Understanding the interplay between covariance forecasting factor models and risk‐based portfolio allocations in currency carry trades

• Author: Pavel V. Shevchenko,Matthew Ames,Gareth W. Peters,Guillaume Bagnarosa
• DOI: http://doi.org/10.1002/for.2505
• Published date: 01 December 2018
• Date: 01 December 2018

Received: 30 November 2015 Revised: 5 June 2017 Accepted: 16 November 2017

DOI: 10.1002/for.2505

RESEARCH ARTICLE

Understanding the interplay between covariance

forecasting factor models and risk-based portfolio

allocations in currency carry trades

Matthew Ames1Guillaume Bagnarosa2Gareth W. Peters3,4,5 Pavel V. Shevchenko6

1The Institute of Statistical Mathematics,

Toky o, Japa n

2Rennes School of Business, Rennes,

France

3Department of Actuarial Mathematics

and Statistics, Heriot-WattUniversity,

Edinburgh, UK

4Oxford-Man Institute, Oxford University,

Oxford, UK

5Systemic Risk Center, London School of

Economics, London, UK

6Department of Applied Finance and

Actuarial Studies, Macquarie University,

Sydney,NSW, Australia

Correspondence

Matthew Ames, Department of Statistical

Modeling, The Institute of Statistical

Mathematics, 10-3 Midori-cho,

Tachikawa,Tokyo 190-8562, Japan.

Email: m-ames@ism.ac.jp

Funding information

Australian Research Council′sDiscovery

Projects, Grant/AwardNumber:

DP160103489

Abstract

With the exception of naive methods for portfolio selection, such as the equal

weighted approaches, all other methods of portfolio allocation are more or less

sensitive to the quality of the inputs considered in constructing the models and

risk measures utilized in the allocation framework. The extensively used fac-

tor model proposed initially by Sharpe in 1963 has provided a robust backdrop

for development of relevant, micro, macro, and context-specific or asset spe-

cific explanatory variables to be incorporated in a statistical manner as inputs to

forecasting models that can then be used to obtain risk measures upon which

portfolio allocations are based. However, like all statistical models, a set of sta-

tistical assumptions accompany this factor model regression framework, one of

which has recently been highlighted as seemingly nonvalidatedin financial data.

This is, of course, the assumption such factor models make on homoskedasticity

or weak-sense covariance stationarity of the returns processes being modeled.

Such factor models, therefore, have typically failed to cope with an important

and ubiquitous feature of financial assets data, which often demonstrates het-

eroskedasticity of the returns variances and covariances. We propose a novel

generalized multifactor forecasting structure utilizing a covariance regression

model, which allows us to incorporate the required heteroskedasticity effects

while also admitting potential dependence in the idiosyncratic error terms. We

argue that such a modeling approach allows for more explicit relationships to

be interpreted between the driving factors and the conditional responses of the

portfolio returns. We then compare the forecasting performances of our model

with the multifactor model and the time series dynamic conditional correlation

model through a currency portfolio application.

KEYWORDS

covariance forecasting, currency carry trade, covariance regression, generalizedmultifactor model,

portfolio optimization

Journal of Forecasting. 2018;37:805–831. wileyonlinelibrary.com/journal/for Copyright © 2018 John Wiley & Sons, Ltd. 805

806 AMES ET AL.

1INTRODUCTION

The advent of modern portfolio theory, with the semi-

nal mean–variance model proposed by Markowitz (1952)

forged new frontiers for a large area of finance literature

and certainly contributed to significant developments

within the asset management industry. Nevertheless, the

performance of such models and, more importantly,

the validity of the accompanying statistical assumptions

underpinning the application of such models to portfolio

selection have been questioned due to widely documented

observed inconsistencies in the model assumptions and

the practical applications. This has resulted in numer-

ous interrogations about the practical implementation of

this seminal model and subsequent model extensions to

the original framework to address such issues. Before

proceeding we will split the problem of portfolio alloca-

tion into four stylized nonindependent stages: The first

stage typically involves statistical model estimation and

model selection of the portfolio constituent multivariate

return processes historically; the second stage typically

involves some form of forecasting under the estimated

model selected; the third stage involves selection and esti-

mation of a risk measure on which to measure perfor-

mance of the portfolio; and the fourth stage involves an

optimization criterion upon which one performs portfolio

allocation based on the portfolio forecasted risk measure.

With these four stages in mind, and returning to the

considerations of portfolio allocation under the classical

mean–variance-based models, we note that several chal-

lenging model prerequisites for such a framework arise.

Most notably, these include the estimation of essential but

unknown parameters such as each portfolio component's

drift and diffusion terms as well as the dependence struc-

ture between them, as often measured through corre-

lation and covariance relationships, but sometimes also

through other concordance measures such as tail depen-

dence. When such statistical models are then utilized for

stage two (forecasting) and then subsequently for stages

three and four (portfolio selection), it is often important

to study the influence of the model assumptions, model

choice, model estimation and model forecast accuracy on

the performance of the portfolio allocation method in

stages three and four. In this regard, several works have

undertaken analysis of such considerations in terms of

considering the sensitivity of the mean–variance optimal

portfolio behavior; examples can be found in both the aca-

demic and practitioner literature (Broadie, 1993; Chopra

& Ziemba, 1993; Frost & Savarino, 1988; Jobson & Korkie,

1981; Michaud, 1989). For instance, it has been shown

that the basic mean–variance quadratic program happens

to be highly sensitive to models which fail to account

for heteroskedasticity in the covariance, and such models

have been shown to be equivalent to a reexpression of

the estimation problem as a measurement error maxi-

mization program, further highlighting the importance

of this covariance modeling feature (see Michaud, 1989;

Nawrocki, 1996).

Several of these studies have demonstrated that, indeed,

one of the most important features to capture in the real

portfolio data returns is, in fact, the trend structure of

the portfolio returns and, even more importantly, the het-

eroskedastic nature of the portfolio covariance structure

over time. While trend is widely considered to be noto-

riously difficult and unpredictable even with the most

carefully developed models, the heteroskedastic nature of

the covariance structure is definitely considered tobe more

reliably predictable and amenable to model developments.

Not only have these features been shown to be important

model components to capture accurately in stages one and

two of the process but, in addition, since the portfolio allo-

cation and subsequently portfolio performance in terms of

returns and risk performance is highly sensitive to the abil-

ity of the model to correctly capture these dynamic features

over time, they also affect directly stages three and four.

Therefore, several approaches have subsequently been

developed in the academic literature to address these prob-

lems, and generally they can be split into two categories,

depending on which aspect of the four stages they mod-

ify to try to address the above identified issues, partic-

ularly on heteroskedasticity of the portfolio covariance;

that is, at the modeling stage, the forecasting stage, risk

measure specification stage or in the portfolio optimiza-

tion program objective function in stage four. We refer to

stages one and two as “upstream” approaches and stages

three and four as “downstream” approaches. In upstream

approaches the natural solution would be to improve the

model development and forecasting framework, that is,

the input estimation that produces the risk measure of

the portfolio and acts as input to portfolio optimization.

Improving the modeling at this stage is a statistical pursuit

and, if achieved, has the effect of reduction of variability

and noise on the input sources. An alternative set of solu-

tions considers instead the input noise as an inexorable

feature of financial market data and accordingly focuses

on downstream components, that is, stages three and four

in the risk measure and optimization program objective

function and the various constraints generally going with

it. Such methods amount to adjusting the optimization

program through reformulation of the loss function or

through refinement of optimization constraints in order to

restrain the estimator bias and its effect upon the optimal

portfolio allocation solution. In summary, one could make

more robust model estimations and forecasts and uti-

lize existing portfolio allocation methods, or alternatively

one can make more resilient and constrained portfolio