Strategic asset allocation by mixing shrinkage, vine copula and market equilibrium

• Date: 01 April 2018
• Author: Zhichao Zhang,Fan Zhang
• DOI: http://doi.org/10.1002/for.2506
• Published date: 01 April 2018

RESEARCH ARTICLE

Strategic asset allocation by mixing shrinkage, vine copula

and market equilibrium

Fan Zhang

1

| Zhichao Zhang

2

1

Liverpool Business School, Liverpool

John Moores University, Liverpool, UK

2

Durham University Business School,

Durham, UK

Correspondence

Fan Zhang, Liverpool Business School,

Liverpool John Moores University,

Liverpool, L3 5UG, UK.

Email: f.zhang@ljmu.ac.uk

Abstract

We propose a new portfolio optimization method combining the merits of the

shrinkage estimation, vine copula structure, and Black–Litterman model. It is

useful for many investors to satisfy simultaneously the three investment objec-

tives: estimation sensitivity, asymmetric risks appreciation, and portfolio stabil-

ity. A typical investor with such objectives is a sovereign wealth fund (SWF).

We use China's SWF as an example to empirically test the method based on a

15‐asset strategic asset allocation problem. Robustness tests using subsamples

not only show the method's overall effectiveness but also manifest that the

function of each component is as expected.

KEYWORDS

asymmetric risk,Bayesian forecast, estimation risk, portfolio management, views blending

1|INTRODUCTION

China Investment Corporation (CIC), the relatively young

sovereign wealth fund (SWF) of China, has attracted

much attention since its inception on September 19,

2007. Owing to the huge amount of foreign exchange

reserves it can tap into, many are curious about its iden-

tity as an international investor, its investment objective,

and its strategic asset allocation (SAA). This specific

instance and many others alike motivate us to find a port-

folio optimization method to suit the demands for such

long‐term institutional investors’SAA decisions.

The three features of financial efficiency, good risk

appraisal, and allocation efficacy have intuitive impor-

tance to portfolio management, and therefore each of

these aspects has been well developed. It is interesting to

ask whether it is possible to combine the three elements

together for investors with all three investment objectives

simultaneously.

With respect to allocation efficacy, by which we mean

stability of portfolio as well as level of diversification, the

mean–variance analysis has been criticized. The most fre-

quently applied solution is that proposed by Black and

Litterman (1991, 1992) and further developed by He and

Litterman (1999) and Satchell and Scowcroft (2000). They

utilize the Bayesian rule to combine analysts’forecasts

with the market equilibrium. This differs from the

mean–variance method where the forecasts for every asset

return are derived from historic data. Based on the effi-

cient market hypothesis, this method incorporates the

market view as the basis for forecasting future returns.

With respect to good risk appraisal for SAA, many

papers discover the asymmetric dependence feature in

asset returns (Ang & Chen, 2002; Bae, Karolyi, & Stulz,

2003; Balla, Ergen, & Migueis, 2014; Hong, Tu, & Zhou,

2007; Longin & Solnik, 2001; Wang, Wu, & Lai, 2013).

Some assets are more likely to go down together, thus

diminishing the effect of diversification. In the multivari-

ate backdrop, asymmetric dependence, distinct from

asymmetry in marginal distributions, has also been

proven to influence asset allocation decisions (Boubaker

& Sghaier, 2013; Leal & Mendes, 2013). In addition, the

fat‐tail feature means that extreme losses would be

underestimated if the common Gaussian distribution

were assumed, as in mean–variance analysis. Therefore,

the copula method is important for risk management in

Received: 10 June 2015 Revised: 5 December 2016 Accepted: 16 November 2017

DOI: 10.1002/for.2506

340 Copyright © 2018 John Wiley & Sons, Ltd. Journal of Forecasting. 2018;37:340–351.wileyonlinelibrary.com/journal/for