Chris Kirby

The Economic Value of Volatility Timing Using 'Realized' Volatility

Recent work suggests that intradaily returns can be used to construct estimates of daily return volatility that are more precise than those constructed using daily returns. We measure the economic value of this “realized” volatility approach in the context of investment decisions. Our results indicate that the value of switching from daily to intradaily returns to estimate the conditional covariance matix can be substantial. We estimate that a risk-averse investor would be willing to pay 50 to 200 basis points per year to capture the observed gains in portfolio performance. Moreover, these gains are robust to transaction costs, estimation risk regarding expected returns, and the performance measurement horizon. JEL classification: G11, G14

Stochastic Volatility, Trading Volume, and the Daily Flow of Information

We use state-space methods to investigate the relation between volume, volatility, and ARCH effects within a mixture of distributions hypothesis (MDH) framework. Most recent studies of the MDH fit AR(1) specifications that require the information flow to be highly persistent. Using a more general specification, we find evidence of a large nonpersistent component of volatility that is closely related to the contemporaneous nonpersistent component of volume. However, in contrast to studies that fit volume-augmented GARCH models, we find no evidence that volume subsumes ARCH effects. Since volume-augmented GARCH models are subject to simultaneity bias, our findings should be more robust than these prior results.

Long Memory in Volatility and Trading Volume

We use fractionally-integrated time-series models to investigate the joint dynamics of equity trading volume and volatility. Bollerslev and Jubinski (1999) show that volume and volatility have a similar degree of fractional integration, and they argue that this evidence supports a long-run view of the mixture-of-distributions hypothesis. We examine this issue using more precise volatility estimates obtained using high-frequency returns (i.e., realized volatilities). Our results indicate that volume and volatility both display long memory, but we can reject the hypothesis that the two series share a common order of fractional integration for a fifth of the firms in our sample. Moreover, we find a strong correlation between the innovations to volume and volatility, which suggests that trading volume can be used to obtain more precise estimates of daily volatility for cases in which high-frequency returns are unavailable.

Multivariate Stochastic Volatility Models with Correlated Errors

We develop a Bayesian approach for parsimoniously estimating the correlation structure of the errors in a multivariate stochastic volatility model. Since the number of parameters in the joint correlation matrix of the return and volatility errors is potentially very large, we impose a prior that allows the off-diagonal elements of the inverse of the correlation matrix to be identically zero. The model is estimated using a Markov chain simulation method that samples from the posterior distribution of the volatilities and parameters. We illustrate the approach using both simulated and real examples. In the real examples, the method is applied to equities at three levels of aggregation: returns for firms within the same industry, returns for different industries, and returns aggregated at the index level. We find pronounced correlation effects only at the highest level of aggregation.

Locally Adaptive Semiparametric Estimation of the Mean and Variance Functions in Regression Models

This article proposes a Bayesian method for estimating a heteroscedastic regression model with Gaussian errors, where the mean and the log variance are modeled as linear combinations of explanatory variables. We use Bayesian variable selection priors and model averaging to make the estimation more efficient. The model is made semiparametric by allowing explanatory variables to enter the mean and log variance flexibly by representing a covariate effect as a linear combination of basis functions. Our methodology for estimating flexible effects is locally adaptive in the sense that it works well when the flexible effects vary rapidly in some parts of the predictor space but only slowly in other parts. Our article develops an efficient Markov chain Monte Carlo simulation method to sample from the posterior distribution and applies the methodology to a number of simulated and real examples.

Optimizing the Performance of Sample Mean-Variance Efficient Portfolios

We propose a comprehensive empirical strategy for optimizing the out-of-sample performance of sample mean-variance efficient portfolios. After constructing a sample objective function that accounts for the impact of estimation risk, specification errors, and transaction costs on portfolio performance, we maximize the function with respect to a set of tuning parameters to obtain plug-in estimates of the optimal portfolio weights. The methodology offers considerable flexibility in specifying objectives, constraints, and modeling techniques. Moreover, the resulting portfolios have well-behaved weights, reasonable turnover, and substantially higher Sharpe ratios and certainty-equivalent returns than benchmarks such as the 1/N portfolio and S&P 500 index.

Discrete Stochastic Autoregressive Volatility

We use Markov chain methods to develop a flexible class of discrete stochastic autoregressive volatility (DSARV) models. Our approach to formulating the models is straightforward, and readily accommodates features such as volatility asymmetry and time-varying volatility persistence. Moreover, it produces models with a low-dimensional state space, which greatly enhances computational tractability. We illustrate the proposed methodology for both individual stock and stock index returns, and show that simple first- and second-order DSARV models outperform generalized autoregressive conditional heteroscedasticity and Markov-switching multifractal models in forecasting volatility.

Component-Driven Regime-Switching Volatility

We develop a new class of regime-switching volatility models that are characterized by high-dimensional state spaces, parsimonious transition matrices, and ARMA dynamics for the log volatility process. This combination of features is achieved by assuming that we can decompose the Markov chain that describes regime dynamics into a number of two-state component chains that evolve independently through time. Using daily data for S&P 500 index and IBM shares, we show that our component-driven regime-switching (CDRS) models are capable of outperforming GARCH, component GARCH, regime-switching GARCH, and Markov-switching multifractal models in forecasting realized variances out of sample. Interestingly, we find that CDRS models with simple AR(1) dynamics perform well across the board. Copyright The Author, 2012. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.

ARCH Effects and Trading Volume

Studies that fit volume-augmented GARCH models often find support for the hypothesis that trading volume explains ARCH effects in daily stock returns. We show that this finding is due to an unrecognized constraint imposed by the GARCH specification used for the analysis. Using a more flexible specification, we find no evidence that inserting volume into the conditional variance function of the model reduces the importance of lagged squared returns in capturing volatility dynamics. Volume is strongly correlated with contemporaneous return volatility, but the correlation is driven largely by transitory volatility shocks that have little to do with the highly persistent component of volatility captured by standard volatility models.

Bootstrap Tests of Multiple Inequality Restrictions on Variance Ratios

We develop a block bootstrap method for testing multiple inequality restrictions on variance ratios. The proposed test has reasonable size and power in the presence of strong persistence in conditional variances, making it well suited to applications in financial econometrics.