资产配置模型的选择:回报、风险抑或二者兼具

近年来以风险平价为代表的基于风险的配置模型广为流行。这些模型的一大特点是放弃回报信息。而以均值方差模型代表的基于回报的配置模型则认为回报很重要而且默认对回报的预测是准确的。这两种做法都有问题。考虑到回报的可预测性得到了大量经验研究的支持,那么对于基于风险的配置模型而言,完全放弃回报则意味着有关回报的有用信息得不到充分利用。对于基于回报的配置模型而言,不考虑参数估计误差而且对输入参数敏感的缺点也大大抵消了它们利用回报信息带来的好处。那么,回报是否重要以及应该如何使用回报成了资产配置研究所面临的一个重大问题。为此,本文提出以风险平价为配置基准,以贝叶斯VAR回报预测为主观观点的Black-Litterman(贝叶斯BL)模型回答这一命题。利用1952-2016年的美国股票和债券季度数据,本文将贝叶斯BL模型与现有配置模型进行比较研究。实证结果表明,相比基于回报的配置模型,贝叶斯BL模型降低了组合风险;相比基于风险的配置模型,贝叶斯BL模型增强了组合回报。这些特性来自于它既能利用回报可预测性带来的有用信息,又能够发挥基于风险的配置模型在控制风险方面的优势。因此该模型表现出增强回报和控制风险兼具的特点,是一条具有潜力的资产配置新方案。     

LOG-PERIODOGRAM ESTIMATION OF LONG MEMORY VOLATILITY DEPENDENCIES WITH CONDITIONALLY HEAVY TAILED RETURNS

Many recent papers have used semiparametric methods, especially the log-periodogram regression, to detect and estimate long memory in the volatility of asset returns. In these papers, the volatility is proxied by measures such as squared, log-squared, and absolute returns. While the evidence for the existence of long memory is strong using any of these measures, the actual long memory parameter estimates can be sensitive to which measure is used. In Monte-Carlo simulations, I find that if the data is conditionally leptokurtic, the log-periodogram regression estimator using squared returns has a large downward bias, which is avoided by using other volatility measures. In United States stock return data, I find that squared returns give much lower estimates of the long memory parameter than the alternative volatility measures, which is consistent with the simulation results. I conclude that researchers should avoid using the squared returns in the semiparametric estimation of long memory volatility dependencies.     

LOG-PERIODOGRAM ESTIMATION OF LONG MEMORY VOLATILITY DEPENDENCIES WITH CONDITIONALLY HEAVY TAILED RETURNS

ABSTRACT

Many recent papers have used semiparametric methods, especially the log-periodogram regression, to detect and estimate long memory in the volatility of asset returns. In these papers, the volatility is proxied by measures such as squared, log-squared, and absolute returns. While the evidence for the existence of long memory is strong using any of these measures, the actual long memory parameter estimates can be sensitive to which measure is used. In Monte-Carlo simulations, I find that if the data is conditionally leptokurtic, the log-periodogram regression estimator using squared returns has a large downward bias, which is avoided by using other volatility measures. In United States stock return data, I find that squared returns give much lower estimates of the long memory parameter than the alternative volatility measures, which is consistent with the simulation results. I conclude that researchers should avoid using the squared returns in the semiparametric estimation of long memory volatility dependencies.     

APPROXIMATING VOLATILITIES BY ASYMMETRIC POWER GARCH FUNCTIONS

ARCH/GARCH representations of financial series usually attempt to model the serial correlation structure of squared returns. Although it is undoubtedly true that squared returns are correlated, there is increasing empirical evidence of stronger correlation in the absolute returns than in squared returns. Rather than assuming an explicit form for volatility, we adopt an approximation approach; we approximate the γth power of volatility by an asymmetric GARCH function with the power index γ chosen so that the approximation is optimum. Asymptotic normality is established for both the quasi-maximum likelihood estimator (qMLE) and the least absolute deviations estimator (LADE) in our approximation setting. A consequence of our approach is a relaxation of the usual stationarity condition for GARCH models. In an application to real financial datasets, the estimated values for γ are found to be close to one, consistent with the stylized fact that the strongest autocorrelation is found in the absolute returns. A simulation study illustrates that the qMLE is inefficient for models with heavy-tailed errors, whereas the LADE is more robust.     

A Stochastic Volatility Model With Conditional Skewness

We develop a discrete-time affine stochastic volatility model with time-varying conditional skewness (SVS). Importantly, we disentangle the dynamics of conditional volatility and conditional skewness in a coherent way. Our approach allows current asset returns to be asymmetric conditional on current factors and past information, which we term contemporaneous asymmetry. Conditional skewness is an explicit combination of the conditional leverage effect and contemporaneous asymmetry. We derive analytical formulas for various return moments that are used for generalized method of moments (GMM) estimation. Applying our approach to S&P500 index daily returns and option data, we show that one- and two-factor SVS models provide a better fit for both the historical and the risk-neutral distribution of returns, compared to existing affine generalized autoregressive conditional heteroscedasticity (GARCH), and stochastic volatility with jumps (SVJ) models. Our results are not due to an overparameterization of the model: the one-factor SVS models have the same number of parameters as their one-factor GARCH competitors and less than the SVJ benchmark.     

Non-traditional analysis of stock returns

SUMMARY An investigation of the prices of eight individual stocks showed that pricechange returns are significantly less complex than are time-dependent returns. Timedependent returns computed every 15, 30 and 45 minutes were found to be more complex, using a complexity measure. Complexity is quantified by measuring the number of times that the estimated correlation dimension of an observed series is multiplied by when its original sequence is randomly shuffled.     

Bayesian modeling of dynamic extreme values: extension of generalized extreme value distributions with latent stochastic processes

This paper develops Bayesian inference of extreme value models with a flexible time-dependent latent structure. The generalized extreme value distribution is utilized to incorporate state variables that follow an autoregressive moving average (ARMA) process with Gumbel-distributed innovations. The time-dependent extreme value distribution is combined with heavy-tailed error terms. An efficient Markov chain Monte Carlo algorithm is proposed using a state-space representation with a finite mixture of normal distributions to approximate the Gumbel distribution. The methodology is illustrated by simulated data and two different sets of real data. Monthly minima of daily returns of stock price index, and monthly maxima of hourly electricity demand are fit to the proposed model and used for model comparison. Estimation results show the usefulness of the proposed model and methodology, and provide evidence that the latent autoregressive process and heavy-tailed errors play an important role to describe the monthly series of minimum stock returns and maximum electricity demand.     

Estimates of the likelihood of extreme returns in international stock markets

This study applies extreme-value theory to daily international stock-market returns to determine (1) whether or not returns follow a heavy-tailed stable distribution, (2) the likelihood of an extreme return, such as a 20% drop in a single day, and (3) whether or not the likelihood of an extreme event has changed since October 1987. Empirical results reject a heavy-tailed stable distribution for returns. Instead, a Student-t distribution or an autoregressive conditional heteroscedastic process is better able to capture the salient features of returns. We find that the likelihood of a large single-day return diff ers widely across markets and, for the G-7 countries, the 1987 stock-market drop appears to be largely an isolated event. A drop of this magnitude, however, is not rare in the case of Hong Kong. Finally, there is only limited evidence that the chance of a large single-day decline is more likely since the October 1987 market drop; however, exceptions include stock markets in Germany, The Netherlands and the UK.     

The Distribution of Stock Returns When the Market Is Up

Abstract

For some investments, the relation between stock returns and the market proxy is conventionally described by a linear regression model with the normality assumption. This paper derives the distribution of stock returns for a security in an upgrade (or downgrade) market with the assumption that the log stock returns of the market proxy follow a mixture of normal distributions. We discuss MLE and the method of moment estimation for parameters involved in the model. An analysis of stock data in Johannesburg Stock Exchange is included to illustrate the model. This note explains the phenomenon in financial analysis regarding the shape of the distribution of long-run stock returns limited on an upgrade or downgrade market index.     

Finite nonparametric grach model for foreign exchange volatility

GARCH model has been commonly used to describe the volatility of foreign exchange returns, which typically depends on returns many lags before, While the GARCH model provides a simple geometric decaying structure for persistence in time, it restricts tiie impact of variables to Quadratic functions. A finite nonparametric GARCH model is proposed that allows the variables' impact to be a smooth function of any form. A direct local polynomial estimation method for this finite GARCH model is proposed based on results on proportional additive model, and is applied to the German Mark (DEM)/US Dollar (USD) daily returns data. Estimators uf both the decaying rate and the impact function are obtained. Diagnostics show satisfactory out-of-sampie prediction based on the proposed model, which helps to better understand the dynamics of foreign exchange volatility.     

A semi-parametric method for estimating the beta coefficients of the hidden two-sided asset return jumps

ABSTRACT

We introduce a new methodology for estimating the parameters of a two-sided jump model, which aims at decomposing the daily stock return evolution into (unobservable) positive and negative jumps as well as Brownian noise. The parameters of interest are the jump beta coefficients which measure the influence of the market jumps on the stock returns, and are latent components. For this purpose, at first we use the Variance Gamma (VG) distribution which is frequently used in modeling financial time series and leads to the revelation of the hidden market jumps' distributions. Then, our method is based on the central moments of the stock returns for estimating the parameters of the model. It is proved that the proposed method provides always a solution in terms of the jump beta coefficients. We thus achieve a semi-parametric fit to the empirical data. The methodology itself serves as a criterion to test the fit of any sets of parameters to the empirical returns. The analysis is applied to NASDAQ and Google returns during the 2006–2008 period.     

Flexible modeling of conditional distributions using smooth mixtures of asymmetric student t densities

A general model is proposed for flexibly estimating the density of a continuous response variable conditional on a possibly high-dimensional set of covariates. The model is a finite mixture of asymmetric student t densities with covariate-dependent mixture weights. The four parameters of the components, the mean, degrees of freedom, scale and skewness, are all modeled as functions of the covariates. Inference is Bayesian and the computation is carried out using Markov chain Monte Carlo simulation. To enable model parsimony, a variable selection prior is used in each set of covariates and among the covariates in the mixing weights. The model is used to analyze the distribution of daily stock market returns, and shown to more accurately forecast the distribution of returns than other widely used models for financial data.     

Option pricing for generalized distributions

The Black Scholes formula has been widely used to price financial instruments. The derivation of this formula is based on the assumption of lognormally distributed returns which is often in poor agreement with actual data. An option pricing formula based on the generalized beta of the second kind (GB2) is presented. This formula includes the Black Scholes formula as a special case and accommodates a wide variety of nonlognormally distributed returns. The sensitivity of option values to departures from the skewness and kurtosis associated with the lognormal distribution is investigated.     

Inference for Local Autocorrelations in Locally Stationary Models

For nonstationary processes, the time-varying correlation structure provides useful insights into the underlying model dynamics. We study estimation and inferences for local autocorrelation process in locally stationary time series. Our constructed simultaneous confidence band can be used to address important hypothesis testing problems, such as whether the local autocorrelation process is indeed time-varying and whether the local autocorrelation is zero. In particular, our result provides an important generalization of the R function acf() to locally stationary Gaussian processes. Simulation studies and two empirical applications are developed. For the global temperature series, we find that the local autocorrelations are time-varying and have a “V” shape during 1910–1960. For the S&P 500 index, we conclude that the returns satisfy the efficient-market hypothesis whereas the magnitudes of returns show significant local autocorrelations.     

Quantile Plots,Partial Orders,and Financial Risk

Quantile-quantile plots are most commonly used to compare the shapes of distributions, but they may also be used in conjunction with partial orders on distributions to compare the level and dispersion of distributions that have different shapes. We discuss several easily recognized patterns in quantile-quantile plots that suffice to demonstrate that one distribution is smaller than another in terms of each of several partial orders. We illustrate with financial applications, proposing a quantile plot for comparing the risks and returns of portfolios of investments. As competing portfolios have distributions that differ in level, dispersion, and shape, it is not sufficient to compare portfolios using measures of location and dispersion, such as expected returns and variances; however, quantile plots, with suitable scaling, do aid in such comparisons. In two plots, we compare specific portfolios to the stock market as a whole, finding these portfolios to have higher returns, greater risks or dispersion, thicker tails than their greater dispersion alone would justify. Nonetheless, investors in these risky portfolios are more than adequately compensated for the risks undertaken.     

Testing Hypotheses in Nonparametric Models of Production

Data envelopment analysis (DEA) and free disposal hull (FDH) estimators are widely used to estimate efficiency of production. Practitioners use DEA estimators far more frequently than FDH estimators, implicitly assuming that production sets are convex. Moreover, use of the constant returns to scale (CRS) version of the DEA estimator requires an assumption of CRS. Although bootstrap methods have been developed for making inference about the efficiencies of individual units, until now no methods exist for making consistent inference about differences in mean efficiency across groups of producers or for testing hypotheses about model structure such as returns to scale or convexity of the production set. We use central limit theorem results from our previous work to develop additional theoretical results permitting consistent tests of model structure and provide Monte Carlo evidence on the performance of the tests in terms of size and power. In addition, the variable returns to scale version of the DEA estimator is proved to attain the faster convergence rate of the CRS-DEA estimator under CRS. Using a sample of U.S. commercial banks, we test and reject convexity of the production set, calling into question results from numerous banking studies that have imposed convexity assumptions. Supplementary materials for this article are available online.     

流动性信息与资产收益：基于非参数模型的分析

本文首先从全新的角度给出市场深度指标的求解方法,然后结合条件资产定价模型和自回归条件异方差模型的优势建立半变系数模型,并应用于我国股票市场每日收益率的研究,得出四点判断：1、通过非参数方法求解得到的指标值具有显著的平稳性。2、流动性信息的时变性对股票市场存在显著的非线性冲击,而且流动性信息的持续性变化与收益之间存在负向关系。3、得到和经典资产定价模型相同的结论,即市场综合指数对个股具有显著的影响。4、模型验证了流动性信息通过波动性将信息非线性传导给投资者的假设,伴随着流动性信息的时变性,投资者所得到的风险补偿也具备时变性。5、通过实际数据的验证,我们所建立的半变系数模型能够较好的解释流动性信息的传递,也为我们以后的实证研究提供了一个估计和检验流动性信息传导和时变型风险补偿的新方法。     

我国期货市场期货价格收益、交易量、波动性关系的动态分析

我国期货市场发展至今已有十多年的时间 ,但对期货市场内部结构、运行特征的研究非常缺乏 ,本文以国内期货市场最为活跃的期货品种上海期货交易所铜、铝 ,大连商品交易所大豆为代表 ,研究期货价格收益、交易量、波动性之间的动态关系 ,揭示出我国期货市场的内在特征 ,填补国内这方面研究的空白。研究期货价格收益、交易量、波动性之间的动态关系对我们全面认识和把握期货市场具有重要的意义。对期货价格收益与交易量之间关系的研究有助于对期货市场内部结构 ,市场信息传播方式的了解 ;有助于对期货价格分布特征的解释 ;在期货价格收益与交易…     

Long memory stochastic volatility : A bayesian approach

We propose a simulation-based Bayesian approach to the analysis of long memory stochastic volatility models, stationary and nonstationary. The main tool used to reduce the likelihood function to a tractable form is an approximate state-space representation of the model, A data set of stock market returns is analyzed with the proposed method. The approach taken here allows a quantitative assessment of the empirical evidence in favor of the stationarity, or nonstationarity, of the instantaneous volatility of the data.     

Interval estimation for the Sharpe Ratio when returns are not i.i.d. with special emphasis on the GARCH(1,1) process with symmetric innovations

In this paper, assuming that returns follows a stationary and ergodic stochastic process, the asymptotic distribution of the natural estimator of the Sharpe Ratio is explicitly given. This distribution is used in order to define an approximated confidence interval for the Sharpe ratio. Particular attention is devoted to the case of the GARCH(1,1) process. In this latter case, a simulation study is performed in order to evaluate the minimum sample size for reaching a good coverage accuracy of the asymptotic confidence intervals.