Generalized Method of Integrated Moments for High‐Frequency Data

We propose a semiparametric two‐step inference procedure for a finite‐dimensional parameter based on moment conditions constructed from high‐frequency data. The population moment conditions take the form of temporally integrated functionals of state‐variable processes that include the latent stochastic volatility process of an asset. In the first step, we nonparametrically recover the volatility path from high‐frequency asset returns. The nonparametric volatility estimator is then used to form sample moment functions in the second‐step GMM estimation, which requires the correction of a high‐order nonlinearity bias from the first step. We show that the proposed estimator is consistent and asymptotically mixed Gaussian and propose a consistent estimator for the conditional asymptotic variance. We also construct a Bierens‐type consistent specification test. These infill asymptotic results are based on a novel empirical‐process‐type theory for general integrated functionals of noisy semimartingale processes.     

Time‐Varying Risk Premium in Large Cross‐Sectional Equity Data Sets

We develop an econometric methodology to infer the path of risk premia from a large unbalanced panel of individual stock returns. We estimate the time‐varying risk premia implied by conditional linear asset pricing models where the conditioning includes both instruments common to all assets and asset‐specific instruments. The estimator uses simple weighted two‐pass cross‐sectional regressions, and we show its consistency and asymptotic normality under increasing cross‐sectional and time series dimensions. We address consistent estimation of the asymptotic variance by hard thresholding, and testing for asset pricing restrictions induced by the no‐arbitrage assumption. We derive the restrictions given by a continuum of assets in a multi‐period economy under an approximate factor structure robust to asset repackaging. The empirical analysis on returns for about ten thousand U.S. stocks from July 1964 to December 2009 shows that risk premia are large and volatile in crisis periods. They exhibit large positive and negative strays from time‐invariant estimates, follow the macroeconomic cycles, and do not match risk premia estimates on standard sets of portfolios. The asset pricing restrictions are rejected for a conditional four‐factor model capturing market, size, value, and momentum effects.     

Demand–Supply Mismatches and Stock Market Performance: A Retailing Perspective

We provide empirical evidence that the volatility of inventory productivity relative to the volatility of demand is a predictor of future stock returns in a sample of publicly listed U.S. retailers over the period 1985–2013. This key performance indicator, entitled demand–supply mismatch (DSM), captures the fact that low variation in inventory productivity relative to variation in demand is indicative of the superior synchronization of demand‐ and supply‐side operations. Applying the Fama and French (1993) three‐factor model augmented with a momentum factor (Carhart 1997), we find that zero‐cost portfolios formed by buying the two lowest and selling the two highest quintiles of DSM stocks yield abnormal stock returns of up to 1.13%. These strong market anomalies related to DSM are observed over the entire sample period and persist after controlling for alternative inventory productivity measures and firm characteristics that are known to predict future stock returns. Further, we reveal that DSM is indicative of lower future earnings and lower sales growth and provide evidence that the observed market inefficiency results from investors’ failure to incorporate all of the information that inventory contains into the pricing of stocks.     

Correcting the Errors: Volatility Forecast Evaluation Using High‐Frequency Data and Realized Volatilities

We develop general model‐free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit recent nonparametric asymptotic distributional results, are both easy‐to‐implement and highly accurate in empirically realistic situations. We also illustrate that properly accounting for the measurement errors in the volatility forecast evaluations reported in the existing literature can result in markedly higher estimates for the true degree of return volatility predictability.     

Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals

This paper studies nonparametric estimation of conditional moment restrictions in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estimators, which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite‐dimensional function parameter space. Some of the PSMD procedures use slowly growing finite‐dimensional sieves with flexible penalties or without any penalty; others use large dimensional sieves with lower semicompact and/or convex penalties. We establish their consistency and the convergence rates in Banach space norms (such as a sup‐norm or a root mean squared norm), allowing for possibly noncompact infinite‐dimensional parameter spaces. For both mildly and severely ill‐posed nonlinear inverse problems, our convergence rates in Hilbert space norms (such as a root mean squared norm) achieve the known minimax optimal rate for the nonparametric mean IV regression. We illustrate the theory with a nonparametric additive quantile IV regression. We present a simulation study and an empirical application of estimating nonparametric quantile IV Engel curves.     

基于非参数与L-Moment估计的股市动态极值ES风险测度研究

通过运用带宽非参数方法、AR-GARCH模型对时间序列的条件均值、条件波动性进行建模估计出标准残差序列,再运用L-Moment与MLE(maximum Likelihood estimation)估计标准残差的尾部的GPD参数,进而运用实验方法测度出风险VaR(value at Risk)及ES(ExpectedShortfall),最后运用Back-Testing方法检验测度准确性。结果表明,基于带宽的非参数估计模型比GARCH簇模型在测度ES上具有更高的可靠性;基于非参数模型与L-Moment的风险测度模型能够有效测度沪深股市的动态VaR与ES。     

Nonparametric Identification under Discrete Variation

This paper provides weak conditions under which there is nonparametric interval identification of local features of a structural function that depends on a discrete endogenous variable and is nonseparable in latent variates. The function delivers values of a discrete or continuous outcome and instruments may be discrete valued. Application of the analog principle leads to quantile regression based interval estimators of values and partial differences of structural functions. The results are used to investigate the nonparametric identifying power of the quarter‐of‐birth instruments used in Angrist and Krueger's 1991 study of the returns to schooling.     

The Realized Laplace Transform of Volatility

We introduce and derive the asymptotic behavior of a new measure constructed from high‐frequency data which we call the realized Laplace transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace transform function of the latent stochastic volatility process over a given interval of time and is robust to the presence of jumps in the price process. With a long span of data, that is, under joint long‐span and infill asymptotics, the statistic can be used to construct a nonparametric estimate of the volatility Laplace transform as well as of the integrated joint Laplace transform of volatility over different points of time. We derive feasible functional limit theorems for our statistic both under fixed‐span and infill asymptotics as well as under joint long‐span and infill asymptotics which allow us to quantify the precision in estimation under both sampling schemes.     

Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models

This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. These models are often ill‐posed and hence it is difficult to verify whether a (possibly nonlinear) functional is root‐n estimable or not. We provide computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is root‐n estimable or not. We establish the following new useful results: (1) the asymptotic normality of a plug‐in penalized sieve minimum distance (PSMD) estimator of a (possibly nonlinear) functional; (2) the consistency of simple sieve variance estimators for the plug‐in PSMD estimator, and hence the asymptotic chi‐square distribution of the sieve Wald statistic; (3) the asymptotic chi‐square distribution of an optimally weighted sieve quasi likelihood ratio (QLR) test under the null hypothesis; (4) the asymptotic tight distribution of a non‐optimally weighted sieve QLR statistic under the null; (5) the consistency of generalized residual bootstrap sieve Wald and QLR tests; (6) local power properties of sieve Wald and QLR tests and of their bootstrap versions; (7) asymptotic properties of sieve Wald and SQLR for functionals of increasing dimension. Simulation studies and an empirical illustration of a nonparametric quantile IV regression are presented.     

Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions

We propose an estimation method for models of conditional moment restrictions, which contain finite dimensional unknown parameters (θ) and infinite dimensional unknown functions (h). Our proposal is to approximate h with a sieve and to estimate θ and the sieve parameters jointly by applying the method of minimum distance. We show that: (i) the sieve estimator of h is consistent with a rate faster than n^‐1/4 under certain metric; (ii) the estimator of θ is √n consistent and asymptotically normally distributed; (iii) the estimator for the asymptotic covariance of the θ estimator is consistent and easy to compute; and (iv) the optimally weighted minimum distance estimator of θ attains the semiparametric efficiency bound. We illustrate our results with two examples: a partially linear regression with an endogenous nonparametric part, and a partially additive IV regression with a link function.     

惯性因子跟踪策略的有效性：来自中国股票市场的证据

基于惯性/反转效应普遍存在的现象以及中国股票市场上不能直接实施惯性/反转投资策略的事实,提出能灵活抓住惯性/反转效应的惯性因子跟踪策略。通过建立和求解惯性因子跟踪策略模型,我们发现,在允许卖空的条件下,最优惯性因子跟踪组合满足两基金分离定理,两基金分别是惯性因子模仿组合和最小方差组合。选择沪深300十大行业指数作为风险资产的代表,实证考察惯性因子跟踪组合的业绩,并与等权组合和最小方差组合的业绩进行比较。结果发现：惯性因子跟踪组合可以在保持和等权组合、最小方差组合风险水平相当的情况下带来更高的收益水平和夏普比率,平均而言,惯性因子跟踪组合的年化超额收益率(8.88%)比等权组合的年化超额收益率高出3.7%,夏普比率(0.42)高出0.18;即便在考虑交易成本的情况下,惯性因子跟踪组合的净夏普比率仍然高出等权组合0.16;综合上方获利和下方风险控制两个方面看,惯性因子跟踪组合优于等权组合。惯性因子跟踪策略的有效性相对于惯性因子的计算方法和样本数据选择区间具有稳健性。     

Ambiguity,Learning, and Asset Returns

We propose a novel generalized recursive smooth ambiguity model which permits a three‐way separation among risk aversion, ambiguity aversion, and intertemporal substitution. We apply this utility model to a consumption‐based asset‐pricing model in which consumption and dividends follow hidden Markov regime‐switching processes. Our calibrated model can match the mean equity premium, the mean risk‐free rate, and the volatility of the equity premium observed in the data. In addition, our model can generate a variety of dynamic asset‐pricing phenomena, including the procyclical variation of price–dividend ratios, the countercyclical variation of equity premia and equity volatility, the leverage effect, and the mean reversion of excess returns. The key intuition is that an ambiguity‐averse agent behaves pessimistically by attaching more weight to the pricing kernel in bad times when his continuation values are low.     

Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods1

We investigate a class of semiparametric ARCH(∞) models that includes as a special case the partially nonparametric (PNP) model introduced by Engle and Ng (1993) and which allows for both flexible dynamics and flexible function form with regard to the “news impact” function. We show that the functional part of the model satisfies a type II linear integral equation and give simple conditions under which there is a unique solution. We propose an estimation method that is based on kernel smoothing and profiled likelihood. We establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model. We also discuss efficiency of both the parametric part and the nonparametric part. We investigate the performance of our procedures on simulated data and on a sample of S&P500 index returns. We find evidence of asymmetric news impact functions, consistent with the parametric analysis.     

基于半鞅过程的中国股市随机波动、跳跃和微观结构噪声统计特征研究

本文基于半鞅过程和非参数统计推断方法,利用已实现幂变差的渐进统计特性,构造检验统计量,在统一的分析框架下,对金融资产价格中随机波动、跳跃和微观结构噪声等问题进行全面系统的研究。并根据上海证券交易所不同行业的股票,上证50 股票指数及其成分股的高频数据进行实证研究。结果表明,我国A 股市场中,噪音交易显著;约43%的风险来源于资产收益过程的随机波动风险,可用股票期权交易对冲;不同来源风险的重要性程度依次为:随机波动的风险、系统性跳跃风险以及异质性跳跃风险;流动性越好的股票越显示出跳跃、尤其是无限小跳的证据。     

稳健非参数VaR建模及风险量化研究

参数VaR模型被广泛应用于风险测量中,然而需要给出具体的结构形式,这就容易发生模型错误设定的灾难,使风险计量的精确性易于产生较大偏差。针对参数VaR模型的设定误差问题,本文构建了SQ-ARCH和Nop-Quantile两个非参数VaR模型,诣在提高传统风险计量模型的灵活性、稳定性和准确性。采用稳健的分位数回归方法,得到了计算这两个VaR模型的具体表达式并给出了模型估计的算法和步骤。Monte Carlo模拟发现无论模型正确还是错误设定非参数VaR模型比参数ARCH类VaR模型更稳健。此外,把这两个稳健非参数VaR模型应用于我国股票市场风险量化的实证分析中。研究结果表明稳健非参数VaR模型比参数ARCH类VaR模型度量风险更准确。     

Nonparametric Estimation of Triangular Simultaneous Equations Models

This paper presents a simple two-step nonparametric estimator for a triangular simultaneous equation model. Our approach employs series approximations that exploit the additive structure of the model. The first step comprises the nonparametric estimation of the reduced form and the corresponding residuals. The second step is the estimation of the primary equation via nonparametric regression with the reduced form residuals included as a regressor. We derive consistency and asymptotic normality results for our estimator, including optimal convergence rates. Finally we present an empirical example, based on the relationship between the hourly wage rate and annual hours worked, which illustrates the utility of our approach.     

Local Partitioned Regression

In this paper, we introduce a kernel‐based estimation principle for nonparametric models named local partitioned regression (LPR). This principle is a nonparametric generalization of the familiar partition regression in linear models. It has several key advantages: First, it generates estimators for a very large class of semi‐ and nonparametric models. A number of examples that are particularly relevant for economic applications will be discussed in this paper. This class contains the additive, partially linear, and varying coefficient models as well as several other models that have not been discussed in the literature. Second, LPR‐based estimators achieve optimality criteria: They have optimal speed of convergence and are oracle‐efficient. Moreover, they are simple in structure, widely applicable, and computationally inexpensive. A Monte Carlo simulation highlights these advantages.     

基于波动持续性的最优组合构建与分散化研究

构建恰当资产组合来减少风险, 是投资组合理论研究的重要目标.由于金融时间序列的波动往往会伴随着持续性特征, 该种特性会增大组合未来收益的风险.本文通过构建随机波动模型序列持续性最优投资组合模型, 以降低金融资产波动的持续性特征对组合收益波动的影响;并通过研究其分散化水平, 考察该投资组合构建方法的有效性与稳健性.研究发现:与均值方差的组合模型相比较, 序列持续性组合的风险分散化水平更好.此研究在资产组合选择方面, 具有较为重要的理论价值及实践意义.     

尾风险度量与定价能力分析

经典资本资产定价模型假设资产收益服从正态分布或者投资者效用函数是二次型,然而实际中资产收益的分布呈现尖峰厚尾特征,因而无法在均值-方差框架下分析风险与收益的关系。与资产收益正常变化相比,极端变化带来的尾风险会对市场风险和投资者的决策行为产生更为显著的影响,因此研究尾风险的度量方法和定价能力具有一定理论和实践意义。 依据极值理论,基于Fama-French的3因子模型无法解释的收益残差构建尾风险度量模型。选取中国股票市场沪深A股作为研究对象,以历史滑动窗估计尾风险,投资组合分析和横截面回归分析的结果都表明尾风险可以稳定地负向预测股票收益,在控制规模、交易量、非流动性、短期反转、中期动量、特质波动率、特质偏度等股票特征后,尾风险的负向预测能力依然显著。引入融资融券交易,发现融资融券标的股票的尾风险显著低于非融资融券标的股票的尾风险,而且可以消除尾风险的负向溢价,因而中国资本市场尚未完全开放融资融券交易机制可能是产生尾风险负向溢价的主要原因。 通过买多-卖空组合构建尾风险定价因子,发现尾风险因子比投资因子和盈利因子有更高的风险价格,而且并不是相对于Fama-French的5因子的冗余因子。与Fama-French的3因子模型和5因子模型相比,Fama-French的3因子或5因子基础上包含尾风险因子的定价模型对股票横截面收益有更好的解释能力,因而有更高的定价效率。 2008年全球金融危机爆发后,对尾风险定价能力的忽略使已有资产定价模型受到广泛批评。因此,探究尾风险的度量方法以及分析尾风险的定价能力,不仅有助于完善和拓展资产定价理论,而且有助于降低投资者对股票价格的认知偏差,提升市场资源配置效率和维护市场稳定性。     

股票收益的截面差异与三因素资产定价模型来自A股市场的经验研究

本文研究沪深A股市场股票收益率的截面性质,并检验Fama-French三因素资产定价模型在中国A股市场的适用性。结果表明,沪深A股市场存在着公司规模效应和股东权益帐面市值比效应,基于市场组合、公司规模和股东权益帐面市值比的Fama-French三因素模型基本上可以解释A股市场收益率的截面差异,但不能完全解释惯性与反转投资策略的超额收益。