Conditional Distribution Of Returns Research Articles

Risk parity portfolio optimization under heavy‐tailed returns and dynamic correlations

Risk parity portfolio optimization, using expected shortfall as the risk measure, is investigated when asset returns are fat‐tailed and heteroscedastic with regime switching dynamic correlations. The conditional return distribution is modeled by an elliptical multi‐variate generalized hyperbolic distribution, allowing for fast parameter estimation via an expectation‐maximization algorithm, and a semi‐closed form of the risk contributions. A new method for efficient computation of non‐Gaussian risk parity weights sidesteps the need for numerical simulations or Cornish–Fisher‐type approximations. Accounting for fat‐tailed returns, the risk parity allocation is less sensitive to volatility shocks, thereby generating lower portfolio turnover, in particular during market turmoils such as the global financial crisis or the COVID shock. While risk parity portfolios are rather robust to the misuse of the Gaussian distribution, a sophisticated time series model can improve risk‐adjusted returns, strongly reduces drawdowns during periods of market stress and enables to use a holistic risk model for portfolio and risk management.

A method for predicting VaR by aggregating generalized distributions driven by the dynamic conditional score

Constructing a more effective value at risk (VaR) prediction model has long been a goal in financial risk management. In this paper, we propose a novel parametric approach and provide a standard paradigm to demonstrate the modeling. We establish a dynamic conditional score (DCS) model based on high-frequency data and a generalized distribution (GD), namely, the GD-DCS model, to improve the forecasts of daily VaR. The model assumes that intraday returns at different moments are independent of each other and obey the same kind of GD, whose dynamic parameters are driven by DCS. By predicting the motion law of the time-varying parameters, the conditional distribution of intraday returns is determined; then, the bootstrap method is used to simulate daily returns. An empirical analysis using data from the Chinese stock market shows that Weibull-Pareto -DCS model incorporating high-frequency data is superior to traditional benchmark models, such as RGARCH, in the prediction of VaR at high risk levels, which proves that this approach contributes to the improvement of risk measurement tools.

Dynamic Black Litterman portfolios with views derived via CNN-BiLSTM predictions

We use daily price and technical indicators' data for the ten MSCI Asia Pacific sector indices for the past 20 years and find that our hybrid multivariate Convolutional Neural Network - Bidirectional Long Short-Term Memory (CNN-BiLSTM) deep learning model gives reasonably better predictions when predicting index closing prices out-of-sample than using either CNN or BiLSTM alone. After utilizing these predictions as investor views inside the Black-Litterman model with time variation in the conditional distribution of returns, we find that the portfolios generated outperform all benchmark model portfolios by a considerable margin in terms of financial efficiency and diversification.

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.

Degree and structure of return dependence among commodities, energy stocks and international equity markets during the post-COVID-19 period

This paper examines the safe-haven role of copper, iron, gold, silver, and energy stocks for international equity markets during the COVID-19 pandemic. Specifically, the degree and structure of return dependence at different points of conditional return distributions are examined for the pre-COVID and post-COVID periods. The results show that copper is a weak safe-haven for the US equity market at the upper-tail of conditional distribution of cooper returns during the post-COVID period. Gold loses its hedge status during the post-COVID period while silver is a strong safe-haven against international equity markets at the upper-tail of conditional return distribution of silver. Further, iron pose weak safe-haven properties against international equity markets when iron returns are extremely positive. However, neither conventional nor green energy stocks act as safe-haven against international equity markets. Current results may provide guidance for risk management, portfolio management and policy decisions during the post-COVID-19 period.

Impact of COVID-19 on the quantile connectedness between energy, metals and agriculture commodities

With many studies highlighting the heterogeneous impact of the COVID-19 pandemic on different commodity markets, this study provides evidence of quantile connectedness between energy, metals, and agriculture commodity markets before and during the COVID-19 outbreak. Since mean-based measures of connectedness are not necessarily suitable to measure connectedness in the crisis period, especially in the tails of the return distribution, thus in this study, we use the newly developed approach of quantile-based connectedness. The full-sample analysis results show that return shocks only propagate within the energy commodity group. The findings manifest that transmission of return spillovers is stronger in the left and right tails of the conditional return distribution. In addition, the results unveil that degree of tail-dependence between energy, metals, and agriculture commodities are time-varying. Meanwhile, our sub-sample analysis clearly shows that the commodity market return connectedness demonstrates a significant shift over time due to COVID-19 shocks. There is evidence of strong transmission of return shocks between energy, metals, and agriculture commodities during the COVID-19 fiasco. Finally, the results also illustrate that softs and livestock commodities hold significant diversification benefits for energy market investors.

A semi-parametric conditional autoregressive joint value-at-risk and expected shortfall modeling framework incorporating realized measures

A class of realized semi-parametric conditional autoregressive joint Value-at-Risk (VaR) and Expected Shortfall (ES) models is proposed. This class includes novel specifications that allow separate dynamics for VaR and ES, driven by realized measures of volatility. A measurement equation is included in the model class for risk modeling, meaning it generalizes the parametric Realized-GARCH model into the semi-parametric realm. The proposed models implicitly allow the conditional return distribution to change over time via the relationship between VaR and ES. Employing a quasi-likelihood built on the asymmetric Laplace distribution, a Bayesian Markov Chain Monte Carlo method is used for model estimation, whose finite sample properties are assessed via simulation. In a forecasting study applied to 7 indices and 7 assets, one-day-ahead 1% and 2.5% VaR and ES forecasting results support the proposed model class.

Predicting the return on the spot price of crude oil out-of-sample by conditioning on news-based uncertainty measures: Some new empirical results

This study contributes to the growing literature that focuses on predicting crude oil spot price returns out-of-sample by conditioning on the news-based uncertainty measures pioneered by Baker et al. (2016). With the aim of providing new empirical results useful for future research, we apply a comprehensive Bayesian model averaging (BMA) framework that incorporates the following aspects: (i): Parameter instability, (ii): Model uncertainty, and (iii): Besides the conditional mean process, it allows predictors of the candidate models in the model set to impact the variable being predicted through the conditional volatility process or both processes. Applied to monthly news-based uncertainty and crude oil price data from 1985m1 through 2020m12, we observe that accounting for model uncertainty and allowing predictors to impact crude oil price returns exclusively through the conditional volatility process lead to the most consistent pattern of point (density) prediction accuracy gains relative to the benchmark. In contrast, the approach predominately relied on in the current literature, namely, allowing predictors to impact returns only through the conditional mean process does not lead to the same degree of point (density) prediction accuracy gains. Likewise, any further prediction accuracy gains from (i) are at best modest once (ii) and (iii) are accounted for. The largest relative gain occurs when predicting the left tail of the conditional return distribution one-month ahead. The statistical evidence of predictability also translates to economic gains.

A dynamic conditional score model for the log correlation matrix

This paper proposes a new model for the dynamics of correlation matrices, where the dynamics are driven by the likelihood score with respect to the matrix logarithm of the correlation matrix. In analogy to the exponential GARCH model for volatility, this transformation ensures that the correlation matrices remain positive definite, even in high dimensions. For the conditional distribution of returns, we assume a student-t copula to explain the dependence structure and univariate student-t for the marginals with potentially different degrees of freedom. The separation into volatility and correlation parts allows for a two-step estimation, which facilitates estimation in high dimensions. We derive estimation theory for one-step and two-step estimation. In an application to a set of six asset indices including financial and alternative assets we show that the model performs well in terms of diagnostics, specification tests, and out-of-sample forecasting.

Modeling heterogeneous treatment effects in the presence of endogeneity

An inappropriate handling of cross-sectional heterogeneity renders estimates of causal effects inaccurate and uninformative. The present paper discusses how the direct modeling of cross-sectional differences via semiparametric models represents a useful bridge between a statistical approach, where the conditional distribution of the dependent variable returns any value of the outcome given any value of the explanatory variables, and an econometric analysis, where functions and parameters have direct policy implications. The explicit modeling of heterogeneity across different groups improves the quality of the estimates, mitigates their dependence upon the chosen instrumental variable, diminishes the self-selection problem, and fosters the acquisition of useful information for the entire sample.

Predicting Extreme Daily Regime Shifts in Financial Time Series Exchange/Johannesburg Stock Exchange—All Share Index

During the past decades, seasonal autoregressive integrated moving average (SARIMA) had become one of a prevalent linear models in time series and forecasting. Empirical research advocated that forecasting with non-linear models can be an encouraging alternative to traditional linear models. Linear models are often compared to non-linear models with mixed conclusions in terms of superiority in forecasting performance. Therefore, the aim of this study is to build an early warning system (EWS) model for extreme daily losses for financial stock markets. A logistic model tree (LMT) is used in collaboration with a seasonal autoregressive integrated moving average-Markov-Switching exponential generalised autoregressive conditional heteroscedasticity-generalised extreme value distribution (SARIMA-MS-EGARCH-GEVD) estimates. A time series of the study is a five-day financial time series exchange/Johannesburg stock exchange-all share index (FTSE/JSE-ALSI) for the period of 4 January 2010 to 31 July 2020. The study is set into a two-stage framework. Firstly, SARIMA model is fitted to stock returns in order to obtain independently and identically distributed (i.i.d) residuals and fit the MS(k)-EGARCH(p,q)-GEVD to i.i.d residuals; while, in the second stage, we set-up an EWS model. The results of the estimated MS(2)-EGARCH(1,1) -GEVD revealed that the conditional distribution of returns is highly volatile giving the expected duration to approximately 36 months and 4 days in regime one and 58 months and 2 days in regime two. We further found that any degree losses above 25% implies that there will be no further losses. Using the seven statistical loss functions, the estimated SARIMA(2,1,0)×(2,1,0)240−MS(2)−EGARCH(1,1)−GEVD proved to be the most appropriate model for predicting extreme regimes losses as it was ranked at 71%. Finally, the results of EWS model exhibit reasonably an overall performance of 98%, sensitivity of 79.89% and specificity of 98.40% respectively. The model further indicated a success classification rate of 89% and a prediction rate of 95%. This is a promising technique for EWS. The findings also confirmed 63% and 51% of extreme losses for both training sample and validation sample to be correctly classified. The findings of this study are useful for decision makers and financial sector for future use and planning. Furthermore, a base for future researchers for conducting studies on emerging markets, have been contributed. These results are also important to risk managers and and investors.

A non-elliptical orthogonal GARCH model for portfolio selection under transaction costs

Covariance matrix forecasts for portfolio optimization have to balance sensitivity to new data points with stability in order to avoid excessive rebalancing. To achieve this, a new orthogonal GARCH model for a multivariate set of non-Gaussian asset returns is proposed. The conditional return distribution is multivariate generalized hyperbolic and the dispersion matrix dynamics are driven by the leading factors in a principal component decomposition. Each of these leading factors is endowed with a univariate GARCH structure, while the remaining eigenvalues are kept constant over time. Joint maximum likelihood estimation of all model parameters is performed via an expectation maximization algorithm, and is applicable in high dimensions. The new model generates realistic correlation forecasts even for large asset universes and captures rising pairwise correlations in periods of market distress better than numerous competing models. When applied to portfolio optimization, it generates strategies with lower turnover and maximum drawdown, and superior risk-adjusted returns net of transaction costs. Moreover, unlike its competitors, it performs well in the sudden market downturn triggered by the global COVID-19 pandemic.

Intraday conditional value at risk: A periodic mixed‐frequency generalized autoregressive score approach

AbstractWe propose a copula‐based periodic mixed frequency generalized autoregressive (GAS) framework in order to model and forecast the intraday exposure conditional value at risk (ECoVaR) for an intraday asset return and the corresponding market return. In particular, we analyze GAS models that account for long‐memory‐type of dependencies, periodicities, asymmetric nonlinear dependence structures, fat‐tailed conditional return distributions, and intraday jump processes for asset returns. We apply our framework in order to analyze the ECoVaR forecasting performance for a large data set of intraday asset returns of the S&P500 index.

Dynamics of Equity Factor Returns and Asset Pricing

AbstractIn empirical equity asset pricing, the stochastic discount factor (SDF) is implicitly modeled as a linear function of equity factors and is influenced by the empirical properties of the factor returns. We investigate the pricing error introduced by a misspecified SDF which ignores each of the following established empirical phenomena: autocorrelation, dynamics of covariances, dynamics of correlations, and heavy tails for the conditional factor return distribution. We consider near-linear SDFs and nonlinear specifications characterized by a high degree of risk aversion. We find that assuming constant covariances or constant correlations can significantly overprice certain equity portfolios at all risk-aversion levels and that ignoring fat tails can lead to large pricing errors for some derivative assets for highly nonlinear SDFs.

Cross-sectional Variation of Option Implied Volatility Skew

The slope of the option implied volatility plot against the strike reflects the risk-neutral skewness of the underlying security's conditional return distribution. We identify two principal risk sources that contribute to the cross-sectional variation of individual stock options' implied volatility skew: the market risk exposure of the stock's return and the company's default risk. Once controlled for these two risk exposures and the implied volatility level, the remaining idiosyncratic variation of the implied volatility skew reflects more of investor expectation and sentiment on the stock's future price movement and can be used to predict future stock returns with more accuracy.

The effects of investor attention and policy uncertainties on cross-border country exchange-traded fund returns

Using a new panel quantile regression approach, this research explores how investor attention and policy uncertainties affect conditional return distributions for 126 cross-border U.S. trading single-country exchange traded funds (ETFs). We find that economic, fiscal, and monetary policy uncertainties negatively impact most of the ETF return quantiles, implying that a non-linear relationship exists, but trade policy uncertainty has asymmetric impacts on current returns that are salient positive in the following period. Therefore, considering four policy uncertainties allows us to completely analyze a single-country ETF market, thus providing valuable insights for ETF portfolio investors, hedge trading, and policymakers.

Predictability of China’s Stock Market Returns Based on Combination of Distribution Forecasting Models

No consensus exists in the literature on whether stock prices can be predicted, with most existing studies employing point forecasting to predict returns. By contrast, this study adopts the new perspective of distribution forecasting to investigate the predictability of the stock market using the model combination strategy. Specifically, the Shanghai Composite Index and the Shenzhen Component Index are selected as research objects. Seven models – GARCH-norm, GARCH-sstd, EGARCH-sstd, EGARCH-sstd-M, one-component Beta-t-EGARCH, two-component Beta-t-EGARCH, and the EWMA-based nonparametric model – are employed to perform distribution forecasting of the returns. The results of out-of-sample forecasting evaluation show that none of the individual models is “qualified” in terms of predictive power. Therefore, three combinations of individual models were constructed: equal weight combination, log-likelihood score combination, and continuous ranked probability score combination. The latter two combinations were found to always have significant directional predictability and excess profitability, which indicates that the two combined models may be closer to the real data generation process; from the perspective of economic evaluation, they may have a predictive effect on the conditional return distribution in China’s stock market.

Does the price of strategic commodities respond to U.S. partisan conflict?

A noteworthy feature of U.S. politics in recent years is serious partisan conflict, which has led to intensifying polarization and exacerbating high policy uncertainty. The US is a significant player in oil and gold markets. Oil and gold also form the basis of important strategic reserves in the US. We investigate whether U.S. partisan conflict affects the returns and price volatility of oil and gold using a parametric test of Granger causality in quantiles. The empirical results suggest that U.S. partisan conflict has an effect on the returns of oil and gold, and the effects are concentrated at the tail of the conditional distribution of returns. More specifically, the partisan conflict mainly affects oil returns when the crude oil market is in a bearish state (lower quantiles). By contrast, partisan conflict matters for gold returns only when the gold market is in a bullish scenario (higher quantiles). In addition, for the volatility of oil and gold, the predictability of partisan conflict index virtually covers the entire distribution of volatility.

Predicting Aggregate and State-Level US House Price Volatility: The Role of Sentiment

This paper examines the predictive ability of housing-related sentiment on housing market volatility for 50 states, District of Columbia, and the aggregate US economy, based on quarterly data covering 1975:3 and 2017:3. Given that existing studies have already shown housing sentiment to predict movements in aggregate and state-level housing returns, we use a k-th order causality-in-quantiles test for our purpose, since this methodology allows us to test for predictability for both housing returns and volatility simultaneously. In addition, this test being a data-driven approach accommodates the existing nonlinearity (as detected by formal tests) between volatility and sentiment, besides providing causality over the entire conditional distribution of (returns and) volatility. Our results show that barring 5 states (Connecticut, Georgia, Indiana, Iowa, and Nebraska), housing sentiment is observed to predict volatility barring the extreme ends of the conditional distribution. As far as returns are concerned, except for California, predictability is observed for all of the remaining 51 cases.

Testes para avaliação das previsões de value-at-risk e expected shortfall

A avaliação das previsões de medidas de risco, como o Value-at-Risk (VaR) e o Expected Shortfall (ES), é uma atividade muito relevante para as instituições financeiras. Os testes que realizam esta avaliação foram introduzidos com o objetivo de verificar a efiiência destas previsões. Neste trabalho comparamos o poder empírico de novas classes de testes de avaliação presentes na literatura. Além disso, utilizamos estes procedimentos para avaliar a efiiência das previsôes geradas pelo método de simulação histórica e baseados na distribuição generalizada de Pareto. Para avaliar previsões de VaR, a classe de testes Geométrico-VaR destacou-se por ter um poder empírico maior que os outros testes nos cenários simulados. Isto evidencia as vantagens de trabalhar com durações discretas e incluir covariáveis nos modelos de testes. Para avaliar previsões de ES, aqueles baseados em distribuições condicionais do retorno ao VaR mostraram um alto poder para grandes tamanhos amostrais. Adicionalmente, mostramos que o método baseado na distribuição generalizada de Pareto utilizando durações e covariáveis resulta em ótimo desempenho nas previsões de VaR e ES.