Standard Errors of Risk and Performance Estimators with Serially Correlated Returns

58 Pages Posted: 12 Dec 2017 Last revised: 17 Jul 2019

See all articles by Xin Chen

Xin Chen

University of Washington - Department of Applied Mathematics

Doug Martin

University of Washington

Date Written: June 2019

Abstract

A new method for computing the standard errors of returns-based risk and performance estimators for serially correlated returns is developed. The method uses the fact that any such estimator can be represented as the sum of returns that are transformed using the estimator’s influence function, and the fact that the variance of such a sum can be estimated by estimating the zero-frequency value of the spectral density of the influence function transformed returns. The spectral density is estimated by fitting a polynomial to the periodogram using a generalized linear model for exponential distributions, with elastic net regularization. An adaptive prewhitening is used to obtain good performance for large as well as small serial correlation of returns. We show that the method works much better in comparison to conventional standard error computational methods, for a collection of 13 hedge funds whose returns have varying degrees of serial correlation. Extensive Monte Carlo mean-squared error performance studies for a number of commonly used risk and performance estimators, using first-order autoregression returns, show that the new method delivers good performance for serial correlations ranging from 0.0 to 0.9, over which range it has better performance than alternative Newey-West methods. Simulations also show that the new method works well for Garch(1,1) returns processes

Keywords: Risk/Performance Measure, Maximum-Likelihood Estimator (MLE), Influence Functions, Estimator Variance, Estimator Standard Error, Generalized Linear Model (GLM), Elastic Net Regularization, Serial Correlation

JEL Classification: C3, C14, G10

Suggested Citation

Chen, Xin and Martin, R. Douglas, Standard Errors of Risk and Performance Estimators with Serially Correlated Returns (June 2019). Available at SSRN: https://ssrn.com/abstract=3085672 or http://dx.doi.org/10.2139/ssrn.3085672

Xin Chen

University of Washington - Department of Applied Mathematics ( email )

Box 352420
Seattle, WA 98195-2420
United States

R. Douglas Martin (Contact Author)

University of Washington ( email )

Applied Mathematics & Statistics
Dept. of Statistics
Seattle, WA 98195
United States

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