Financial Asset Returns Research Articles

Power transformations of absolute returns and long memory estimation

Abstract Different power transformations of absolute returns of various financial assets have been found to display different magnitudes of sample autocorrelations, a property referred to as the Taylor effect. In this paper, we consider the long memory stochastic volatility model for the returns, under which, the asymptotic rate of decay of the autocorrelations of powers of absolute returns is governed by their long memory parameter. Although the true long memory parameter of powers of absolute returns is the same across different powers, we show that the local Whittle estimator of the long memory parameter has finite-sample bias that differs across the power transformations chosen. A Monte-Carlo experiment provides evidence in support of our theoretical finding that the reported variation of the estimates of the long memory parameter for power transformations of returns could be due to finite-sample bias of the estimator. The local Whittle estimates of powers of absolute returns for the S&P500 index and the DM/USD exchange rate are also examined.

215 Years of Global Multi-Asset Momentum: 1800-2014 (Equities, Sectors, Currencies, Bonds, Commodities and Stocks)

Extending price return momentum tests to the longest available histories of global financial asset returns, including country-specific sectors and stocks, fixed income, currencies, and commodities, as well as U.S. stocks, we create a 215-year history of multi-asset momentum, and we confirm the significance of the momentum premium inside and across asset classes. Consistent with stock-level results, we document a large variation of momentum portfolio betas, conditional on the direction and duration of the return of the asset class in which the momentum portfolio is built. A significant recent rise in pair-wise momentum portfolio correlations suggests features of the data important for empiricists, theoreticians and practitioners alike.

Análise da eficiência de mercado do Ibovespa: uma abordagem com o modelo autorregressivo quantílico

Dependency on financial asset returns has received considerable attention in the finance literature in order to assist in the formulation of strategies of expected positive return and portfolio risk management. However, the market efficiency hypothesis assumes that new information is immediately incorporated to the asset and that the dependency among the returns is null or not significant. Based on this idea, this research aims to analyze the behavior of serial dependence of stock returns of the Ibovespa using the quantile autoregression model (QAR). Daily log-returns of the Bovespa Index from January 2, 2008 to June 13, 2012 have been used. The results indicate that the extreme qua ntiles are associated with positive or negative returns and have a strong and distinct dependence on each other. The dependence of central quantiles is close to zero and similar to the model of ordinary least squares (OLS). The study also identified an asymmetric effect of investors, which was associated with the market state and the location in the quantile. Besides, high past positive or negative autoregressive coefficients lead to future coefficients of the same sign. It is clear, therefore, that the Ibovespa behaves differently from the assumptions of the hypothesis of market efficiency in the weak form. Keywords: quantile autoregression model, market efficiency, dependence.

Detection of Multiple Structural Breaks in Multivariate Time Series

We propose a new nonparametric procedure (referred to as MuBreD) for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second-order) piecewise stationary process, which also identifies the components of the series where the breaks occur. MuBreD is based on a comparison of the estimated spectral distribution on different segments of the observed time series and consists of three steps: it starts with a consistent test, which allows us to prove the existence of structural breaks at a controlled Type I error. Second, it estimates sets containing possible break points and finally these sets are reduced to identify the relevant structural breaks and corresponding components which are responsible for the changes in the autocovariance structure. In contrast to all other methods proposed in the literature, our approach does not make any parametric assumptions, is not especially designed for detecting one single change point, and addresses the problem of multiple structural breaks in the autocovariance function directly with no use of the binary segmentation algorithm. We prove that the new procedure detects all components and the corresponding locations where structural breaks occur with probability converging to one as the sample size increases and provide data-driven rules for the selection of all regularization parameters. The results are illustrated by analyzing financial asset returns, and in a simulation study it is demonstrated that MuBreD outperforms the currently available nonparametric methods for detecting breaks in the dependency structure of multivariate time series. Supplementary materials for this article are available online.

Optimal positioning in financial derivatives under mixture distributions

In this paper, we study and extend the optimal portfolio positioning problem introduced by Brennan and Solanki (1981) and by Leland (1980). For that purpose, we introduce mixtures of probability distributions to model the log returns of financial assets. In this framework, we provide and analyze the general solution for log return with mixture distributions, in particular for the mixture Gaussian case. Our solution is characterized for arbitrary utility functions and for any risk neutral probability. Moreover, we illustrate the solution for a CRRA utility and for the minimal risk-neutral probability. Lastly, we compare our solution with the optimal portfolio within ambiguity. Our results have significant implications to improve the management of structured financial portfolios.

Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance

Modeling covariance structures are known to suffer from the curse of dimensionality. In order to avoid the problem for forecasting, the paper proposes a new factor multivariate stochastic volatility (fMSV) model for realized covariance measures that accommodates asymmetry and long memory. Using the basic structure of the fMSV model, the paper extends the dynamic correlation MSV model, the conditional/stochastic Wishart autoregressive models, the matrix-exponential MSV model, and the Cholesky MSV model. Empirical results for 7 financial asset returns for the US stock returns indicate that the new fMSV models outperform existing dynamic conditional correlation models for forecasting future covariances. Regarding the forecasting performance for one-day, five-day and ten-day horizons, the recommended specification among the new fMSV models is the stochastic Wishart autoregressive specification with asymmetric effects for the periods during and after the global financial crisis, while the Cholesky fMSV model with long memory and asymmetry displays the best performance for periods without the financial turbulence.

COMFORT: A common market factor non-Gaussian returns model

A new multivariate time series model with various attractive properties is motivated and studied. By extending the CCC model in several ways, it allows for all the primary stylized facts of financial asset returns, including volatility clustering, non-normality (excess kurtosis and asymmetry), and also dynamics in the dependency between assets over time. A fast EM-algorithm is developed for estimation. Each element of the vector return at time t is endowed with a common univariate shock, interpretable as a common market factor. This leads to the new model being a hybrid of GARCH and stochastic volatility, but without the estimation problems associated with the latter, and being applicable in the multivariate setting for potentially large numbers of assets. A feasible technique which allows for multivariate option pricing is presented, along with an empirical illustration.

The relationship between South Asian stock returns and macroeconomic variables

This article investigates whether economic variables have explanatory power for share returns in South Asian stock markets. In particular, using data for four South Asian emerging stock markets over the period 1998–2012, the article examines the influence of a selection of local, regional and global economic variables in explaining equity returns; most previous studies that have examined this issue have tended to focus on only local and/or global factors. Important factors are identified by distilling the macroeconomic variables into principal components. Economic activities, real interest rates, real exchange rates and the trade balance represent local factors. Regional factors are represented by interregional trade and regional economic activity while global factors are represented by world financial asset returns and world economic activity. The vector autoregression results suggest that the South Asian markets examined are not efficient. Both local and regional factors can directly and indirectly explain Bangladeshi, Pakistani and Sri Lankan stock returns while the lagged returns of the Pakistani stock market and world economic activity can explain Indian stock returns.

Multivariate Time-VaryingG-HCopula GARCH Model and Its Application in the Financial Market Risk Measurement

Taking full advantage of the strengths ofG-Hdistribution, Copula function, and GARCH model in depicting the return distribution of financial asset, we construct the multivariate time-varyingG-HCopula GARCH model which can comprehensively describe “asymmetric, leptokurtic, and heavy-tail” characteristics, the time-varying volatility characteristics, and the extreme-tail dependence characteristics of financial asset return. Based on the conditional maximum likelihood estimator and IFM method, we propose the estimation algorithm of model parameters. Using the quantile function and simulation method, we propose the calculation algorithm of VaR on the basis of this model. To apply this model on studying a real financial market risk, we select the SSCI (China), HSI (Hong Kong, China), TAIEX (Taiwan, China), and SP500 (USA) from January 3, 2000, to June 18, 2010, as the samples to estimate the model parameters and to measure the VaRs of various index risk portfolios under different confidence levels empirically. The results of the application example are in line with the actual situation and the risk diversification theory of portfolio. To a certain extent, these results also justify the feasibility and effectiveness of the multivariate time-varyingG-HCopula GARCH model in depicting the return distribution of financial assets.

Stock Market Investment: The Role of Human Capital

Portfolio choice models counter factually predict (or advise) almost universal equity market participation and a high share for equity in wealth early in life. Empirically consistent predictions have proved elusive without participation costs, informational frictions, or non standard preferences. We demonstrate that once human capital investment is allowed, standard theory predicts portfolio choices much closer to those empirically observed. Two intuitive mechanisms are at work: For participation, human capital returns exceed financial asset returns for most young households and, as households age, this is reversed. For shares, risks to human capital limit the household's desire to hold wealth in risky financial equity.

Is volatility clustering of asset returns asymmetric?

Volatility clustering is a well-known stylized feature of financial asset returns. This paper investigates asymmetric pattern in volatility clustering by employing a univariate copula approach of Chen and Fan (2006). Using daily realized kernel volatilities constructed from high frequency data from stock and foreign exchange markets, we find evidence that volatility clustering is highly nonlinear and strongly asymmetric in that clusters of high volatility occur more often than clusters of low volatility. To the best of our knowledge, this paper is the first one to address and uncover this phenomenon. In particular, the asymmetry in volatility clustering is found to be more pronounced in the stock markets than in the foreign exchange markets. Further, the volatility clusters are shown to remain persistent for over a month and asymmetric across different time periods. Our findings have important implications for risk management. A simulation study indicates that models which accommodate asymmetric volatility clustering can significantly improve the out-of-sample forecasts of Value-at-Risk.

Construction of Value-at-Risk Forecasts Under Different Distributional Assumptions within a BEKK Framework

Financial asset returns are known to be conditionally heteroskedastic and generally non-normally distributed, fat-tailed and often skewed. In order to account for both the skewness and the excess kurtosis in returns, we combine the BEKK model from the multivariate GARCH literature with different multivariate densities for the returns. The set of distributions we consider comprises the normal, Student, Multivariate Exponential Power and their skewed counterparts. Applying this framework to a sample of ten assets from the Dow Jones Industrial Average Index, we compare the performance of equally- weighted portfolios derived from the symmetric and skewed distributions in forecasting out-of-sample Value-at-Risk. The accuracy of the VaR forecasts is assessed by implementing standard statistical backtesting procedures. The results unanimously show that the inclusion of fat-tailed densities into the model specification yields more accurate VaR forecasts, while the further addition of skewness does not lead to significant improvements.

Leverage and Returns: A Cross-Country Analysis of Public Real Estate Markets

The theoretical literature suggests a positive relation between financial leverage and asset returns, but the empirical evidence on this effect is mixed. We examine leverage effects in public real estate markets across eight countries with active public real estate markets. Cross-country public real estate markets provide an interesting testing ground given the significant use of leverage in real estate markets, the variation in REIT capital structures within and across countries, and the cross-country differences in liquidity, ownership, economic, institutional, and capital market structures. After carefully isolating leverage effects in firm-level returns, we find that leverage has a significant effect on returns both unconditionally and conditionally using standard asset pricing models. In addition, greater use of leverage during the 2007–2008 REIT crisis period is associated with larger share price declines.

Sampling-based Inference of Time Deformation Models with Heavy Tail Distributions

This article focuses on simulation-based inference for the time-deformation models directed by a duration process. In order to better capture the heavy tail property of the time series of financial asset returns, the innovation of the observation equation is subsequently assumed to have a Student-t distribution. Suitable Markov chain Monte Carlo (MCMC) algorithms, which are hybrids of Gibbs and slice samplers, are proposed for estimation of the parameters of these models. In the algorithms, the parameters of the models can be sampled either directly from known distributions or through an efficient slice sampler. The states are simulated one at a time by using a Metropolis-Hastings method, where the proposal distributions are sampled through a slice sampler. Simulation studies conducted in this article suggest that our extended models and accompanying MCMC algorithms work well in terms of parameter estimation and volatility forecast.

The role of orthogonal polynomials in adjusting hyperpolic secant and logistic distributions to analyse financial asset returns

In this paper, we will tackle the issue of accounting for skewness and potentially severe excess kurtosis of the empirical distribution of a random variable of interest by adjusting a parent leptokurtic distribution, using orthogonal polynomials. We will show that the polynomial shape adapter that allows the transformation from a given parent to a target distribution is a linear combination of the orthogonal polynomials associated to the former with coefficients depending on the difference between the moments of these two distributions. A recent work (Zoia, Commun Stat Theory Methods 39(1):52–64, 2010) has shown how to adjust the normal density by using Hermite polynomials but this application is suitable only for series with moderate kurtosis (lower than 5). This is why we provide two other parent distributions, the logistic and the hyperbolic secant which, once polynomially adjusted, can be used to reshape series with higher degrees of kurtosis. We will apply these results for modelling heavy-tailed and skewed distributions of financial asset returns by using both the conditional and unconditional approaches. We empirically demonstrate the advantages of using the polynomially adapted distributions in place of popular alternatives.

Normex, a new method for evaluating the distribution of aggregated heavy tailed risks

We develop theoretically as well as numerically a new method, Normex, for the sum of independent heavy tailed distributed random variables, to obtain the most accurate evaluation of its entire distribution. Normex provides sharp results, whatever the number of summands and the tail index are. It is particularly suited when the Central Limit Theorem (CLT) applies but with slow convergence of the mean and with a poor approximation for the tail. Hence, it is filling up a gap in the literature by giving an appropriate limit distribution in this case, in general better than with most standard methods. An application is developed to evaluate the Value-at-Risk of the yearly log returns of financial assets.

Joint extremal behavior of hidden and observable time series with applications to GARCH processes

For a class of generalized hidden Markov models \((X_{t},Y_{t})_{t \in \mathbb {Z}}\) we analyze the limiting behavior of the (suitably scaled) unobservable part \((Y_{t})_{t\in \mathbb Z}\) under an observable extreme event |X 0|>x, as \(x \to \infty \). We discuss sufficient conditions for the existence of this limit and characterize its special structure. Our approach gives rise to an efficient and flexible algorithm for the Monte Carlo evaluation of extremal characteristics (such as the extremal index) of the observable process. Further, our setup allows to evaluate extremal measures which depend on the extremal behavior of X −1,X −2,…, i.e. before X 0. An application to financial asset returns is given by the asymmetric GARCH(1,1) model whose extremal behavior has not been considered before. Our results complement the findings of Segers on the tail chains of single time series (Segers 2007).

Computing equal risk contribution portfolios

For institutional investors, optimizing the trade-off between risk and reward poses significant modeling and computational challenges. Notably, small errors in the estimated returns of financial assets can lead to optimized portfolios that incur far too much risk for the returns they actually deliver. Given these adverse effects, portfolio construction techniques that are based exclusively on risk have grown in popularity. For instance, equal risk contribution (ERC) portfolios seek to equalize the risk contributions of all assets, so that the portfolio is fully diversified from a risk perspective. This paper reviews the nonlinear optimization models that underlie the ERC approach and, in response to the reported difficulty of solving such optimization problems, compares the performance of several nonlinear programming algorithms when constructing ERC portfolios. Our results suggest that performance worsens with a poor choice of algorithm or a bad problem formulation. We provide alternative formulations and also develop heuristic procedures that construct an approximation to the ERC portfolio in an efficient manner.

The relationship between financial asset returns and the well-being of US households

This note considers the effect of changes on the well-being of US residents owing to changes in the value of various financial assets. Ordinary least squares estimates reveal that equity market returns have a significant and asymmetric, impact on the well-being. This result is likely the result of a wealth effect whereby rising (falling) stock markets increase (decrease) the ability to meet basic needs and this contributes to a shifting assessment of life-situation and overall well-being.

A clustering time series model for the optimal hedge ratio decision making

In this study, a novel procedure combining computational intelligence and statistical methodologies is proposed to improve the accuracy of minimum-variance optimal hedge ratio (OHR) estimation over various hedging horizons. The time series of financial asset returns are clustered hierarchically using a growing hierarchical self-organizing map (GHSOM) based on the dynamic behaviors of market fluctuation extracted by measurement of variances, covariance, price spread, and their first and second differences. Instead of using original observations, observations with similar patterns in the same cluster and weighted by a resample process are collected to estimate the OHR. Four stock market indexes and related futures contracts, including Taiwan Weighted Index (TWI), Standard & Poor׳s 500 Index (S&P 500), Financial Times Stock Exchange 100 Index (FTSE 100), and NIKKEI 255 Index, are adopted in empirical experiments to investigate the correlation between hedging horizon and performance. Results of the experiments demonstrate that the proposed approach can significantly improve OHR decisions for mid-term and long-term hedging compared with traditional ordinary least squares and naïve models.