Short‐run wavelet‐based covariance regimes for applied portfolio management

• Author: Ramazan Gençay,Theo Berger
• Date: 01 July 2020
• Published date: 01 July 2020
• DOI: http://doi.org/10.1002/for.2650

Received: 13 April 2019 Revised: 7 August 2019 Accepted: 3 January 2020

DOI: 10.1002/for.2650

RESEARCH ARTICLE

Short-run wavelet-based covariance regimes for applied

portfolio management

Theo Berger1Ramazan Gençay2

1Department of Business and

Administration, University of Bremen,

Bremen, Germany

2Department of Economics, Simon Fraser

University, Burnaby,British Columbia,

Canada

Correspondence

Theo Berger, Department of Business and

Administration, University of Bremen,

Wilhelm-Herbst-Str. 5, D-28359 Bremen,

Germany.

Email: thberger@uni-bremen.de

Funding information

Natural Sciences and Engineering

Research Council of Canada and the

Social Sciences and Humanities Research

Council of Canada, Grant/Award

Number: N/A

Abstract

Decisions on ass et allocations are often determined by covariance estimates

from historical market data. In this paper, we introduce a wavelet-based port-

folio algorithm, distinguishing between newly embedded news and long-run

information that has already been fully absorbed by the market. Exploiting

the wavelet decomposition into short- and long-run covariance regimes, we

introduce an approach to focus on particular covariance components. Using

generated data, we demonstrate that short-run covariance regimes comprise

the relevant information for periodical portfolio management. In an empirical

application to US stocks and other international markets for weekly, monthly,

quarterly, and yearly holding periods (and rebalancing), we present evidence

that the application of wavelet-based covariance estimates fromshort-run infor-

mation outperforms portfolio allocations that are based on covariance estimates

from historical data.

KEYWORDS

portfolio management, short-run trends, wavelet decomposition

1INTRODUCTION

Capital allocation between volatile stocks is at the center

of portfolio formation decisions, and adequate estimates

of the unknown covariance matrix describe crucial infor-

mation for strategic portfolio allocations. Historical data

contain information about both short- and long-run infor-

mation, and conclusions drawn from respective covari-

ance estimates provide limited insight regarding periodical

diversification opportunities.

In this paper, we introduce a wavelet-basedapproach to

improve the future performance of portfolio allocations.

Employing a multi-horizon nonparametric filter—the

wavelet transformation—we develop a covariance estima-

tor to distinguish between newly embedded information

content of underlying historical market prices and news

Ramazan Gençay passed awayafter this manuscript had been completed.

that has been fully absorbed by the market.1To assess

the relevance of competing information components, we

apply a simple mean-variance efficient portfolio alloca-

tion algorithm and study the out-of-sample performance

of wavelet-based covariance estimates.2

1Wavelet decomposition describes an adequate approach to filter finan-

cial time series. In comparison to alternative filtering methods—that

is, Fourier analysis—waveletdecomposition does not require periodicity

in financial time series, events can be localized, and it is applicable to

multivariate time series. For a thorough study on the advantages of the

application of wavelet transformation to financial time series, we refer to

Gençay et al. (2005), Conlon et al. (2018), and the references therein.

2The concept of mean-variance portfolio optimization, as introduced

by Markowitz (1952), represents a widely accepted approach that takes

account of the quantitative tradeoff between risk and return of an invest-

ment. As described by Kolm et al. (2004), Markowitz's portfolio diversifi-

cation has been instrumental in the development and understanding of

financial markets, whereas adequate estimates of the unknown covari-

ance matrix of the underlying assets represent crucial information that

determines strategic portfolio allocations (see DeMiguel et al., 2009;

Maillet et al., 2015).

This is an open access article under the terms of the Creative Commons AttributionLicense, which permits use, distribution and reproduction in any medium, providedthe

original work is properly cited.

© 2020 The Authors. Journal of Forecasting published by John Wiley & Sons Ltd

Journal of Forecasting. 2020;39:642–660.

wileyonlinelibrary.com/journal/for642

News arrives at markets at certain times expectedly as

proxied by analysts, but also at times it arrives unexpect-

edly. Typically, news would cause the evolution of the

historical price to deviate significantly from its long-term

average; such deviations may or may not be permanent.

Depending on the nature of such news, the historical

volatility pattern of the data, and the nature of the sea-

sonal patterns, the full extent of the news impact may not

be obvious from observing the raw data. Namely, a certain

threshold of newly embedded deviations may be blended

with long-term average features of the data, radiating an

illusion that changes are not as large, attributing short-run

changes falsely to long-term growth. Therefore, it is not

necessarily rewarding to work with raw data directly to

identify shorter term newly embedded covariances, but

to split the raw data into its short-run and long-run

components.

To identify different covariance regimes, we draw on

Berger and Gençay (2018) and Conlon et al. (2018) and

apply wavelet decomposition, which is well suited to iden-

tify short-run and long-run regimes of the underlying

return series. Initially, wavelet decomposition was intro-

duced into financial return series by Percival and Walden

(2000) and Gençay et al. (2001). Since then, the appli-

cation of signal processing techniques to financial data

triggered a growing field of research that mainly deals with

the decomposition of financial return series into short-run

and long-run trends. For instance, Gençay et al. (2010)

provide evidence for the existence of different financial

volatility regimes across different trends, and Gençay et al.

(2005) apply the capital asset pricing model (CAPM) to

deconstructed return series of international stock indices

and illustrate that fundamental risk increases for long-run

trends. Rua and Nunes (2012) confirm this finding for

emerging markets, whereas Gallegati (2012) deconstructs

return series of stock market indices of the G7 coun-

tries, Brazil, and Hong Kong to assess changing correla-

tion regimes between deconstructed return series. Conlon

et al. (2018) also study wavelet-based correlation estimates

of G7 countries and provide evidence for different pat-

terns between deconstructed return series; in particular,

dependence between long-run seasonalities appears to be

stronger than suggested by the original data.3

Moreover, as wavelet transformation does not only

allow for a deconstruction but also for a reconstruction

3Reboredo and Rivera-Castro (2014) assess dependence between decon-

structed European and US stocks and oil prices and find evidence of

increased dependence between long-run seasonalities after 2008. Dewan-

daru et al. (2015) analyze dependence between Asian stocks, Andries

et al. (2014) between interest rates, stock prices, and exchange rates,

and Tan et al. (2014) analyze dependence between US and Asian equity

markets.

of a deconstructed financial return series, Berger and

Gençay (2018) present a novel approach which allows

the investor to reconstruct deconstructed financial return

series by excluding particular information components of

the underlying data. Also, Conlon et al. (2018) reconstruct

financial return series to assess correlation estimates. In

this study, we add to this literature and empirically study

the out-of-sample performance of portfolios that consider

covariance estimates of deconstructed return series. In

contrast to the growing field of literature that deals with

dependence between denoised long-run trends of financial

data, our results provide evidence that it is the covariance

of short-run regimes that describes the relevant informa-

tion for out-of-sample portfolio performances.4

Specifically, we expand the analysis of univariate return

series by Berger and Gençay (2018) and apply a wavelet

filter to deconstruct return series into different covari-

ance regimes and reconstruct the return series by taking

either short-run, middle-run, or long-run regimes into

account. Furthermore, based on the reconstructed ver-

sions of the original return series, we discuss simple

mean-variance efficient portfolio optimization and assess

its out-of-sample performance. Analogous to DeMiguel

et al. (2009) and Maillet et al. (2015) we evaluate the

risk-adjusted performance of competing portfolio alloca-

tions and the setup of the assessment will be twofold.

First, we set up a simulation analysis, and simulate

return series which are described by different patterns of

long-memory effects to assess the relevance of short- and

long-run memory of a return series on portfolio alloca-

tions. By investigatingreconstructed return series that take

either short-run or long-run memory into account, we

shed light on the relevant information for applied portfo-

lio management in the presence of incomplete information

on the underlying market conditions.

Second, we assess the out-of-sample performance of

mean-variance efficient portfolios that are based on recon-

structed return series and compare the performance with

the mean-variance efficient portfolio allocations based on

daily raw data. To take account of different market sizes

and regimes, we assess stocks that are listed at leading

indices of both developed and emerging stock markets.

We also take account of different holding periods and

assess daily, weekly, monthly,quarterly, and yearly portfo-

lio rebalancing. The results indicate that middle-run and

long-run covariance regimes should be excluded from the

original time series, as it impacts the out-of-sample perfor-

mance of daily portfolio management.

The findings add to the results of Berger and Gençay

(2018) and Conlon et al. (2018), and to papers on covari-

4See Gallegati (2012), Berger and Uddin (2016), and the references

therein.

BERGER AND GENÇAY 643