Asymmetry in Higher Moment Spillovers: Evidence from
Sustainable and Traditional Investments
Xie HeShigeyuki Hamori
September 2023
Discussion Paper No. 2316

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITYROKKO, KOBE, JAPANAsymmetry in Higher Moment Spillovers: Evidence from Sustainable andTraditional Investments

Xie HeGraduate School of Economics, Kobe University
2-1, Rokkodai, Nada-Ku, Kobe 657-8501 JAPAN
Shigeyuki Hamori (corresponding author)
Graduate School of Economics, Kobe University
2-1, Rokkodai, Nada-Ku, Kobe 657-8501 JAPAN
Email: hamori@econ.kobe-u.ac.jp

Abstract
This study presents a framework that breaks down kurtosis into positive and negative
shocks, distinguishing between "good" and "bad" kurtosis. We analyze asymmetrickurtosis spillovers among sustainable and traditional investments. Our findings indicatethat within the system encompassing sustainable and traditional investments, good
kurtosis spillover generally surpasses bad kurtosis spillover in the majority of periods.
However, during specific extreme events such as Brexit and COVID-19, bad kurtosis
spillover takes on a dominant role.
Key words: Higher moments; Conditional kurtosis; Spillover effect;
JEL classification: G15; F3; C32
Funding: This work was supported by Sawamura Masaka Foundation.

1

1. Introduction
The presence of asymmetric volatility in financial markets, where good news and badnews have distinct impacts on the evolution of market prices and their volatilities, haslong been acknowledged in the literature. Specifically, volatility stemming from market
downturns is typically more pronounced than the volatility associated with market
upturns of the same magnitude. This raises an essential question: "Does the volatility
resulting from good news propagate across financial markets in the same manner as thevolatility stemming from bad news?" In other words, does asymmetry manifest involatility spillover? This question holds significant importance. For investors, it
constitutes a central concern when managing optimal portfolio diversification and asset
allocation strategies. For policymakers, it plays a pivotal role in crafting policies aimed
at mitigating the transmission of detrimental shocks across markets and enhancing
financial stability (BenSaïda, 2019). In recent years, an increasing number of studies havestarted to center their focus on the asymmetry in volatility spillover.
Volatility is commonly regarded as a risk measure: low volatility implies low
volatility risk, while high volatility implies high volatility risk. Consequently, volatility
spillovers can be interpreted as spillovers of volatility risk (Baruník et al., 2016). Similarly,
kurtosis, which is one of the higher moments, can serve as a proxy for extreme risk, as it
signifies the probability of extreme outcomes, whether they are extremely positive or
negative. Consequently, kurtosis spillovers can be perceived as spillovers of extreme risk.
Here, we raise another question: Does asymmetry also manifest in kurtosis spillovers?
To address this inquiry, we reference the methodology of BenSaïda (2019) and2

employ the GJR with skewness and kurtosis (GJR-SK) model. This model, an extended
version of the GJR model designed for higher moments, allows us to decompose kurtosis
into components of good and bad kurtosis. The partitioning of volatility into bad and goodvolatility can be interpreted as a measure of downside and upside volatility risk (Baruník
et al., 2016). Similarly, the partitioning of kurtosis into bad and good kurtosis can be
regarded as an indicator of extreme downside and upside risk. Guided by this kurtosis
decomposition, we investigate asymmetric kurtosis spillovers within sustainable andtraditional investments. Our aim is to analyze whether the extreme upside risk introducedby positive news propagates across investments in the same manner as the extreme
downside risk stemming from negative news.
To the best of our knowledge, this study is the first to examine the asymmetry inhigher moment (kurtosis) spillover. Our study introduces a novel approach to assess theasymmetry in the transmission of extreme risk. Our research framework allows
researchers to differentiate between upward and downward extreme risk spillovers and toinvestigate them independently.
One of the key findings of this study is that, in most periods, the spillover of extreme
risk among investments predominantly involves the transmission of extreme upside risk
due to good news. However, during specific extreme periods, such as the Brexit vote andthe COVID-19 pandemic, the spillover is more focused on extreme downside risk
resulting from bad news. This result starkly contrasts with the findings related to thegeneral transmission of volatility risk, where, in most periods, the spillover effect ofvolatility risk is greater for bad volatility risk arising from bad news. This result can be3

attributed to two factors: Firstly, the spillover effect of extreme risk in the market is not
as responsive to bad news as the spillover effect of general risk. Only relatively severe
bad news may trigger an increase in the transmission of downward extreme risk. Secondly,
the spillover effect of risk in the market is intertwined with market sentiment. Market
expectations for general risk and extreme risk may not necessarily align. While the market
generally holds a pessimistic outlook on general risk, it is only in highly unstable market
environments that it adopts a pessimistic view of extreme risk.
The structure of the remaining sections of this paper is as follows: Section 2 presents
a literature review of relevant studies. Section 3 outlines the methodology used. Section
4 provides data, summary statistics, and empirical research results along with discussions.
The concluding section presents the final remarks.
2. Related literature
2.1.

Lower moment spillovers and higher moment spillovers

The spillover effect is a vital research topic as it captures the transmission of shocks
and movements across markets or sectors. Understanding these interconnections is crucial
for comprehending systemic risk, formulating effective monetary and fiscal policies, andmaking informed investment decisions. It illuminates the interconnected nature offinancial systems and the potential cascading effects of a crisis or event in one market
onto others. In recent years, the Diebold Yilmaz connectedness (spillover) approach has
gained increasing attention from researchers studying the spillover effect. The approachis both computationally straightforward and yields intuitive results. By utilizing a4generalized vector autoregression framework, it provides a clear depiction of volatility
transmission across markets or sectors. The resulting spillover indices are easilyinterpretable, making it an appealing tool for researchers and policymakers seeking tounderstand market interconnectedness and systemic risk. Drawing from the Diebold
Yilmaz connectedness approach, a significant body of literature has investigated returns
and volatilities spillovers (e.g., Baele, 2005; Chan et al., 2018; X. He et al., 2020; Huo &Ahmed, 2017; Liu & Hamori, 2020; Tiwari et al., 2018).
Indeed, while much of the existing research has focused on lower moment spillovers
such as returns and volatility, delving into higher moment spillovers can yield distinct
insights. Higher moments, such as skewness and kurtosis, can capture more nuanced
characteristics of asset distributions and their extreme movements, providing a deeper
grasp of market dynamics and systemic risks. Unlike volatility spillover, higher moment
spillovers can encompass extreme tail comovements between markets. Additionally,
higher moment spillovers can effectively identify significant events that return andvolatility spillover might not adequately capture (Bouri et al., 2021). To capture timevarying skewness or kurtosis, either realized measures utilizing high-frequency data ormodel-based estimates relying on specific econometric models to predict changes in thesehigher moments over time are necessary. In recent times, an increasing number of studies
have unveiled the presence of higher moment spillovers (such as skewness and kurtosis)
in financial markets (e.g., He & Hamori, 2023; X. He & Hamori, 2021; Nekhili & Bouri,
2023; Nyakurukwa & Seetharam, 2023; H. Zhang et al., 2023).

5

2.2.

Asymmetric spillovers
In the analysis of market dynamics and crisis transmission, understanding how

volatility reacts to shocks (or news) has become a significant concern. However, theasymmetry in volatility spillover has received limited attention, and the identification oftransmission mechanisms heavily relies on model design (BenSaïda, 2019). For instance,
Reboredo et al. (2016) measured downside and upside risk transmission through theconditional value-at-risk (CoVaR) computed from pair copulas. Yarovaya et al. (2017)
employed an asymmetric causality test to investigate pairwise spillovers. By employing
a recently-developed quantile-on-quantile (QQ) method, Duan et al. (2023) analyzed thepotential asymmetry and non-linearity of the market connection between Bitcoin andgreen and traditional assets.
Barndorff‐Nielsen et al. (2010) decomposed realized volatility into a positive
semivariance estimator RS+ and a negative semivariance estimator RS− to capturechanges arising from positive and negative shocks, respectively. Building on these
realized semivariance measures and the Diebold-Yilmaz approach, some researchers have
explored asymmetric volatility spillovers across markets (e.g., Baruník et al., 2016, 2017;
Mensi et al., 2021, 2022).
However, realized measures have their limitations. Firstly, they rely on intraday highfrequency data, which can present certain challenges in data acquisition. Secondly, highfrequency data are affected by microstructure noise, and stock returns include a jumpcomponent, impacting the accuracy of realized volatility estimators. To address theselimitations, BenSaïda (2019) proposed a model-based semivariance estimate based on the
6Glosten Jagannathan-Runkle (GJR) model and explored asymmetric spillovers across G7
stock markets using this model-based estimate.
2.3.

Spillovers in sustainable and traditional investments
Over the past decade, sustainable investing has emerged as a transformative paradigm

in the financial sector, seeking to merge environmental, social, and governance (ESG)
considerations with traditional investment strategies. Rooted in the belief that long-term
success is intricately linked to a broader societal and environmental context, this approachtranscends mere financial returns, emphasizing responsible stewardship of capital. As
global challenges like climate change and social inequities become increasingly pressing,
there's a growing recognition of the pivotal role that finance plays in shaping sustainableoutcomes. Consequently, sustainable investing has not only experienced increased
adoption by institutional and retail investors alike but has also begun to reshape thecontours of the global investment landscape.
Given its relatively nascent emergence, sustainable investments, while promising, still
have limited market depth compared to traditional investments. This results in heightenedrisk associated with sustainable investments. Consequently, it underscores the imperative
to explore effective diversification and risk mitigation strategies for these promising yetinherently riskier sustainable assets.
As the size and number of participants in the carbon market expand, the linkage ofprices between carbon assets and other financial products, such as energy assets, appears
to be growing stronger (Ren et al., 2022a). The nexus between the volatility of energy
markets and the carbon market seems indisputable. However, the connection between the7volatility of the crude oil market and the carbon market remains a subject of divergent
opinions. Indeed, some studies have confirmed a strong bidirectional spillover effectbetween the carbon market and the crude oil market (i.e., Ji et al., 2018; Ren et al., 2022b;
Y. Wang & Guo, 2018). However, there are still some studies that present contraryevidence. For example, Zhang & Sun (2016) argue that no significant volatility spilloveris found between the European carbon trading market and crude oil markets.
As an extension of the widely studied "Carbon-Energy" system, the "Carbon-EnergyFinance" system has gained attention in recent years. This system posits that the carbon
market is interconnected not only with traditional energy markets but also with somefinancial markets. For example, the research of Tan et al. (2020) on the EU ETS indicatesthat the volatility of the carbon market is closely related to the volatility of the stock
market.
Green stocks, renewable energy stocks, and ESG (Environmental, Social, andGovernance) stocks are three crucial stock-based sustainable investments. Green stocks
primarily focus on environmental factors, such as the S&P 500 Bond Investment Grade
Carbon Efficient Index, which mainly involves companies with low carbon emissions
relative to their sales. ESG stocks not only emphasize environmental factors but also
highlight companies that excel in their environmental, social, and governance practices.
The investment scope of renewable energy stocks is even more specific, as it only
encompasses firms in the clean energy sector. Research on the nexus between ESG stocks
and green stocks with the traditional energy market is relatively limited, with most studies
focusing on the relationships between renewable energy stocks and the traditional energy
8market. The volatility spillover effects between new energy stocks and traditional energy
markets have been confirmed by many researchers (i.e., Attarzadeh & Balcilar, 2022;
Caporale et al., 2023; Liu & Hamori, 2020; Song et al., 2019; Umar et al., 2022), andmany studies have found that the spillover effects between the crude oil market and newenergy stocks are the most significant (i.e., Liu & Hamori, 2020; Song et al., 2019; Umar
et al., 2022).
Green bonds are considered essential investment vehicles within sustainable investing.
They represent new forms of asset classes that not only engage in market-centric businesspractices but also derive their legitimacy and innovation by strongly focusing on
environmentally and sustainable capital transactions (Rao et al., 2022).
Most of the research primarily focuses on the spillover effects between green bonds
and the energy market (i.e., Nguyen et al., 2021; Pham, 2016; Reboredo, 2018; Reboredo
et al., 2020). However, some studies have also identified a pronounced spillover effectbetween green bonds and precious metals such as gold and silver (i.e., Naeem et al., 2021).
3. Methodology
3.1.

GJR-GARCH-SK model
We propose to infer the volatility and kurtosis measure of each investment from the

Glosten Jagannathan-Runkle (GJR) with skewness and kurtosis (GJR-SK) model. The
formulation of the GJR-SK model is given as follows.
𝑟𝑟𝑡𝑡 = 𝛼𝛼0 + 𝛼𝛼1 𝑟𝑟𝑡𝑡−1 + 𝜀𝜀𝑡𝑡
−1/2

𝜂𝜂𝑡𝑡 = ℎ𝑡𝑡
9

𝜀𝜀𝑡𝑡

(1a)

(1b)

𝜂𝜂𝑡𝑡 |𝐼𝐼𝑡𝑡−1 ~Δ(0,1, 𝑠𝑠𝑡𝑡 , 𝑘𝑘𝑡𝑡 )

(1c)

2
2
+ 𝛽𝛽2 ℎ𝑡𝑡−1 + 𝛽𝛽3 𝜀𝜀𝑡𝑡−1𝐼𝐼{𝜂𝜂𝑡𝑡−1 <0}ℎ𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1 𝜀𝜀𝑡𝑡−1

(1d)

4
4
𝑘𝑘𝑡𝑡 = 𝛿𝛿0 + 𝛿𝛿1 𝜂𝜂𝑡𝑡−1+ 𝛿𝛿2 𝑘𝑘𝑡𝑡−1 + 𝛿𝛿3 𝜂𝜂𝑡𝑡−1
𝐼𝐼{𝜂𝜂𝑡𝑡−1 <0}

(1f)

3
3
+ 𝛾𝛾2 𝑠𝑠𝑡𝑡−1 + 𝛾𝛾3 𝜂𝜂𝑡𝑡−1
𝐼𝐼{𝜂𝜂𝑡𝑡−1 <0}𝑠𝑠𝑡𝑡 = 𝛾𝛾0 + 𝛾𝛾1 𝜂𝜂𝑡𝑡−1(1e)Here 𝛼𝛼0 , 𝛼𝛼1 are parameters of the AR model and 𝛽𝛽𝑖𝑖−1 , 𝛾𝛾𝑖𝑖−1 , and 𝛿𝛿𝑖𝑖−1 , 𝑖𝑖 = 1,2,3 areparameters of the GJR-SK model. 𝐼𝐼𝐴𝐴 is an indicator function that returns 1 if A is trueand 0 otherwise. Δ is a probability density function with mean 0, variance 1, and time-varying skewness 𝑠𝑠𝑡𝑡 , and kurtosis 𝑘𝑘𝑡𝑡 . The probability density function Δ(0,1, 𝑠𝑠𝑡𝑡 , 𝑘𝑘𝑡𝑡 )can be given by Gram-Charlier expansion using Chebyshev-Hermite polynomials.

+
Next, following BenSaïda (2019) 's line of thought, we define the good volatility ℎ𝑖𝑖,𝑡𝑡−
and bad volatility ℎ𝑖𝑖,𝑡𝑡
to correspond to positive and negative shocks, respectively.
+ℎ𝑖𝑖,𝑡𝑡= ℎ𝑖𝑖,𝑡𝑡 𝐼𝐼{𝜂𝜂𝑡𝑡−1 ≥0}� −ℎ𝑖𝑖,𝑡𝑡 = ℎ𝑖𝑖,𝑡𝑡 𝐼𝐼{𝜂𝜂𝑡𝑡−1 <0}

(2)

𝑘𝑘+
𝑖𝑖,𝑡𝑡 = 𝑘𝑘𝑖𝑖,𝑡𝑡 𝐼𝐼{𝜂𝜂𝑡𝑡−1 ≥0}𝑘𝑘𝑖𝑖,𝑡𝑡 = 𝑘𝑘𝑖𝑖,𝑡𝑡 𝐼𝐼{𝜂𝜂𝑡𝑡−1 <0}

(3)

+
−
Similarly, we also define the good kurtosis 𝑘𝑘𝑖𝑖,𝑡𝑡
and bad kurtosis 𝑘𝑘𝑖𝑖,𝑡𝑡
as follows.

� −We note that the total volatility (kurtosis) of an asset 𝑖𝑖 at any time 𝑡𝑡 is simply the sum+−+ ℎ𝑖𝑖,𝑡𝑡
andof the good and bad volatility (kurtosis) components. Hence, ℎ𝑖𝑖,𝑡𝑡 = ℎ𝑖𝑖,𝑡𝑡+−𝑘𝑘𝑖𝑖,𝑡𝑡 = 𝑘𝑘𝑖𝑖,𝑡𝑡+ 𝑘𝑘𝑖𝑖,𝑡𝑡.

3.2.

TVR-VAR based Asymmetric spillover approach

Antonakakis et al. (2020) introduced a simple measure of dynamic spillovers acrossmarkets by using a time-varying parameter vector autoregressive model (TVP-VAR).
Consider an 𝑁𝑁-variable TVP-VAR(1) model as follows:
10

+ +
+
𝒚𝒚+
𝑡𝑡 = 𝚽𝚽𝑡𝑡 𝒚𝒚𝑡𝑡−1 + 𝜺𝜺𝑡𝑡 ,++𝜺𝜺+𝑡𝑡 |𝛀𝛀𝑡𝑡−1 ~𝑵𝑵(𝟎𝟎, 𝚺𝚺𝑡𝑡 ),

− −
−
𝒚𝒚−
𝑡𝑡 = 𝚽𝚽𝑡𝑡 𝒚𝒚𝑡𝑡−1 + 𝜺𝜺𝑡𝑡 ,−−𝜺𝜺−𝑡𝑡 |𝛀𝛀𝑡𝑡−1 ~𝑵𝑵(𝟎𝟎, 𝚺𝚺𝑡𝑡 ),

(4a)

+ )
vec(𝚽𝚽𝑡𝑡+ ) = vec(𝚽𝚽𝑡𝑡−1
+ 𝜼𝜼+
𝑡𝑡 ,

+
+
𝜼𝜼+
𝑡𝑡 |𝛀𝛀𝑡𝑡−1 ~𝑵𝑵(𝟎𝟎, 𝚵𝚵𝑡𝑡 ),

(4b)

− )
+ 𝜼𝜼−
vec(𝚽𝚽𝑡𝑡− ) = vec(𝚽𝚽𝑡𝑡−1
𝑡𝑡 ,

−
−
𝜼𝜼−
𝑡𝑡 |𝛀𝛀𝑡𝑡−1 ~𝑵𝑵(𝟎𝟎, 𝚵𝚵𝑡𝑡 ),

(4d)

(4c)
′

+
+
where 𝒚𝒚+𝑡𝑡 can be an 𝑁𝑁 × 1 dimensional of good volatilities 𝒉𝒉+𝑖𝑖,𝑡𝑡 = (ℎ1,𝑡𝑡 , ⋯ , ℎ𝑛𝑛,𝑡𝑡 ) or+
+ ′good kurtosis 𝒌𝒌+𝑖𝑖,𝑡𝑡 = (𝑘𝑘1,𝑡𝑡, ⋯ , 𝑘𝑘𝑛𝑛,𝑡𝑡) , while 𝒚𝒚−
𝑡𝑡 can be an 𝑁𝑁 × 1 dimensional bad volatility++−ℎ𝑖𝑖,𝑡𝑡or bad kurtosis 𝑘𝑘𝑖𝑖,𝑡𝑡. 𝛀𝛀+
𝑡𝑡−1 and 𝛀𝛀𝑡𝑡−1 represent all available information up to 𝑡𝑡 − 1.

𝚽𝚽𝑡𝑡+ and 𝚽𝚽𝑡𝑡− are 𝑁𝑁 × 𝑁𝑁 matrices and their vectorization vec(𝚽𝚽𝑡𝑡+ ) or vec(𝚽𝚽𝑡𝑡− ) is an

𝑁𝑁 2 × 1 vector. The shocks 𝜺𝜺𝑡𝑡 and𝜼𝜼𝑡𝑡 are 𝑁𝑁 × 1 and 𝑁𝑁 2 × 1 dimensional vectors,

respectively. Moreover, variance-covariance matrices 𝚺𝚺𝑡𝑡+ , 𝚺𝚺𝑡𝑡− and 𝚵𝚵𝑡𝑡+ , 𝚵𝚵𝑡𝑡− are 𝑁𝑁 × 𝑁𝑁
and 𝑁𝑁 2 × 𝑁𝑁 2 dimensional matrices, respectively.

Using the Wold representation theorem, the TVP-VAR can be transformed into a

TVP-VMA. To ease the notational burden, we replace 𝒚𝒚𝒕𝒕 with either the good volatility(kurtosis) 𝒚𝒚+𝑡𝑡 or bad volatility (kurtosis) 𝒚𝒚−𝑡𝑡 as follows.
∞𝒚𝒚𝒕𝒕 = � 𝚲𝚲𝑗𝑗𝑗𝑗 𝜺𝜺𝑡𝑡−𝑗𝑗 + 𝜺𝜺𝑡𝑡 .
𝑗𝑗=1

(5)

We can then calculate the generalized forecast error variance decomposition (GFEVD),
which was introduced by Koop et al. (1996), and Pesaran & Shin (1998), using TVPVMA coefficients to compute the dynamic connectedness measures (Diebold & Yilmaz,
2009, 2012, 2014).
The 𝐻𝐻-step-ahead GFEVD under the generalized VAR framework can be expressed

as follows:11

𝐻𝐻𝜃𝜃𝑗𝑗𝑗𝑗,𝑡𝑡=−1 ∑𝐻𝐻−1 ′Σ𝑘𝑘𝑘𝑘,𝑡𝑡ℎ=0 �𝑒𝑒𝑗𝑗 𝚲𝚲ℎ,𝑡𝑡 𝚺𝚺𝑡𝑡 𝑒𝑒𝑘𝑘 �
′
′
∑𝐻𝐻−1
ℎ=0 �𝑒𝑒𝑗𝑗 𝚲𝚲ℎ,𝑡𝑡 𝚺𝚺𝑡𝑡 𝚲𝚲ℎ,𝑡𝑡 𝑒𝑒𝑗𝑗 �

2

,

(6)

After the normalization, the pairwise connectedness index from the 𝑘𝑘 −th variable to the𝑗𝑗 −th variable at horizon 𝐻𝐻 at time 𝑡𝑡 can be calculated by𝐻𝐻=𝜃𝜃�𝑗𝑗𝑗𝑗,𝑡𝑡𝐻𝐻𝜃𝜃𝑗𝑗𝑗𝑗,𝑡𝑡

𝐻𝐻∑𝑁𝑁
𝑘𝑘=1 𝜃𝜃𝑗𝑗𝑗𝑗,𝑡𝑡,(7)

Meanwhile, the total connectedness index can be represented as
1
𝑆𝑆𝑡𝑡𝐻𝐻 =𝑁𝑁𝑁𝑁

�𝑗𝑗,𝑘𝑘=1,𝑗𝑗≠𝑘𝑘𝐻𝐻𝜃𝜃�𝑗𝑗𝑗𝑗,𝑡𝑡.

(8)

Moreover, the directional connectedness (From), which measures the total spillover to the𝑘𝑘 −th variable from all remaining variables in the system, can be calculated as
𝑁𝑁

1
𝐻𝐻
𝐻𝐻
𝑆𝑆𝑘𝑘←⋅,𝑡𝑡=� 𝜃𝜃�𝑘𝑘𝑘𝑘,𝑡𝑡.
𝑁𝑁
𝑗𝑗=1,𝑗𝑗≠𝑘𝑘(9)

Similarly, the directional connectedness (To), which measures the total directional
spillover from the 𝑘𝑘 −th variable to all the remaining variables in the system, can becalculated as

3.3.

Spillover asymmetry

𝐻𝐻
𝑆𝑆⋅←𝑘𝑘,𝑡𝑡
=

𝑁𝑁

1
𝐻𝐻
� 𝜃𝜃�𝑗𝑗𝑗𝑗,𝑡𝑡.
𝑁𝑁
𝑗𝑗=1,𝑗𝑗≠𝑘𝑘(10)

To detect the potential asymmetry in the risk transmission across markets, we denotethe good total volatility (kurtosis) spillover index as 𝑆𝑆𝑡𝑡𝐻𝐻+ , and the bad total volatility
12

(kurtosis) spillover index as 𝑆𝑆𝑡𝑡𝐻𝐻− . The total spillover asymmetry 𝐴𝐴𝐻𝐻
𝑡𝑡 , can be defined as

the difference between the good and the bad spillover indices:
𝐻𝐻+
𝐴𝐴𝐻𝐻− 𝑆𝑆𝑡𝑡𝐻𝐻−
𝑡𝑡 = 𝑆𝑆𝑡𝑡

(11)

𝐻𝐻+
𝐻𝐻−
Similarly, the directional spillover measures for 𝑘𝑘 − th variable are (𝑆𝑆𝑘𝑘←⋅,𝑡𝑡, 𝑆𝑆𝑘𝑘←⋅,𝑡𝑡
,

𝐻𝐻+
𝐻𝐻−
, 𝑆𝑆⋅←𝑘𝑘,𝑡𝑡) from equation (9) and (10). Then the directional spillover asymmetry can𝑆𝑆⋅←𝑘𝑘,𝑡𝑡

be calculated as

𝐻𝐻+
𝐻𝐻−
𝐴𝐴𝐻𝐻+
𝑘𝑘←⋅,𝑡𝑡 = 𝑆𝑆𝑘𝑘←⋅,𝑡𝑡 − 𝑆𝑆𝑘𝑘←⋅,𝑡𝑡

𝐻𝐻+
𝐻𝐻−
𝐴𝐴𝐻𝐻+
⋅←𝑘𝑘,𝑡𝑡 = 𝑆𝑆⋅←𝑘𝑘,𝑡𝑡 − 𝑆𝑆⋅←𝑘𝑘,𝑡𝑡

(12a)

(12b)

If the spillover asymmetry indices are null, the contributions from the good and badvolatilities are identical; hence, the risk transmission is symmetric. Alternatively,
asymmetric connectedness in terms of magnitude and direction is the result of different
good and bad spillover indices. A positive asymmetry index means that the good volatility
spills over markets more intensely than the bad volatility. Similarly, a negative
asymmetry index means that the bad volatility spills over markets more intensely than thegood volatility.
3.4.

Bootstrapping the spillover asymmetry

The bootstrapping technique in this paper is summarized as follows:(i)Re-sample, with replacement, the returns as a block, i.e., the re-sampling is
performed with respect to time t. For a given day, we draw the returns of all
markets to keep the connectedness structure between variables;(ii)

Re-estimate the good and bad volatilities (kurtosis);
13

(iii)

Compute the time-varying bootstrap asymmetry spillover indices to check fortime-dependency;
Repeat the previous steps (i) to (iii) B times.

(iv)

4. Empirical study
4.1.

Data and summary statistics
In this paper, we have selected six principal indices under the sustainable investment

theme of S&P Global to represent sustainable investments. These are: S&P Global 1200
ESG Index (ESG), S&P Global 1200 Carbon Efficient Index (CEI), S&P 500 Bond
Investment Grade Carbon Efficient Index (BIGCEI), S&P Green Bond Index (GBI), S&P
Global Clean Energy Index (GCEI), and S&P Global Carbon Index (Carbon).
Collectively, these indices encompass a range of sustainable investment categories,
including green bonds, clean energy equities, ESG investments, and carbon-focusedinvestments.
More specifically, the S&P Global 1200 ESG Index (ESG) ranks and weights its
Global 1200 member companies based on their Environmental, Social, and Governance(ESG) performance. Companies with higher ESG scores have greater weight in this index.
The S&P Global 1200 Carbon Efficient Index (CEI) aligns carbon efficiency with themarket capitalization of its Global 1200 companies. It gives preference to companies thathave lower carbon emissions relative to their market value. The S&P 500 Bond
Investment Grade Carbon Efficient Index (BIGCEI) focuses on investment-gradecompanies within the S&P 500, combining their market capitalization with carbon

14efficiency. Similar to CEI, it favors companies with a lower ratio of carbon emissions tomarket value. The S&P Green Bond Index (GB) tracks global green bonds, which arebonds specifically issued to finance environmentally friendly projects. The S&P Global
Clean Energy Index (GCEI) tracks the stock performance of global clean energy
companies, promoting investment in the clean energy sector. Lastly, the S&P Global
Carbon Index (Carbon) concentrates on the global carbon market, tracking the pricing
and performance of carbon trading.
Moreover, in our study, we also selected four representative traditional investments,
encompassing stocks, gold, crude oil, and bonds. Specifically, these are: S&P GLOBAL
1200 Index (Stock), S&P GSCI Gold Index (Gold), S&P GSCI Crude Oil Index (Oil),and S&P 500 Bond Index (Bond).
All the indices are plotted in Figure 1. The data spans from September 1, 2015, to July
1, 2023. The data used in this study is sourced from S&P Global.
First, we compute the logarithmic returns of each asset's price series. Subsequently,
we estimate conditional volatility and conditional kurtosis based on the GJR-SK model.
Table 1 presents the descriptive statistics of the return series. From Table 1, we observethat the mean and variance of the returns across the series are fairly consistent, nearly
converging to zero. As for skewness and excess kurtosis, it's evident that all series exhibit
negative skewness and positive excess kurtosis. The p-values of the Jarque-Bera (JB) test
are consistently below 0.01, rejecting the null hypothesis that all return series are normally
distributed. The unit root test conducted by Elliott et al. (1996) shows that all return series
exhibit no unit root. The results of the Fisher & Gallagher (2012) weighted portmanteau
15test reveal the presence of ARCH/GARCH type effects in all return series.
The estimated volatility and kurtosis are depicted in Figure 2 and Figure 3,
respectively. It is evident that there exists a certain similarity in the movements ofvolatility and kurtosis across indices, which strongly suggests the presence of a spillover
effect across markets. Furthermore, a discernible distinction between the variations involatility and kurtosis can be observed. This indicates that the patterns of generalvolatility and extreme volatility changes are not identical, displaying significant
disparities. Lastly, there are distinct periods of high (either volatility or extreme) risk,such as the Brexit vote in mid-2016, the outbreak of the COVID-19 pandemic, and theRussia-Ukraine conflict.

16

Fig.1: All price series
Note: ESG, CEI, BIGCEI, GB, and GCEI represent the S&P Global 1200 ESG Index, S&P Global 1200 Carbon
Efficient Index, S&P 500 Bond Investment Grade Carbon Efficient Index, S&P Green Bond Index, and S&P Global
Clean Energy Index, respectively. Stock, Gold, Oil, and Bond refer to the S&P GLOBAL 1200 Index, S&P GSCI Gold
Index, S&P GSCI Crude Oil Index, and S&P 500 Bond Index, respectively.

17

ESG
CEI
BIGCEI
GB
GCEI
Carbon
Stock
Gold
Oil
Bond

Mean

Table 1: Summary statistics
Var
Skew Kurto
JB

ERS

Q(20)

Q2(20)

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

0.00
0.00
0.00
0.00
0.00
0.01
0.00
0.01
0.00
0.00

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

−1.08
−1.10
−0.55
−0.24
−0.41
−1.06
−1.05
−0.05
−2.85
−0.59

16.17
16.99
9.04
4.75
7.89
9.71
15.44
4.25
62.39
11.26

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

Note: The table presents descriptive statistics including the mean, variance (Var), skewness (Skew), excess kurtosis(Kurto), and the p-value of the Jarque-Bera test (JB; 1987), the unit root test by Elliott et al. (1996), and the Fisher &Gallagher (2012) weighted portmanteau test with 20 lags. ESG, CEI, BIGCEI, GB, and GCEI represent the S&P Global
1200 ESG Index, S&P Global 1200 Carbon Efficient Index, S&P 500 Bond Investment Grade Carbon Efficient Index,
S&P Green Bond Index, and S&P Global Clean Energy Index, respectively. Stock, Gold, Oil, and Bond refer to the
S&P GLOBAL 1200 Index, S&P GSCI Gold Index, S&P GSCI Crude Oil Index, and S&P 500 Bond Index,
respectively.

18

Fig.2: All conditional volatility series
Note: ESG, CEI, BIGCEI, GB, and GCEI refer to the S&P Global 1200 ESG Index, S&P Global 1200 Carbon EfficientIndex, S&P 500 Bond Investment Grade Carbon Efficient Index, S&P Green Bond Index, and S&P Global Clean
Energy Index, respectively. Stock, Gold, Oil, and Bond correspond to the S&P GLOBAL 1200 Index, S&P GSCI Gold
Index, S&P GSCI Crude Oil Index, and S&P 500 Bond Index, respectively.

19

Fig.3: All conditional kurtosis series
Note: ESG, CEI, BIGCEI, GB, and GCEI refer to the S&P Global 1200 ESG Index, S&P Global 1200 Carbon
Efficient Index, S&P 500 Bond Investment Grade Carbon Efficient Index, S&P Green Bond Index, and S&P Global
Clean Energy Index, respectively. Stock, Gold, Oil, and Bond correspond to the S&P GLOBAL 1200 Index, S&P
GSCI Gold Index, S&P GSCI Crude Oil Index, and S&P 500 Bond Index, respectively.

4.2.

Traditional volatility and kurtosis spillovers
As a benchmark, we first report the detailed averaged dynamic (symmetric) volatility

and kurtosis spillovers without separating the good from the bad component in Figure 4
and 5, respectively. In fact, we can see that the total volatility spillover across the entire
system stands at 65.424 percentage points, while the total kurtosis spillover stands at
48.337 percentage points. This highlights that volatility risk tends to propagate more
extensively across various investments compared with extreme risk. In terms of volatility
spillover, Oil, CEI, and Stock are the top three investments transmitting spillovers
outward, contributing 9.073%, 8.857%, and 8.376% of volatility spillover to other20

investments, respectively. For kurtosis spillover, Stock, CEI, and ESG are the top three
investments transmitting spillovers outward, contributing 8.001%, 7.894%, and 6.345%
of kurtosis spillover to other investments, respectively. Interestingly, while Oil transmits
higher volatility risk to other investments, it conveys minimal kurtosis risk, accounting
for just 1.493% of kurtosis spillover.

Fig.4: Averaged dynamic volatility spillover index
Note: ESG, CEI, BIGCEI, GB, and GCEI refer to the S&P Global 1200 ESG Index, S&P Global 1200 Carbon
Efficient Index, S&P 500 Bond Investment Grade Carbon Efficient Index, S&P Green Bond Index, and S&P Global
Clean Energy Index, respectively. Stock, Gold, Oil, and Bond correspond to the S&P GLOBAL 1200 Index, S&P
GSCI Gold Index, S&P GSCI Crude Oil Index, and S&P 500 Bond Index, respectively.

21

Fig.5: Averaged dynamic kurtosis spillover index
Note: ESG, CEI, BIGCEI, GB, and GCEI refer to the S&P Global 1200 ESG Index, S&P Global 1200 Carbon
Efficient Index, S&P 500 Bond Investment Grade Carbon Efficient Index, S&P Green Bond Index, and S&P Global
Clean Energy Index, respectively. Stock, Gold, Oil, and Bond correspond to the S&P GLOBAL 1200 Index, S&P
GSCI Gold Index, S&P GSCI Crude Oil Index, and S&P 500 Bond Index, respectively.

4.3.

Averaged dynamic asymmetric spillovers
Next, we present the averaged dynamic good volatility spillover index and theaveraged dynamic bad volatility spillover index in Figures 6 and 7, respectively. In
addition, Figures 8 and 9 depict the averaged dynamic good kurtosis spillover index andthe averaged dynamic bad kurtosis spillover index, respectively.
We find that the contribution of spillovers from volatility shocks among variables tothe total forecast error variance is 49.546% for good shocks, while it is 56.163% for bad
shocks. This suggests that both good and bad shocks significantly contribute to thesystem's volatility, with negative shocks having a slightly greater impact. On the other
hand, the contribution of spillovers from kurtosis shocks among variables to the total
forecast error variance stands at 43.092% for good shocks, compared with an almost equal
42.138% for bad shocks.
22For carbon, we found a relatively strong volatility spillover and kurtosis spillover
between it and both the stock and crude oil markets. This finding supports the "CarbonEnergy-Finance" system, which posits that the Carbon market is interconnected not onlywith traditional energy markets but also with some financial markets. For instance, theresearch of Tan et al. (2020) on the EU ETS also indicates that the volatility of the carbon
market closely relates to the volatility of the stock market. Moreover, we observed thatthe level of bad volatility spillover between them is greater than that of good volatility
spillover. Although we also identified a relatively strong kurtosis spillover effect between
carbon and stocks or crude oil, the kurtosis spillover effect between them appears to besymmetric, meaning that the levels of good kurtosis spillover and bad kurtosis spillover
are nearly equal.
Additionally, for the three stock-based sustainable investments, CEI, GCEI, and ESG,
apart from substantial volatility spillovers with the stock market, they also exhibit
significant volatility spillovers with the crude oil market. Specifically, we found that thebad volatility spillover between them and the crude oil market is stronger than the goodvolatility spillover. Among these three stock-based sustainable investments, the volatility
spillover effect between GCEI and crude oil is the strongest, regardless of whether it isgood or bad volatility and irrespective of the direction of the spillover. The volatility
spillover effects between new energy stocks and traditional energy markets, especiallythe crude oil market, have been confirmed by many researchers (e.g., Attarzadeh &Balcilar, 2022; Caporale et al., 2023; Liu & Hamori, 2020; Song et al., 2019; Umar et al.,2022).
23

In our research, we observe strong spillover effects in kurtosis between the threestock-based sustainable investments (CEI, GCEI, ESG) and crude oil. Similarly, forkurtosis spillover, the level of bad kurtosis spillover is higher than that of good kurtosis
spillover. The only distinction is that CEI transmits the highest kurtosis spillover to crudeoil, rather than GCEI.
Finally, for bond-based sustainable investments like BIGCEI and GB, we identify arobust volatility spillover effect between them and gold, regardless of whether it is goodor bad volatility. Additionally, the bad volatility spillover between them and gold isstronger than the good volatility spillover. The volatility spillover effect between green
bonds and gold is also more pronounced, irrespective of whether it is good or badvolatility.
The findings for kurtosis spillover are generally consistent with these results. The
only distinction in kurtosis spillover is that the levels of bad and good kurtosis spillover
between bond-based sustainable investments (BIGCEI, GB) and gold are almost identical,
indicating symmetrical kurtosis spillover between them.
The strong spillover relationship between green bonds and precious metals can be
attributed to the increasing significance of the green bonds market and the stable value of
precious metals. Precious metals, particularly gold, are considered stable assets, making
them suitable for hedging against market risks. Concurrently, the growing emphasis on
sustainable projects is driving the prominence of green bond markets, which areconsidered effective financial tools for promoting a low-carbon economy. Investors may
switch between green bonds and stable precious metals to optimize returns and manage
24

risks, leading to the strong observed spillover effects between these markets (Naeem etal., 2021).

Fig.6: Averaged dynamic good volatility spillover index
Note: ESG, CEI, BIGCEI, GB, and GCEI refer to the S&P Global 1200 ESG Index, S&P Global 1200 Carbon
Efficient Index, S&P 500 Bond Investment Grade Carbon Efficient Index, S&P Green Bond Index, and S&P Global
Clean Energy Index, respectively. Stock, Gold, Oil, and Bond correspond to the S&P GLOBAL 1200 Index, S&P
GSCI Gold Index, S&P GSCI Crude Oil Index, and S&P 500 Bond Index, respectively.

25

Fig.7: Averaged dynamic bad volatility spillover index
Note: ESG, CEI, BIGCEI, GB, and GCEI refer to the S&P Global 1200 ESG Index, S&P Global 1200 Carbon
Efficient Index, S&P 500 Bond Investment Grade Carbon Efficient Index, S&P Green Bond Index, and S&P Global
Clean Energy Index, respectively. Stock, Gold, Oil, and Bond correspond to the S&P GLOBAL 1200 Index, S&P
GSCI Gold Index, S&P GSCI Crude Oil Index, and S&P 500 Bond Index, respectively.

Fig.8: Averaged dynamic good kurtosis spillover index
Note: ESG, CEI, BIGCEI, GB, and GCEI refer to the S&P Global 1200 ESG Index, S&P Global 1200 Carbon
Efficient Index, S&P 500 Bond Investment Grade Carbon Efficient Index, S&P Green Bond Index, and S&P Global
Clean Energy Index, respectively. Stock, Gold, Oil, and Bond correspond to the S&P GLOBAL 1200 Index, S&P
GSCI Gold Index, S&P GSCI Crude Oil Index, and S&P 500 Bond Index, respectively.

26

Fig.9: Averaged dynamic bad kurtosis spillover index
Note: ESG, CEI, BIGCEI, GB, and GCEI refer to the S&P Global 1200 ESG Index, S&P Global 1200 Carbon
Efficient Index, S&P 500 Bond Investment Grade Carbon Efficient Index, S&P Green Bond Index, and S&P Global
Clean Energy Index, respectively. Stock, Gold, Oil, and Bond correspond to the S&P GLOBAL 1200 Index, S&P
GSCI Gold Index, S&P GSCI Crude Oil Index, and S&P 500 Bond Index, respectively.

4.4.

Dynamic asymmetric spillovers
Conclusions drawn solely based on Averaged dynamic asymmetric spillovers

without further analysis of directional transmission or the evolution of spillover indicesover time could potentially be misleading (BenSaïda, 2019). Therefore, this section shifts
our focus to dynamic asymmetric spillovers. Figure 10 and Figure 11 depict the dynamic
total volatility spillover index and dynamic total kurtosis spillover index, respectively.
Each of these figures contains two lines: black represents positive (good) spillover, andred represents negative (bad) spillover. If both lines coincide, it indicates symmetricspillovers.
Figure 10 reveals that bad volatility spillover exceeds good volatility spillover inmost periods, indicating that the total volatility spillover in the entire system isasymmetric in most cases. Particularly, the outbreak of COVID-19 significantly
27

influenced bad volatility spillover. In other periods, the difference between good and badvolatility spillover was less pronounced, but the onset of COVID-19 in late 2019intensified bad volatility spillover, keeping it high for an extended period. Meanwhile,
while good volatility spillover also increased during this period, it started to decline soonafter, leading to a notable difference between the two during this timeframe.
On the other hand, compared to Figure 10 where bad volatility spillover exceeded
good volatility spillover in most periods, Figure 11 illustrates that periods with bad
kurtosis spillover surpassing good kurtosis spillover are much less frequent. In fact,
instances of bad kurtosis spillover surpassing good kurtosis spillover primarily occurred
during the Brexit referendum in mid-2016 and the period of COVID-19.

Fig.10: Dynamic total volatility spillover
Note: The black line represents the positive (good) total volatility spillover, while the red line indicates the negative(bad) total volatility spillover.

28

Fig.11: Dynamic total kurtosis spillover
Note: The black line represents the positive (good) total kurtosis spillover, while the red line indicates the negative(bad) total kurtosis spillover.

These results are also confirmed by Figures 12 and 13. Respectively, Figures 12 and13 illustrate the total volatility spillover asymmetry and total kurtosis spillover
asymmetry calculated using Equation 11. In these figures, the periods when bad volatility(kurtosis) spillover exceeds good volatility (kurtosis) spillover (indicating negative
asymmetry) are shown by the green shaded areas, while the periods when good volatility(kurtosis) spillover exceeds bad volatility (kurtosis) spillover (indicating positive
asymmetry) are represented by the blue shaded areas. The red lines denote the upper andlower bounds of the time-varying 95% confidence interval.
Figure 12 demonstrates that the volatility spillover asymmetry is predominantly
negative, with a substantial increase in negative spillover asymmetry during the COVID19 period. Meanwhile, Figure 13 indicates that negative kurtosis spillover asymmetry ismost prominent during the Brexit period in 2016 and the onset of the COVID-19
pandemic.
In financial markets, the phenomenon of negative volatility asymmetry is moreprevalent than positive asymmetry, as demonstrated by various studies (e.g., Baruník et29

al., 2016, 2017; Mensi et al., 2021; X. Wang & Wu, 2018). Our research on volatility
spillover asymmetry reaffirms this observation. However, our investigation into kurtosis
spillover asymmetry has yielded contrasting results. The occurrence of negative kurtosis
asymmetry appears to be more common, whereas positive kurtosis asymmetry is observed
only in specific periods.
BenSaïda (2019) and X. Wang & Wu (2018) argue that spillover asymmetry reflects
two key aspects. Firstly, it indicates the sensitivity of market participants to both goodand bad news. Secondly, it captures market sentiment, whether it leans toward optimism
or pessimism, and participants' expectations. Viewing this from the first perspective, it'splausible to assert that market participants are generally more responsive to negative news,
which often triggers herd behavior more readily. Consequently, unfavorable news tends
to lead to more significant volatility, and this effect is more prone to transmission throughspillover channels. This underscores that general volatility risk and volatility spillover are
more influenced by negative news. However, extreme volatility, or extreme risk, is lessaffected by negative news compared to general volatility risk. Only exceptionally severe
negative news might drive an increase in extreme volatility and corresponding extreme
volatility spillover.
Considering the second perspective, the prevalence of negative spillover asymmetry
in most periods indicates that pessimistic sentiment has largely dominated. This has
resulted in an overrepresentation of bad volatility spillover. However, this pessimistic
sentiment primarily pertains to volatility risk rather than extreme risk. Investors'
expectations for volatility risk, reflecting general volatility, and extreme risk, representing
30

extreme volatility, may diverge. In most periods, investors lean toward pessimism
concerning volatility risk but exhibit relatively greater optimism toward extreme risk. Yet,during exceptionally extreme periods like the Brexit vote and COVID-19, investor
sentiment becomes extremely pessimistic. Consequently, investors harbor pessimistic
views not only about volatility risk but also about extreme risk.

Fig.12: Total volatility spillover asymmetry index

Fig.13: Total kurtosis spillover asymmetry index

Figures 14 and 15 illustrate the volatility spillover asymmetry index and the kurtosis
spillover asymmetry index to other investments, as given in equation 12a. Meanwhile,
Figures 16 and 17 present the volatility spillover asymmetry index and the kurtosis
spillover asymmetry index from other investments, following equation 12b. These figures
yield intriguing insights not readily accessible through traditional symmetric spillover31

analysis or averaged dynamic asymmetric spillover analysis.
For instance, two notable findings emerge. Firstly, spillover asymmetry prevails
across various investments, albeit with varying degrees of intensity. Secondly, in thecontext of volatility spillover, most investments during the vast majority of periods tend
to transmit or receive unfavorable volatility spillovers from other investments. However,in the case of kurtosis spillover, there exists greater diversity among investments. For
example, ESG predominantly transmits and receives more favorable kurtosis spillover inmost periods, whereas GCEI and BIGCEI exhibit the opposite trend.

(a) Carbon.

(b) CEI(c) GCEI(d) ESG32

(e) BIGCEI(f) GB(g) Oil(h) Gold(i) Stock(j) Bond
Fig.14: Volatility spillover asymmetry index to other investments.
Note: ESG, CEI, BIGCEI, GB, and GCEI refer to the S&P Global 1200 ESG Index, S&P Global 1200 Carbon
Efficient Index, S&P 500 Bond Investment Grade Carbon Efficient Index, S&P Green Bond Index, and S&P Global
Clean Energy Index, respectively. Stock, Gold, Oil, and Bond correspond to the S&P GLOBAL 1200 Index, S&P
GSCI Gold Index, S&P GSCI Crude Oil Index, and S&P 500 Bond Index, respectively.

(a) Carbon.

(b) CEI(c) GCEI(d) ESG33

(e) BIGCEI(f) GB(g) Oil(h) Gold(i) Stock(j) Bond
Fig.15: Kurtosis spillover asymmetry index to other investments.
Note: ESG, CEI, BIGCEI, GB, and GCEI refer to the S&P Global 1200 ESG Index, S&P Global 1200 Carbon
Efficient Index, S&P 500 Bond Investment Grade Carbon Efficient Index, S&P Green Bond Index, and S&P Global
Clean Energy Index, respectively. Stock, Gold, Oil, and Bond correspond to the S&P GLOBAL 1200 Index, S&P
GSCI Gold Index, S&P GSCI Crude Oil Index, and S&P 500 Bond Index, respectively.

(a) Carbon.

(b) CEI

34

(c) GCEI(d) ESG(e) BIGCEI(f) GB(g) Oil(h) Gold(i) Stock(j) Bond
Fig.16: Volatility spillover asymmetry index from other investments.
Note: ESG, CEI, BIGCEI, GB, and GCEI refer to the S&P Global 1200 ESG Index, S&P Global 1200 Carbon
Efficient Index, S&P 500 Bond Investment Grade Carbon Efficient Index, S&P Green Bond Index, and S&P Global
Clean Energy Index, respectively. Stock, Gold, Oil, and Bond correspond to the S&P GLOBAL 1200 Index, S&P
GSCI Gold Index, S&P GSCI Crude Oil Index, and S&P 500 Bond Index, respectively.

35

(a) Carbon.

(b) CEI(c) GCEI(d) ESG(e) BIGCEI(f) GB(g) Oil(h) Gold36

(i) Stock(j) Bond
Fig.17: Kurtosis spillover asymmetry index from other investments.
Note: ESG, CEI, BIGCEI, GB, and GCEI refer to the S&P Global 1200 ESG Index, S&P Global 1200 Carbon
Efficient Index, S&P 500 Bond Investment Grade Carbon Efficient Index, S&P Green Bond Index, and S&P Global
Clean Energy Index, respectively. Stock, Gold, Oil, and Bond correspond to the S&P GLOBAL 1200 Index, S&P
GSCI Gold Index, S&P GSCI Crude Oil Index, and S&P 500 Bond Index, respectively.

5. Conclusions and discussions
Citing the research of Barndorff‐Nielsen et al. (2010) and BenSaïda (2019), we
expanded the analysis of asymmetric spillover effects to higher moments (kurtosis) using
the GJR-SK model. We explored asymmetric volatility spillover and asymmetric kurtosis
spillover among sustainable and traditional investments.
For carbon, we observed robust volatility and kurtosis spillovers with both stocks andcrude oil. The negative volatility spillover exceeded the positive volatility spillover,whereas the kurtosis spillover exhibited symmetry.
Among the three stock-based sustainable investments—CEI, GCEI, and ESG—weidentified substantial volatility and kurtosis spillovers with crude oil. These spillovers
showed asymmetry, with the negative volatility (kurtosis) spillover surpassing thepositive volatility (kurtosis) spillover.
Regarding the two bond-based sustainable investments, BIGCEI and GB, we notedsignificant volatility and kurtosis spillovers with gold. The adverse volatility spillover
was more pronounced than the favorable volatility spillover, while the kurtosis spillover
demonstrated symmetry.
By investigating the dynamic changes in spillover effects, we have discovered that
good kurtosis spillover generally surpasses bad kurtosis spillover in most periods.
37

However, during specific extreme events such as Brexit and COVID-19, bad kurtosis
spillover becomes predominant. This finding contrasts significantly with the observationin volatility spillover, where bad volatility spillover exceeds good volatility spillover inmost periods. The potential reason for this disparity in results lies in the sensitivity ofkurtosis spillover, which represents extreme volatility spillover, to negative news.
Moreover, market expectations regarding general volatility and extreme volatility may
diverge. While the market commonly adopts a pessimistic stance towards general risk, it
only tends to do so for extreme risk in highly turbulent market conditions.
Hence, through vigilant monitoring of kurtosis spillover, policymakers can acquire
insights into market sentiment and devise timely interventions to stabilize financial
markets during periods of heightened pessimism. Investors can also capitalize on tracking
kurtosis spillover, employing it as an indicator of market sentiment and making wellinformed decisions regarding portfolio diversification and risk management, especiallyduring instances of pronounced market volatility.

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