The Higher the Better? Hedging and Investment Strategies
in Cryptocurrency Markets:
Insights from Higher Moment Spillovers
Xie HeShigeyuki Hamori
September 2023
Discussion Paper No. 2315

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITYROKKO, KOBE, JAPANThe Higher the Better? Hedging and Investment Strategies in Cryptocurrency
Markets: Insights from Higher Moment Spillovers
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 aims to investigate whether conditional higher moments offer additional anddistinct information compared to lower moments in spillover effect analysis, and to
examine their relevance for portfolio construction and hedging strategies. We employ
the autoregressive conditional density (ACD) model to estimate the conditionalskewness and kurtosis of nine major cryptocurrency markets. Furthermore, we explore
the higher moment spillovers among these markets using the Diebold Yilmaz spillover
approach. The results confirm that the magnitude and direction of spillover effects varyacross different moments in the cryptocurrency market, each providing unique insights.
Additionally, we find that although the spillover effects exhibit variations over different
time periods and market conditions, the skewness spillover and kurtosis spillover,which track the transmission of downside (upside) risk and tail risk respectively,
demonstrate similarities in their patterns. These variations differ noticeably from thechanges observed in volatility spillover, which tracks the transmission of volatility risk.
Finally, comparing the minimum connectedness portfolio (MCoP) based on different
moment spillovers, we discover that the MCoP derived from higher moment spillovers
exhibits superior hedge effectiveness and Sharpe ratios.
Key words: Higher moments; Spillover effect; Cryptocurrency markets
JEL classification: G15; F3; C32
Funding: This work was supported by JSPS KAKENHI Grant Number 22K01424
1

1. Introduction
The spectacular collapse of the US housing market and the bursting of the US
mortgage bubble in the summer of 2007 directly triggered a severe financial crisis in
2008. This crisis begins in the US stock market and spreads rapidly to other financial
sectors. The crisis spreads to other countries, transforming a local crisis into a global
one. This event serves as a reminder to closely monitor spillover effects between
markets to prevent shocks from one market from spreading to others.
Numerous techniques can be utilized to measure spillover effects. Some of thecommonly employed techniques include vector autoregression (VAR) models,
multivariate generalized autoregressive conditional heteroskedasticity (M-GARCH)
models such as dynamic conditional correlation (DCC) GARCH, and Copula Models.
In recent years, the Diebold Yilmaz connectedness (spillover) approach has garnered
increasing attention from researchers. It measures the spillover effect in the generalized
VAR framework and was first proposed by Diebold & Yilmaz (2009). It quantifies boththe strength and direction of spillover effects within a fixed investment horizon.
Based on the Diebold Yilmaz connectedness approach, an extensive amount ofliterature has investigated the spillovers of returns and volatilities (e.g., Diebold &Yilmaz, 2009; He et al., 2020; Liu & Hamori, 2020; Sun et al., 2022; Tiwari et al.,2018). Since returns and volatilities track changes in investor expectations and market
volatility risks, return spillover and volatility spillover are considered to track intermarket expectational links and volatility risk links (Diebold & Yilmaz, 2015). Recently,2researchers have started extending spillover analysis to higher moments, such as
skewness and kurtosis. Skewness and kurtosis of returns are considered to measuredownside (upside) risk or tail risk in challenging times and under adverse scenarios infinancial markets (He & Hamori, 2023). Compared with volatility spillover, skewness
spillover and kurtosis spillover can capture extreme tail co-movements between
markets. Higher moment spillovers can effectively detect some important events that
may not be effectively captured by return and volatility spillover (Bouri et al., 2021).
Similar to volatility, both skewness and kurtosis are latent and need to be estimated.
Several higher moment spillover analyses based on realized measures or model-based
estimates have garnered attention (e.g., Finta and Aboura 2020; Gkillas et al. 2022; Heand Hamori 2021; Nekhili and Bouri 2023; Zhang et al. 2022). One major advantageof realized measures is their ease of calculation, and therefore, most of the literature on
higher moment spillover has utilized realized measures. However, model-based
estimates allow for more sophisticated and flexible modeling techniques, such as theautoregressive conditional density (ACD) model and GARCHSK models. Thesemodels capture the conditional dependencies and dynamics in the data, providing moreaccurate and robust volatility estimates. Additionally, model-based estimates ofskewness or kurtosis do not require high-frequency data, unlike realized measures,
which rely on high-frequency data. He and Hamori (2021) conducted pioneering workin spillover analysis of conditional higher moments. They focused on major global
stock markets as the subject of their study and employed the ACD model to estimate3

their conditional higher moments, obtaining robust results in the stock market andconfirming the importance of measuring higher order spillover effects.
In recent years, cryptocurrencies like Bitcoin and Ethereum have gained increasingprominence, reshaping the financial landscape and disrupting conventional
understandings of currency. They have opened up new opportunities for investment andfinancial transactions. Cryptocurrencies have emerged as a noteworthy financial asset
class, displaying distinct features, market structure, price determinants, risk factors, andregulatory considerations in contrast to traditional financial products. Given thesignificance and distinctive nature of the cryptocurrency market, we incorporate highmoment spillover analysis into our study. This approach allows us to examine thesimilarities and differences in high moment spillover effects between cryptocurrencies
and other markets.
The Diebold Yilmaz connectedness approach has long been considered to provide
important information for practical investment decisions, but its specific application
remains a widely discussed issue. However, in recent times, it has found practicalapplication in portfolio construction. Broadstock et al. (2020) introduced a portfolio
technique called the Minimum Connectedness Portfolio (MCoP). This approach aims
to construct a portfolio by minimizing interconnectedness and spillover effects among
investment assets. Several studies related to the MCoP have confirmed the significant
role played by return connectedness or volatility connectedness in portfolio
construction (e.g., Abdullah, Chowdhury, and Sulong 2023; Adekoya et al. 2022; Cui

4and Maghyereh 2023; Tiwari et al. 2021). Additionally, the MCoP has exhibitedfavorable financial performance for certain financial assets. However, there is limited
literature on MCoP based on higher moment connectedness. The applicability of higher
moment connectedness to this strategy, as well as its role in hedging strategies andportfolio construction, still need to be verified.
For these reasons, we follow the approach of He & Hamori (2021) and estimate theconditional skewness and kurtosis using the ACD model. Subsequently, we extend theDiebold-Yilmaz connectedness approach to incorporate higher moments. We
investigate the spillover of skewness and kurtosis among 9 major cryptocurrencies,
analyzing their implications for the transmission of downside (upside) risk and tail risk.
Furthermore, we examine the role of skewness spillover and kurtosis spillover in
portfolio construction, assessing whether the MCoP based on higher moment
connectedness exhibits superior hedge effectiveness compared to that based onvolatility connectedness. To the best of our knowledge, this paper represents the firstresearch endeavor to explore the spillover effects of conditional higher moments across
cryptocurrency markets. Moreover, it contributes to the existing literature by
investigating the role of higher moment spillovers in hedging strategies and portfolio
construction.
Here are some major findings of this paper:First, we find that the total spillovers across cryptocurrency markets decrease as
the order of the moment increases. The total skewness spillover and total kurtosis

5spillover are smaller than the total volatility spillover among all markets. Additionally,
the changes in skewness and kurtosis spillovers display high similarity, implying aconsistent pattern in the transmission of downside (upside) risk and tail risk acrossmarkets over time. However, the changes and fluctuations in downside (upside) risk
and tail risk are notably different from the transmission patterns of volatility risk.
Second, for each cryptocurrency, the spillover from and to other cryptocurrencies
varies across different moments. Binance Coin (BNB) and Bitcoin (BTC) dominate intransmitting volatility and kurtosis, respectively, while Cardano (ADA) exhibits thehighest skewness spillover transmitted to others.
At last, to examine whether higher-moment spillovers can be used in portfolio
construction and hedging strategies, we introduce the higher moment connectedness
into the MCoP and explore the historical investment performance of them throughback-testing.
We find that compared to the MCoP based on volatility, the MCoP based on higher
moments shows better hedge effectiveness and higher Sharpe ratios for volatility, Valueat Risk (VaR), and expected shortfall (ES). Particularly, in terms of hedge effectivenessand Sharpe ratios, the Minimum Connectedness Portfolio (MCoP) based on kurtosis
connectedness and skewness connectedness demonstrates the best performance,
respectively.
The remainder of this paper is organized as follows. Section 2 presents the empiricalmethods, including the ACD model, the Diebold Yilmaz TVP-VAR-based

6connectedness approach, and a novel portfolio technique named MCoP. Section 3
describes the data, reports the summary statistics, and presents the results of the tests.
The results are discussed in Section 4, and Section 5 provides a summary andconclusions.
2. Methodology
2.1.

The Autoregressive Conditional Denity Model
To capture the dynamic behavior of higher moments, such as skewness and kurtosis,

Hansen (1994) introduced the Autoregressive Conditional Density (ACD) model,
which generalizes GARCH type dynamics to time varying conditional higher moments
and such subsumes them.
A first order constant-GARCH(1,1) model with general ACD dynamics can be
written as:
𝑟𝑟𝑡𝑡 = 𝜇𝜇𝑡𝑡 + 𝜖𝜖𝑡𝑡 = 𝜇𝜇𝑡𝑡 + 𝜎𝜎𝑡𝑡 𝑧𝑧𝑡𝑡 ,𝜎𝜎2𝑡𝑡 = 𝜔𝜔 + 𝛼𝛼1 𝜖𝜖2𝑡𝑡−1 + 𝛽𝛽1 𝜎𝜎2𝑡𝑡−1 .

(1a)

(1b)

where 𝜖𝜖𝑡𝑡 is the innovation, and 𝑧𝑧𝑡𝑡 is white noise and assumed to follow someappropriately distribution 𝔇𝔇(0,1, 𝜌𝜌𝑡𝑡 , 𝜁𝜁𝑡𝑡 )1. 𝜌𝜌𝑡𝑡 and 𝜁𝜁𝑡𝑡 are skew parameter and shapeparameter, which control the asymmetry and tail thickness, respectively. The higher
order moments such as skewness and kurtosis could be calculated by the two parameters.

This paper uses the normal inverse Gaussian (NIG) distribution which follows He andHamori (2021).

1

7

In the ACD model, the dynamics for the two parameters can be modeled by the
first-order quadratic-type dynamics:
𝜌𝜌𝑡𝑡 = Φ�𝜌𝜌� t � = 𝐿𝐿𝜌𝜌�t +(𝑈𝑈𝜌𝜌� −𝐿𝐿𝜌𝜌� )tt

1+𝑒𝑒−𝜌𝜌� t

�

(2a)

,,

𝜁𝜁𝑡𝑡 = Φ�𝜁𝜁�t � = 𝐿𝐿𝜁𝜁�t + 𝑈𝑈𝜁𝜁�t 𝑒𝑒−𝜐𝜐𝜁𝜁t ,

(2b)

2
̅ .
𝜁𝜁t̅ = 𝑏𝑏0 + 𝑏𝑏1 𝑧𝑧𝑡𝑡−1 + 𝑏𝑏2 𝑧𝑧𝑡𝑡−1+ 𝑑𝑑1 𝜁𝜁t−1(2d)2
𝜌𝜌̅t = 𝑎𝑎0 + 𝑎𝑎1 𝑧𝑧𝑡𝑡−1 + 𝑎𝑎2 𝑧𝑧𝑡𝑡−1+ 𝑐𝑐1 𝜌𝜌̅t−1 ,(2c)Where 𝜌𝜌̅t and 𝜁𝜁t̅ are the unconstrained motion dynamics of the skew parameter 𝜌𝜌𝑡𝑡

and 𝜁𝜁𝑡𝑡 respectively. Φ(⋅) represents an appropriate transformation function. 𝐿𝐿 and𝑈𝑈 are the lower and upper bounds of the distributional parameters.
2.2.

The Diebold–Yilmaz TVP-VAR-based Approach

In this research, a TVP-VAR with one lag will be employed based on the Schwartz
information criterion (SC). Consider an 𝑁𝑁-variable TVP-VAR(1) model as follows:
𝜺𝜺𝒕𝒕 |𝛀𝛀𝑡𝑡−1 ~𝑵𝑵(𝟎𝟎, 𝚺𝚺𝑡𝑡 ),𝒚𝒚𝑡𝑡 = 𝚽𝚽1𝑡𝑡 𝒚𝒚𝑡𝑡−1 + 𝜺𝜺𝑡𝑡 ,(3a)vec(𝚽𝚽𝑡𝑡 ) = vec(𝚽𝚽𝑡𝑡−1 ) + 𝜼𝜼𝑡𝑡 , 𝜼𝜼𝑡𝑡 |𝛀𝛀𝑡𝑡−1 ~𝑵𝑵(𝟎𝟎, 𝚵𝚵𝑡𝑡 ),(3b)where 𝛀𝛀𝑡𝑡−1 represents all available information up to 𝑡𝑡 − 1 , the endogenous

variables 𝒚𝒚𝑡𝑡 is an 𝑁𝑁 × 1 dimensional vector. 𝚽𝚽𝑡𝑡 is an 𝑁𝑁 × 𝑁𝑁 matrix and its

vectorization vec(𝚽𝚽𝑡𝑡 ) is an 𝑁𝑁 2 × 1 vector. The shocks 𝜺𝜺𝑡𝑡 and𝜼𝜼𝑡𝑡 are 𝑁𝑁 × 1 and𝑁𝑁 2 × 1 dimensional vectors, respectively. Moreover, variance-covariance matrices 𝚺𝚺𝑡𝑡
and 𝚵𝚵𝑡𝑡 are 𝑁𝑁 × 𝑁𝑁 and 𝑁𝑁 2 × 𝑁𝑁 2 dimensional matrices, respectively.

8

According to the Wold representation theorem, we can transform the TVP-VAR
into a TVP-VMA as follows:∞𝒚𝒚𝒕𝒕 = � 𝚲𝚲𝑗𝑗𝑗𝑗 𝜺𝜺𝑡𝑡−𝑗𝑗 + 𝜺𝜺𝑡𝑡 .

(4)

𝑗𝑗=1

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: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

,

(5)

where 𝐻𝐻 is the forecast horizon that is set to 10 in this paper. 𝑒𝑒𝑖𝑖 is a selection vector

with one on the 𝑖𝑖 −th position and zeros elsewhere. 𝚲𝚲ℎ,𝑡𝑡 represents the coefficientmatrix multiplying the ℎ-lagged shock vector in the TVP-VMA at time 𝑡𝑡, and Σ𝑘𝑘𝑘𝑘,𝑡𝑡
is the 𝑘𝑘-th diagonal element of the covariance matrix 𝚺𝚺𝑡𝑡 .

After the normalization, the pairwise connectedness index from the 𝑘𝑘 −th variable

to the 𝑗𝑗 −th variable at horizon 𝐻𝐻 at time 𝑡𝑡 can be calculated by𝐻𝐻𝜃𝜃�𝑗𝑗𝑗𝑗,𝑡𝑡=𝐻𝐻𝜃𝜃𝑗𝑗𝑗𝑗,𝑡𝑡

𝐻𝐻∑𝑁𝑁
𝑘𝑘=1 𝜃𝜃𝑗𝑗𝑗𝑗,𝑡𝑡,

Meanwhile, the total connectedness index can be represented as
9(6)

𝑆𝑆𝑡𝑡𝐻𝐻 =

1
𝑁𝑁

𝑁𝑁

�

𝑗𝑗,𝑘𝑘=1,𝑗𝑗≠𝑘𝑘𝐻𝐻𝜃𝜃�𝑗𝑗𝑗𝑗,𝑡𝑡.

(7)

Moreover, the directional connectedness (From), which measures the averaged
spillover to the 𝑘𝑘 − th variable from all remaining variables in the system, can becalculated as

𝐻𝐻
𝑆𝑆𝑘𝑘←⋅,𝑡𝑡
=

𝑁𝑁

1
𝐻𝐻
� 𝜃𝜃�𝑘𝑘𝑘𝑘,𝑡𝑡
.
𝑁𝑁

(8)

𝑗𝑗=1,𝑗𝑗≠𝑘𝑘

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

𝐻𝐻𝑆𝑆⋅←𝑘𝑘,𝑡𝑡
=

1.

𝑁𝑁

1
𝐻𝐻
� 𝜃𝜃�𝑗𝑗𝑗𝑗,𝑡𝑡
.
𝑁𝑁

(9)

𝑗𝑗=1,𝑗𝑗≠𝑘𝑘

The above-defined measures of connectedness at time 𝑡𝑡 are summarized in Table
Table 1: Averaged Diebold–Yilmaz connectedness index table

𝑦𝑦1

𝑦𝑦1

𝐻𝐻
𝜃𝜃�11

𝑦𝑦2

…

𝐻𝐻
𝑆𝑆2←⋅

⋯

𝐻𝐻
𝜃𝜃�𝑁𝑁𝑁𝑁

𝐻𝐻
𝑆𝑆𝑁𝑁←⋅⋱𝑦𝑦N

𝐻𝐻
𝜃𝜃�𝑁𝑁1

𝐻𝐻
𝜃𝜃�𝑁𝑁2

𝐻𝐻
𝑆𝑆⋅←1

𝐻𝐻
𝜃𝜃�2𝑁𝑁

⋮

𝐻𝐻
𝜃𝜃�22

To

⋯

⋯

𝐻𝐻
𝜃𝜃�21

⋮

From

𝐻𝐻
𝜃𝜃�12

𝑦𝑦2
⋮

𝑦𝑦N

𝐻𝐻
𝑆𝑆⋅←2

⋯

Note: Adapted from (Diebold & Yilmaz, 2015).
10

𝐻𝐻𝜃𝜃�1𝑁𝑁⋮

𝐻𝐻
𝑆𝑆⋅←𝑁𝑁

𝐻𝐻
𝑆𝑆1←⋅

⋮

𝑆𝑆 𝐻𝐻

2.3.

Portfolio back-testing models

2.3.1

Minimum Connectedness Portfolio

In the spirit of the minimum variance portfolio and minimum correlation portfolio,(Broadstock et al., 2020) proposed the MCoP by using all Diebold-Yilmaz pairwise
spillover indices instead of the variance or correlation matrix in the minimum variance
portfolio or minimum correlation portfolio. By minimizing the interconnectedness andspillover effects among variables, a more resilient investment portfolio can be achieved,
which is less susceptible to the adverse impacts of network shocks. Consequently,
variables (investment instruments) that neither affect nor are influenced by others will
receive higher weights within the portfolio. This can be expressed as follows:𝝎𝝎𝑅𝑅𝑅𝑅 =𝑷𝑷𝑷𝑷𝑷𝑷−1
𝑡𝑡 𝑰𝑰.
𝑰𝑰𝑷𝑷𝑷𝑷𝑷𝑷−1
𝑡𝑡 𝑰𝑰

(10)

Where 𝑷𝑷𝑷𝑷𝑰𝑰𝑡𝑡 is the pairwise connectedness index matrix, and 𝑰𝑰 is the identity matrix.
2.3.2

Portfolio evaluation

To evaluate the effectiveness of the hedging and portfolio strategy, on the one hand,
we calculate the hedge effectiveness as proposed by (EDERINGTON, 1979) which canbe calculated as:

𝐻𝐻𝐻𝐻 = 1 −𝑉𝑉𝑉𝑉𝑉𝑉(𝑦𝑦𝑝𝑝 ).
𝑉𝑉𝑉𝑉𝑉𝑉(𝑦𝑦𝑢𝑢𝑢𝑢ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 )(11)

𝑉𝑉𝑉𝑉𝑉𝑉(𝑦𝑦𝑢𝑢𝑢𝑢ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 ) is the variance of the portfolio returns, and 𝑉𝑉𝑉𝑉𝑉𝑉(𝑦𝑦𝑝𝑝 ) represents thevariance of the un-hedged asset.

11

The hedge effectiveness reflects the percent reduction in the variance of the unhedged position. The higher the hedge effectiveness the larger is the volatility risk
reduction and vice versa. Following this line of thought, to measure the ability of thehedging portfolio to reduce extreme risks, we adapted Ederington's hedge efficiency forvolatility risk, and calculated the hedge efficiency for VaR and for ES accordingly. The
calculations are conducted as follows:

𝐻𝐻𝐻𝐻𝐸𝐸𝐸𝐸 = 1 −𝑉𝑉𝑉𝑉𝑉𝑉�𝑦𝑦𝑝𝑝 �,(12𝑎𝑎)

𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉(𝑦𝑦𝑝𝑝 ).
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶(𝑦𝑦𝑢𝑢𝑢𝑢ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 )(12b)

𝐻𝐻𝐻𝐻𝑉𝑉𝑉𝑉𝑉𝑉 = 1 −𝑉𝑉𝑉𝑉𝑉𝑉�𝑦𝑦𝑢𝑢𝑢𝑢ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 �

Where 𝐻𝐻𝐻𝐻𝑉𝑉𝑉𝑉𝑉𝑉 and 𝐻𝐻𝐻𝐻𝐸𝐸𝐸𝐸 are hedge efficiency for VaR and for ES, respectively.

On the other hand, we calculate the Sharpe ratio of return over volatility (SR),which proposed by Sharpe (1994), is calculated as follows.
𝑆𝑆𝑆𝑆 =

𝑟𝑟̅𝑝𝑝

�𝑣𝑣𝑣𝑣𝑣𝑣(𝑟𝑟𝑝𝑝 )

(13)

.

Where 𝑟𝑟𝑝𝑝 is the portfolio returns assuming that the risk-free rate is equal to zero. In
addition, similar to the hedge effectiveness, we also calculate the Sharpe ratios of return
over VaR (𝑆𝑆𝑆𝑆𝑉𝑉𝑉𝑉𝑉𝑉 ) and ES (𝑆𝑆𝑆𝑆𝐸𝐸𝐸𝐸 ) 2 as follows.
𝑆𝑆𝑆𝑆𝑉𝑉𝑉𝑉𝑉𝑉 =𝑟𝑟̅𝑝𝑝

𝑉𝑉𝑉𝑉𝑉𝑉�𝑟𝑟𝑝𝑝 �,(13𝑎𝑎)

The confidence levels for both VaR and ES are 95%, the same as that in hedge
effectiveness.

2

12

𝑆𝑆𝑆𝑆𝐸𝐸𝐸𝐸 =𝑟𝑟̅𝑝𝑝

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶�𝑟𝑟𝑝𝑝 �

.

(13b)

The 𝑆𝑆𝑆𝑆 , 𝑆𝑆𝑆𝑆𝑉𝑉𝑉𝑉𝑉𝑉 , and 𝑆𝑆𝑆𝑆𝐸𝐸𝐸𝐸 indicate which portfolio has the highest return given thesame volatility, VaR, and ES, respectively.
3. Data and Descriptive Statistics
At Binance, more than 350 cryptocurrencies are being traded. For this study, we
have selected the top 9 cryptocurrencies with the highest market capitalization as ofJanuary 2023, excluding stablecoins such as Tether (USDT), USD Coin (USDC), andBinance USD (BUSD), which are highly pegged to the US dollar. The selected
cryptocurrencies are Bitcoin (BTC), Binance Coin (BNB), Ethereum (ETH), XRP,
Cardano (ADA), Dogecoin (DOGE), Polygon (MATIC), Polkadot (DOT), and Solana(SOL). As of January 2023, these 9 cryptocurrencies collectively account for over 65%
of the total market. Our data covers the period from August 18, 2020, to January 1,
2023. We selected this time period for two reasons: firstly, the data for DOT and SOL
became available only from August 2020 onwards, and secondly, prior to 2020, mostcryptocurrencies experienced only minor fluctuations within a narrow price range. All
the cryptocurrencies analyzed in this paper are spot trading pairs, and the data is sourced
from Binance, with units denominated in USDT.
After obtaining the raw data for the cryptocurrencies, we calculate the returns foreach trading pair using a logarithmic difference transformation. Then, we utilize the
ACD-NIG model to estimate the conditional volatility, conditional skewness, and13

conditional kurtosis series. Table 2 presents a range of summary statistics for all series.
Regarding the return series, except for BTC, ETH, and SOL, the returns of all othercryptocurrencies exhibit a right-skewed distribution, indicating the potential for
exceptionally high returns, albeit with a low probability. Additionally, all return series
exhibit leptokurtosis, except for BTC and ADA, which display platykurtic andmesokurtic distributions, respectively. A leptokurtic distribution suggests that returns
are prone to extreme values, both negative and positive, indicating a higher tail risk.
The p-values of the Jarque and Bera (Jarque & Bera, 1980) normality test confirm thatnone of the return series follow a normal distribution. The unit root test conducted by
Elliott et al. (1996) shows that all return series exhibit no unit root. The results of theFisher & Gallagher (2012) weighted portmanteau test reveal the presence of
ARCH/GARCH type effects in all return series. In terms of conditional volatility,
conditional skewness, and conditional kurtosis, the results of the Jarque and Bera
(Jarque & Bera, 1980) normality test indicate that they are also non-normally
distributed. Furthermore, the results of the unit root test developed by Elliott et al. (1996)
indicate the absence of unit roots in the data.

14

Table 2: Summary statistics
Returns
BTC

BNB

ETH

XRP

ADA

DOGE

MATIC

DOT

SOL

Mean

0.000

0.003

0.001

0.000

0.001

0.003

0.004

0.000

0.001

Variance

0.001

0.003

0.003

0.004

0.003

0.009

0.006

0.004

0.006

Skewness−0.2360.622−0.413

0.15

0.255

5.977

0.969

0.233

−0.368

Ex.Kurtosis

2.713

14.491

3.791

12.5383.000

92.500

6.057

7.532

6.019

JB

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

ERS

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

𝑸𝑸𝟐𝟐 (𝟓𝟓)

0.02

0.00

0.00

0.00

0.00

0.03

0.00

0.00

0.00

Mean

0.036

0.05

0.049

0.058

0.055

0.068

0.074

0.063

0.073

Variance

0.000

0.001

0.000

0.001

0.000

0.005

0.001

0.001

0.001

Skewness

0.754

3.494

2.217

2.467

1.576

7.603

2.226

2.023

3.008

Ex.Kurtosis

0.439

16.956

7.434

7.385

3.113

86.492

6.664

4.750

12.869

JB

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

ERS

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Conditional Volatilities

Conditional Skewness
Mean−0.054−0.227−0.219−0.042

0.063

0.541

0.44

0.115

0.132

Variance

0.285

0.37

0.196

0.659

0.149

1.498

1.031

0.475

0.378

Skewness−2.9660.414−1.272−0.745−2.684

3.008

2.019

0.104

−2.524

Ex.Kurtosis

16.473

1.862

8.708

8.15

10.61114.729

8.531

1.003

10.256

JB

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

ERS

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Conditional Kurtosis
Mean

4.646

4.379

2.492

6.278

3.059

11.756

5.733

3.825

2.944

Variance

8.249

0.902

2.426

24.1170.432

161.686

72.043

1.572

3.518

Skewness

7.692

4.346

15.78911.018

8.186

6.437

5.806

4.548

14.539

Ex.Kurtosis

85.11127.302355.963

195.264

75.61949.15237.38534.845286.902

JB

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

ERS

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Note: The table presents the descriptive statistics includes the mean, variance, skewness, excess kurtosis,
and the p-value of the test of Jarque and Bera (JB; 1987), the Elliott et al., (1996) unit root test. and theFisher & Gallagher (2012) weighted portmanteau test with 5 lags.

15

4. Empirical Results and Discussion
4.1.

Averaged dynamic spillovers
Let's begin by focusing on the averaged spillover measures. Tables 3, 4, and 5

present the averaged volatility spillovers, averaged skewness spillovers, and averaged
kurtosis spillovers among the cryptocurrency markets, respectively. The values on themain diagonal of each table are not our main concern as they correspond to shocks
within the same variable. Our interest lies in the off-diagonal values, which represent
the interactions and spillovers between different markets. The last row and the lastcolumn in each table represent directional spillover (to) and directional spillover (from),
respectively. They indicate the average spillover level from a specific market to all othermarkets and the average spillover level from all other markets to a specific market.
Lastly, the value at the bottom right corner of each table represents the total spillover,indicating the overall spillover level of all markets. By comparing and analyzing theresults of Tables 3, 4, and 5, we can draw the following key findings.
First, we observe that in the cryptocurrency markets, as the order of the moment
increases, the total spillover decreases. The total volatility spillover among markets is
the highest (64.11%), followed by the skewness spillover (59.27%), and the kurtosis
spillover is the smallest (29.82%). This finding is consistent with the results of He &Hamori (2021).
Secondly, the spillovers from and to other cryptocurrencies vary across different
moments for each cryptocurrency. For instance, in terms of volatility, BNB exhibits the16highest volatility spillover to other currencies, while ETH receives the highest volatility
spillover. However, when it comes to skewness, ADA shows the highest skewness
spillover to other currencies while also receiving the highest skewness spillover. In thecase of kurtosis, BTC transmits the highest kurtosis spillover to other currencies,
whereas ETH receives the highest kurtosis spillover. These findings imply that BNB,
ADA, and BTC are likely to transfer the most volatility risk, downside (upside) risk,
and tail risk to other markets, respectively. At the same time, ETH is likely to receive
the most volatility risk and tail risk, while ADA is likely to receive the most downside(upside) risk. The transmission of volatility risk, downside (upside) risk, and tail risk
among different cryptocurrency markets varies in magnitude and direction. Thissuggests that we can obtain unique information regarding the transmission of various
types of risk from volatility spillover, skewness spillover, and kurtosis spillover. This
information can enable more tailored risk management approaches, potentiallyenhancing the efficiency and effectiveness of investment strategies.

17

Table 3: Averaged dynamic volatility spillover index table
BTC

BNB

ETH

XRP

ADA

DOGE

MATIC

DOT

SOL

From

BTC

33.46

10.87

12.52

5.97

6.75

9.10

7.53

7.31

6.49

7.39

BNB

10.15

33.13

8.94

8.32

6.46

9.23

8.13

7.98

7.66

7.43

ETH

11.06

11.41

27.00

6.11

7.43

11.84

6.79

8.86

9.51

8.11

XRP

7.05

8.56

7.42

40.80

6.16

10.33

6.52

6.85

6.30

6.58

ADA

6.41

8.96

12.81

8.58

28.39

11.82

7.07

8.01

7.96

7.96

DOGE

6.54

6.21

5.87

5.98

4.37

58.29

3.69

4.96

4.10

4.64

MATIC

9.37

12.20

11.43

6.72

6.88

9.27

29.64

6.74

7.73

7.82

DOT

6.97

9.33

8.13

6.60

7.29

6.02

5.89

41.82

7.95

6.46

SOL

5.35

12.12

10.61

8.99

8.04

8.53

7.30

8.60

30.47

7.73

To

6.99

8.85

8.64

6.36

5.93

8.46

5.88

6.59

6.41

64.11

Table 4: Averaged dynamic skewness spillover index table
BTC

BNB

ETH

XRP

ADA

DOGE

MATIC

DOT

SOL

From

BTC

49.65

6.50

10.08

4.64

11.17

1.79

2.39

6.33

7.44

5.59

BNB

4.39

34.29

9.08

8.87

12.23

4.62

8.53

13.31

4.69

7.30

ETH

6.80

9.31

33.63

8.35

13.29

3.81

5.45

12.14

7.23

7.38

XRP

3.53

9.71

9.03

39.69

11.49

4.41

6.63

10.94

4.57

6.70

ADA

6.84

11.09

11.41

9.66

30.17

4.01

6.26

11.24

9.31

7.76

DOGE

2.03

7.24

7.60

6.76

6.20

54.90

5.19

7.56

2.52

5.01

MATIC

2.33

11.18

7.63

7.84

9.36

5.33

40.79

11.07

4.47

6.58

DOT

3.51

12.47

10.77

9.60

10.86

3.60

7.07

36.59

5.53

7.05

SOL

7.74

6.46

8.01

5.31

13.07

1.87

3.09

7.60

46.86

5.91

To

4.13

8.22

8.18

6.78

9.74

3.27

4.96

8.91

5.08

59.27

Table 5: Averaged dynamic kurtosis spillover index table
BTC

BTC

BNB

ETH

XRP

ADA

DOGE

MATIC

DOT

SOL

From

72.53

0.54

9.45

5.68

0.49

1.69

4.64

2.92

2.06

3.05

BNB

1.65

66.81

0.60

0.51

13.81

2.94

3.75

6.04

3.90

3.69

ETH

10.65

0.61

62.00

4.32

0.12

9.44

4.54

5.64

2.69

4.22

XRP

6.08

0.72

5.38

73.95

0.14

3.13

6.49

2.57

1.54

2.89

ADA

0.37

13.72

0.11

0.10

70.21

3.23

0.38

6.29

5.59

3.31

DOGE

1.22

2.46

2.47

2.33

2.07

84.71

1.32

2.42

1.01

1.70

MATIC

7.80

3.34

10.26

5.68

0.34

3.34

64.09

3.15

2.00

3.99

DOT

3.29

5.25

4.87

2.38

5.46

1.48

2.91

68.84

5.53

3.46

SOL

8.08

4.14

2.69

1.38

6.15

0.88

1.87

6.32

68.51

3.50

To

4.35

3.42

3.98

2.49

3.18

2.90

2.88

3.93

2.70

29.82

18

4.2.

Dynamic total spillovers
To investigate how the spillover effects evolve over time and how extreme eventsaffect them, we will focus on the results of dynamic total spillovers. In addition, tobetter illustrate the results, we present in the topmost panel of Figure 1 a price chartover time for the S&P cryptocurrency top 10 equal weight index, which reflects theoverall price movements of the top 10 ranked cryptocurrencies. The second to fourth
panels from the top downward show the dynamic changes in total volatility spillover,total skewness spillover, and total kurtosis spillover, respectively.
To investigate the evolution of spillover effects over time and their response to
extreme events, we focus on the dynamic total spillovers. To enhance the understandingof the results, Figure 1 presents a price chart for the S&P cryptocurrency top 10 equal
weight index in the topmost panel. This index reflects the overall price movements ofthe top 10 ranked cryptocurrencies. The second to fourth panels, from top to bottom,
display the dynamic changes in total volatility spillover, total skewness spillover, andtotal kurtosis spillover, respectively.
Analyzing Figure 1, let's first examine the overall trend of the cryptocurrency
market from August 2020 to January 2023. As depicted in the figure, the cryptocurrency
market has undergone an extended period of bullish behavior until May 2021, withprices steadily and significantly rising. However, from May to July 2021, the market
experienced a sharp decline, with prices plummeting by over 50%. Subsequently, prices
gradually recovered until approximately November 2021. However, starting from
November 2021, the cryptocurrency market gradually entered another phase of decline,
19

characterized as a bear market. Overall, during this period, the cryptocurrency market
has exhibited highly volatile and unpredictable behavior.
More specifically, prior to May 2021, the cryptocurrency market is characterized
by a steady upward trend, during which the volatility spillover, skewness spillover, andkurtosis spillover exhibit a decreasing trend or remain at relatively low levels. On May
19th, 2021, the cryptocurrency market experiences a significant downturn, with major
cryptocurrencies like Bitcoin and Ethereum plunging by over 30% within hours. Thissudden crash is triggered by a combination of factors, including regulatory crackdowns
on cryptocurrency exchanges and Tesla's announcement that it no longer accepts
Bitcoin as payment. Subsequently, the volatility spillover experiences a sharp increase,
while skewness spillover and kurtosis spillover steadily rise. From July to November
2021, the cryptocurrency market witnesses a price rebound. During this period,
volatility spillover remains consistently high with minimal variation. In contrast,
skewness spillover and kurtosis spillover exhibit a continuous and gradual increase. In
October, this upward trend briefly pauses. However, following the resumption of thedecline in cryptocurrency market prices after November, the skewness spillover andkurtosis spillover resume their steady rise. This rise persists until March 2023, spanningthe entirety of the bear market.

20

Fig.1: Cryptocurrency index and dynamic total spillovers

4.3.

Portfolio and hedging strategies analysis
In this section, we present investment portfolios constructed using the MCoP

(Minimum Connectedness Portfolio) based on the Diebold-Yilmaz connectedness
index at different moments.
To provide a more concrete understanding of the composition of the individual
portfolios, we illustrate the dynamic portfolio weights of the MCoP calculated based on
the connectedness measures of different moments in Figures 2, 3, and 4, respectively.
By definition, the weights of the MCoP reflect the level of volatility connectedness(spillover) and aim to minimize the transmission of volatility risk across markets.
Similarly, the weights of the MCoP for minimum kurtosis connectedness portfolios are
determined by the level of kurtosis connectedness (spillover), with the objective ofminimizing the transmission of tail risk across markets. Lastly, the weights of the MCoP
for minimum skewness connectedness portfolios are determined by the size of21

skewness connectedness (spillover) and serve the purpose of minimizing thetransmission of downside (upside) risk across markets.
Based on Figures 2, 3, and 4, it is evident that the weight changes of portfolios
based on skewness connectedness and those based on kurtosis connectedness exhibit
similarities for certain cryptocurrencies. Specifically, prior to 2021, the portfolios'
weights based on volatility connectedness undergo significant fluctuations. In contrast,
the weight changes in portfolios based on skewness connectedness and kurtosis
connectedness are relatively stable. Nevertheless, there are still notable differences in
the weight changes across the three moments. These disparities arise due to variationsin the dynamic spillovers of cryptocurrencies under different moments, despite somesimilarities in the dynamic changes of skewness spillover and kurtosis spillover. As theportfolio weights are determined by minimizing interconnectedness and spillover
effects among the variables, assets that neither impact nor are influenced by others
receive higher weights within the portfolio. Consequently, the weights assigned to each
cryptocurrency adjust according to its dynamic spillover patterns.

22Fig.2: Dynamic multivariate portfolio weights: minimum volatility connectedness portfolio

Fig.3: Dynamic multivariate portfolio weights: minimum skewness connectedness portfolio

23

Fig.4: Dynamic multivariate portfolio weights: minimum kurtosis connectedness portfolio

In relation to the hedge effectiveness ratios presented in Table 6, the findings forthe minimum volatility connectedness portfolio indicate that allocating an average of
12% to BTC, 6% to BNB, 3% to ETH, 13% to XRP, 12% to ADA, 22% to DOGE, 13%
to MATIC, 10% to DOT, and 10% to SOL would lead to reductions in asset volatilityof −102%, 15%, −9%, 37%, 19%, 70%, 56%, 37%, and 54%, respectively. Additionally,
the Value at Risk (VaR) for each asset in this portfolio would decrease by −34%, −12%,−3%, 8%, 7%, 14%, 19%, 16%, and 23%, while the Expected Shortfall (ES) would

decrease by −40%, 1%, −6%, 14%, 0%, 22%, 18%, 11%, and 28%. Comparing the threeportfolios, it is evident that the MCoP based on skewness connectedness or kurtosis
connectedness demonstrates enhanced hedge effectiveness in terms of volatility, VaR,
and ES, compared to the MCoP based on volatility connectedness. Furthermore, the24minimum kurtosis connectedness portfolio exhibits superior performance, showcasing
the highest hedge effectiveness in reducing volatility, VaR, and ES.
The findings for the minimum kurtosis connectedness portfolio suggest that byallocating an average of 11% to BTC, 11% to BNB, 8% to ETH, 13% to XRP, 12% toADA, 14% to DOGE, 11% to MATIC, 9% to DOT, and 12% to SOL, the volatility ofeach asset in this portfolio would decrease by −83%, 23%, 1%, 43%, 27%, 73%, 60%,
43%, and 58% respectively. Similarly, the Value at Risk (VaR) of each asset in thisportfolio would decrease by −28%, −7%, 2%, 13%, 11%, 18%, 23%, 20%, and 27%,
while the Expected Shortfall (ES) would decrease by −36%, 2%, −3%, 17%, 3%, 24%,
21%, 14%, and 30%.
Our findings regarding the enhanced hedge effectiveness of the MCoP based on
skewness connectedness or kurtosis connectedness are consistent with the research
conducted by Cui and Maghyereh (2023) on realized skewness and realized kurtosis.
In their study, the MCoP based on realized skewness or realized kurtosis also improved
the hedge effectiveness of volatility. Furthermore, our study extends these findings byconfirming that the hedge effectiveness of VaR and ES is also improved.
Additionally, it is worth noting that the volatility of dynamic portfolio weights in
the MCoP based on skewness connectedness or kurtosis connectedness is lower
compared to that in the MCoP based on volatility.
Finally, the Sharpe ratios for the three portfolios are presented in Table 7. Similar
to hedge effectiveness, we found that compared to the MCoP based on volatility

25connectedness, the MCoP based on skewness connectedness or kurtosis connectedness
also exhibits enhanced Sharpe ratios for return over standard deviation, VaR, and ES.
However, this time, it is the minimum skewness portfolio that demonstrates the best
performance, rather than the minimum kurtosis portfolio.

26

Table 6: Averaged portfolio weights and hedge effectiveness
Minimum volatility connectedness portfolio
Mean

Std.Dev.

5%

95%

HE

BTC

0.12

0.08

0.00

0.28

−1.02

BNB

0.06

0.08

0.00

0.19

0.15

ETH

0.03

0.06

0.00

0.13

𝐇𝐇𝐇𝐇𝐕𝐕𝐕𝐕𝐕𝐕

𝐇𝐇𝐇𝐇𝐄𝐄𝐄𝐄

−0.34

−0.40

−0.12

−0.01

−0.09

−0.03

−0.06

XRP

0.13

0.06

0.02

0.24

0.37

0.08

0.14

ADA

0.12

0.05

0.00

0.18

0.19

0.07

0.00

DOGE

0.22

0.08

0.12

0.36

0.70

0.14

0.22

MATIC

0.13

0.07

0.00

0.20

0.56

0.19

0.18

DOT

0.10

0.06

0.00

0.20

0.37

0.16

0.11

SOL

0.10

0.06

0.00

0.18

0.54

0.23

0.28

Minimum skewness connectedness portfolio
BTC

0.21

0.05

0.15

0.30

−0.89

−0.32

−0.38

BNB

0.05

0.04

0.00

0.11

0.20

−0.10

0.00

ETH

0.04

0.04

0.00

0.12

−0.02

−0.01

−0.04

XRP

0.11

0.03

0.05

0.16

0.41

0.10

0.15

ADA

0.00

0.01

0.00

0.03

0.24

0.09

0.01

DOGE

0.20

0.04

0.15

0.26

0.72

0.15

0.23

MATIC

0.17

0.05

0.09

0.24

0.59

0.21

0.20

DOT

0.04

0.03

0.00

0.09

0.41

0.17

0.13

SOL

0.17

0.04

0.11

0.24

0.57

0.25

0.29

Minimum kurtosis connectedness portfolio
BTC

0.11

0.02

0.08

0.15

−0.83

−0.28

−0.36

BNB

0.11

0.01

0.09

0.13

0.23

−0.07

0.02

ETH

0.08

0.04

0.01

0.12

0.01

0.02

−0.03

XRP

0.13

0.01

0.11

0.15

0.43

0.13

0.17

ADA

0.12

0.03

0.06

0.16

0.27

0.11

0.03

DOGE

0.14

0.04

0.10

0.22

0.73

0.18

0.24

MATIC

0.11

0.02

0.08

0.15

0.60

0.23

0.21

DOT

0.09

0.05

0.00

0.14

0.43

0.20

0.14

SOL

0.12

0.02

0.08

0.15

0.58

0.27

0.30

Note: The table presents the means (Mean), standard deviations (Std.Dev.), 5 percentiles (5%), 95thth

percentiles (95%) of dynamic portfolio weights, and hedge effectiveness in terms of volatility (HE),Value at Risk (HEVaR ), and expected shortfall (HEES ).

27

Table 7: Sharpe Ratio
𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝒗𝒗𝒗𝒗𝒗𝒗

𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔

𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝒌𝒌𝒌𝒌𝒌𝒌𝒌𝒌𝒌𝒌

𝑺𝑺𝑺𝑺

𝑺𝑺𝑺𝑺𝑽𝑽𝑽𝑽𝑽𝑽
0.017

0.008

0.019

0.009

0.031

0.018

0.009

0.028
0.032

𝑺𝑺𝑺𝑺𝑬𝑬𝑬𝑬

Note: The table presents the Sharpe ratios of return over standard deviation (SR), Value at Risk (SR VaR ),and expected shortfall (SR ES ). 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣 , 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 , and 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘 refer to the MCoP based onvolatility, skewness, and kurtosis, respectively.

5. Conclusions and Discussions
In this study, we conduct a comprehensive analysis of nine major cryptocurrencies
traded on Binance, focusing on the spillover effects of conditional volatility andconditional higher moments, including skewness and kurtosis. Our data span the period
from August 18, 2020, to January 1, 2023. Here are some key findings and conclusions.
First, we find that volatility, skewness, and kurtosis spillovers exhibit distinct
patterns across different moments, with the total spillover decreasing as the order of the
moment increases. Each cryptocurrency manifests a unique pattern of risk transmission
across these moments. For instance, BNB and BTC dominate in transmitting volatility
and kurtosis, respectively, while ADA shows the highest skewness spillover transmitted
to others. These findings imply that BNB, ADA, and BTC are likely to transfer the mostvolatility risk, downside (upside) risk, and tail risk to other markets, respectively. Thesefindings may be particularly useful for investors in formulating accurate strategies toguard against specific types of risks. The differential risk transference characteristics ofthese cryptocurrencies can enable more tailored risk management approaches,
potentially improving the efficiency and effectiveness of investment strategies.
28

Second, we also observe dynamic changes in spillover effects, which are
influenced by the overall market conditions and extreme events. The changes inskewness and kurtosis spillovers display high similarity, implying a consistent patternin the transmission of downside (upside) risk and tail risk across markets over time. Thechanges and fluctuations in downside (upside) risk and tail risk are notably different
from the transmission patterns of volatility risk. These findings carry significant
implications for investors and risk managers. By understanding the unique transmission
patterns of different types of risks across the cryptocurrency markets, they can better
design their investment strategies and risk management practices. For instance, if aninvestor is more concerned about tail risk (which involves the risk of extreme market
movements), they might pay more attention to the changes in kurtosis spillover overtime, given that it behaves differently from volatility spillover. This would enable them
to better anticipate and hedge against tail risk. Moreover, the high degree of similarity
in the changes of skewness and kurtosis spillovers indicates that downside (upside) risk
and tail risk often change hand-in-hand. This can help investors improve their risk
diversification strategies by simultaneously considering these two types of risks.
The study further examines and compares the performances of the MCoP based onvolatility, skewness, and kurtosis spillovers. We find that compared to the MCoP basedon volatility, the MCoP based on higher moments shows enhanced hedge effectivenessand higher Sharpe ratios for volatility, VaR, and ES. Specifically, our results reveal that
the MCoP based on kurtosis connectedness offers the highest hedge effectiveness, while29the MCoP based on skewness connectedness offers the highest Sharpe ratios.
In conclusion, this study provides valuable insights into the dynamic spillover
effects among cryptocurrencies and their implications for risk management andportfolio construction. The findings highlight the importance of considering higher
moments like skewness and kurtosis, in addition to volatility, for effective risk
management in the cryptocurrency market. Understanding the higher moment spillover
effects across cryptocurrency markets can help investors determine the transmission
mechanism of risk more comprehensively and understand how markets are linked by
the level of asymmetry and tailedness of their returns, which relates to upside (downside)risks and tail risks. These insights not only offer fresh and helpful perspectives on
hedging strategies but also enrich the knowledge required for effective portfolio
diversification and the management of extreme risks. Future research could expand onthese findings by exploring other portfolio techniques or hedging strategies based onhigher moment connectedness or by incorporating data from other markets.

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