Distribution Of Asset Returns Research Articles

Climate risks and the realized higher-order moments of financial markets: Evidence from China

The return distribution of energy assets deviates from the normal distribution, making volatility a partial measure of risk, and climate risk tend to affect the skewness preferences of environmentally conscious investors. However, limited evidence exists on the impact of climate risk on higher-order moments of asset returns, especially in China. Using data from December 2013 to June 2022, we study the time-varying Granger causal flow from two Chinese climate uncertainty indices (Chinese climate policy uncertainty (CPU) and Chinese climate uncertainty (CU)) to the realized high-order moments (volatility, skewness, and kurtosis) of various Chinese assets covering green energy, carbon emission allowances, and brown energy indices. The main results show evidence of time-variation in the causal flows from climate risks, without ignoring the heterogeneity between the two climate risk measures and across the three assets under study. Granger causality spans various time periods, and is generally more significant for the realized volatility. These results are robust to the specification of the time-varying causality analysis. They also remain significant when accounting for the impact of Chinese economic policy uncertainty, which further supports their robustness. These findings highlight the ability of climate risk to affect higher-order moments of asset returns through the channels of strong deviation of returns from the normal distribution, the preference of investors for skewness, and the frequent occurrence of crisis periods.

Portfolio optimisation of international real estate investment trusts market during COVID-19: A behavioural perspective

This paper employs the cumulative prospect theory to investigate how deviation from rational investor asset selection improves portfolio optimisation. Firstly, asset portfolios are constructed by utilising the cumulative prospect theory, which captures investors’ psychology and risk tolerance and is herein referred to as a behavioural portfolio (BF). Secondly, the cluster technique is also used to build behavioural-centred investment portfolios that capture all the relevant moment properties of the asset return distribution as well as investors’ psychological dynamics and risk appetite, herein called the cluster moment behavioural portfolio (CMBF). The constructed portfolios are optimised by copula and differential evolution techniques. The analysis of optimisation of the constructed portfolios indicates that for behavioural portfolios (BF), in all phases of our sample period, portfolios with higher behavioural scores outperformed those with lower behavioural scores. And in the cluster moment behavioural portfolio (CMBP), for the pre-COVID and the COVID phases, the portfolios with lower behavioural scores outperform those with higher behavioural scores; however, for the full sample phase, the portfolio with a higher behavioural score outperforms the portfolio with the lower behavioural scores. The optimisation results of all the constructed portfolios largely favour portfolios with higher behavioural scores over those with lower scores. The results offer investment suggestions to guide investors with varying risk tolerance levels and those who deviate from the rational investor on how they can enhance their portfolio optimisation.

Multiportfolio Optimization: A Fairness-Aware Target-Oriented Model

Problem definition: We consider a multiportfolio optimization problem in which nonlinear market impact costs result in a strong dependency of one account’s performance on the trading activities of the other accounts. Methodology/results: We develop a novel target-oriented model that jointly optimizes the rebalancing trades and the split of market impact costs. The key advantages of our proposed model include the consideration of clients’ targets on investment returns and the incorporation of distributional uncertainty. The former helps fund managers to circumvent the difficulty in identifying clients’ utility functions or risk parameters, whereas the latter addresses a practical challenge that the probability distribution of risky asset returns cannot be fully observed. Specifically, to evaluate the quality of multiple portfolios’ investment payoffs in achieving targets, we propose a new class of performance measures, called fairness-aware multiparticipant satisficing (FMS) criteria. These criteria can be extended to encompass distributional uncertainty and have the salient feature of addressing the fairness issue with the collective satisficing level as determined by the least satisfied participant. We find that, structurally, the FMS criteria have a dual connection with a set of risk measures. For multiportfolio optimization, we consider the FMS criterion with conditional value-at-risk being the underlying risk measure to further account for the magnitude of shortfalls against targets. The resulting problem, although nonconvex, can be solved efficiently by solving an equivalent converging sequence of tractable subproblems. Managerial implications: For the multiportfolio optimization problem, the numerical study shows that our approach outperforms utility-based models in achieving targets and in out-of-sample performance. More generally, the proposed FMS criteria provide a new decision framework for operational problems in which the decision makers are target-oriented rather than being utility maximizers and issues of fairness and ambiguity should be considered. Funding: This work was supported by the Hong Kong Research Grants Council [Grants 14210821, 16204521], Leading Talent Program of Guangdong Province [Grant 2016LJ06D703], and the National Natural Science Foundation of China [Grants 71971187, 72171156, 72231002, 72331009]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.0363 .

Measuring systemic risk contribution: A higher-order moment augmented approach

Marginal contributions of individual institutions to the systemic risk contain predictive power for potential future exposures and provide early warning signals to regulators and the public. In this paper, the higher-order co-skewness and co-kurtosis are used to construct systemic risk contribution measures, which allow us to identify and characterize the co-movement driving the asymmetry and tail behavior of the joint distribution of asset returns. We illustrate the usefulness of higher-order moment augmented approach by using 4868 stocks living in the Chinese market from June 2002 to March 2022. The empirical results show that these higher-order moment measures convey useful information for systemic risk contribution measurement and portfolio selection, complementary to the information extracted from a standard principal components analysis.

Loss Aversion Robust Optimization Model Under Distribution and Mean Return Ambiguity

From the aspect of behavioral finance, which is an emerging area integrating human behavior into finance, this work studies a robust portfolio problem for loss-averse investors under distribution and mean return ambiguity. A loss-aversion distributionally-robust optimization model is constructed if the return distribution of risky assets is unknown. Then, under the premise that the mean returns of risky assets belong to an ellipsoidal uncertainty set, a model under joint ambiguity in distribution and mean returns is constructed. This study solves both robust models and derives their analytical solutions, respectively. Moreover, the effect of ambiguity aversion and loss aversion on robust optimal portfolio returns is studied. The results show that ambiguity-neutral investors who do not know the return distribution obtain more robust optimal portfolio returns than ambiguity-averse investors who are unaware of both the distribution and mean return. The difference between them decreases with the increase of loss aversion coefficients and increases with ambiguity aversion coefficients. Both loss aversion and ambiguity aversion play important roles in investors’ behavioral portfolio selection.

Dynamic robust portfolio selection under market distress

This article proposes a dynamic robust portfolio selection model that is based on minimizing portfolio’s worst case scenarios using the Conditional Value at Risk as relevant risk measure. Our proposed empirical model for the dynamics of portfolio constituents has three main features: i) accommodates tail dependence between assets by means of a mixture of copula functions; ii) conditional heteroscedasticity and leverage effects are considered through the implementation of a GJR-GARCH model; and iii) extreme events are taken into account by considering parametric and semiparametric hybrid models for the marginal distribution of asset returns. We illustrate the performance of this portfolio before and during the COVID-19 pandemic using statistical measures such as the Sharpe ratio, cumulative returns, and volatility. The results show the outperformance of our WCVaR portfolio during the turmoil period against benchmark portfolios commonly used by practitioners. The method also exhibits good performance during calm periods.

Swap variance hedging and efficiency: The role of high moments

AbstractIn this article, we propose a new theoretical approach for developing hedging strategies based on swap variance (SwV). SwV is a generalized risk measure equivalent to a polynomial combination of all moments of a return distribution. Using the S&P 500 index and West Texas Intermediate (WTI) crude oil spot and futures price data, as well as simulations by varying the distribution of asset returns, we investigate the dynamic differences between hedge ratios and portfolio performances based on SwV (with high moments) and variance (without high moments). We find that, on average, the minimizing‐SwV hedging suggests more short futures contracts than minimizing‐variance hedging; however, when market conditions deteriorate, the minimizing‐SwV hedging suggests fewer short positions in futures. The superior posthedge performances of the mean‐SwV hedged portfolios over the mean‐variance hedged portfolios in highly volatile or extremely calm markets confirm the efficiency of the mean‐SwV hedging strategy.

Cardinality-constrained distributionally robust portfolio optimization

This paper studies a distributionally robust portfolio optimization model with a cardinality constraint for limiting the number of invested assets. We formulate this model as a mixed-integer semidefinite optimization (MISDO) problem by means of the moment-based ambiguity set of probability distributions of asset returns. To exactly solve large-scale problems, we propose a specialized cutting-plane algorithm that is based on bilevel optimization reformulation. We prove the finite convergence of the algorithm. We also apply a matrix completion technique to lower-level SDO problems to make their problem sizes much smaller. Numerical experiments demonstrate that our cutting-plane algorithm is significantly faster than the state-of-the-art MISDO solver SCIP-SDP. We also show that our portfolio optimization model can achieve good investment performance compared with the conventional robust optimization model based on the ellipsoidal uncertainty set.

Multivariate Option Pricing with Gaussian Mixture Distributions and Mixed Copulas

Recently, it has been reported that the hypothesis proposed by the classical black scholes model to price multivariate options in finance were unrealistic, as such, several other methods have been introduced over the last decades including the copulas methods which uses copulas functions to model the dependence structure of underlying assets. However, the previous work did not take into account the use of mixed copulas to assess the underlying assets' dependence structure. The approach we propose consists of selecting the appropriate mixed copula’s structure which captures as much information as possible about the asset’s dependence structure and apply a copulas-based martingale strategy to price multivariate equity options using monte Carlo simulation. A mixture of normal distributions estimated with the standard EM algorithm is also considered for modeling the marginal distribution of financial asset returns. Moreover, the Monte Carlo simulation is performed to compute the values of exotic and up and out barrier options such as worst of, spread, and rainbow options, which shows that the clayton gumble and clayton gaussian have relatively large values for all the options. Our results further indicate that the mixed copula-based approach can be used efficiently to capture heterogeneous dependence structure existing in multivariate assets, price exotic options and generalize the existing results.

Asset Allocation in Indonesian Stocks Using Portfolio Robust

The mean-variance portfolio has several weaknesses. It does not accommodate the uncertainty of parameters, tends to be sensitive to the changes of parameter input, and tends to be unreliable on extreme observations. Moreover, it cannot accommodate the changes in investor preferences regarding the evidence of abnormal and asymmetric asset return distribution. To overcome these three weaknesses, we can use the robust mean-variance portfolio that is based on the uncertainty of parameters. However, the robust mean-variance portfolio has not included skewness in its optimization. Therefore, here in this paper, we use the robust mean-variance-skewness portfolio which includes skewness in its optimization. So it can be used for the condition where the data return is skewed asymmetric and contains extreme values. An empirical study of robust mean-variance and robust mean-variance-skewness portfolios has been conducted on four banking stocks in Indonesia, i.e AGRS.JK, BTPN.JK, BBNI.JK, and BBCA.JK. The data used in this study is the daily closing price of the company's stock price for the period January 2, 2020 – January 2, 2022 (489 days) obtained from Yahoo! Finance. From the results of the data analysis, it can be concluded that the variance still plays an important role in determining the weight of the allocation of a portfolio. Meanwhile, the large value of skewness leads to the allocation of the same weight for each stock in a portfolio.

Distributionally robust portfolio optimization with second-order stochastic dominance based on wasserstein metric

In portfolio optimization, we may be dealing with misspecification of a known distribution, that stock returns follow it. The unknown true distribution is considered in terms of a Wasserstein-neighborhood of P to examine the tractable formulations of the portfolio selection problem. This study considers a distributionally robust portfolio optimization problem with an ambiguous stochastic dominance constraint by assuming the unknown distribution of asset returns. The objective is to maximize the worst-case expected return and subject to an ambiguous second-order stochastic dominance constraint. The expected return robustly stochastically dominates the benchmark in the second order over all possible distributions within an ambiguity set. It is also shown that the Wasserstein-moment ambiguity set-based distributionally robust portfolio optimization can be reduced to a semidefinite program and second-order conic programming. We use a cutting plane to solve our second-order stochastic dominance constraint portfolio optimization problem with ambiguity sets based on the Wasserstein metric. Then we decompose this class of distributionally robust portfolio optimization into semi-infinite programming and apply the cutting surface method to solve it. The captured optimization programs are applied to real-life data for more efficient comparison. The problems are examined in depth using the optimal solutions of the optimization programs based on the different setups.

Estimating the Tail Index of Conditional Distribution of Asset Returns

Massive stock market failures in the past decades cast a doubt on the standard normality assumption of many economic models. Despite decent research on the non-Gaussian characteristics of many financial time series, the question of tail heaviness still remains open. We conduct diagnostic analysis on the conditional distribution of asset returns of small/large companies (Russell 2000 and S&P 500) to look for clear evidence on the presence of heavy tails. We employ extreme value (EVT) tools in order to estimate the shape parameter () of Generalized Pareto distribution (GPD) using a well-known “Hill estimator”. It turns out that the shape parameter lies in the interval implying that the conditional distribution of asset returns supposedly has finite mean and variance. We also find an evidence that the tail estimates experience structural breaks during 2008 Global Financial Crisis.

Detecting Investment Fraud Using the Bias Ratio

Hedge funds play an important role in investment markets, but high-profile frauds and market manipulation have necessitated increased scrutiny for the detection and prevention of such activities. Market metrics which signal fraudulent activity quickly, early, and reliably are scarce and sometimes provide fallacious results. The bias ratio in conjunction with other metrics could provide a solution as it compares the real asset return distribution to that of unbiased returns. High bias ratios combined with statistical moments which differ considerably from those expected from normal distributions provide compelling evidence for possible return manipulation. Application of these metrics to known fraud cases shows that—used historically and in tandem—they would have provided powerful early indicators of suspicious investment activity. Uncovering these frauds earlier could have potentially saved investors considerable resources. The bias ratio also shows promising results in detecting other possible market scams such as insider trading.

A tail-revisited Markowitz mean-variance approach and a portfolio network centrality

A measure for portfolio risk management is proposed by extending the Markowitz mean-variance approach to include the left-hand tail effects of asset returns. Two risk dimensions are captured: asset covariance risk along risk in left-hand tail similarity and volatility. The key ingredient is an informative set on the left-hand tail distributions of asset returns obtained by an adaptive clustering procedure. This set allows a left tail similarity and left tail volatility to be defined, thereby providing a definition for the left-tail-covariance-like matrix. The convex combination of the two covariance matrices generates a “two-dimensional” risk that, when applied to portfolio selection, provides a measure of its systemic vulnerability due to the asset centrality. This is done by simply associating a suitable node-weighted network with the portfolio. Higher values of this risk indicate an asset allocation suffering from too much exposure to volatile assets whose return dynamics behave too similarly in left-hand tail distributions and/or co-movements, as well as being too connected to each other. Minimizing these combined risks reduces losses and increases profits, with a low variability in the profit and loss distribution. The portfolio selection compares favorably with some competing approaches. An empirical analysis is made using exchange traded fund prices over the period January 2006–February 2018.

The Performance Measurement of Generalized Sharpe Ratio and Economic Performance Measure: A Hedge Funds Example

Prior literature documents that the Sharpe ratio (SR) generates biases in performance evaluation if returns distribution deviates from normal distribution because SR is derived under the mean-variance model with the strict assumption of either quadratic preferences or customarily distributed returns. When the return distributions deviate from normality, it may lead to unreasonable results. Therefore, this study examines which performance measurement approaches are efficient for non-normality on the distribution of asset returns. We collect monthly returns of 14 Credit Suisse (CS) hedges fund indexes from April 1994 to June 2021. The hedge fund index returns exhibit high negative skewness or high positive kurtosis, implying non-normal distribution. Then, we employ the Sharpe ratio (SR) and two performance measures, which extend the Sharpe ratio, the generalized Sharpe ratio (GSR), and the economic performance measure (EPM), to evaluate the performances of hedge funds. In addition, both the nonparametric and parametric estimation methods of the GSR and the EPM are utilized. Our findings indicate that the nonparametric GSR and the nonparametric EPM produce more similar rankings than the SR. Among the three parametric estimation methods of the GSR and EPM, only the method proposed by [1] produces similar rankings with the nonparametric GSR and the nonparametric EPM. Finally, our study contributes the practical approach for fund managers to evaluate their fund performance efficiently.

Can Mixed-Frequency Data Improve the Higher-Order Moments Portfolio Performance?

ABSTRACT In the presence of non-normally distributed asset returns, an optimal portfolio selection should consider higher-order (co-)moments when no sampling errors exist. However, the curse of dimensionality has already been a serious concern in mean-variance analyses; higher-order (co-)moments also face the same dilemma. This study uses mixed-frequency (MF) data under the assumption that stock returns are generated by a mixed-data sampling (MIDAS) regression model, which shows to provide well-improved estimates for the covariance, co-skewness, and co-kurtosis matrices for higher dimension. We discover that the new, improved estimates used in higher-order (co-)moment portfolio selections can dominate the other existing structured estimates from an out-of-sample perspective in most instances.

Pricing Multivariate European Equity Option Using Gaussians Mixture Distributions and EVT-Based Copulas

In this article, we present an approach which allows taking into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associated options. Specifically, the marginal distribution of asset returns is modelled by a mixture of two Gaussian distributions. Moreover, we model the joint dependence structure of the returns using a copula function, the extremal one, which is suitable for our financial data, particularly the extreme values copulas. Applications are made on the Atos and Dassault Systems actions of the CAC40 index. Monte Carlo method is used to compute the values of some equity options such as the call on maximum, the call on minimum, the digital option, and the spreads option with the basket (Atos, Dassault systems) as underlying.

Fat‐Tailed Kelly

Asset returns have fat tails. Traditional mean-variance analysis, however, assumes that asset returns are normally distributed, with thin tails. A natural extension of the normal distribution is the α-stable distribution, which has fat tails, skewness—and infinite variance, which makes mean-variance optimization impossible. In this white paper, I review the data, examine the investment implications, and do the math of fat tailed, α-stably distributed asset returns.

Sampling distributions of optimal portfolio weights and characteristics in small and large dimensions

Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realize the position suggested by the optimal portfolios, he/she needs to estimate the unknown parameters and to account for the parameter uncertainty in the decision process. Most often, the parameters of interest are the population mean vector and the population covariance matrix of the asset return distribution. In this paper, we characterize the exact sampling distribution of the estimated optimal portfolio weights and their characteristics. This is done by deriving their sampling distribution by its stochastic representation. This approach possesses several advantages, e.g. (i) it determines the sampling distribution of the estimated optimal portfolio weights by expressions, which could be used to draw samples from this distribution efficiently; (ii) the application of the derived stochastic representation provides an easy way to obtain the asymptotic approximation of the sampling distribution. The later property is used to show that the high-dimensional asymptotic distribution of optimal portfolio weights is a multivariate normal and to determine its parameters. Moreover, a consistent estimator of optimal portfolio weights and their characteristics is derived under the high-dimensional settings. Via an extensive simulation study, we investigate the finite-sample performance of the derived asymptotic approximation and study its robustness to the violation of the model assumptions used in the derivation of the theoretical results.

Taming Tail Risk: Regularized Multiple β Worst-Case CVaR Portfolio

The importance of proper tail risk management is a crucial component of the investment process and conditional Value at Risk (CVaR) is often used as a tail risk measure. CVaR is the asymmetric risk measure that controls and manages the downside risk of a portfolio while symmetric risk measures such as variance consider both upside and downside risk. In fact, minimum CVaR portfolio is a promising alternative to traditional mean-variance optimization. However, there are three major challenges in the minimum CVaR portfolio. Firstly, when using CVaR as a risk measure, we need to determine the distribution of asset returns, but it is difficult to actually grasp the distribution; therefore, we need to invest in a situation where the distribution is uncertain. Secondly, the minimum CVaR portfolio is formulated with a single β and may output significantly different portfolios depending on the β. Finally, most portfolio allocation strategies do not account for transaction costs incurred by each rebalancing of the portfolio. In order to improve these challenges, we propose a Regularized Multiple β Worst-case CVaR (RM-WCVaR) portfolio. The characteristics of this portfolio are as follows: it makes CVaR robust with worst-case CVaR which is still an asymmetric risk measure, it is stable among multiple β, and against changes in weights over time. We perform experiments on well-known benchmarks to evaluate the proposed portfolio.RM-WCVaR demonstrates superior performance of having both higher risk-adjusted returns and lower maximum drawdown.