# Browsing by Author "Bollerslev, Tim"

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Item Restricted A Capital Asset Pricing Model with Time Varying Covariances(Journal of Political Economy, 1988) Bollerslev, Tim; Engle, Robert F; Wooldridge, Jeffrey MItem Open Access ARCH Models(1994) Bollerslev, Tim; Engle, Robert F; Nelson, Daniel BThis chapter evaluates the most important theoretical developments in ARCH type modeling of time-varying conditional variances. The coverage include the specification of univerate parametric ARCH models, general inference procedures, conditions for stationarity and ergodicity, continuous time methods, aggregation and forecasting of ARCH models, multivariate conditional covariance formulations, and the use of model selection criteria in an ARCH context. Additionally, the chapter contains a discussion of the empirical regularities pertaining to the temporal variation in financial market volatility. Motivated in part by recent results on optimal filtering, a new conditional variance model for better characterizing stock return volatility is also presented.Item Open Access Common Persistence in Conditional Variances(Econometrica, 1994) Bollerslev, Tim; Engle, Robert FItem Open Access Daily House Price Indexes: Volatility Dynamics and Longer-Run Predictions(2014) Wang, WenjingThis dissertation presents the construction procedure of “high-frequency” daily measure of changes in housing valuations, and analyzes its return dynamics, as well as investigates its relationship to capital markets. The dissertation consists of three chapters. The first chapter introduces the house price index methodologies and housing transaction data, and reviews the related literature. The second chapter shows the construction and modeling of daily house price indexes and highlights the informational advantage of the daily indexes. The final chapter provides detailed empirical and theoretical investigations of housing index return volatilities.

Chapter 2 discusses the relationship of the housing market with the other markets, such as consumer good market and financial markets. Different housing price indexes and their construction methodologies are introduced, with emphases on the repeat sales model and S&P/Case Shiller Home Price Index. A detailed description of the housing transaction data I use in the dissertation is also provided in this chapter.

Chapter 3 is co-authored with Professor Tim Bollerslev and Professor Andrew Patton. We construct daily house price indexes for ten major U.S. metropolitan areas. Our calculations are based on a comprehensive database of several million residential property transactions and a standard repeat-sales method that closely mimics the procedure used in the construction of the popular monthly Case-Shiller house price indexes. Our new daily house price indexes exhibit dynamic features similar to those of other daily asset prices, with mild autocorrelation and strong conditional heteroskedasticity. The correlations across house price index returns are low at the daily frequency, but rise monotonically with the return horizon, and are commensurate with existing empirical evidence for existing monthly and quarterly house price series. Timely and accurate measures of house prices are important in a variety of applications, and are particularly valuable during times of turbulence, such as the recent housing crisis. To quantify the informational advantage of our daily index, we show that a relatively simple multivariate time series model for the daily house price index returns, explicitly allowing for commonalities across cities and GARCH effects, produces forecasts of monthly house price changes that are superior to various alternative forecast procedures based on lower frequency data.

Chapter 4 investigates the properties of housing index return volatilities. Similar to stock market volatility, housing volatilities are found to respond asymmetrically to negative and positive returns. A direct test of volatility on changes in loan-to-value ratio suggests that the observed volatility asymmetry does not stem from changes in degree of housing financial leverage, but could result from the risk premium carried by housing volatility, which is supported by a consumption-based asset pricing model with housing. Moreover, housing and stock volatilities are found to be positively correlated from a set of predictive regressions based on realized variances of housing and stock markets, in which higher (lower) volatility in one market will be followed by higher (lower) volatility in the other. Finally, housing and stock cross-sectional return dispersions are shown to contain useful information in predicting both within-market and cross-market realized volatilities.

Item Open Access Dan Nelson Remembered(Journal of Business and Economic Statistics, 1995) Bollerslev, Tim; Rossi, Peter EItem Open Access Equity Clusters Through the Lens of Realized SemicorrelationsBollerslev, Tim; Patton, Andrew J; Zhang, HaozheItem Open Access Essays in Empirical Asset Pricing(2017) Zhao, BingzhiThis dissertation consists of three essays that shed light on various problems in empirical asset pricing and portfolio management by applying high frequency econometric techniques. Chapter 1, An Efficient Factor from Basis “Anomalies”, examines the challenges brought by the massive asset-pricing “anomalies” and develops a novel method to construct a highly ex-post efficient portfolio that prices asset returns in a one-factor model, Relative Asset Pricing Model (RAP). The one single empirical factor outperforms and drives out 11 of the most acclaimed multi-factors combined. It provides evidence that the massive amount of asset pricing “anomalies” are in fact manifested by non-linear effects of three basic stock characteristics, size, book-to-market and momentum. It also demonstrates that an arbitrary number of trading signals can be engineered to pass existing asset pricing tests as new “unique anomalies”, even though they are purely the projections of the efficient factor beta onto a set of characteristics. Chapter 2, Good Volatility, Bad Volatility and the Cross Section of Stock Returns, documents that relative good-minus-bad jump measure extracted from high frequency intra-day data have strong cross-sectional return predictability. Chapter 3, Factors and Their Economic Value in Volatility Forecast, develops a simple and reliable volatility forecast model in large cross-section that incorporates volatility factor structure and add significant values to investors in portfolio optimization.

Item Open Access Essays on Financial Econometrics(2018) Xue, YuanThis dissertation consists of three essays. The first essay, "Volume, volatility and Macroeconomic Announcements" studies the relationship between trading intensity and price volatility and how it is affected by investors' disagreement on a common public signal around macroeconomic announcements. Inspired by a difference-of-opinion model in which investors agree to disagree, we use high frequency data and empirically show that the volume-volatility elasticity of SP 500 ETF is uniformly below 1. Besides, the elasticity decreases with disagreement measures such as the forecast dispersion on unemployment rate and uncertainty measures, as well as a textual based tone measure constructed using FOMC statements. This paper provides new evidences on how information is processed in financial market.

The second essay, "Investor Sentiment and Volume Volatility Relationship" shows that investor sentiment plays a role on information processing in financial markets. We incorporate a one-factor asset pricing model into the difference-of-opinion model to derive the volume-volatility relationship for individual stocks. We separate the sample into high and low sentiment periods and use high frequency data to show that investors' disagreement measures only significantly reduce volume-volatility elasticity around macroeconomic announcements during high-sentiment periods, for both the S&P 500 ETF and Dow Jones

30 components. This result is consistent with

changes in the confidence level of investors when sentiment regime shifts. Our estimates of elasticity also decrease significantly with the

ratio of idiosyncratic variance, which indicates that higher idiosyncratic risks introduce larger dispersion among investors.

In the third essay, "Efficient Estimation of Integrated Functional of Variance with Irregular

Observation Time", we propose an efficient estimator of the integrated functional of the variance with irregular observation time of prices. We propose the consistency and central limit theorems, and then validate the theorems through proofs and simulations.

Item Open Access Essays on Financial Econometrics: Analysis of Classical Problems with Novel Econometric Methods(2021) Zhang, QiushiThe dissertation consists of two essays that apply nonparametric econometric tools to studying the financial market. The first essay, “Sentiment and Volume-Volatility Elasticity” is presented in Chapter 2 and explores the relationship between sentiment and market participants' trading activities around public news announcements. We develop a theoretical model under the short-sale constraint and the model predicts a nonlinear relationship between sentiment and the volume-volatility elasticity. We estimate parametric regression models and carry out nonparametric series estimation around important macroeconomic news announcements with high-frequency intraday trading volume and transaction price data of the S&P 500 E-mini futures contract. Empirical results not only corroborate predictions of the theoretical model, but also suggest varying effects of sentiment on the volume-volatility elasticity around announcements of different importance.

Chapter 3 presents the second essay, “Conditional Superior Performing Assets”. We utilize a novel functional test for conditional moment inequalities to select conditional superior performing assets (CSPA). We apply the CSPA test to evaluate the performance of U.S. mutual funds. The test is carried out with gross as well as risk-adjusted returns of domestic equity mutual funds bearing various investment objectives. By inverting the CSPA test for sets of benchmark assets, we obtain confidence sets for the uniformly most superior asset. Empirical results indicate superior performance of funds with various investment objectives over certain conditioning states of measures from various aspects of the economy. Additionally, the CSPA confidence sets can serve as criteria for fund selection. The usefulness of the CSPA test on fund evaluation is demonstrated through identifying significant conditional superior performance from assets that are indistinguishable unconditionally.

Item Open Access Essays on High-Frequency Factors(2024) Aleti, SakethThis dissertation provides an empirical analysis of asset pricing factors in a continuous-time framework. The value of such a framework is that it affords a distinction between continuous returns, generally modelled by Brownian motion, and discontinuous returns, often referred to as "jumps.'' The focus of the dissertation is on how the asset pricing implications of these two types of risk differ.

To measure these types of risk, it is crucial to use high-frequency return data to justify the use of infill asymptotic arguments that enable the identification of price jumps and volatility functionals. Correspondingly, in the first essay, I develop a dataset of high-frequency factor portfolio returns that allows for exactly this and, armed with this dataset, I further engage in a continuous-time econometric study of factor jump risk as well as factor continuous and (semi)jump risk premia. To begin, I study the jumps embedded in the factor portfolio returns, finding significant evidence thereof and suggesting that non-market systematic jump risk is non-trivial. These findings motivate a deeper analysis of said risk and, in particular, its pricing implications. To this end, I estimate the risk premia of each factor in my dataset, first estimating continuous/jump betas using high-frequency regressions and second estimating the risk premia using cross-sectional regressions. My results show that these two categories of risk draw different premia with jump risk being far more important for explaining cross-sectional return variation.

Having illustrated the existence and importance of non-market jump risk, I then go on to study exactly what economic events drive said risk in the second essay of my dissertation, co-authored with Tim Bollerslev. In this latter essay, we construct an estimate of the tangency portfolio using the high-frequency factor returns previously defined; this portfolio serves as a univariate representation of all systematic risk and thus facilitates a straightforward analysis of both systematic market and non-market jumps. We then connect the jumps in this portfolio, again with identification leaning on infill asymptotics, with a large dataset of newswire articles to understand what news topics drive the jumps. We further price each of these topics, estimating their risk premia to understand the economic significance of each. We find that monetary policy and finance news is the most important followed by news about international affairs and macroeconomic data. We also decompose the jumps into more primitive economic shocks, finding that these systematic equity jumps primarily correspond to growth and short-rate shocks and that there exists substantial heterogeneity in what news topics drive the different primitive shocks.

The third essay of this dissertation, co-authored with Tim Bollerslev and Mathias Siggaard, takes a different angle, instead trying to understand whether the market portfolio can be predicted using the lagged high-frequency factor returns. Our analysis in this essay similarly exploits the precision of jump detection afforded by the high-frequency data but uses the separated continuous/discontinuous returns to explore heterogeneity in the predictive content therein. Moreover, we consider using the continuous returns as regressands in our in-sample regressions, leaning on the well-established theoretical no-arbitrage argument that any predictability should lie solely in the continuous component of returns. Our forecasts, constructed using Lasso regressions to handle the high-dimensionality of our features, corroborate this idea, evincing market return predictability with strong statistical and economic significance. In addition, much of the predictive content of our forecasts can be traced back to a few factors related to turnover, connecting our results to past work on volume and information absorption.

Item Open Access Financial Market Volatility and Jumps(2007-05-07T19:07:04Z) Huang, XinThis dissertation consists of three related chapters that study financial market volatility, jumps and the economic factors behind them. Each of the chapters analyzes a different aspect of this problem. The first chapter examines tests for jumps based on recent asymptotic results. Monte Carlo evidence suggests that the daily ratio z-statistic has appropriate size, good power, and good jump detection capabilities revealed by the confusion matrix comprised of jump classification probabilities. Theoretical and Monte Carlo analysis indicate that microstructure noise biases the tests against detecting jumps, and that a simple lagging strategy corrects the bias. Empirical work documents evidence for jumps that account for seven percent of stock market price variance. Building on realized variance and bi-power variation measures constructed from high-frequency financial prices, the second chapter proposes a simple reduced form framework for modelling and forecasting daily return volatility. The chapter first decomposes the total daily return variance into three components, and proposes different models for the different variance components: an approximate long-memory HAR-GARCH model for the daytime continuous variance, an ACH model for the jump occurrence hazard rate, a log-linear structure for the conditional jump size, and an augmented GARCH model for the overnight variance. Then the chapter combines the different models to generate an overall forecasting framework, which improves the volatility forecasts for the daily, weekly and monthly horizons. The third chapter studies the economic factors that generate financial market volatility and jumps. It extends the recent literature by separating market responses into continuous variance and discontinuous jumps, and differentiating the market’s disagreement and uncertainty. The chapter finds that there are more large jumps on news days than on no-news days, with the fixed-income market being more responsive than the equity market, and non-farm payroll employment being the most influential news. Surprises in forecasts impact volatility and jumps in the fixed-income market more than the equity market, while disagreement and uncertainty influence both markets with different effects on volatility and jumps. JEL classification: C1, C2, C5, C51, C52, F3, F4, G1, G14Item Open Access High-Frequency Financial Volatility and the Pricing of Volatility Risk(2009) Sizova, NataliaThe idea that integrates parts of this dissertation is that high-frequency data allow for more precise and robust methods for forecasting financial volatility and elucidating the role of volatility in forming asset prices. Thus, the first two chapters compare the performance of model-free forecasts specifically designed to employ high-frequency data with the performance of "classical" forecasts developed for daily data. The final chapter of the dissertation incorporates high-frequency data to verify the predictions of asset pricing models about the risk-return relationships at the very shortest horizons. The results are arranged in the following order.

Chapter 1 presents the analytical comparison of feasible reduced-form forecasts designed to employ high-frequency data and model-based forecasts updated to use high-frequency data. The prediction errors of both forecast groups are calculated using the ESV-representation of Meddahi (2003), which allows one to generalize the statements from this analysis to a wider class of volatility processes. The results show that reduced-form forecasts outperform model-based forecasts at longer horizons and perform just as well for day-ahead forecasts.

Chapter 2 expands the conclusions from Chapter 1 to economic measures of forecast performance. These performance measures are constructed within a microeconomic framework that mimics the decision making process of a variance trader who uses volatility forecasts to predict the future profitability of a trade. The results support the theoretical predictions of Chapter 1.

Chapter 3 is co-authored with Professor Tim Bollerslev and Professor George Tauchen. It extends the "long-run risk" model of Bansal and Yaron(2004) to consistently price volatility risks and to be applicable to high-frequency data. The hypothesis at the outset is that while financial volatility is a long-memory process (it exhibits long-range dependence), its own variance (volatility-of-volatility) is a short memory one. Then the presented model implies that the volatility premium (the measure of the difference between option-implied and expected variances) should be short-memory as well. This insight is confirmed by studying cross correlations of returns and volatility measures. Horizons at which cross correlations are considered are unique for the literature; they start at intra-day values, as short as five minutes.

Item Open Access Macro Announcement Disagreement with Jump Regressions(2021) Salim Saker Chaves, LeonardoThis dissertation consists of two main essays in which it extends our knowledge on how stock market investors process the information from macro announcements. In the first essay, we extend the existing econometric theory to study the relation between jumps in multiple processes at a high-frequency. More specifically, we develop new high-frequency-based inference procedures for analyzing the relationship between jumps in instantaneous moments of stochastic processes. The estimation consists of two steps: the nonparametric determination of the jumps as differences in local averages, followed by a minimum-distance type estimation of the parameters of interest under general loss functions that include both least-square and more robust quantile regressions as special cases. The resulting asymptotic distribution of the estimator, derived under an infill asymptotic setting, is highly nonstandard and generally not mixed normal. In addition, we establish the validity of a novel bootstrap algorithm for making feasible inference including bias-correction. In the second essay, the new methods are applied to determine whether investors disagree when they process relevant macro-news announcements. If investors do disagree, we investigate the systematic components that drive disagreement. The high frequency data on stocks price and trade enable us to precisely isolate the news impact, and we use the volume-volatility elasticity framework to interpret our estimation. We consider a set of stock characteristics that might contribute to investor disagreement: idiosyncratic volatility, market size, value, and institutional ownership. Our findings suggest that investors do disagree whenever there is more uncertainty about future payoffs. Furthermore, the different stock characteristics explain, to a large extent, the deviation from the case of no disagreement. For last, we explore how the direction of stock misprice affects the elasticity and verify that the overall investor disagreement may not be entirely observed due to arbitrage constraints.

Item Open Access Realized Semibetas: Signs of Things to Come(2020-02-20) Bollerslev, Tim; Patton, Andrew J; Quaedvlieg, RogierItem Open Access Realized Semicovariances(Econometrica: journal of the Econometric Society, 2020) Bollerslev, Tim; Li, Jia; Patton, Andrew; Quaedvlieg, RogierWe propose a decomposition of the realized covariance matrix into components based on the signs of the underlying high‐frequency returns, and we derive the asymptotic properties of the resulting realized semicovariance measures as the sampling interval goes to zero. The first‐order asymptotic results highlight how the same‐sign and mixed‐sign components load differently on economic information related to stochastic correlation and jumps. The second‐order asymptotic results reveal the structure underlying the same‐sign semicovariances, as manifested in the form of co‐drifting and dynamic “leverage” effects. In line with this anatomy, we use data on a large cross‐section of individual stocks to empirically document distinct dynamic dependencies in the different realized semicovariance components. We show that the accuracy of portfolio return variance forecasts may be significantly improved by exploiting the information in realized semicovariances.Item Open Access Three Essays on High-Frequency and High-Dimensional Financial Data Analysis(2013) Li, ZhengziIn recent decades, financial market data has become available with increasingly higher frequency and higher dimension. This rapidly growing amount of financial data has created many research opportunities and challenges. In this dissertation, I address several important issues in the areas of asset pricing, financial econometrics, and computational statistics using large-scale financial data techniques. In terms of asset pricing (Chapter 2), I investigate the relationship between the cross-section of expected stock returns and the associated market risks. In terms of financial econometrics (Chapter 3), I uncover the sources of extreme dependence risks between assets. In terms of computational statistics (Chapter 4), I design novel algorithms for efficiently estimating large-scale covariance matrices.

In Chapter 2, using a large novel high-frequency dataset, I investigate how individual stock returns respond to two different market changes: continuous and discontinuous (jump) movements. I also explore whether the different systematic risks associated with those two distinct movements are priced in the cross-section of expected stock returns. I show that the cross-section of expected stock returns reflects a risk premium for the systematic discontinuous risk but not for the systematic continuous risk. An investment strategy that goes long stocks in the highest discontinuous beta decile and shorts stocks in the lowest discontinuous beta decile produces average excess returns of 17% per annum. I estimate the risk premium for the systematic discontinuous risk is approximately 3% per annum after controlling for the usual firm characteristic variables including size, book-to-market ratio, momentum, idiosyncratic volatility, coskewness, cokurtosis, realized-skewness, realized-kurtosis, maximum daily return, and illiquidity.

In Chapter 3, co-authored with Professor Tim Bollerslev and Professor Viktor Todorov, we provide a new framework for estimating the systematic and idiosyncratic jump tail risks in the financial asset prices. Our estimates are based on in-fill asymptotics for directly identifying the jumps, together with Extreme Value Theory (EVT) approximations and methods-of-moments for assessing the tail decay parameters and the tail dependencies. On implementing the aforementioned procedures with a panel of intraday prices for a large cross-section of individual stocks and the S&P 500 market portfolio, we find that the distributions of the systematic and idiosyncratic jumps are both generally heavy-tailed and close to symmetric. We also show that the jump tail dependencies deduced from the high-frequency data together with the day-to-day variation in the diffusive volatility account for the "extreme" joint dependencies observed at the daily level.

When it comes to estimating large covariance matrices, a major challenge is the number of observations is often only comparable or even smaller than the number of parameters. Therefore, in Chapter 4, co-authored with Professor Hao Wang, we induce sparsity via graphical models in order to produce stable and robust covariance matrix estimates. We propose a new algorithm for Bayesian model determination in Gaussian graphical models under G-Wishart prior distributions. We first review recent developments in sampling from G-Wishart distributions for given graphs, with a particular interest in the efficiency of the block Gibbs samplers and other competing methods. We generalize the maximum clique block Gibbs samplers to a class of flexible block Gibbs samplers and prove its convergence. This class of block Gibbs samplers substantially outperforms its competitors along a variety of dimensions. We next develop the theory and computational details of a novel Markov chain Monte Carlo sampling scheme for Gaussian graphical model determination. Our method relies on the partial analytic structure of the G-Wishart distributions integrated with the exchange algorithm. Unlike existing methods, the new method requires neither proposal tuning nor evaluation of normalizing constants of the G-Wishart distributions.

Item Open Access What About Short Run?(2014) Xu, LaiThis dissertation explores issues regarding the short-lived temporal variation of the equity risk premium. In the past decade, the equity risk premium puzzle is resolved by many competing consumption-based asset pricing models. However, before \cite{btz:vrp:rfs}, the return predictability as an outcome of such models has limited empirical support in the short-run. Nowadays, there has been a consensus of the literature that the short-run equity return's predictability is intimately linked with the variance risk premium---the difference between options-implied and actual realized variation measures.

In this work, I continue to argue the importance of the short-lived components in the equity risk premium. Specifically, I first provide simulation evidence of the strong return predictability based on the variance risk premium in the U.S. aggregate market, and document new empirical findings in the international setting. Then I attempt to use a structural macro-finance model to guide through the predictability estimation with much more efficiency gain. Finally I decompose the equity risk premium into two short-lived parts --- tail risk and diffusive risk --- and propose a semi-parametric estimation method for each part. The results are arranged in the following order.

Chapter 1 of the dissertation is co-authored with Tim Bollerslev, James Marrone and Hao Zhou. In this chapter, we demonstrate that statistical finite sample biases cannot ``explain'' this apparent predictability in U.S. market based on variance risk premium. Further corroborating the existing evidence of the U.S., we show that country specific regressions for France, Germany, Japan, Switzerland, the Netherlands, Belgium and the U.K. result in quite similar patterns. Defining a ``global'' variance risk premium, we uncover even stronger predictability and almost identical cross-country patterns through the use of panel regressions.

Chapter 2 of the dissertation is co-authored with Tim Bollerslev and Hao Zhou. In this chapter, we examine the joint predictability of return and cash flow within a present value framework, by imposing the implications from a long-run risk model that allow for both time-varying volatility and volatility uncertainty. We provide new evidences that the expected return variation and the variance risk premium positively forecast both short-horizon returns \textit{and} dividend growth rates. We also confirm that dividend yield positively forecasts long-horizon returns, but that it does not help in forecasting dividend growth rates. Our equilibrium-based ``structural'' factor GARCH model permits much more accurate inference than %the reduced form VAR and

univariate regression procedures traditionally employed in the literature. The model also allows for the direct estimation of the underlying economic mechanisms, including a new volatility leverage effect, the persistence of the latent long-run growth component and the two latent volatility factors, as well as the contemporaneous impacts of the underlying ``structural'' shocks.

In Chapter 3 of the dissertation, I develop a new semi-parametric estimation method based on an extended ICAPM dynamic model incorporating jump tails. The model allows for time-varying, asymmetric jump size distributions and a self-exciting jump intensity process while avoiding commonly used but restrictive affine assumptions on the relationship between jump intensity and volatility. The estimated model implies that the average annual jump risk premium is 6.75\%. The model-implied jump risk premium also has strong explanatory power for short-to-medium run aggregate market returns. Empirically, I present new estimates of the model based equity risk premia of so-called "Small-Big", "Value-Growth" and "Winners-Losers" portfolios. Further, I find that they are all time-varying and all crashed in the 2008 financial crisis. Additionally, both the jump and volatility components of equity risk premia are especially important for the "Winners-Losers" portfolio.