RESTRICTED TWO-SCALES COVARIANCE AND RISK CORRECTION IN THE CONTEXT OF HIGH-FREQUENCY FINANCIAL TRADING

• Activity Number: 554
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Scientific and Public Affairs Advisory Committee
• Author(s): Cyrille Nzouda* and Shunpu Zhang and Kent Eskridge
• Companies: University of Nebraska - Lincoln and University of Central Florida and University of Nebraska - Lincoln
• Keywords: Two Scales Covariance (TSCV) ; risk estimator ; Pairwise refresh method ; All-refresh method

Abstract

The Two Scales Covariance estimator is a consistent estimator of the true covariance matrix used to evaluate the portfolio risk (Zhang et al. 2005). Used in the context of high frequency financial data, Fan et al (2012) demonstrated that the portfolio risk estimator using the pairwise refresh synchronization method and the portfolio risk estimator using the all-refresh synchronization method converged to the true risk. Moreover, they showed that the portfolio risk estimator using the pairwise refresh synchronization method converged faster. But, their simulation and empirical results showed that as the gross exposure increased, the estimated portfolio risks diverged from the true risk. They argued that the reason could be that the TSCV produced non positive definite matrices. We prove that forcing non positive definite matrices to be positive definite has negative consequences. We suggest a risk based on restricted TSCV - based on positive definite covariance matrices --, however that risk is not unbiased. This article suggests an expression of that bias and proposes a corrected portfolio risk estimator which is unbiased and based on positive definite TSCV. Simulations demonstrate that the estimated risks based on the restricted TSCV are more stable as the gross exposure increases, and we can correct for the bias.