499 research outputs found
What About Short Run?
No full textThis 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 andunivariate 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.</p
Cointegration, Fractional Cointegration, and Exchange Rate Dynamics.
No full textMultivariate tests due to Soren Johansen, as implemented by Richard T. Baillie and Tim Bollerslev (1989) and Francis X. Diebold, Javier Gardeazabal, and Kamil Yilmaz (1994), reveal mixed evidence on whether a group of exchange rates are cointegrated. Further analysis of the deviations from the cointegrating relationship suggests that it possesses long memory and may possibly be well described as a fractionally integrated process. Hence, the influence of shocks to the equilibrium exchange rates may only vanish at very long horizons. Copyright 1994 by American Finance Association.
High-Frequency Financial Volatility and the Pricing of Volatility Risk
No full textThe 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.</p
Exchange Rate Returns Standardized by Realized Volatility Are (Nearly) Gaussian
No full textThe prescriptions of modern financial risk management hinge critically on the associated characterization of the distribution of future returns (cf., Diebold, Gunther and Tay, 1998, and Diebold, Hahn and Tay, 1999). Because volatility persistence renders high-frequency returns temporally dependent (e.g., Bollerslev, Chou and Kroner, 1992), it is the conditional return distribution, and not the unconditional distribution, that is of relevance for risk management. This is especially true in high-frequency situations, such as monitoring and managing the risk associated with the day-to-day operations of a trading desk, where volatility clustering is omnipresent. Exchange rate returns are well-known to be unconditionally symmetric but highly leptokurtic. Standardized daily or weekly returns from ARCH and related stochastic volatility models also appear symmetric but leptokurtic; that is, the distributions are not only unconditionally, but also conditionally leptokurtic, although less so than unconditionally.1 A sizable literature explicitly attempts to model the fat-tailed conditional distributions, including, for example, Bollerslev (1987), Engle and Gonzalez-Rivera (1991), and Hansen (1994).
Three Essays on High-Frequency and High-Dimensional Financial Data Analysis
No full textIn 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.</p
Daily House Price Indexes: Volatility Dynamics and Longer-Run Predictions
No full textThis 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.</p
Modeling and Forecasting Realized Volatility
No full textThis paper provides a general framework for integration of high-frequency intraday data into the measurement, modeling and forecasting of daily and lower frequency volatility and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on restrictive and complicated parametric multivariate ARCH or stochastic volatility models, which often perform poorly at intraday frequencies. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we formally develop the links between the conditional covariance matrix and the concept of realized volatility. Next, using continuously recorded observations for the Deutschemark/Dollar and Yen /Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatitilies perform admirably compared to popular daily ARCH and related models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to well-calibrated density forecasts of future returns, and correspondingly accurate quintile estimates. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications.
Correcting the Errors : A Note on Volatility Forecast Evaluation Based on High-Frequency Data and Realized Volatilities
No full textThis note develops general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit the recent asymptotic distributional results in Barndorff-Nielsen and Shephard (2002a), are both easy to implement and highly accurate in empirically realistic situations. On properly accounting for the measurement errors in the volatility forecast evaluations reported in Andersen, Bollerslev, Diebold and Labys (2003), the adjustments result in markedly higher estimates for the true degree of return-volatility predictability.Cette note développe des méthodes d’ajustement, sans spécifier le modèle, qui corrigent le biais induit par les erreurs de mesures de la volatilité dans la mesure de performance des méthodes de prévision de la volatilité. Les procédures, qui utilisent la récente théorie asymptotique de Barndorff-Nielsen et Shephard (2002a), sont faciles à mettre en oeuvre et très performantes dans les situations empiriques usuelles. En particulier, la prise en compte des erreurs de mesures dans les procédures de prévision de Andersen, Bollerslev, Diebold et Labys (2003), amène à des performances de prévision de la volatilité très élevées
Modeling and Forecasting Realized Volatility
No full textThis paper provides a general framework for integration of high-frequency intraday data into the measurement forecasting of daily and lower frequency volatility and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on restrictive and complicated parametric multivariate ARCH or stochastic volatility models, which often perform poorly at intraday frequencies. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we formally develop the links between the conditional covariancematrix and the concept of realized volatility. Next, using continuously recorded observations for the Deutschemark Dollar and Yen / Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatilities perform admirably compared to popular daily ARCH and related models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to well-calibrated density forecasts of future returns, and correspondingly accurate quantile estimates. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications.
Correcting the Errors : A Note on Volatility Forecast Evaluation Based on High-Frequency Data and Realized Volatilities
No full textThis note develops general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit the recent asymptotic distributional results in Barndorff-Nielsen and Shephard (2002a), are both easy to implement and highly accurate in empirically realistic situations. On properly accounting for the measurement errors in the volatility forecast evaluations reported in Andersen, Bollerslev, Diebold and Labys (2003), the adjustments result in markedly higher estimates for the true degree of return-volatility predictability.Cette note développe des méthodes d’ajustement, sans spécifier le modèle, qui corrigent le biais induit par les erreurs de mesures de la volatilité dans la mesure de performance des méthodes de prévision de la volatilité. Les procédures, qui utilisent la récente théorie asymptotique de Barndorff-Nielsen et Shephard (2002a), sont faciles à mettre en oeuvre et très performantes dans les situations empiriques usuelles. En particulier, la prise en compte des erreurs de mesures dans les procédures de prévision de Andersen, Bollerslev, Diebold et Labys (2003), amène à des performances de prévision de la volatilité très élevées
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