Asymmetric Correlations in Predicting Portfolio Returns*

• Published date: 01 March 2021
• Author: Nianling Wang,Lijie Zhang,Zhuo Huang,Yong Li
• Date: 01 March 2021
• DOI: http://doi.org/10.1111/irfi.12255

Asymmetric Correlations in

Predicting Portfolio Returns*

NIANLING WANG

†

,LIJIE ZHANG

†

,ZHUO HUANG

‡

AND YONG LI

†

†

Hanqing Advanced Institute of Economics and Finance, Renmin University of China,

Beijing, China and

‡

National School of Development, Peking University, Beijing, China

ABSTRACT

Rigorous statistical tests have been designed to detect the existence of asym-

metric correlations. However, these tests can hardly further facilitate future

investment or risk management because asymmetric correlations are time-

varying and difficult to predict. In this paper, we construct a unified state-

space model, which not only measures in-sample asymmetric correlations,

but also exploit out-of-sample asymmetric correlations in the context of pre-

dicting portfolio returns. First, we regard time-varying correlation between

market returns and portfolio returns as a state variable and model it as an

AR(1) process. Then, we measure future asymmetric correlations based on

correlation coefficients between two unpredictable components in market

returns and correlation, respectively. Third, we clarify the intuition, calculate

asymmetric correlations for two portfolio sets and estimate the economic

value of applying our model in asset allocation. Finally, we try to search for

potential variables that can explain future asymmetric correlations. The

results show that market-wide liquidity, variance, earning price ratio, and

investor sentiment can partially explain the asymmetry correlation

phenomenon.

JEL Codes: G10; G11

Accepted: 28 January 2019

INTRODUCTION

Evidence of time-varying asymmetric correlations between portfolio returns has

been long-standing in finance literature. As shown in Ang and Chen (2002)

and Hong et al. (2007), correlations between portfolio returns and market

returns are much higher when both returns are below some criteria, but rela-

tively lower when both returns are above some criteria. This phenomenon is

called asymmetric correlations between returns and has attracted lots of atten-

tion since discovered. Besides, the evidence for asymmetric correlations also

comes from international markets, as shown in Longin and Solnik (1995,

* Yong Li gratefully acknowledges the financial support of the Fundamental Research Funds for the

Central Universities, and the Research Funds of Renmin University of China (No. 14XNI005).

© 2019 International Review of Finance Ltd. 2019

International Review of Finance, 21:1, 2021: pp. 97–120

DOI: 10.1111/irfi.12255

2001), Ang and Bekaert (2002), Campbell et al. (2002), Okimoto (2008), and

Toyoshima and Hamori (2013). They found that correlations between market

returns in different countries were higher during bear market periods. The

asymmetry of correlations really matters because the benefits of diversification

will decline dramatically when portfolios become high-correlated and prices

decline all together in downside markets. Consequently, both asset allocation

and risk management fail. Therefore, it is important to have a better under-

standing of the asymmetric correlations between portfolio returns.

However, the previous literature focused on realized asymmetric correlations

calculated from historical returns (henceforth realized asymmetric correlations).

As a consequence, those statistical tests can only summarize asymmetry of cor-

relations in the past and provide no direct guidance to deal with future situa-

tions. Therefore, previous studies, such as Patton (2004) and Hong et al. (2007),

resorted to copula functions for investment in real time. On one hand, Jiang

et al. (2015) showed that the downside asymmetric correlation structure was

time-varying and it was difficult to predict based on past values and firm char-

acteristics. On the other hand, it is unarguable that out-of-sample prediction of

asymmetry in correlations is of crucial importance because it affects both

returns and risks in the future. For example, Patton (2004), Gupta and Don-

leavy (2009), and Virbickait _

e et al. (2016) all showed that asymmetric correla-

tions were very important in out-of-sample asset allocation.

Realizing both the importance and difficulty in enhancing predicting power

for an asymmetric correlation model, this paper makes efforts to study asym-

metric correlations in the context of predicting future portfolio returns and tries

to capture the effects of future asymmetric correlations on asset allocations. Dif-

ferent from traditional definition for asymmetric correlations, which is subject

to a certain criteria level and makes it difficult to apply in real-time investment,

we put forward a new definition of asymmetric correlations from the perspec-

tive of forecasting portfolio returns, hence is especially useful and convenient

for future asset allocation and risk management.

Particularly, our model is a state-space model, with time-varying correlation

between market returns and portfolio returns as the state variable (referred to as

correlation). Both market returns and the correlation are assumed to follow

AR(1) processes, similar to Cappiello et al. (2006) and Ang and Chen (2007).

Then, we decompose both market returns and the correlation into a predictable

component and an unpredictable component as implied by the

AR(1) processes. We measure asymmetric correlations as the correlation coeffi-

cients between the two unpredictable components of market returns and corre-

lation, respectively. Using Bayesian approach, we can estimate posterior

distribution of the correlation coefficients and figure out how future correla-

tions will change conditional on the change in future market returns in terms

of probability.

As for asymmetric correlations tests, Ang and Chen (2002) was the first to

construct a rigorous statistical test for realized asymmetric correlations. The so-

called Hstatistics were proposed to test whether the exceedance correlations

© 2019 International Review of Finance Ltd. 201998

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