Kevin Sheppard

Evaluating Volatility and Correlation Forecasts

This chapter considers the problems of evaluation and comparison of volatility forecasts, both univariate (variance) and multivariate (covariance matrix and/or correlation). We pay explicit attention to the fact that the object of interest in these applications is unobservable, even ex post, and so the evaluation and comparison of volatility forecasts often rely on the use of a “volatility proxy”, i.e. an observable variable that is related to the latent variable of interest. We focus on methods that are robust to the presence of measurement error in the volatility proxy, and to the conditional distribution of returns.

Good Volatility, Bad Volatility: Signed Jumps and The Persistence of Volatility

Using estimators of the variation of positive and negative returns (realized semivariances) and high-frequency data for the S&P 500 Index and 105 individual stocks, this paper sheds new light on the predictability of equity price volatility.We showthat future volatility is more strongly related to the volatility of past negative returns than to that of positive returns and that the impact of a price jump on volatility depends on the sign of the jump, with negative (positive) jumps leading to higher (lower) future volatility. We show that models exploiting these findings lead to significantly better out-of-sample forecast performance.

Ambiguity and the Historical Equity Premium

This paper assesses the quantitative impact of ambiguity on historically observed financial asset returns and growth rates. The single agent, in a dynamic exchange economy, treats the conditional uncertainty about the consumption and dividends next period as ambiguous. We calibrate the agents ambiguity aversion to match only the first moment of the risk-free rate in data and measure the uncertainty each period on the actual, observed history of (U.S.) macroeconomic growth outcomes. Ambiguity aversion accentuates the conditional uncertainty endogenously in a dynamic way, depending on the history; e.g., it increases during recessions. We show the model implied time series of asset returns substantially match the first and second conditional moments of observed return dynamics. In particular, we find the time-series properties of our model generated equity premium, which may be regarded as an index measure of revealed uncertainty, relates closely to those of the macroeconomic uncertainty index recently developed in Jurado, Ludvigson, and Ng (2013).

Multivariate Rotated ARCH Models

This paper introduces a new class of multivariate volatility models which is easy to estimate using covariance targeting, even with rich dynamics. We call them rotated ARCH (RARCH) models. The basic structure is to rotate the returns and then to ?t them using a BEKK-type parameterization of the time-varying covariance whose long-run covariance is the identity matrix. The extension to DCC-type parameterizations is given, introducing the rotated conditional correlation (RCC) model. Inference for these models is computationally attractive, and the asymptotics are standard. The techniques are illustrated using data on some DJIA stocks.

Efficient and Feasible Inference for the Components of Financial Variation Using Blocked Multipower Variation

High frequency financial data allows us to learn more about volatility, volatility of volatility and jumps. One of the key techniques developed in the literature in recent years has been bipower variation and its multipower extension, which estimates time-varying volatility robustly to jumps. We improve the scope and efficiency of multipower variation by the use of a more sophisticated exploitation of high frequency data. This suggests very significant improvements in the power of jump tests. It also yields efficient estimates of the integrated variance of the continuous part of a semimartingale. The paper also shows how to extend the theory to the case where there is microstructure in the observations and derive the first nonparametric high frequency estimator of the volatility of volatility. A fundamental device in the paper is a new type of result showing path-by-path (strong) approximation between multipower and the (unobserved) RV based on the continuous part of the process.

Econometric Analysis of Vast Covariance Matrices Using Composite Realized Kernels and Their Application to Portfolio Choice

We propose a composite realized kernel to estimate the ex-post covariation of asset prices. These measures can in turn be used to forecast the covariation of future asset returns. Composite realized kernels are a data-efficient method, where the covariance estimate is composed of univariate realized kernels to estimate variances and bivariate realized kernels to estimate correlations. We analyze the merits of our composite realized kernels in an ultra high-dimensional environment, making asset allocation decisions every day solely based on the previous day’s data or a short moving average over very recent days. The application is a minimum variance portfolio exercise. The dataset is tick-by-tick data comprising 437 U.S. equities over the sample period 2006–2011. We show that our estimator is able to outperform its competitors, while the associated trading costs are competitive.

On the Computational Complexity of Consumer Decision Rules

A consumer entering a new bookstore can face more than 250,000alternatives. The efficiency of compensatory and noncompensatory decisionrulesfor finding a preferred item depends on the efficiency of their associatedinformation operators. At best, item-by-item information operators lead tolinear computational complexity; set information operators, on the other hand,can lead to constant complexity. We perform an experiment demonstrating thatsubjects are approximately rational in selecting between sublinear and linearrules. Many markets are organized by attributes that enable consumers toemploya set-selection-by-aspect rule using set information operations. In cyberspacedecision rules are encoded as decision aids.

An ordering experiment

Binary comparison operators form the basis of consumer set theory. If humans could only perform binary comparisons, the most efficient procedure a human might employ to make a complete preference ordering of n items would be a n log2n algorithm. But, if humans are capable of assigning each item an ordinal utility value, they are capable of implementing a more efficient linear algorithm. In this paper, we consider six incentive systems for ordering three different sets of objects: pens, notebooks, and Hot Wheels. All experimental evidence indicates that humans are capable of implementing a linear algorithm, for small sets.

Factor High-Frequency Based Volatility (HEAVY) Models

We propose a new class of multivariate volatility models utilizing realized measures of asset volatility and covolatility extracted from high-frequency data. Dimension reduction for estimation of large covariance matrices is achieved by imposing a factor structure with time-varying conditional factor loadings. Statistical properties of the model, including conditions that ensure covariance stationary or returns, are established. The model is applied to modeling the conditional covariance data of large U.S. financial institutions during the financial crisis, where empirical results show that the new model has both superior in- and out-of-sample properties. We show that the superior performance applies to a wide range of quantities of interest, including volatilities, covolatilities, betas and scenario-based risk measures, where the models performance is particularly strong at short forecast horizons.