensions of the theory of induced order statistics, with which we are able to characterize the distribution of residual returns of individual assets ranked by the impact factor. Our framework provides a toolkit for practitioners to construct impact portfolios and quantify their performance based on real data. This allows impact investors to achieve higher risk-adjusted returns than those with impact portfolios constructed using simpler heuristics such as negative or positive screening.

Quantile coherency across bonds, commodities, currencies, and equities

This paper examines quantile coherency in bonds, commodities, currencies, and equities using a novel quantile coherency approach. While recent literature has explored single-frequency tail- and time-frequency dependence in asset returns, we provide fresh evidence on asset return dependence across quantiles (proxying business cycles or market conditions) at different frequencies (representing investment horizons). Considering sixty-seven individual asset return series in four asset classes, we observe that low frequency (yearly) dependence is stronger in the bond, foreign exchange, and equity markets. Specifically, we find strong dependence between the German and French bond markets, heating oil and crude oil, gold and silver, British Pound, and Euro, French and German and Canadian and US equities. As we report asset return interdependence in different business cycles and at different time horizons, these results have important implications for portfolio allocation and investment strategy formulation.

Credibilistic portfolio optimization with higher-order moments using coherent triangular fuzzy numbers

Financial portfolio formation is usually a multi-objective decision-making problem concerning return and risk on the investment. In this study, we make use of an extension of regular triangular fuzzy numbers, known as coherent triangular fuzzy numbers, to describe portfolio returns in a credibility-based framework. The paper’s novelty lies in proposing and deriving a crisp equivalent for computing the coherent triangular fuzzy number-based credibilistic semivariance, credibilistic skewness, and credibilistic semikurtosis. Utilizing these analytical expressions, along with additional formulations found in existing literature, we present three multi-objective portfolio optimization models involving the practical constraints related to investment decisions. All the proposed analytical expressions, when used with the returns of the portfolio as a whole, help to overcome the computationally expensive process of simulating results using the returns of individual assets. The proposed models differ with respect to different risk measures, viz. semivariance, Mean-Absolute-Semi-Deviation (MASD), and Conditional Value-at-Risk (CVaR). These models are solved using an adaptation of an efficient Multi-Objective Genetic Algorithm (MOGA) specifically designed to solve portfolio optimization problems with practical constraints. Data from the National Stock Exchange (NSE) in Mumbai, India and the New York Stock Exchange (NYSE) in New York, USA, are used to demonstrate the effectiveness of the proposed portfolio optimization models and solution methodology. All the proposed models are compared with respect to each other and the benchmarks considered in this study to bring out the performance stability.

Robust Portfolio Optimization with Respect to Spectral Risk Measures Under Correlation Uncertainty

This paper proposes a distributionally robust multi-period portfolio model with ambiguity on asset correlations with fixed individual asset return mean and variance. The correlation matrix bounds can be quantified via corresponding confidence intervals based on historical data. We employ a general class of coherent risk measures namely the spectral risk measure, which includes the popular measure conditional value-at-risk (CVaR) as a particular case, as our objective function. Specific choices of spectral risk measure permit flexibility for capturing risk preferences of different investors. A semi-analytical solution is derived for our model. The prominent stochastic dual dynamic programming (SDDP) algorithm adapted with intricate modifications is developed as a numerical method under the discrete distribution setting. In particular, our new formulation accounts for the unknown worst-case distribution in each iteration. We verify the convergence property of this algorithm under the setting of finite scenarios. Our results show that the optimal solution favours a certain degree of anti-diversification due to dependence ambiguity and exhibits its protection ability during the financial crisis period.

Impact of macroeconomic variables on the topological structure of the Brazilian stock market: A complex network approach

Complex networks is an interdisciplinary field of study, effective in modeling various phenomena of strategic and/or market interest. Complex correlation networks between financial assets are mathematical abstractions that represent the relations between the financial returns of certain assets in a given period. The present work analyzed the Brazilian stock market, as well as the macroeconomic variables and indicators correlated to it in the context of complex networks. Based on the concept moving networks, 43 monthly complex networks were developed with relationships based on Pearson correlations between the logarithms of individual asset returns. To evaluate the impact of the oscillations of macroeconomic indicators on the topological structure of the network of assets, autoregressive vector models were used, as well as variance decomposition and Granger causality. The results of the Granger causality tests suggest that Gross Domestic Product, Risk Brazil, Ibovespa points and Interest rate influence the metrics density and number of components. The macroeconomic variables Gross Domestic Product, Risk Brazil and Ibovespa points presented, in general, higher explanatory power in relation to the variances of the density, transitivity and components number metrics. Among the positive and practical aspects related to this work, it is possible to highlight the use of global metrics of complex networks of assets as a support tool for investors and financial analysts in the detection of risk and volatility through oscillations in macroeconomic variables and policies.

Dynamic portfolio rebalancing through reinforcement learning

Portfolio managements in financial markets involve risk management strategies and opportunistic responses to individual trading behaviours. Optimal portfolios constructed aim to have a minimal risk with highest accompanying investment returns, regardless of market conditions. This paper focuses on providing an alternative view in maximising portfolio returns using Reinforcement Learning (RL) by considering dynamic risks appropriate to market conditions through dynamic portfolio rebalancing. The proposed algorithm is able to improve portfolio management by introducing the dynamic rebalancing of portfolios with vigorous risk through an RL agent. This is done while accounting for market conditions, asset diversifications, risk and returns in the global financial market. Studies have been performed in this paper to explore four types of methods with variations in fully portfolio rebalancing and gradual portfolio rebalancing, which combine with and without the use of the Long Short-Term Memory (LSTM) model to predict stock prices for adjusting the technical indicator centring. Performances of the four methods have been evaluated and compared using three constructed financial portfolios, including one portfolio with global market index assets with different risk levels, and two portfolios with uncorrelated stock assets from different sectors and risk levels. Observed from the experiment results, the proposed RL agent for gradual portfolio rebalancing with the LSTM model on price prediction outperforms the other three methods, as well as returns of individual assets in these three portfolios. The improvements of the returns using the RL agent for gradual rebalancing with prediction model are achieved at about 27.9–93.4% over those of the full rebalancing without prediction model. It has demonstrated the ability to dynamically adjust portfolio compositions according to the market trends, risks and returns of the global indices and stock assets.

Realized semibetas: Disentangling “good” and “bad” downside risks

We propose a new decomposition of the traditional market beta into four semibetas that depend on the signed covariation between the market and individual asset returns. We show that semibetas stemming from negative market and negative asset return covariation predict significantly higher future returns, while semibetas attributable to negative market and positive asset return covariation predict significantly lower future returns. The two semibetas associated with positive market return variation do not appear to be priced. The results are consistent with the pricing implications from a mean-semivariance framework combined with arbitrage risk driving a wedge between the risk premiums for long and short positions. We conclude that rather than betting against the traditional market beta, it is better to bet on and against the “right” semibetas.

Behavioral Portfolio Management with Layered ESG Goals and Ai Estimation of Asset Returns

Portfolio managers and individual investors alike are in quest of efficient asset allocation models that simultaneously express environmental, social, and governance (ESG) considerations along with investor behavioral biases. The current study presents a novel approach to optimize the behavioral portfolio management model in the presence of investor biases for ESG sustainability, loss aversion, and cognitive dissonance. We extend the factor pricing literature by implementing a factor extraction protocol to identify three unique and pervasive ESG factors. Upon examining the interconnectedness of the factors, machine learning methods are applied to a production-theoretic six-factor Fama and French model to predict individual asset returns. Enumeration of efficient asset allocations is obtained by solving a hierarchical multiobjective portfolio optimization model. simulation results from solving alternate specifications of the layered goal ESG-driven model corroborate and extend emergent research on portfolio sustainability, network theory, and the interconnectedness of financial returns. Additionally, we provide results to amplify the existence of a hump-shaped ESG efficiency frontier. The results provide new information about the trade-offs available for resolving cognitive dissonance when investors are conflicted between holding ‘green’ versus ‘brown’ asset diversification plans.

Realized Semibetas: Signs of Things to Come

We propose a new decomposition of the traditional market beta into four semibetas depending on the signed covariation between the market and individual asset returns. Consistent with the pricing implications from a mean-semivariance framework, we show that higher semibetas defined by negative market and negative (positive) asset return covariation predict significantly higher (lower) future returns, while the other two semibetas do not appear to be priced. The results are robust to an array of alternative test specifications and additional controls. Rather than betting on or against beta, we conclude that it is better to bet on and against the right semibetas.

A Biased-Randomized Iterated Local Search Algorithm for Rich Portfolio Optimization

This research develops an original algorithm for rich portfolio optimization (ARPO), considering more realistic constraints than those usually analyzed in the literature. Using a matheuristic framework that combines an iterated local search metaheuristic with quadratic programming, ARPO efficiently deals with complex variants of the mean-variance portfolio optimization problem, including the well-known cardinality and quantity constraints. ARPO proceeds in two steps. First, a feasible initial solution is constructed by allocating portfolio weights according to the individual return rate. Secondly, an iterated local search framework, which makes use of quadratic programming, gradually improves the initial solution throughout an iterative combination of a perturbation stage and a local search stage. According to the experimental results obtained, ARPO is very competitive when compared against existing state-of-the-art approaches, both in terms of the quality of the best solution generated as well as in terms of the computational times required to obtain it. Furthermore, we also show that our algorithm can be used to solve variants of the portfolio optimization problem, in which inputs (individual asset returns, variances and covariances) feature a random component. Notably, the results are similar to the benchmark constrained efficient frontier with deterministic inputs, if variances and covariances of individual asset returns comprise a random component. Finally, a sensitivity analysis has been carried out to test the stability of our algorithm against small variations in the input data.

Cross-Sectional Learning of Extremal Dependence Among Financial Assets

We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint heavy-tailed random vectors featuring not only distinct marginal tail heaviness, but also flexible tail dependence structure. The novelty lies in that pairwise tail dependence between any two dimensions is modeled separately from their correlation, and can vary respectively according to its own parameter rather than the correlation parameter, which is an essential advantage over many commonly used methods such as multivariate $t$ or elliptical distribution. It is also intuitive to interpret, easy to track, and simple to sample comparing to the copula approach. We show its flexible tail dependence structure through simulation. Coupled with a GARCH model to eliminate serial dependence of each individual asset return series, we use this novel method to model and forecast multivariate conditional distribution of stock returns, and obtain notable performance improvements in multi-dimensional coverage tests. Besides, our empirical finding about the asymmetry of tails of the idiosyncratic component as well as the market component is interesting and worth to be well studied in the future.

Robust Nearly-Efficient Estimation of Large Panels With Factor Structures

This paper studies estimation of linear panel regression models with heterogeneous coefficients, when both the regressors and the residual contain a possibly common, latent, factor structure. Our theory is (nearly) efficient, because based on the GLS principle, and also robust to the specification of such factor structure, because it does not require any information on the number of factors nor estimation of the factor structure itself. We first show how the unfeasible GLS estimator not only affords an efficiency improvement but, more importantly, provides a bias-adjusted estimator with the conventional limiting distribution, for situations where the OLS is affected by a first-order bias. The technical challenge resolved in the paper is to show how these properties are preserved for a class of feasible GLS estimators in a double-asymptotics setting. Our theory is illustrated by means of Monte Carlo exercises and, then, with an empirical application using individual asset returns and firms' characteristics data.

Investigating the Drivers of International Comovement in Real Financial Asset Returns

There is a substantial body of theoretical and empirical research on asset price comovement and determinants. The empirical analysis in this paper differs in that it incorporates a channel for cross-country comovement in asset prices as well in a set of proposed asset price determinants, across a sample of 9 OECD countries. A Bayesian dynamic factor model is utilised to isolate common, or ‘world’, and country-specific shocks in stock, bond, currency, and house markets and in variables representing monetary policy, fiscal policy, productivity, demand, relative commodity prices and macroeconomic sentiment. The results are used to gauge the degree of financial and economic integration. Individual asset returns are then regressed on factors extracted from the driving variables to examine the relative importance of the common and country shocks. Stock and bond markets in particular are found to be driven largely by shocks which are common across all countries and asset markets, though a country level cycle in returns is also evident. Together the world factors in the driving variables are found to be a relatively large source of shocks for all asset markets, with shocks to fiscal policy variables, productivity and sentiment appearing to underpin international linkages in asset return volatility. The country-specific component in relative commodity price growth is a large driving force for individual returns.

Diversifying portfolios of U.S. stocks with crude oil and natural gas: A regime-dependent optimization with several risk measures

We build a portfolio encompassing U.S. crude oil, natural gas and stocks to study the diversification power of energy commodities. Such diversification power depends on the joint dependence structure of the three types of assets. According to Gatfaoui (2016a), the dependence structure is time-varying because individual asset returns exhibit several variance regimes. We identify the corresponding regime-specific multivariate copulas, and incorporate them to well-chosen risk measures. Specifically, we minimize the portfolio's variance, semi-variance and tail risk, in the presence and the absence of constraints on the portfolio's expected return and/or stock investment. First, the return constraint reduces the performance of the optimal portfolio. Second, the regime-specific portfolio optimization implements an enhanced active management strategy over the whole sample period. Finally, the tail-risk optimal portfolio offers the most interesting risk-return tradeoff. However, variance and semi-variance optimal portfolios can also be considered in the absence of a return constraint.

Modelling the Dependence Structure of Financial Assets: A Bivariate Extreme Data Study

Quantifying dependence among variables is the core of all modelling efforts in financial econometrics. In the recent years, copula was introduced to model the dependence structure among financial assets return, and its application developed fast. A large number of studies on copula have been performed, but the study of multivariate extremes related with copulas was quite behind in comparison with the research on copulas. In order to predict extreme losses in finance, extreme value copulas play more important role than copulas. In this paper, we study the modelling of extreme value dependence using extreme value copulas on finance data and introducing a negative dependence between the assets return. This model was applied in the portfolio of the IDX Composite Index (IHSG) and the exchange rate for Indonesia Rupiah to United States Dollar (NT). Each individual asset return is modelled by the AR-GARCH and the joint distribution is modelled using extreme value copulas. As a comparison, the joint distribution is also modelled using the copulas. The result shows that the dependence between IHSG and NT is negative. Therefore, in this paper, we tested the extreme value copulas and the copulas which were rotated 270 degree and 90 degree. The empirical study showed that the extreme value copulas rotated with 270 degree are relatively more appropriate model than the copulas. Quantifying dependence among variables is the core of all modelling efforts in financial econometrics. In the recent years, copula was introduced to model the dependence structure among financial assets return, and its application developed fast. A large number of studies on copula have been performed, but the study of multivariate extremes related with copulas was quite behind in comparison with the research on copulas. In order to predict extreme losses in finance, extreme value copulas play more important role than copulas. In this paper, we study the modelling of extreme value dependence using extreme value copulas on finance data and introducing a negative dependence between the assets return. This model was applied in the portfolio of the IDX Composite Index (IHSG) and the exchange rate for Indonesia Rupiah to United States Dollar (NT). Each individual asset return is modelled by the AR-GARCH and the joint distribution is modelled using extreme value copulas. As a comparison, the joint distribution is also modelled using the copulas. The result shows that the dependence between IHSG and NT is negative. Therefore, in this paper, we tested the extreme value copulas and the copulas which were rotated 270 degree and 90 degree. The empirical study showed that the extreme value copulas rotated with 270 degree are relatively more appropriate model than the copulas.

Efficient Factor Selection: Explaining Risk and Mean Returns Jointly

An asset pricing model is customarily evaluated by how well it explains means of returns. But how well the model explains fluctuations of returns is similarly important though often overlooked in the literature. We derive “efficient” factors that combine both objectives and turn out to maximize average time-series (first-pass) R-square for given cross-sectional (second-pass) R-square. Efficient factors work better out of sample and even explain mean returns better than structural models. The reason is that structural models emphasize factors that as a group are close to the tangency portfolio. But this portfolio, by necessity, has relatively low variance that explains individual asset return fluctuations poorly and impedes factor identification. These findings explain many of the puzzling results in empirical asset pricing. Further, intended holding period becomes essential now for model evaluation and shorter holding periods require more emphasis on first-pass fit, which is another key issue overlooked in the literature.

'Know When to Hodl Em, Know When to Fodl Em': An Investigation of Factor Based Investing in the Cryptocurrency Space

It has been known since at least the groundbreaking work of Fama and French (1992) that there are specific attributes, so called factors, that can help predict the returns of individual assets above the return of the broader market. Since these predictive characteristics arise out of sample (with currently observable factor values predicting future returns), investors can earn excess returns with portfolios that are constructed to align with the factors. First introduced in the cross section of returns and focusing on individual equity securities, the efficacy of such factors has since been demonstrated at the asset class level as well, and found to work not only in the cross section but also longitudinally (for individual assets, through time). Factors like value, momentum, and carry have been found to work so broadly across different asset classes, security universes, countries, and time periods, that Asness et al. simply titled their influential 2013 Journal of Finance paper “Value and Momentum Everywhere”. Our paper provides a first application of momentum, value, and carry based factor investing to the cryptocurrencies. We show that these same factors are effective in this relatively new and unexplored asset class, permitting the construction of portfolios that can earn excess returns over the cryptocurrency “market” as a whole.

Risk measures in a quantile regression credibility framework with Fama/French data applications

In this paper we extend the idea of embedding the classical credibility model into risk measures, as was presented by Pitselis (2016), to the idea of embedding regression credibility into risk measures. The resulting credible regression risk measures capture the risk of individual insurer’s contract (in finance, the individual asset return portfolio) as well as the portfolio risk consisting of several similar but not identical contracts (in finance, several similar portfolios of asset returns), which are grouped together to share the risk. In insurance, credibility plays a special role of spreading the risk. In financial terminology, credibility plays a special role of diversification of risk. For each model, regression credibility models are established and the robustness of these models is investigated. Applications to Fama/French financial portfolio data are also presented.