Using High-Frequency Data in Dynamic Portfolio Choice

This article evaluates the economic benefit of methods that have been suggested to optimally sample (in an MSE sense) high-frequency return data for the purpose of realized variance/covariance estimation in the presence of market microstructure noise (Bandi and Russell, 2005a, 2008). We compare certainty equivalents derived from volatility-timing trading strategies relying on optimally-sampled realized variances and covariances, on realized variances and covariances obtained by sampling every 5 minutes, and on realized variances and covariances obtained by sampling every 15 minutes. In our sample, we show that a risk-averse investor who is given the option of choosing variance/covariance forecasts derived from MSE-based optimal sampling methods versus forecasts obtained from 5- and 15-minute intervals (as generally proposed in the literature) would be willing to pay up to about 80 basis points per year to achieve the level of utility that is guaranteed by optimal sampling. We find that the gains yielded by optimal sampling are economically large, statistically significant, and robust to realistic transaction costs.     

Using High-Frequency Data in Dynamic Portfolio Choice

This article evaluates the economic benefit of methods that have been suggested to optimally sample (in an MSE sense) high-frequency return data for the purpose of realized variance/covariance estimation in the presence of market microstructure noise (Bandi and Russell, 2005a Bandi , F. M. , Russell , J. R. ( 2005a ). Realized covariation, realized beta, and microstructure noise . Working paper . [Google Scholar], 2008 Bandi , F. M. , Russell , J. R. ( 2008 ). Microstructure noise, realized variance, and optimal sampling . Review of Economic Studies , forthcoming . [Google Scholar]). We compare certainty equivalents derived from volatility-timing trading strategies relying on optimally-sampled realized variances and covariances, on realized variances and covariances obtained by sampling every 5 minutes, and on realized variances and covariances obtained by sampling every 15 minutes. In our sample, we show that a risk-averse investor who is given the option of choosing variance/covariance forecasts derived from MSE-based optimal sampling methods versus forecasts obtained from 5- and 15-minute intervals (as generally proposed in the literature) would be willing to pay up to about 80 basis points per year to achieve the level of utility that is guaranteed by optimal sampling. We find that the gains yielded by optimal sampling are economically large, statistically significant, and robust to realistic transaction costs.     

Recent developments in high dimensional covariance estimation and its related issues,a review

In this paper we review some of recent developments in high dimensional data analysis, especially in the estimation of covariance and precision matrix, asymptotic results on the eigenstructure in the principal components analysis, and some relevant issues such as test on the equality of two covariance matrices, determination of the number of principal components, and detection of hubs in a complex network.     

Estimation of High-Frequency Volatility: An Autoregressive Conditional Duration Approach

We propose a method to estimate the intraday volatility of a stock by integrating the instantaneous conditional return variance per unit time obtained from the autoregressive conditional duration (ACD) model, called the ACD-ICV method. We compare the daily volatility estimated using the ACD-ICV method against several versions of the realized volatility (RV) method, including the bipower variation RV with subsampling, the realized kernel estimate, and the duration-based RV. Our Monte Carlo results show that the ACD-ICV method has lower root mean-squared error than the RV methods in almost all cases considered. This article has online supplementary material.     

Forecasting realized volatility: A review

Forecast methods for realized volatilities are reviewed. Basic theoretical and empirical features of realized volatilities as well as versions of estimators of realized volatility are briefly investigated. Major forecast models featuring the empirical aspects of persistency and asymmetry are discussed in terms of forecasting models for which the heterogeneous autoregressive (HAR) model is one of the most basic one in the recent literature. Forecast methods addressing the issues of jump, break, implied volatility, and market microstructure noise are reviewed. Forecasting realized covariance matrix is also considered.     

Faster Convergence to the Estimation of Quadratic Variation with Microstructure Noise

The continuous quadratic variation of asset return plays a critical role for high-frequency trading. However, the microstructure noise could bias the estimation of the continuous quadratic variation. Zhang et al. (2005 Zhang, L., Mykland, P., Ait-Sahalia, Y. (2005). A tale of two time scales: determining integrated volatility with noisy high-frequency data. J. Amer. Statist. Assoc. 100(472):1394–1411.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) proposed a batch estimator for the continuous quadratic variation of high-frequency data in the presence of microstructure noise. It gives the estimates after all the data arrive. This article proposes a recursive version of their estimator that outputs variation estimates as the data arrive. Our estimator gives excellent estimates well before all the data arrive. Both real high-frequency futures data and simulation data confirm the performance of the recursive estimator.     

Moving Average-Based Estimators of Integrated Variance

We examine moving average (MA) filters for estimating the integrated variance (IV) of a financial asset price in a framework where high-frequency price data are contaminated with market microstructure noise. We show that the sum of squared MA residuals must be scaled to enable a suitable estimator of IV. The scaled estimator is shown to be consistent, first-order efficient, and asymptotically Gaussian distributed about the integrated variance under restrictive assumptions. Under more plausible assumptions, such as time-varying volatility, the MA model is misspecified. This motivates an extensive simulation study of the merits of the MA-based estimator under misspecification. Specifically, we consider nonconstant volatility combined with rounding errors and various forms of dependence between the noise and efficient returns. We benchmark the scaled MA-based estimator to subsample and realized kernel estimators and find that the MA-based estimator performs well despite the misspecification.     

Moving Average-Based Estimators of Integrated Variance

We examine moving average (MA) filters for estimating the integrated variance (IV) of a financial asset price in a framework where high-frequency price data are contaminated with market microstructure noise. We show that the sum of squared MA residuals must be scaled to enable a suitable estimator of IV. The scaled estimator is shown to be consistent, first-order efficient, and asymptotically Gaussian distributed about the integrated variance under restrictive assumptions. Under more plausible assumptions, such as time-varying volatility, the MA model is misspecified. This motivates an extensive simulation study of the merits of the MA-based estimator under misspecification. Specifically, we consider nonconstant volatility combined with rounding errors and various forms of dependence between the noise and efficient returns. We benchmark the scaled MA-based estimator to subsample and realized kernel estimators and find that the MA-based estimator performs well despite the misspecification.     

Sampling Returns for Realized Variance Calculations: Tick Time or Transaction Time?

This article introduces a new model for transaction prices in the presence of market microstructure noise in order to study the properties of the price process on two different time scales, namely, transaction time where prices are sampled with every transaction and tick time where prices are sampled with every price change. Both sampling schemes have been used in the literature on realized variance, but a formal investigation into their properties has been lacking. Our empirical and theoretical results indicate that the return dynamics in transaction time are very different from those in tick time and the choice of sampling scheme can therefore have an important impact on the properties of realized variance. For RV we find that tick time sampling is superior to transaction time sampling in terms of mean-squared-error, especially when the level of noise, number of ticks, or the arrival frequency of efficient price moves is low. Importantly, we show that while the microstructure noise may appear close to IID in transaction time, in tick time it is highly dependent. As a result, bias correction procedures that rely on the noise being independent, can fail in tick time and are better implemented in transaction time.     

Sampling Returns for Realized Variance Calculations: Tick Time or Transaction Time?

This article introduces a new model for transaction prices in the presence of market microstructure noise in order to study the properties of the price process on two different time scales, namely, transaction time where prices are sampled with every transaction and tick time where prices are sampled with every price change. Both sampling schemes have been used in the literature on realized variance, but a formal investigation into their properties has been lacking. Our empirical and theoretical results indicate that the return dynamics in transaction time are very different from those in tick time and the choice of sampling scheme can therefore have an important impact on the properties of realized variance. For RV we find that tick time sampling is superior to transaction time sampling in terms of mean-squared-error, especially when the level of noise, number of ticks, or the arrival frequency of efficient price moves is low. Importantly, we show that while the microstructure noise may appear close to IID in transaction time, in tick time it is highly dependent. As a result, bias correction procedures that rely on the noise being independent, can fail in tick time and are better implemented in transaction time.     

On testing for an identity covariance matrix when the dimensionality equals or exceeds the sample size

This article explores the problem of testing the hypothesis that the covariance matrix is an identity matrix when the dimensionality is equal to the sample size or larger. Two new test statistics are proposed under comparable assumptions to those statistics in the literature. The asymptotic distribution of the proposed test statistics are found and are shown to be consistent in the general asymptotic framework. An extensive simulation study shows the newly proposed tests are comparable to, and in some cases more powerful than, the tests for an identity covariance matrix currently in the literature.     

Predicting the Daily Covariance Matrix for S&P 100 Stocks Using Intraday Data—But Which Frequency to Use?

This article investigates the merits of high-frequency intraday data when forming mean-variance efficient stock portfolios with daily rebalancing from the individual constituents of the S&P 100 index. We focus on the issue of determining the optimal sampling frequency as judged by the performance of these portfolios. The optimal sampling frequency ranges between 30 and 65 minutes, considerably lower than the popular five-minute frequency, which typically is motivated by the aim of striking a balance between the variance and bias in covariance matrix estimates due to market microstructure effects such as non-synchronous trading and bid-ask bounce. Bias-correction procedures, based on combining low-frequency and high-frequency covariance matrix estimates and on the addition of leads and lags do not substantially affect the optimal sampling frequency or the portfolio performance. Our findings are also robust to the presence of transaction costs and to the portfolio rebalancing frequency.     

Predicting the Daily Covariance Matrix for S&P 100 Stocks Using Intraday Data—But Which Frequency to Use?

This article investigates the merits of high-frequency intraday data when forming mean-variance efficient stock portfolios with daily rebalancing from the individual constituents of the S&P 100 index. We focus on the issue of determining the optimal sampling frequency as judged by the performance of these portfolios. The optimal sampling frequency ranges between 30 and 65 minutes, considerably lower than the popular five-minute frequency, which typically is motivated by the aim of striking a balance between the variance and bias in covariance matrix estimates due to market microstructure effects such as non-synchronous trading and bid-ask bounce. Bias-correction procedures, based on combining low-frequency and high-frequency covariance matrix estimates and on the addition of leads and lags do not substantially affect the optimal sampling frequency or the portfolio performance. Our findings are also robust to the presence of transaction costs and to the portfolio rebalancing frequency.