Revisiting Fama–French factors' predictability with Bayesian modelling and copula‐based portfolio optimization

• Date: 01 October 2019
• DOI: http://doi.org/10.1002/ijfe.1742
• Published date: 01 October 2019
• Author: Georgios Sermpinis,Charalampos Stasinakis,Yang Zhao,Filipa Da Silva Fernandes

RESEARCH ARTICLE

Revisiting Fama–French factors' predictability with Bayesian

modelling and copula-based portfolio optimization

Yang Zhao

1

| Charalampos Stasinakis

2

| Georgios Sermpinis

2

| Filipa Da Silva Fernandes

3

1

Chinese Academy of Finance and

Development, Central University of Finance

and Economics, Beijing, China

2

Adam Smith Business School, University

of Glasgow, Glasgow,UK

3

Aberdeen Business School, University of

Aberdeen, Aberdeen, UK

Correspondence

Charalampos Stasinakis, Adam Smith

Business School, University of Glasgow,

Adam Smith Building, Glasgow G12 8QQ,

UK.

Email: charalampos.stasinakis@glasgow.ac.

uk

Abstract

This study is investigating the predictability of the five Fama–French factors and

explores their optimal portfolio allocation for factor investing during 2000–2017.

Firstly, we forecast each factor with a pool of linear and nonlinear models. Next,

the individual forecasts are combined through dynamic model averaging, and their

performance is benchmarked by the best performing individual predictor and other

forecast combination techniques. Finally, we use the generalized autoregressive

score model and the skewed tcopula method to estimate the correlation of assets.

The generalized autoregressive score performance is also compared with other

traditional approaches such as dynamic conditional correlation model and

asymmetric dynamic conditional correlation. The performance of the constructed

portfolios is assessed through traditional metrics and ratios accounting for the

conditional value-at-risk and the conditional diversification benefits approach.

Our results show that combining Bayesian forecast combinations with copulas is

leading to significant improvements in the portfolio optimization process, and

forecasting covariance accounting for asymmetric dependence between the factors

adds diversification benefits to the obtained portfolios.

KEYWORDS

dynamic model averaging, factor investing, forecastcombinations, portfolio optimization

1|INTRODUCTION

It is a well-known fact that reduced-form factor models

are useful in asset pricing, as they provide a parsimonious

summary of the cross section of asset returns (Fama &

French, 1993Fama & French, 1995). The economic premise

of factor-modelling is based on the fact that covariances have

explanatory power over the cross-sectional expected returns

and that factors are able to capture to a large extent the time

series comovements of stock returns. Therefore, it is

expected that an investor who wants to benefit from this must

accept exposure to factor risk (Kozak, Nagel, & Santosh,

2018). As a consequence, factor models are accepted as an

econometric tool for analysing portfolio risk exposures.

Decomposing risk exposure into factors not only allows for

an independent vetting of managers offering investment

opportunities but also quantifies the risk exposure overlap

with other funds during periods of high volatility or liquidity

draughts (Luo & Mesomeris, 2015).

Factor investing has gained increased popularity over the

past decades among academics and market participants

(Cerniglia & Fabozzi, 2018). This is based on the fact that

investors believe that portfolio returns' expectations should

be evidence based and that factor-based portfolios are con-

sidered a solid example of long-term investment (Briere &

Szafarz, 2018; Dimson, Marsh, & Staunton, 2017). A large

number of studies have identified that some style factors

have historically earned attractive risk–return profiles over

DOI: 10.1002/ijfe.1742

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time (Ang, 2014; Carhart, 1997; Fama & French, 1993,

2015 and Ferson, Siegel, & Xu, 2006). There are two main

types of factors that drive returns: macroeconomic factors,

which capture broad risks across asset classes, and style

factors, which explain returns and risk within asset classes. If

an investor holds (optimized) diversified portfolios, better

risk–return trade-offs can be attained in comparison to

holding individual assets. This is the foundation of the

traditional mean–variance (M-V) approach of Markowitz

(1952). Assuming that this investor can invest directly in a

security that replicates the return on individual factors, then

it is possible to obtain diversification benefits from investing

in a portfolio of stock factors. Thus, if factor investing can be

implemented cheaply, it significantly raises the bar for active

management.

Although practitioners have to face structural or regula-

tory barriers to short-selling when they construct long-short

portfolios, factors still can be tradeable via different ways.

Some factor premiums can be captured through long-short

combinations of existing index-based instruments (Br iere &

Szafarz, 2018). For instance, MSCI factor indexes provide

flexible access to factor investing, such as value, low size,

low volatility, high yield, quality, and momentum. Studies

such as the works of Ferson et al. (2006); Bender, Briand,

Nielsen, and Stefek (2010); and Bender, Briand, Melas, and

Subramanian (2013) explain how portfolios are constructed

in an effort to obtain factor risk premium. This is very

important, as such risk premiums are required to compen-

sate for their underlying risk and allow risk hedging through

application of different types of factors in the same portfo-

lio. Several techniques are developed to improve upon the

passive capitalization of weighted equity market portfolios

through intelligent integration of factor returns. Common

factors of interest are the market, size, and value factors

introduced by Fama and French (1993), the momentum

factor introduced by Jegadeesh and Titman (1993) and

Carhart (1997), the liquidity factor identified by Pástor and

Stambaugh (2003), and the profitability factor and invest-

ment patterns' factor found in Fama and French (2015). In

general, the seminal studies of Fama and French (2015,

2016, 2018) confirm that the five-factor model is capturing

adequately the returns' movements. This literature brings

forward the fact that many institutions are increasingly

interested in factors' congruence and how their optimal

allocation can improve the risk-adjusted performance of

their equity portfolios. This interest, though, goes beyond

the traditional approach of Markowitz (1952).

This motivates us to explore optimal allocation methods

for factor investing. Several studies postulate that portfolio

optimization can yield substantial diversification benefits in

terms of risk–return trade-off mainly depending on the fore-

casting accuracy of conditional moments of asset returns

(Chan, Karceski, & Lakonishok, 1999). Consequently, more

accurate estimates can generate more successful and active

investment strategies. Knowing that the expected returns

and correlation (covariance matrix) of assets are the primar y

inputs for portfolio optimization, the aim of this study is

twofold. The first target is to select superior factor return

predictions. The second goal is to exploit the time-varying

correlations of factor returns and their asymmetric depen-

dence in order to maximize the diversification benefits

derived from factor-based portfolios.

Miralles-Quiros and Miralles-Quiros (2017) suggest that

portfolio optimization literature tends to neglect the impor-

tance of return predictability. The voluminous financial fore-

casting literature should be ideal for practitioners aiming at

the first target mentioned above. Through that they are able

to select and/or combine linear and nonlinear models that

apply constant or time-varying parameterization processes.

Bayesian models constitute a prominent class of such tech-

niques able to encompass the forecasting power of large

number of individual predictors given powerful computa-

tional resources. Wright (2008, 2009) apply Bayesian min

forecasting exchange rates and U.S. inflation. Feldkircher,

Horvath, and Rusnak (2014) utilize also the same technique

in the FX markets too. The dynamic model averaging

(DMA) is used by Koop and Korobilis (2012) to forecasting

inflation based on a set of predictors, as a recursive extension

of the Bayesian approach. Another class of available fore-

casting tools is the support vector regressions (SVRs). They

are regression-based models able to explore the nonlinear

and data-adaptive dynamics of financial time series given a

set of inputs (Vapnik, 1995). Their applications in finance

are numerous (see among others Lu, Lee, and Chiu, 2009;

Wang and Zhu, 2010; and Yao, Crook, and Andreeva

(2015). They exhibit, though, high sensitivity to the calibra-

tion of their parameters. For that reason, many studies in the

area of heuristic and metaheuristic optimization are invested

into this task, as especially the latter are able to avoid local

optima trapping, over-fitting, and computational costs

(Parejo, Ruiz-Cortés, Lozano, & Fernandez, 2012). Nature-

inspired metaheuristic approaches in particular that are moti-

vated by the evolution of species or their swarm movement

behaviour have received research traction (Gandomi & Alavi,

2012; Yang, 2010; Yang & Gandomi, 2012). Mirjalili (2016)

proposed the sine cosine (SC) algorithm that is based on

mathematical objective functions rather than bio-inspired

ones. This was recently adopted couple of studies, Li, Fang,

and Liu (2018) and Fernandes, Stasinakis, and Zekaite

(2018) in a hybrid SC-SVR model. Their results indicate that

SC is providing better SVR optimization compared with

other robust bio-inspired algorithms.

On the other hand, portfolio researchers that focus on the

univariate distributions of the individual assets and the

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