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Dependence structure between NFT, DeFi and cryptocurrencies in turbulent times: An Archimax copula approach

January 2024
The North American Journal of Economics and Finance 70(8):102079

DOI:10.1016/j.najef.2024.102079

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Authors:

Mohamed Fakhfekh

Faculté des Sciences Économiques et de Gestion de Sfax

Azza Béjaoui

Institut Supérieur de Gestion de Tunis

Aurelio F. Bariviera

Universidad Rovira i Virgili

Ahmed Jeribi

Faculty of Economics and Management of Mahdia, Tunisia

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North American Journal of Economics and Finance 70 (2024) 102079

Available online 23 January 2024

(http://creativecommons.org/licenses/by/4.0/).

Contents lists available at ScienceDirect

North American Journal of Economics and Finance

journal homepage: www.elsevier.com/locate/najef

Dependence structure between NFT, DeFi and cryptocurrencies in

turbulent times: An Archimax copula approach

Mohamed Fakhfekh a, Azza Bejaoui b, Aurelio F. Bariviera c,∗, Ahmed Jeribi d

aHigher Institute of Business Administration of Sfax-Tunisia, Tunis, Tunisia

bHigher School of Commerce, Tunis, Tunisia

cUniversitat Rovira i Virgili, Department of Business & ECO-SOS, Av. Universitat 1, Reus, 43204, Spain

dFaculty of Economics and Management of Mahdia, Mahdia, Tunisia

ARTICLE INFO

JEL classification:

G10

G11

C58

Keywords:

Non fungible token

DeFi

Hedge ratio

Archimax copula

ABSTRACT

This paper investigates the connectedness among eighteen cryptocurrency assets including

NFT, DeFi, gold-backed cryptocurrencies, and traditional cryptocurrencies. We also compute

the Optimal hedge ratio for each pair of (gold-backed) cryptocurrency-NFT/DeFi and assess

their hedge effectiveness. To this end, we use a combination of econometric methods. Our

sample period goes from 01/11/2021 to 21/02/2023, making the empirical analysis insightful

and interesting as it includes the Covid-19 health crisis and the Russia–Ukraine war. Our

empirical findings highlight the dissimilarities between different cryptocurrencies in terms of

connectedness with NFT/DeFi assets. They also reflect the diversification benefits generated by

the inclusion of gold-backed cryptocurrencies into NFT/DeFi portfolios, in particular in times

of unprecedented events. These findings could be useful for crypto-investors who search to

diversify their portfolios.

1. Introduction

Cryptocurrencies have been subject to increasing scrutiny in the financial economics realm. This market experienced an explosive

evolution, that departed from the original idea of Nakamoto (2009) of establishing a peer-to-peer payment system that could bypass

the traditional banking system. In fact, this market has evolved into a complex cobweb of different but interrelated instruments such

as plain cryptocurrencies, fungible tokens, non-fungible tokens (NFT), and Decentralized Finance projects (DeFi). Daily volume

exceeds 60 USD billion, thus their importance in the investment strategy of many people cannot be ignored.

Bariviera and Merediz-Solà (2021) provide a comprehensive landscape of the scientific production around cryptocurrencies

in the financial economics realm. Three closely related research lines emerge in the literature: assets’ correlations, safe haven

characteristics, and portfolio formation.

Regarding the first topic, Corbet et al. (2018) and Aslanidis et al. (2019) find that cryptocurrencies are relatively isolated from

traditional assets (stocks, bonds, or gold), but they exhibit similar mean correlations among them. Additionally, Koutmos (2018)

find that there is a bidirectional linkage between Bitcoin returns and transaction activity, whereas Giudici and Abu-Hashish (2019)

report a strong price correlation of Bitcoin across different exchange markets. More recently, Aslanidis et al. (2022) uncover that

cryptocurrency returns and volatilities are not linked to broad uncertainty indices (e.g. measured by Google Trends), but to market-

specific uncertainty proxies. Consequently, the literature agrees that the different assets in the cryptocurrency market are correlated

and that they do not comove with other financial assets.

∗Correspondence to: Av. Universitat 1, 4320 Reus, Spain.

E-mail addresses: fakhfekh_moh@yahoo.fr (M. Fakhfekh), bjaouiazza2@yahoo.fr (A. Bejaoui), aurelio.fernandez@urv.cat (A.F. Bariviera),

ahmedjeribi07@yahoo.fr (A. Jeribi).

https://doi.org/10.1016/j.najef.2024.102079

Received 15 June 2023; Received in revised form 6 December 2023; Accepted 2 January 2024

North American Journal of Economics and Finance 70 (2024) 102079

M. Fakhfekh et al.

Regarding the second topic, the use of cryptocurrencies as a safe haven is controversial. Bouri et al. (2017) report that Bitcoin

acts as a poor hedge and is more suitable for diversification purposes. However, according to Urquhart and Zhang (2019) it can be

an intraday hedge against some fiat currencies, whereas it acts as a diversifier for other fiat currencies.

Finally, portfolio management seems to be an active research area involving cryptocurrencies. Liu (2019) use data from ten major

cryptocurrencies, finding some diversification benefits. Similarly, Platanakis and Urquhart (2019) compares naïve diversification

with more advanced portfolio models, finding that the latter yield superior risk-adjusted returns.

With the advent of Covid-19 pandemic, many researchers have endeavored to understand the impact of health crises on

international financial markets and cross-market linkages (Arouxet et al.,2022;Bariviera et al.,2023;Corbet et al.,2023;Salisu

& Vo,2020;Zhang et al.,2020). Not only that, but they have also investigated the features of cryptocurrencies as hedge and safe

haven against other assets (Bedowska-Sójka & Kliber,2022;Yousaf & Yarovaya,2022). In this regard, an increasing number of

papers focus on the connections between cryptocurrencies and traditional assets. Nevertheless, research on the potential roles of

(gold-backed) cryptocurrencies in portfolios including NFT and DeFi still remains under-explored. Also, when comparing the large

literature on Bitcoin and other cryptocurrencies, papers on DeFi and NFTs markets seem to be scanty (Maouchi et al.,2022). Very

few issues related to such assets start to be under study such as NFts pricing and relationship with other cryptocurrencies (Dowling,

2022a). Therefore, the empirical literature lacks evidence on the diversification advantages of different cryptocurrencies against

new digital crypto assets.

Considering the relatively recent introduction of NFT and DeFi, the outbreak of stressing market situations (Covid-19 and Russia–

Ukraine war), as well as the dynamic characteristics of this market, it is worth researching the linkage structure and hedge ratio of

a set of representative crypto-assets during turbulent times.

In this sense, this paper studies a comprehensive sample of five NFTs, five DeFi projects, four traditional cryptocurrencies and

tokens, and four gold-backed cryptocurrencies. Their interrelationship is not trivial, and investors would benefit from different

hedging strategies, in order to reduce risks and generate the highest possible returns. In this paper, we use a sequential approach of

quantitative methodologies, comprising Extreme Value Theory, and Archimax copula. The latter is a flexible class of copulas that

have recently gained popularity in the field of finance. In particular, they are a type of copula that is based on the generalized

extreme value distribution, which allows for the flexible modeling of tail dependence.

More precisely, the purpose of this study is two-fold. First, we investigate the dependence structure between gold-backed and

traditional cryptocurrencies and tokens, and NFTs/DeFi assets through a four-step approach. Such a multi-step procedure allows

us to examine and better understand the interdependence between new and traditional crypto-assets, specially at the tails of their

distributions. Second, we also compute the hedge ratios and assess the hedge effectiveness which could further help to understand

to what extent gold-backed and traditional crypto-assets could diminish the downside risk of NFT and DeFi crypto-portfolios. Then,

we study the potential impact of the Covid-19 pandemic and the geopolitical risk. This could help cryptocurrency investors and

portfolio managers to curb loss under extreme market conditions.

This study contributes to the literature in three key aspects. First, it expands the vast research on crypto-market linkages by

considering the combination of gold-backed and plain cryptocurrencies and tokens with new digital currencies (DeFi and NFTs)

in a portfolio, and assesses if (or to what extent) such dependence structure could offer further diversification benefits. Second,

it contributes to the study of hedging, diversification, and safe-haven features between traditional versus new cryptocurrencies

during turbulent economic conditions. In this regard, it provides a close look at the potential impact of geopolitical risk (and the

derived economic uncertainty) on the (new/traditional) cryptocurrency connectedness. Particularly, we investigate if different digital

currencies tend to exhibit (dis)similar connectedness reaction patterns to a political event. Third, this study offers some interesting

information about the possibility of predicting NFTs/DeFi prices based on price formation from other cryptocurrencies’ prices.

The remaining of the paper is organized as follows. Section 2conducts a brief literature review. Section 3explains the

methodology. Section 4describes the data. Sections 5and 6display the results and discuss the main empirical findings, respectively.

Finally, Section 7offers some concluding remarks.

2. Literature review

Many researchers have extensively investigated the hedging and safe-haven properties of new and traditional crypto-assets

(e.g. Bitcoin and NFTs) against various assets (e.g. stock indices, crude oil). For instance, Klein et al. (2018) investigate and compare

conditional variance features of gold, Bitcoin, and other assets, showing a discrepancy between them. Using a BEKK-GARCH model,

they report that gold is relevant for stock markets as a flight-to-quality vehicle during turbulent times. They also reveal that

Bitcoin could be correlated positively with downward markets. Mensi et al. (2019) show that forming different portfolios based

on cryptocurrencies (e.g. Bitcoin, Monero, Litecoin, and Bitcoin) offers better diversification advantages for portfolio managers and

investors. Wang et al. (2019) report that cryptocurrency could generally serve as a safe haven, but it is not a hedge for most stock

markets. They also show that the safe-haven feature tends to be more pronounced in developed markets. Le et al. (2021) study

the frequency-based dependency networks of different financial assets in the tails of return distributions. They report increases in

the network density in both upper and lower regions of the distributions of asset returns. In particular, an asymmetric effect of the

Covid-19 pandemic is well-documented. They also display that the cross-asset tail-dependency of currency, equity, and commodity

markets raises significantly in the left tails, which implies a higher degree of tail contagion effects. Wang et al. (2020) investigate the

safe-haven, hedging, and diversifying features of stablecoins against classical digital currencies. They show that USD-pegged (resp.

gold-pegged) stablecoins tend to perform better (resp. worse) than their corresponding underlying assets. They afterward show

that USD-pegged stablecoins perform better than gold-pegged stablecoins in extreme risk reductions. Aloui et al. (2021) evaluate

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M. Fakhfekh et al.

the effect of geopolitical risk on conventional and Islamic gold-backed gold cryptocurrencies using M-GARCH model. They reveal

that Islamic gold-backed cryptocurrencies behave differently from their conventional counterparts. They show that geopolitical risk

increases the connectedness of gold-backed cryptocurrencies to gold volatility and returns. Bouri et al. (2020) compare the hedging

and safe-haven properties of Bitcoin and gold against the G7 stock markets. They show that gold can be considered a suitable hedge

and safe-haven asset for many G7 stock indices, while Bitcoin takes such properties only for the Canadian stock market. They also

report that gold provides many conditional diversification benefits and more stable linkage for the G7 stock markets compared to

Bitcoin.

(Jalan et al.,2021) investigate the performance of five gold-backed stablecoins during the Covid-19 pandemic and compare

them to Bitcoin, Tether, and gold. They show that gold-backed cryptocurrencies seem to be susceptible to volatility transmitted

from gold markets during the Covid-19 pandemic period. They also report that the volatility of such assets is similar to that of

Bitcoin. Wasiuzzaman and Rahman (2021) study the performance of gold-backed cryptocurrencies during the Covid-19 pandemic

and the bear market of 2020. They record that the mean returns of such assets rise insignificantly during crisis periods. They

also reveal that PAX Gold displays increased volatility over the Covid-19 pandemic and the bear market, but its increase can

be insignificant. Jareno et al. (2021) study potential asymmetric and nonlinear interdependencies between cryptocurrencies and

oil price shocks over the period 20/11/2018-30/06/2020. Using the NARDL model, they also analyze the connectedness between

cryptocurrencies and crude oil. They afterward report that demand shocks display the highest association with cryptocurrencies.

The long and short-run analysis proves a strong connection between cryptocurrencies and oil during turbulent times. Dowling

(2022a) examines the relationship between NFT pricing and cryptocurrency pricing. The empirical results show limited volatility

transmission between NFTs and other crypto-assets, given the value of the spillover index. This seems to indicate that cryptocurrency

pricing behavior can help to recognize NFT pricing patterns. Nevertheless, the low volatility transmission reveals that NFTs could be

considered as low-correlation assets, and different from traditional cryptocurrencies. Bedowska-Sójka and Kliber (2022) investigate

the hedging potential of cryptocurrencies against Brent crude oil during the period 10/02/2020-10/02/2022. In this context, the

advent of the Covid-19 pandemic has increasingly impacted oil prices by raising the economic uncertainty and mobility factor.

They clearly display that stablecoins constitute the best hedge against downward fluctuations in oil prices, but do not decrease

investment volatility. Maouchi et al. (2022) analyze digital financial bubbles during the Covid-19 pandemic period using Bitcoin,

Ethereum, nine DeFi tokens, and three NFTs. They identify many overlapping bubbles. In particular, they detect NFT and DeFi

bubbles, which tend to be less recurrent with high magnitude than the other crypto-assets. The outbreak of the Covid-19 pandemic

increased bubble occurrences. Mokni et al. (2022) examine if cryptocurrencies and gold tend to be safe-haven assets and hedge

against economic policy uncertainty (EPU) before and during the health crisis. They disclose that cryptocurrencies and gold cannot

act as safe haven or hedge against EPU before and during the health crisis. Dunbar and Owusu-Amoako (2022) indicate that causality

seems to flow from equity returns to cryptocurrencies. They afterward show that equities tend to be more inversely related to

cryptocurrencies during the Covid-19 pandemic period. This suggests that equities could be a suitable hedge against cryptocurrency

risks. Based on rolling window regressions, they display that the equity risk premium decreases downside risk during a substantial

crisis event (e.g. the Covid-19 pandemic). Gadi and Sicilia (2022) investigate the safe-haven, hedging, and diversifying abilities

of cryptocurrencies against stock indices in G7 and BRICS regions during the period 01/01/2018-30/09/2022. Based on the Baur

and McDermott model, they show that blockchain technology pre/during the Covid-19 pandemic period could play a crucial role

in the safe-haven, hedging, and diversifying features linked to such assets. More precisely, stablecoins tend to sustain hedging

features in most stock markets before and during the health crisis. Nevertheless, Bitcoin investment features tend to change after

the beginning of such a crisis. Shahzad, Bouri, Ahmad, and Naeem (2022) study the safe-haven and hedging properties of traditional

currencies for Bitcoin, Litecoin, Ethereum, and Ripple. They report that the Japanese yen is an effective hedge for digital currencies,

followed by the British pound, and the Chinese yuan. The safe-haven proprieties for the yen, euro, and yuan are maintained during

the adverse explosiveness periods of the cryptocurrency market. Díaz et al. (2023) evaluate the capacity of stablecoins to reduce

the downside risk of a traditional cryptocurrency portfolio. They detail the low conditional correlations between dollar-backed

stablecoins and cryptocurrency portfolios, clearly showing that they can be considered as hedges for cryptocurrencies. They also

report that all stablecoins tend to have great diversification abilities by decreasing portfolio tail risk. Khaki et al. (2023) re-examine

the portfolio diversification properties of cryptocurrencies, using mean–variance and higher-order moments optimization techniques.

They conclude that expanding the set of digital currencies can achieve only marginal advantages given the substantial comovements

between cryptocurrencies. Finally, Nedved and Kristoufek (2023) show that stock markets tend to move along with Bitcoin, whereas

gold and crude oil could be considered safe havens. In particular, gold tends to be a strong safe haven for Bitcoin.

From a methodological standpoint, many researchers have increasingly tried to use advanced econometric models to better

understand interconnections between cryptocurrencies and other assets (Burnie,2018;Caferra et al.,2022;Giudici & Polinesi,2021),

analyze the tail risk of cryptocurrency prices (Ahelegbey et al.,2021;Bouteska et al.,2023) and construct portfolios using machine

learning models (Babaei et al.,2022;Jiang & Liang,2016). For instance, Burnie (2018) uses the correlation networks method

to identify features that highly affect the evolution of cryptocurrency prices. They show a positive relationship among different

cryptocurrencies, except for USD Tether. Ho et al. (2020) study the features and dynamic evolution of 120 cryptocurrencies during

the period 2013–2020 by performing network analysis. They show that the cross-returns between cryptocurrencies are decreasing

during 2013–2016 and increased after that period. They also display that cryptocurrencies used for transaction payment tend to be

dominant in the market until mid-2016, followed by those developed for applications based on Blockchain. Using the correlation

networks method, Giudici and Polinesi (2021) scrutinize the dynamics of cryptocurrencies’ prices and how price information is

conveyed between the different Bitcoin exchanges and between Bitcoin markets and traditional ones. They reveal that Bitcoin

exchange prices tend to be positively linked to each other. They also report that traditional asset volatilities (resp. prices) affect

North American Journal of Economics and Finance 70 (2024) 102079

M. Fakhfekh et al.

(resp. cannot influence) Bitcoin prices with adverse and lagged effects. Nie (2022) examines the evolution of correlations in the

cryptocurrency market by using a network method. Such a method is also employed to detect critical events in the correlation

dynamics of cryptocurrencies. The empirical results show great fluctuations in the market index near such events. This indicates

the existence of a relationship between the correlation matrix dynamics and market states. The empirical findings also display

a synchronization among changes in correlation and changes in network structures. Caferra et al. (2022) study if and how

cryptocurrency ecosystem network connectivity could predict Bitcoin returns through quantiles of the return distribution. They

show the effectiveness of many connectivity measures in predicting both price downfalls and spikes, but in a different way before

and during the Covid-19 pandemic. Briola and Aste (2022) analyze cross-correlations of 25 liquid cryptocurrencies at various time

horizons. Using the network, they show that a decrease in correlation among pairs of cryptocurrencies for finner time sampling

resolutions is well-documented. They also display a growing framework for coarser resolutions, indicating multiple changes in the

hierarchical reference role played by cryptocurrencies. Jing and Rocha (2023) employ network methods to choose cryptocurrencies

and the Markowitz Portfolio Theory to establish portfolios that are agnostic for further market behavior. They show that the

performance of their network-based portfolios tends to be optimal with 46 cryptocurrencies and higher to benchmarks for short-term

investments, achieving up to mean expected returns within 1 day. Ma et al. (2023) try to explore if crypto tokens could improve

portfolio performance and how crypto tokens could be interesting alternatives for portfolio diversification. Using correlation-based

networks, they report tokens with great Sharp ratios but low centrality could boost the portfolio performance. They also report that

the market is dominated by tokens from GameFi sectors, DeFi, and Blockchain infrastructure.

Borri (2019) estimate the conditional tail-risk in the cryptocurrency markets (Ripple, Litecoin, Bitcoin, and Ether) by employing

CoVaR. The empirical results show that even though cryptocurrency returns tend to be greatly linked one to another, idiosyncratic

risk could be substantially decreased and cryptocurrency portfolios provide better conditional and risk-adjusted returns than

individual cryptocurrencies. Canh et al. (2019) study the structural breaks and volatility spillovers in different cryptocurrencies.

They use the Granger Causality test, LM test for ARCH and Dynamic conditional correlation MGARCH model, and Cumulative sum

test for parameter stability. They report that structural breaks exist in many cryptocurrencies. They also show the shifts from smaller

cryptocurrencies to larger ones in terms of market capitalization. Opala et al. (2022) study the risk measurement of Ethereum,

Bitcoin, and Litecoin using different models such as the extreme value theory. They report that the extreme value theory with

the peaks-over-threshold method shows satisfactory backtesting results at a 99% confidence level. They show that the greatly

volatile market phases may not be observed from the short time series. Ahn (2022) examines extreme tail dependence between

cryptocurrencies and the S&P500 index using a model-free approach. The empirical results show that any symmetric model cannot

succeed in explaining the correlation framework in major cryptocurrency returns. The sample upward tail correlations among digital

currencies and the equity market are lower than the downward tail ones. Ahelegbey et al. (2021) study the links between market

assets during turbulent times using the extreme downside hedge and the extreme downside correlation. They show that crypto-assets

could be divided into two sets: technical assets (e.g. Ethereum) which are receivers of tail contagion whereas speculative assets are

transmitters of contagion.

Umar et al. (2022) analyze tail dependence of higher-order moments and portfolio features using NFTs and other assets.

Using Conditional Value-at-Risk (CoVaR) and 𝛥CoVaRs along with different copula functions, they show that NFTs have beneficial

investment and hedging features under all market conditions. Bouteska et al. (2023) analyze the interconnections among the

cryptocurrency volatilities, the US equity and bond markets’ volatility, and the effects of Covid-19 pandemic. They also explore the

potential presence of structural breaks in the volatility of Dash, Monero, Bitcoin, and Stellar. They use GARCH models and Inclán and

Tiao (1994) Cumulative Sums of Squares algorithm and Simultaneous Equation Model. They report the presence of return-volatility

spillovers among Dash, Bitcoin, and Stellar while Monero is the main transmitter of shocks. Fang et al. (2023) employ 𝛥CoVaR and

MES to forecast the systemic risk in the cryptocurrency markets. They display that EOS, Aoen, and Sinacoin tend to better forecast

systemic risk. Jalan and Matkovskyy (2023) show the lack of substantial decreases and increases in liquidity and systemic risk,

respectively.

Jiang and Liang (2016) employ a convolutional neural network with historic prices of cryptocurrencies to provide forecasts.

They provide interesting results for portfolio management. Borges and Neves (2020) develop a system using machine learning

methods to establish an investment strategy to trade cryptocurrency exchange markets. They show that all learning algorithms tend

to outperform the buy-and-hold strategy in most markets. Using ARIMA, convolutional neural network, and long/short-run memory

methods, Ramkumar (2021) attempts to forecast the cryptocurrency prices. The empirical results display that multiple portfolios

are established using equal-weighted portfolios, modern portfolio theory, cointegrated pairs, Kelly criterion, and risk parity. They

show that a portfolio constructed using a cointegrated pair has outperformed and the annualized returns are maximized based on

a pair trading strategy. Sebastiao and Godinho (2021) analyze the predictability of three cryptocurrencies (Bitcoin, Ethereum and

Litecoin) and the profitability of trading strategies using machine learning techniques during the period 15/08/2015-03/03/2019.

Overall, they report that machine learning methods offer robust results concerning the predictability of cryptocurrencies. Babaei

et al. (2022) propose an explainable portfolio management approach for cryptocurrencies using a machine learning model. Using

such an approach they are able to understand what is behind the chosen portfolio weights, providing useful hints for portfolio

managers (better risk adjustment) and policymakers (implementation of better financial regulation).

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3. Methodology

This paper investigates the dependence structure and optimal hedge ratios between NFT, DeFi, and traditional and gold-backed

cryptocurrencies. To do so, a four-step approach is used. First, we filter residuals using an AR(1)-FIEGARCH(1, 𝑑, 1) model. Second,

we employ the Extreme Values Theory (EVT) to identify extreme events (e.g. the Covid-19 pandemic and the Russia–Ukraine war).

We particularly adopt the Peaks Over Thresholds (POT) method. Before estimating the GEV distribution parameters of extreme

values, we choose 30% of the observations; 15% of them are related to the large-value (resp. small-value) observations. Finally, we

employ the copula method to estimate the extreme series interdependence structures.

We employ a FIEGARCH(𝑝, 𝑑, 𝑞 )model to deal with autocorrelations, shock asymmetry, and shock persistence of the time series.

Such a model also enables us to take into consideration both ARCH and long-memory effects. Developed by Bollerslev and Mikkelsen

(1996), the model is given as follows:

ln(ℎ𝑡) = 𝜔+𝜙(𝐿)−1(1 − 𝐿)−𝑑[1 + 𝛼(𝐿)]𝑔(𝑧𝑡−1 )

with 𝑔(𝑧𝑡) = 𝛾1𝑧𝑡+𝛾2[𝑧𝑡−𝐸𝑧𝑡](1)

The FIEGARCH(𝑝, 𝑑, 𝑞 )model can be transformed into an EGARCH model (resp. an integrated EGARCH) when 𝑑= 0 (resp. 𝑑= 1).

Analogous to the ARFIMA model, ln (ℎ𝑡)is covariance-stationary and invertible for 𝑑∈ [−0.5,0.5] (Bollerslev & Mikkelsen,1996).

Additionally, the long-memory feature dissipates for all the values of 𝑑 < 1. We thereafter assume that the return equation is given

as follows :

𝑟𝑡=𝛼0+𝛼1𝑟𝑡−1 +𝜀𝑡(2)

where 𝑟𝑡(resp. 𝑟𝑡−1) denotes the return index at time 𝑡(resp. 𝑡− 1), and 𝛼0, 𝛼1are parameters.

Needless to say, analyzing the cross-market linkages among several assets requires information regarding the underlying

dependence associations. To do so, a flexible copula framework is selected. Following the Sklar (1959) theorem, the joint

distributions of two continuous random variables 𝑋and 𝑌,𝐹𝑋𝑌 (𝑥, 𝑦), with marginal functions 𝐹𝑋(𝑥)and 𝐹𝑌(𝑦), are described using

the following copula function 𝐶:

𝐹𝑋𝑌 (𝑥, 𝑦)=𝐶𝐹𝑋(𝑥), 𝐹𝑌(𝑦)(3)

There is a critical issue related to multivariate distribution modeling. To obviate any complexity, one might use the bivariate

distribution copula method to model the dependence relationship among two variables. In particular, the Archimax copulas

developed by Capéraà et al. (2000) are used in this study. Indeed, they combine the Extreme Value Theory and Archimedean copula

classes into a single class. Extreme value theory is a branch of the theory of order statistics, which dates back to the pioneering works

by Fisher and Tippett (1928). Extreme value theory is concerned with the asymptotic distribution of standardized maxima from a

series of i.i.d random variables. Extreme Value Theory provides a strong framework to formally analyze the behavior of extreme

observations (Marimoutou et al.,2009). Essentially, there are two main methods to apply the EVT, i.e. to model extreme values of

a random variable. First, we have the Block Maxima Method (BMM); it divides the time horizon into periods (i.e. blocs) in which

the maximum values of the variable in each period are retained. These observations are considered as extreme events. However,

taking into account merely the maximum return in each period induces the exclusion of many data points from the analysis. Hence,

the BMM does not allow enough study of the volatility clustering. Second, to overcome such shortcomings, the so-called Peak-Over

Threshold (POT) method was developed. This method takes into consideration all the values above a given (high) threshold.

The Archimax copulas are given by:

𝐶(𝑢, 𝑣) = 𝜑−1 (𝜑(𝑥) + 𝜑(𝑦))𝐴𝜑(𝑢)

𝜑(𝑢) + 𝜑(𝑣) (4)

where 𝐴(𝑡)is a valid dependence function, and 𝜑is a valid Archimedean generator. Archimax copulas reduce to Archimedean copulas

for 𝐴(𝑡)=1and to EV copulas for 𝜑(𝑡) = − ln(𝑡).

In this context, the BB4 Archimax copula with

𝜑(𝑡) = 𝑡−𝜃− 1 and 𝐴(𝑡) = 1 − 𝑡−𝛿+ (1 − 𝑡)−𝛿−1∕𝛿(5)

is called the BB4 copula and is given by the following formula:

𝐶(𝑢, 𝑣) = 𝑢−𝜃+𝑣−𝜃−1−(𝑢−𝜃− 1)−𝛿+ (𝑣−𝜃− 1)−𝛿−1∕𝛿−1∕𝜃(6)

with 𝜃≥0and 𝛿 > 0.

Afterward, the dependence coefficient could be used to compute the optimal hedge ratios. In this way, investors could learn how

NFT and DeFi can be effectively hedged by other assets (i.e. plain and gold-backed cryptocurrencies and tokens).

To illustrate, let an investor want to hedge his/her portfolio position against cryptocurrency market price fluctuations. From a

portfolio perspective, the investor wants to minimize the portfolio risk without diminishing the expected returns. Following Kroner

and Sultan (1993), the optimal hedge ratio of his/her portfolio is determined as follows:

𝛽𝑆𝑂

𝑡=ℎ𝑆𝑂

𝑡

ℎ𝑆

𝑡

(7)

where:

North American Journal of Economics and Finance 70 (2024) 102079

M. Fakhfekh et al.

•𝛽𝑡refers to the risk-minimizing hedge ratio about assets.

•ℎ𝑠

𝑡refers to the conditional variances of the assets.

•ℎ𝑠𝑜

𝑡corresponds to the conditional covariance between digital assets at time 𝑡.

Hedging strategies can be used to reduce market risk by offsetting losses in one asset with gains in another. In this study,

we investigate the effectiveness of hedging plain and gold-backed cryptocurrencies with NFT and DeFi tokens. We find that the

optimal hedge ratio, which is the amount of NFT and DeFi tokens to sell (𝛽) for every dollar invested in plain and gold-backed

cryptocurrencies, varies depending on the specific cryptocurrency. We then use the hedge effectiveness (HE) index to assess the

performance of various optimal hedge ratios.

Following Ku et al. (2007) and Chang et al. (2011), the HE index is computed as follows:

𝐻𝐸 =𝑣𝑎𝑟𝑢𝑛ℎ𝑒𝑑 𝑔𝑒𝑑 −𝑣𝑎𝑟ℎ𝑒𝑑𝑔𝑒𝑑

𝑣𝑎𝑟𝑢𝑛ℎ𝑒𝑑𝑔𝑒𝑑

(8)

4. Data

This paper uses daily data from 01/11/2021 to 21/02/2023 of eighteen digital assets1:

•five NFTs: Metaverse NFT index (PLAY), Unicly CryptoPunks Collection (UPUNK), Sandbox (SAND), NFTLaunch (NFTL), and

xNFT Protocol (xNFT).

•five DeFi projects: DeFi Pulse Index (DPI), Terra Classic (LUNC), Avalanche (AVAX), Wrapped Bitcoin (WBTC), and Chainlink

(UNK).

•four plain cryptocurrencies and tokens: Bitcoin (BTC), Ethereum (ETH), Binance Coin (BNB), and FTX Token (FTT).

•four gold-backed cryptocurrencies: Pax Gold (PAXG), Tether Gold (XAUT), Perth Mint Gold Token (PMGT), and Digix Global

(DGX).

Data were downloaded from www.coinmarketcap.com Thus, the sample has 477 daily observations.

The rationale behind choosing (five) NFTs, (five) DeFi and (four) cryptocurrencies, and (four) gold-backed cryptocurrencies

is based on two criteria: the availability of the data and the market capitalization. According to Karim et al. (2022), such

cryptocurrencies, seem to be mature and have strong market capitalization whereas DeFis and NFTs remain emerging and show

different market capitalization. We also chose four gold-backed cryptocurrencies as stablecoins which are different from those used

by Díaz et al. (2023) to better understand and assess the ability of such assets against new digital assets in terms of portfolio

diversification.

All the price series are transformed into logreturns as 𝑅𝑖,𝑡 = log(𝑃𝑖,𝑡) − log(𝑃𝑖,𝑡−1 ), where 𝑃𝑖,𝑡 (resp. 𝑃𝑖,𝑡−1) corresponds to the asset

𝑖closing price at time 𝑡(resp. 𝑡− 1).

Table 1 reports the sample statistics for assets under consideration. It is worth mentioning that the highest (resp. the lowest)

mean return is recorded for LUNC (resp. PAXG and PMGT) which is equal to 0.0317 (resp. 0). All the mean values of assets are

positive whereas median of some assets presents negative values such as LINK and BNB. We also report that the highest standard

deviation is recorded for LUNC (0.3888) whereas the lowest one is for PAXG (0.0080). The results of the Jarque–Bera test reject

the null hypothesis of normal distribution for returns.

Fig. 1 illustrates the daily return movements over the period 01/11/2021-30/11/2022. From Fig. 1, all daily return series seem

to fluctuate over time, indicating the existence of some turning points. All daily returns series tend to show a volatility clustering

behavior.

Fig. 2 illustrates the correlation among different assets. Recall that the diagonal elements of the matrix correspond to the variances

(dark blue color) whereas the off-diagonal elements refer to the covariances between all potential pairs of assets. At first sight, the

pairwise correlations between assets tend to be positive and vary from 0 and 0.9. Some dissimilarities in the correlation framework

are well-documented. Indeed, some correlations are low whereas other ones are high. For instance, the pairs ETH/DPI, BTC/WBTC,

and XAU/PAXG are highly and positively related, with a value of about 0.8. However, SAN/UPUNK, FTT/PLAY are weakly and

positively linked, with a value of around 0.1.

1Díaz et al. (2023) show that three stablecoins (Tether, USD coins and Digix Gold) are characterized by higher diversifying and hedging potential against

traditional cryptocurrencies (Bitcoin, Ethereum, Ripple, Cardano and Litecoin). Many researchers have studied the hedging, diversifying, and safe-haven features

of different assets against cryptocurrencies (Dunbar & Owusu-Amoako,2022;Nekhili & Sultan,2022;Shahzad, Bouri, Ahmad, & Naeem,2022;Shahzad, Bouri,

Rehman, & Roubaud,2022). In our paper, we analyze the interrelatedness of NFTs and DeFi to evaluate the ability of different asset classes (gold-backed

cryptocurrencies and traditional cryptocurrencies). Four gold-backed cryptocurrencies (i.e. Pax Gold, Tether Gold, Perth Mint Gold Token, and Digix Glod) which

are stablecoins are used in our study. Among them, Digix Gold has already been used as a stablecoin by Díaz et al. (2023). We also chose four gold-backed

cryptocurrencies as stablecoins which are different from those used by Díaz et al. (2023) to better understand and assess the ability of such assets against new

digital assets in terms of portfolio diversification.

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M. Fakhfekh et al.

Table 1

Descriptive statistics.

Asset Mean Median Max. Min. Std. Dev. Skewness Kurtosis Jarque–Bera Q(16) Q2(16)

PLAY −0.524 0.000 83.509 −81.830 13.584 0.236 21.069 6493.27*** 123.720*** 136.640***

UPUNK −0.253 −0.039 28.137 −27.455 5.506 −0.568 9.942 983.51*** 38.694*** 114.790***

SAND −0.208 −0.170 37.499 −28.576 6.615 0.503 7.137 360.23*** 19.719 47.402***

NFTL −0.319 −1.127 58.159 −53.078 9.172 1.460 14.546 2819.04*** 12.960 56.737***

XNFT −0.788 −0.663 57.812 −53.957 8.811 1.451 17.586 4395.61*** 20.599 22.675

DPI −0.293 −0.014 18.914 −25.108 4.967 −0.521 5.800 177.44*** 14.591 43.585***

LUNC −2.618 −0.376 150.364 −554.678 35.408 −11.186 157.847 486502.50*** 155.430*** 174.190***

AVAX −0.238 −0.078 22.299 −36.414 6.038 −0.497 6.213 224.87*** 22.200 40.545***

WBTC −0.192 −0.013 13.548 −17.460 3.275 −0.574 7.187 374.69*** 18.562 17.642

LINK −0.297 0.000 14.770 −21.502 5.100 −0.545 4.429 64.15*** 23.356 112.530***

BTC −0.192 −0.111 13.576 −17.405 3.271 −0.536 7.180 370.17*** 18.978 16.890

ETH −0.201 −0.138 16.648 −19.185 4.305 −0.404 5.904 180.57*** 23.367 46.347***

BNB −0.104 0.179 20.546 −19.376 3.878 −0.604 7.994 524.80*** 11.171 86.481***

FTT −0.747 −0.202 42.555 −194.000 10.935 −11.482 207.091 838337.40*** 33.920*** 2.219

PAXG 0.002 0.001 3.000 −3.068 0.774 −0.054 5.129 90.34*** 29.133** 35.551***

XAUT 0.005 0.011 2.745 −2.848 0.700 −0.148 5.126 91.55*** 24.645* 17.793

PMGT 0.005 0.000 11.365 −13.226 1.325 −0.783 33.707 18789.63*** 30.865*** 106.290***

DGX 0.009 −0.141 186.727 −151.260 16.542 1.994 59.993 64873.88*** 61.472*** 43.946***

Table 2

FIEGARCH estimation results.

C AR(1) A GARCH(1) ARCH(1) LEV(1) Fraction

PLAY 0.0112*** −0.1183*** −0.1088*** 0.6318 0.3104*** 0.2312*** 0.8743***

UPUNK 0.0072*** −0.0829* −0.4273** 0.8638*** 0.1473*** −0.1832 0.4402**

SAND 0.0039* 0.0125 −0.3582*** 0.3528* 0.2743*** 0.0482** 0.5703***

NFTL 0.0072*** −0.0765** −0.9752*** 0.1122 0.4219*** 0.1983*** 0.4038***

XNFT 0.0032 −0.1214*** −1.8732*** 0. 7148* 0.1993*** 0.2438*** 0.1183**

DPI 0.0082* 0.0195 −0.4478** 0. 7153** 0.1473** 0.2731*** 0.3274**

LUNC 0.0061** −0.0406* −0.7532*** 0.7012*** 0.2842*** 0.1704*** 0.0329

AVAX 0.0033** 0.0337 −0.7632** 0. 6731*** 0.3422*** 0.1392*** 0.3521

WBTC 0.0044** 0.0041 −0,6429 0.6662* 0.1288** 0.2231*** 0.1099

LINK 0.0021 0.0039 −0.8652 0.6991*** 0.2626*** 0.0904** 0.0438

BTC 0.0043** −0.0019 −15,095 0.5723* 0.1629** 0.2520*** 0.1275

ETH 0.006 0.0308 −17,753 0.7629*** 0.1852*** 0.2187*** 0.0184

BNB 0.0023 0.0886** −0.7459** 0.6982*** 0.1399** 0.2762*** 0.2067*

FTT 0.0011 −0.0773* 0.0195 0.6421*** 0.2862*** 0.7896*** 0.4208***

PAXG 0.0002 0.0028 −11,642 0.8751*** 0.0847* −0.0628** 0.4401**

XAUT 0.0001 0.0209 −12,406 0.8621*** 0.0642 −0.1382*** 0.4502**

PMGT −0.0002 −0.2127*** −14,175 0.7230*** 0.1851* −0.1421** 0.3217

DGX 0.0113** −0.1578*** −0.4652*** 0.9261*** 0.0632*** −0.6413*** 0.1982

Note: *,** and *** denote significance at 10%, 5%, and 1%, respectively.

5. Results and discussion

5.1. FIEGARCH model

Since ours is a sequential multi-model approach, it is important to select the more appropriate model at each stage. Thus, we

first estimate different GARCH-type models (i.e. GARCH, EGARCH, TGARCH and FIGARCH), with their corresponding information

criteria, which allow us to choose the best model. Table 4 in the Appendix reports the results from the calculation of the usual

information criteria. The lowest values of different information criteria clearly show the FIEGARCH model is preferred, indicating

that this model offers the best fit for our data.

As aforementioned, the AR(1)-FIEGARCH(1, 𝑑, 1) model allows us to evaluate the asymmetric shock effect on volatility (i.e. the

leverage effect) and the long memory persistence. Table 2 reports the estimation results.

Table 2 reveals that the leverage effect coefficient LEV(1) is significant for all assets. That is, all time series show significant and

positive leverage effects whereas gold-backed cryptocurrencies show significant and negative effects. Indeed, a negative leverage

effect indicates that negative shocks raise volatility less than positive ones. Such empirical results confirm those reported by Jeribi

and Fakhfekh (2021), Choi and Shin (2022), and Fakhfekh et al. (2016) for financial time series. According to Wang (1993)

and Gajurel and Chawla (2022) an (in)decrease in volatility can be attributed to the behavior of (un)informed investors. The

price changes due to the presence of uninformed market participants will be reversed, raising volatility by more than those

attributed to informed ones (Avramov et al.,2006;Gajurel & Chawla,2022). In particular, for NFT, DeFi, and plain and gold-backed

cryptocurrencies, the invested asymmetric effect can be attributed to the herding (resp. the contrarian behavior) of uninformed

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M. Fakhfekh et al.

Fig. 1. Daily Return of the different assets in the sample.

investors (resp. informed investors) when assets’ prices increase (resp. decrease). Such finding seems to be in line with Fakhfekh

and Jeribi (2020) and Charfeddine et al. (2020).

The positive (inverted) asymmetric volatility effect is well-documented for NFT, DeFi, and cryptocurrencies. As mentioned, both

NFT series (i.e. PLAY and SAND) exhibit the persistence of volatility shocks, given that the persistence degree 𝑑is greater than 0.5.

This situation shows a strong persistence and might be explained by the structural changes in the variance process (Lamoureux &

Lastrapes,1990). In addition, PLAY reveals a strong persistence, implying that the effect of the shock on the volatility of this asset is

long-lasting. However, the shock impact on the rest of return volatilities seems to exhibit transitory persistence of volatility shocks.

5.2. Extreme value theory

Once the FIEGARCH model is estimated, the estimation results are used to identify extreme losses based on the Extreme Value

Theory. In this study 30% of the residuals series are considered as outliers (i.e. 15% represent the highest values and 15% the

lowest ones). Using Generalized Pareto Distribution (GPD), the upper and lower tails’ estimations are displayed in Table 3. The POT

method is performed through the GPD for tail estimation while accounting for 30% of the sample residuals. It can be observed in

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M. Fakhfekh et al.

Fig. 2. Correlation Matrix among time series.

Table 3

EVT estimation results.

Upper tail Lower tail

PLAY 𝜉0.327 0.0294

𝛽0.4378 0.6643

UPUNK 𝜉0.0742 −0.2696

𝛽0.8962 1.2843

SAND 𝜉−0.0724 0.2038

𝛽0.7534 0.7083

NFTL 𝜉−0.0908 0.1628

𝛽0.7962 0.6843

XNFT 𝜉−0.0352 0.3099

𝛽0.5973 0.4473

DPI 𝜉−0.2861 −0.0632

𝛽0.8633 0.7039

LUNC 𝜉0.0799 −0.7392

𝛽0.6621 0.7382

AVAX 𝜉−0.1853 −0.4281

𝛽0.8963 0.6643

WBTC 𝜉−0.3907 −0.0125

𝛽1.0842 0.5944

LINK 𝜉−0.3536 −0.1782

𝛽0.7952 0.5399

BTC 𝜉−0.4399 −0.0639

𝛽1.1974 0.6224

ETH 𝜉−0.3082 −0.0108

𝛽0.8236 0.6482

BNB 𝜉−0.1904 −0.231

𝛽1.1774 0.6284

FTT 𝜉0.5538 0.0799

𝛽0.4293 0.3298

PAXG 𝜉−0.2744 −0.0432

𝛽0.9071 0.6674

XAUT 𝜉−0. 5457 −0.1264

𝛽1.1823 0.8094

PMGT 𝜉−0.4632 −0.4263

𝛽0.796 0.8894

DGX 𝜉0.904 0.4092

𝛽0.2742 0.4483

Note: Coefficients 𝛽and 𝜉are, respectively, the shape and scale parameters of

the fitted generalized Pareto distribution (GPD)

Table 3 that, regarding the upper tail, all time series show a short-tailed feature. As a matter of fact, 𝜉values are negative, except

for PLAY, UPUNK, LUNC, FTT and DGX, which exhibit long-tailedness. Regarding the lower tail, it can be noticed that only PLAY,

SAND, NFTL, XNFT, FTT, and DGX show long-tail features.

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M. Fakhfekh et al.

Fig. 3. Spearman’s Rho and Kendall’s Tau for all the pairs.

5.3. Copula estimation results

After computing the GPD and residual parameters, we estimate the Archimax copula for each of the NFT/DeFi-plain/gold-backed

cryptocurrency pairs. Table 5 (Appendix) displays the estimation results of Archimax copula dependence parameters (𝛿and 𝜃),

Kendall’s Tau, and Spearman’s Rho correlation coefficients.

It can be observed that the dependence between PLAY and Ethereum is the highest, with 𝜃= 0.1904 and 𝛿= 0.4870. On the

contrary, the lowest dependence is recorded for the PLAY/DGX, with 𝜃= 0 and 𝛿= 0.3050. These results are in agreement with the

values of the nonparametric correlations coefficients, showing that the values of Kendall’ Tau and Spearman’s Rho coefficients for

the pair PLAY/ETH (resp. PLAY/DGX) are equal to 0.2594 and 0.3777 (resp. 0.0788 and 0.1177). In particular, Fig. 3 illustrates

that all the correlation coefficients are positive, although at different levels. This allows us to better understand the nature of the

relationship between different assets.

5.4. Optimal hedge ratio and hedge effectiveness

In this sub-section, we report the estimation results related to optimal hedge ratio and hedge effectiveness in order to analyze

the implications of the different crypto-assets from a portfolio management perspective. Table 6 (Appendix) and Fig. 4 present the

estimation results related to the optimal hedge ratios and hedge effectiveness for each asset pair.

Table 6 (Appendix) reports a high correlation for the WBTC-BTC pair (0.9954) followed by the WBTC-Ethereum pair (0.8906).

Differently, low correlations are noticed for the XNFT-PMGT and the XNFT-DGX pairs. Overwhelmingly, the cross-market linkages

seem to be low, implying that gold-backed cryptocurrencies seem suitable for enhancing portfolio diversification.

Afterward, we focus on the values of the hedge ratios (𝛽) between the NFT/DeFi markets and plain/gold-backed cryptocurrencies

using FIEGARCH-EVT Copula modeling. Table 5 shows that the estimated coefficients are positive. This implies that a long position

of one dollar in the four plain and the four gold-backed cryptocurrencies could be hedged by a short position of 𝛽in DeFi and NFT.

Nevertheless, some heterogeneity in the hedge ratio values according to assets is well-documented. The level of the hedge ratio

considerably varies across assets. In this regard, the values of the hedge ratio are lower than 1 for the pairs involving WBTC.

Some patterns are documented for the pairs including UPUNK. The values of SAND/other assets and AVAX/other assets are

generally lower than 1, except for BTC and ETH. But, for the couples of NFTL/other assets and DPI/other assets, only the hedge

ratio related to Bitcoin has a value of less than 1. The XNFT/PAXG and XNFT/XAUT (resp. LINK/BTC and LINK/PMGT) pairs are

higher than 1, which the 𝛽s are equal to 2.6036 and 2.8130 (resp. 1.1869 and 1.8474). The number of hedge ratios greater than 1

seems to be high for LUNC/other assets. In particular, the couples of LUNC/BTC (𝛽= 2.0064), LUNC/ETH (𝛽= 1.5984), LUNC/BNB

(𝛽= 1.0880), and LUNC/XAUT (𝛽= 1.0952) clearly show this fact.

Regarding the HE hedging indices, the PLAY/DGX and UPUNK/DGX portfolios are superior to the portfolio index integrating

other cryptocurrencies and backed gold. This finding suggests that higher hedge effectiveness and greater risk reduction benefits

could have been secured for investors by applying the DGX index as hedging instruments for both NFT series (i.e., PLAY and UPUNK).

In addition, the PMGT index is an effective hedging instrument for the following series: SAND, XNFT, DPI and AVAX, while

the XAUT index is an effective hedging instrument and reduces the risk for movements in the returns of NFTL, WBTC, and LINK

indices. PAXG presents the best hedging instrument for the LUNC index. According to this result, we can notice that gold-backed

North American Journal of Economics and Finance 70 (2024) 102079

M. Fakhfekh et al.

Fig. 4. Overview of hedging strategies.

assets are the best hedging instruments compared to those of cryptocurrencies. Indeed, investors could use these assets to hedge

their portfolios and reduce their likely risk.

Overall, the empirical findings display that gold-backed cryptocurrencies seem to show more effectiveness in portfolio diversifi-

cation efficiency. So, they can be considered as hedging tools. Such findings can provide insightful information for several reasons.

First and foremost, they help investors for effective decision-making regarding optimal portfolio choices. This can be achieved using

the nonlinear dependence framework among NFT/DeFi-gold-backed cryptocurrencies. Afterward, they may help portfolio managers

adjust their strategies and grasp better opportunities. In this regard, the conditional EVT approach (i.e. the FIEGARCH-EVT-Coula

method) seems to be an interesting econometric tool to diminish financial losses and curb portfolio risk.

6. Discussion

Hedging the extreme risk in cryptocurrency is a crucial issue for risk-averse investors and portfolio managers during episodes of

turbulent market conditions, which are frequent in this market. Such a situation justifies the interest of the literature in the hedging

and safe-haven features of cryptocurrencies (e.g. Conlon and McGee 2020,Goodell and Goutte 2021), which gain relevance as an

emerging asset class (Dunbar & Owusu-Amoako,2022). For instance, Charfeddine et al. (2020) examine the diversification and

hedging abilities of cryptocurrencies under different economic and political situations. They show that cryptocurrencies could be

used for portfolio diversification. However, this market is in continuous evolution. In addition to plain cryptocurrencies and tokens,

other new digital assets emerged. For instance, gold-backed cryptocurrencies (whose value is pegged to the value of gold), NFTs,

and DeFi projects have increasingly attracted investors’ attention and media coverage (Aloui et al.,2021;Maouchi et al.,2022).

In particular, the prompt evolution of DeFi and NFTs was contemporaneous with the upsurge of the health crisis (Maouchi et al.,

2022) and was characterized by the bubble formation in such markets (Kyriazis et al.,2020).

Intending to contribute to the ongoing aforementioned literature, this study investigates the dependence structure among

NFT/DeFi assets and plain/gold-backed cryptocurrencies and evaluates hedge effectiveness based on a multi-method approach

during the geopolitical event.

Our empirical findings clearly show dissimilarities in the dependence structure among different crypto-asset classes during the

period 01/11/2021-05/10/2023. This period was crossed by the Covid-19 pandemic and by the war in Ukraine. Afterward, a short

position of 𝛽in NFT and DeFi could hedge a long position of one dollar in the four plain and gold-backed cryptocurrencies. However,

some discrepancies among different couples of NFT/DeFi-traditional/gold-backed cryptocurrencies in terms of hedge ratio values

are clearly reported. In particular, the pairs of SAND/other cryptocurrencies and AVAX/other cryptocurrencies tend to be less than

1. As far as the hedging effectiveness is concerned, portfolios including PLAY and DGX or UPUNK and DGX outperform the other

ones. This shows that greater hedge effectiveness and higher portfolio risk diminution could offer interesting benefits for investors

and portfolio managers when including DGX index as a hedging instrument for an NFT portfolio. The PMGT index can be also

considered an effective hedging instrument for SAND, AVAX, XNFT, and DPI; whereas the XAUT index is an effective hedging

instrument and successfully can diminish the NFT portfolio risk. From the foregoing, gold-backed assets seem to be the best hedging

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M. Fakhfekh et al.

assets in comparison to traditional cryptocurrencies and show more effectiveness in portfolio diversification. This finding indicates

that adding such an asset class contributes to decreasing the downside risk during crucial crisis events, such as the Covid-19 pandemic

and the Ukraine-Russia war. Even though the relationship between NFT/DeFi and other asset classes remains under-explored (Umar

et al.,2022) and despite their distinguishable features such as the non-fungibility (Corbet et al.,2023;Nadini et al.,2021), our

results confirm recent findings by Díaz et al. (2023), who report the added value of stablecoins and gold-backed cryptocurrencies to

systematically reduce the tail risk of portfolios composed by traditional cryptocurrencies. Moreover, they confirm findings reported

by Wasiuzzaman and Rahman (2021), who argue that gold-backed cryptocurrencies could serve as safe-haven investments during

crisis periods. Nevertheless, Bitcoin fails somewhat to be a useful hedging asset. They are also in line with findings found by some

researchers who have shown that the prices of NFTs could be influenced by Ethereum and Bitcoin (Ante,2023) and that there are

low spillovers among cryptocurrency and NFT markets (Dowling,2022b).

7. Conclusions

Overall, DeFi and NFTs price dynamics and their increased demand have attracted individual and institutional investors. In this

regard, the current study examines the dependence structure of such new digital assets and gold-backed cryptocurrencies with the

traditional ones. We also compute the optimal hedge ratio for different pairs and assess the portfolio hedge effectiveness. With this

aim, this study applies a multi-method approach to the returns of five NFTs, five DeFi projects, four plain cryptocurrencies, and

four gold-backed cryptocurrencies.

Overwhelmingly, the findings show different behavior displayed by various dependence structures, which greatly depends

on the currency pair under consideration. We also report that plain cryptocurrencies (particularly, Bitcoin) could not offer

portfolio diversification benefits during some periods. Nevertheless, gold-backed cryptocurrencies exhibit more effective portfolio

diversification efficiency during geopolitical and health crises. Such findings could lay the foundations for future discussion about

the issue of safe-haven features of gold-backed/traditional cryptocurrencies from a dynamic perspective during extreme events.

Our empirical findings are important for investors and traders as they shed light upon the (dis)similarities of gold-backed/plain

cryptocurrencies with respect to DeFi/NFT. They show suitable investment strategies by comparing the potential diversification

benefits of portfolios composed of gold-backed/plain cryptocurrencies, NFT, and DeFi portfolios during the outbreak of extreme

events. Our results offer DeFi and NFTs investors a better understanding of the connectedness with other asset classes during

unforeseeable and disrupting events.

Some limitations of this study correspond to the small period, given that the purpose of our paper is to assess the ability of

gold-backed cryptocurrencies and traditional cryptocurrencies vis-à-vis NFTs/DeFis. So, a future extension of our study would be

to extend the sample backward and forward to better apprehend the nature of the correlation structure between assets. Another

limitation of this study refers to the static nature of volatilities and correlation structure which leads to static optimal hedging ratios.

Therefore, an interesting extension would be to take into account the time-varying nature of volatility and correlation structures

which would allow us to analyze the dynamic behavior of the optimal hedge ratio by using the three models. This implies varying

costs for hedging risk and a demand for frequent portfolio rebalancing.

CRediT authorship contribution statement

Mohamed Fakhfekh: Data curation, Formal analysis, Methodology, Software, Visualization, Writing – original draft, Writing

– review & editing. Azza Bejaoui: Data curation, Formal analysis, Methodology, Software, Visualization, Writing – original draft,

Writing – review & editing. Aurelio F. Bariviera: Conceptualization, Supervision, Writing – original draft, Writing – review &

editing. Ahmed Jeribi: Conceptualization, Formal analysis, Methodology, Software, Supervision, Writing – original draft, Writing

– review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared

to influence the work reported in this paper.

Data availability

Data will be made available on request.

Appendix

See Tables 4–6.

North American Journal of Economics and Finance 70 (2024) 102079

M. Fakhfekh et al.

Table 4

Information criteria results of the best GARCH models’ estimations.

Asset Information Criterion GARCH FIEGARCH EGARCH TGARCH FIGARCH

BTC

Akaike 5.0229 5.0121 5.0233 5.0230 5.0135

Bayesian 5.0448 5.0376 5.0421 5.0486 5.0426

Shibata 5.0229 5.0121 5.0231 5.0230 5.0134

Hannan-Quinn 5.0311 5.0216 5.0342 5.0326 5.0243

ETH

Akaike 5.5716 5.5602 5.5762 5.5726 5.5608

Bayesian 5.5935 5.5857 5.5862 5.5981 5.5899

Shibata 5.5716 5.5602 5.5731 5.5725 5.5607

Hannan-Quinn 5.5798 5.5697 5.5749 5.5821 5.5717

BNB

Akaike 5.4668 5.4528 5.4631 5.4670 5.4669

Bayesian 5.4887 5.4783 5.4832 5.4925 5.4960

Shibata 5.4668 5.4527 5.4603 5.4670 5.4668

Hannan-Quinn 5.4750 5.4623 5.4732 5.4765 5.4778

FTT

Akaike 6.9305 6.9045 6.9193 6.9184 6.9059

Bayesian 6.9524 6.9300 6.9431 6.9439 6.9350

Shibata 6.9305 6.9045 6.9264 6.9183 6.9058

Hannan-Quinn 6.9387 6.9140 9.9235 6.9279 6.9168

PAXG

Akaike 2.4836 2.4743 2.4781 2.4829 2.4793

Bayesian 2.5055 2.4998 2.5036 2.5084 2.5085

Shibata 2.4836 2.4743 2.4781 2.4829 2.4793

Hannan-Quinn 2.4918 2.4839 2.4876 2.4924 2.4902

XAUT

Akaike 5.4890 5.4357 5.4899 5.4843 5.4366

Bayesian 5.5109 5.4632 5.5154 5.5098 5.4658

Shibata 5.4889 5.4374 5.4899 5.4842 5.4376

Hannan-Quinn 5.4971 5.4472 5.4994 5.4938 5.4475

PMGT

Akaike 6.2848 6.2730 6.2793 6.2767 6.2744

Bayesian 6.3067 6.2985 6.3048 6.3023 6.3035

Shibata 6.2848 6.2729 6.2793 6.2767 6.2743

Hannan-Quinn 6.2930 6.2825 6.2888 6.2863 6.2852

DGX

Akaike 6.2650 6.2452 6.2653 6.2585 6.2598

Bayesian 6.2869 6.2708 6.2909 6.2840 6.2890

Shibata 6.2650 6.2452 6.2653 6.2584 6.2598

Hannan-Quinn 6.2732 6.2548 6.2749 6.2680 6.2707

PLAY

Akaike 6.2543 6.2384 6.2514 6.2446 6.2396

Bayesian 6.2762 6.2639 6.2770 6.2701 6.2688

Shibata 6.2543 6.2384 6.2514 6.2446 6.2396

Hannan-Quinn 6.2625 6.2479 6.2610 6.2541 6.2505

UPUNK

Akaike 6.2497 6.2438 6.2504 6.2491 6.2451

Bayesian 6.2716 6.2693 6.2759 6.2746 6.2743

Shibata 6.2497 6.2437 6.2503 6.2491 6.2451

Hannan-Quinn 6.2579 6.2533 6.2599 6.2586 6.2560

SAND

Akaike 6.1262 6.1216 6.1272 6.1271 6.1265

Bayesian 6.1480 6.1471 6.1527 6.1526 6.1557

Shibata 6.1261 6.1215 6.1272 6.1271 6.1265

Hannan-Quinn 6.1343 6.1311 6.1367 6.1366 6.1374

NFTL

Akaike 5.9806 5.9728 5.9784 5.9809 5.9740

Bayesian 6.0025 5.9983 6.0040 6.0064 6.0032

Shibata 5.9806 5.9727 5.9784 5.9809 5.9740

Hannan-Quinn 5.9888 5.9823 5.9880 5.9904 5.9849

XNFT

Akaike 6.6156 6.6101 6.6168 6.6176 6.6113

Bayesian 6.6374 6.6356 6.6424 6.6431 6.6405

Shibata 6.6155 6.6101 6.6168 6.6176 6.6112

Hannan-Quinn 6.6237 6.6196 6.6264 6.6271 6.6222

DPI

Akaike 6.7381 6.7293 6.7357 6.7312 6.7321

Bayesian 6.7599 6.7548 6.7612 6.7567 6.7613

Shibata 6.7380 6.7292 6.7357 6.7312 6.7321

Hannan-Quinn 6.7462 6.7388 6.7453 6.7407 6.7430

LUNC

Akaike 5.0240 5.0121 5.0121 5.0128 5.0243

Bayesian 5.0495 5.0376 5.0413 5.0456 5.0498

Shibata 5.0240 5.0120 5.0121 5.0128 5.0242

Hannan-Quinn 5.0335 5.0216 5.0230 5.0251 5.0338

AVAX

Akaike 5.5726 5.5597 5.5618 5.5622 5.5723

Bayesian 5.5981 5.5852 5.5909 5.5950 5.5978

Shibata 5.5725 5.5596 5.5617 5.5621 5.5722

Hannan-Quinn 5.5821 5.5692 5.5726 5.5744 5.5818

WBTC

Akaike 5.4677 5.4657 5.4657 5.4670 5.4681

Bayesian 5.4932 5.4912 5.4949 5.4998 5.4936

Shibata 5.4677 5.4657 5.4657 5.4670 5.4680

Hannan-Quinn 5.4772 5.4752 5.4766 5.4793 5.4776

LINK

Akaike 6.9093 6.9052 6.9173 6.9066 6.9289

Bayesian 6.9348 6.9343 6.9428 6.9394 6.9544

Shibata 6.9093 6.9051 6.9173 6.9065 6.9288

Hannan-Quinn 6.9188 6.9161 6.9268 6.9188 6.9384

North American Journal of Economics and Finance 70 (2024) 102079

M. Fakhfekh et al.

Table 5

Archimax copula estimation results.

Copula Kendall’s Spearman’s Copula Kendall’s Spearman’s

Parameter Value Tau Rho Parameter Value Tau Rho

PLAY/BTC 𝜃0.1768 0.2461 0.3591 DPI/BTC 𝜃0.1975 0.5687 0.7577

𝛿0.4708 𝛿1.3959

PLAY/ETH 𝜃0.1904 0.2594 0.3777 DPI/ETH 𝜃0.2655 0.6372 0.8238

𝛿0.487 𝛿1.7209

PLAY/BNB 𝜃0.0737 0.2056 0.3021 DPI/BNB 𝜃0.0000*** 0.3321 0.4768

𝛿0.4655 𝛿0.7713

PLAY/FTT 𝜃0.0693 0.1877 0.2766 DPI/FTT 𝜃00.2912 0.4217

𝛿0.4374 𝛿0.6805

PLAY/PAXG 𝜃0.0753 0.1572 0.2676 DPI/PAXG 𝜃0.1123 0.0747 0.1116

𝛿0.3972 𝛿0.1976

PLAY/XAUT 𝜃0.0642 0.1684 0.2636 DPI/XAUT 𝜃0.1177 0.0556 0.0833

𝛿0.4001 𝛿0.0287

PLAY/PMGT 𝜃0.0597 0.1498 0.2852 DPI /PMGT 𝜃0.0353 0.0267 0.04

𝛿0.4153 𝛿0.1584

PLAY/DGX 𝜃00.0788 0.1177 DPI /DGX 𝜃0.1354 0.1679 0.2481

𝛿0.305 𝛿0.359

UPUNK/BTC 𝜃0.1623 0.1514 0.2241 LUNC/BTC 𝜃0.0367 0.3217 0.4628

𝛿0.3112 𝛿0.7194

UPUNK/ETH 𝜃0.2284 0.1868 −0.1879 LUNC/ETH 𝜃00.3574 0.5101

𝛿0.3301 𝛿0.8326

UPUNK/BNB 𝜃0.0218 0.1594 0.2359 LUNC/BNB 𝜃00.2007 0.2955

𝛿0.4219 𝛿0.5076

UPUNK/FTT 𝜃0.1322 0.1864 0.2438 LUNC/FTT 𝜃00.1537 0.2277

𝛿0.3541 𝛿0.4277

UPUNK /PAXG 𝜃0.035 0.0414 0.062 LUNC/PAXG 𝜃00.0269 0.0403

𝛿0.2022 𝛿0.2075

UPUNK/XAUT 𝜃0.1513 0.1652 0.2486 LUNC/XAUT 𝜃00.0341 0.051

𝛿0.3354 𝛿0.2233

UPUNK/PMGT 𝜃0.1494 0.176 0.2597 LUNC/PMGT 𝜃00.0293 0.0438

𝛿0.3635 𝛿0.2128

UPUNK/DGX 𝜃0.0403 0.0454 0.0679 LUNC /DGX 𝜃00.1024 0.1525

𝛿0.2057 𝛿0.3439

SAND/BTC 𝜃0.098 0.53 0.7171 AVAX/BTC 𝜃0.1645 0.5465 0.7346

𝛿1.3135 𝛿1.3225

SAND/ETH 𝜃0.0308 0.5416 0.7297 AVAX/ETH 𝜃0.3388 0.5799 0.7689

𝛿1.4348 𝛿1.3212

SAND/BNB 𝜃00.2643 0.3848 AVAX/BNB 𝜃00.289 0.4188

𝛿0.6256 𝛿0.676

SAND/FTT 𝜃00.1963 0.2891 AVAX/FTT 𝜃00.2209 0.3241

𝛿0.4997 𝛿0.5436

SAND/PAXG 𝜃0.0922 0.044 0.066 AVAX/PAXG 𝜃0.089 0.0501 0.0749

𝛿0.0267 𝛿0.1513

SAND/XAUT 𝜃0.0855 0.0409 0.0614 AVAX/XAUT 𝜃0.0904 0.0568 0.0849

𝛿0.0281 𝛿0.174

SAND/PMGT 𝜃0.0478 0.0233 0.035 AVAX/PMGT 𝜃0.096 0.0458 0.0686

𝛿0.0252*** 𝛿0.0274***

SAND/DGX 𝜃0.064 0.1564 0.2315 AVAX/DGX 𝜃0.1376 0.1901 0.2799

𝛿0.4457 𝛿0.396

NFTL/BTC 𝜃0.0976 0.2899 0.4196 WBTC/BTC 𝜃1.0819 0.9388 0.9945

𝛿0.6079 𝛿9.8921

NFTL/ETH 𝜃0.1159 0.2919 0.4223 WBTC/ETH 𝜃0.2735 0.6994 0.8762

𝛿0.5994 𝛿2.2157

NFTL/BNB 𝜃0.0414 0.2641 0.3843 WBTC/BNB 𝜃00.3243 0.4664

𝛿0.5956 𝛿0.7532

NFTL/FTT 𝜃00.1919 0.2828 WBTC/FTT 𝜃00.3218 0.4631

𝛿0.4922 𝛿0.7475

NFTL/PAXG 𝜃0.0206 0.034 0.0509 WBTC/PAXG 𝜃0.0907 0.0756 0.1129

𝛿0.2007 𝛿0.2225

NFTL/XAUT 𝜃0.0451 0.0221 0.0331 WBTC/XAUT 𝜃0.1001 0.0502 0.0752

𝛿0.0303*** 𝛿0.1227

NFTL/PMGT 𝜃0.0963 0.0535 0.0801 WBTC/PMGT 𝜃0.0622 0.056 0.0838

𝛿0.152 𝛿0.2069

NFTL/DGX 𝜃0.0000*** 0.0622 0.093 WBTC/DGX 𝜃0.2382 0.2166 −0.1344

𝛿0.2766 𝛿0.3779

XNFT/BTC 𝜃0.0261 0.1869 0.2755 LINK/BTC 𝜃0.088 0.5342 0.7216

𝛿0.4654 𝛿1.3416

XNFT/ETH 𝜃0.064 0.1904 0.2805 LINK/ETH 𝜃0.1317 0.5627 0.7516

𝛿0.4457 𝛿1.4316

XNFT/BNB 𝜃00.1517 0.2247 LINK/BNB 𝜃00.2654 0.3864

𝛿0.4243 𝛿0.6279

XNFT/FTT 𝜃00.1279 0.2137 LINK/FTT 𝜃00.2338 0.3423

𝛿0.4214 𝛿0.5412

XNFT/PAXG 𝜃00.1401 0.2351 LINK/PAXG 𝜃0.1058 0.0627 0.0938

𝛿0.4417 𝛿0.1708

XNFT/XAUT 𝜃00.1502 0.2019 LINK/XAUT 𝜃0.0857 0.0485 0.0726

𝛿0.4532 𝛿0.1509

XNFT/PMGT 𝜃00.0061 0.0091 LINK/PMGT 𝜃00.2217 0.3321

𝛿0.1435 𝛿0.5021

XNFT/DGX 𝜃00.0149 0.0225 LINK/DGX 𝜃0.0917 0.1535 0.2272

𝛿0.1765 𝛿0.364

Note: *,** and *** denote statistical significance at 10%, 5%, and 1% level.

North American Journal of Economics and Finance 70 (2024) 102079

M. Fakhfekh et al.

Table 6

Hedging strategy results estimation.

𝛽mean var corr HE 𝛽mean var corr HE

PLAY/BTC 1.2670 0.0029 0.0192 0.3770 −2.4875 DPI /BTC 1.1636 0.0004 0.0041 0.7791 −0.8824

PLAY/ETH 1.0014 0.0039 0.0194 0.3963 −2.5195 DPI/ETH 0.9465 0.0013 0.0043 0.8419 −0.9750

PLAY/BNB 1.0089 0.0060 0.0185 0.3174 −2.3669 DPI /BNB 0.6898 0.0023 0.0032 0.4984 −0.4792

PLAY/FTT 0.3187 0.0014 0.0180 0.2906 −2.2671 DPI /FTT 0.2618 0.0019 0.0030 0.4416 −0.3829

PLAY/PAXG 3.9484 0.0076 0.0183 0.2906 −2.3344 DPI /PAXG 0.7533 0.0041 0.0027 0.1171 −0.2211

PLAY/XAUT 4.3396 0.0072 0.0183 0.2906 −2.3349 DPI /XAUT 0.6044 0.0041 0.0026 0.0872 −0.2139

PLAY/PMGT 3.0370 0.0077 0.0183 0.2906 −2.3333 DPI /PMGT 0.2038 0.0042 0.0026 0.0420 −0.2070

PLAY/DGX 0.1146 0.0067 0.0171 0.1235 −2.1065 DPI /DGX 0.1150 0.0043 0.0027 0.2608 −0.2576

UPUNK/BTC 0.4128 0.0024 0.0037 0.2355 −0.4141 LUNC /BTC 2.0064 0.0292 0.1697 0.4841 −34.7269

UPUNK/ETH 0.3826 0.0028 0.0038 0.2892 −0.4469 LUNC /ETH 1.5984 0.0257 0.1742 0.5325 −35.6876

UPUNK /BNB 0.4030 0.0033 0.0037 0.2478 −0.4208 LUNC /BNB 1.0880 0.0338 0.1510 0.3102 −30.8018

UPUNK/FTT 0.2068 0.0024 0.0037 0.2730 −0.4234 LUNC /FTT 0.3419 0.0311 0.1451 0.2391 −29.5643

UPUNK/PAXG 0.4803 0.0037 0.0035 0.0650 −0.3502 LUNC /PAXG 0.8106 0.0306 0.1398 0.0422 −28.4340

UPUNK/XAUT 2.1627 0.0037 0.0038 0.2730 −0.4434 LUNC /XAUT 1.0952 0.0305 0.1399 0.0535 −28.4653

UPUNK/PMGT 1.5144 0.0040 0.0038 0.2730 −0.4428 LUNC /PMGT 0.6519 0.0308 0.1398 0.0459 −28.4431

UPUNK /DGX 0.0361 0.0037 0.0035 0.0712 −0.3491 LUNC /DGX 0.2391 0.0328 0.1425 0.1601 −29.0128

SAND/BTC 1.3849 −0.0017 0.0063 0.7397 −1.0874 AVAX /BTC 1.3634 −0.0003 0.0061 0.7568 −1.2397

SAND/ETH 1.0618 −0.0002 0.0063 0.7518 −1.0924 AVAX /ETH 1.0684 0.0007 0.0063 0.7901 −1.2864

SAND/BNB 0.6990 0.0023 0.0048 0.4033 −0.5910 AVAX /BNB 0.7277 0.0027 0.0047 0.4386 −0.7208

SAND/FTT 0.2265 0.0016 0.0045 0.3034 −0.4810 AVAX /FTT 0.2433 0.0021 0.0044 0.3401 −0.5911

SAND/PAXG 0.5534 0.0032 0.0042 0.0691 −0.3906 AVAX /PAXG 0.6100 0.0040 0.0040 0.0786 −0.4722

SAND/XAUT 0.5536 0.0032 0.0042 0.0643 −0.3897 AVAX /XAUT 0.7450 0.0040 0.0040 0.0891 −0.4748

SAND/PMGT 0.2210 0.0033 0.0042 0.0367 −0.3859 AVAX /PMGT 0.4213 0.0041 0.0040 0.0719 −0.4707

SAND/DGX 0.1336 0.0033 0.0043 0.2433 −0.4384 AVAX /DGX 0.1570 0.0042 0.0042 0.2942 −0.5480

NFTL/BTC 1.0320 0.0035 0.0091 0.4398 −1.3018 WBTC /BTC 0.9978 0.0000 0.0022 0.9954 −1.1990

NFTL/ETH 0.7848 0.0043 0.0091 0.4426 −1.2970 WBTC /ETH 0.6763 0.0013 0.0020 0.8906 −0.9682

NFTL/BNB 0.8776 0.0053 0.0089 0.4030 −1.2426 WBTC /BNB 0.4588 0.0020 0.0014 0.4877 −0.3979

NFTL/FTT 0.2796 0.0047 0.0082 0.2969 −1.0815 WBTC /FTT 0.1957 0.0015 0.0014 0.4843 −0.3521

NFTL/PAXG 0.5347 0.0068 0.0078 0.0534 −0.9573 WBTC /PAXG 0.5127 0.0032 0.0012 0.1186 −0.1631

NFTL/XAUT 0.3745 0.0068 0.0077 0.0347 −0.9541 WBTC /XAUT 0.3674 0.0032 0.0012 0.0788 −0.1543

NFTL/PMGT 0.6349 0.0069 0.0078 0.0840 −0.9653 WBTC /PMGT 0.2872 0.0033 0.0012 0.0879 −0.1559

NFTL/DGX 0.0665 0.0069 0.0078 0.0976 −0.9645 WBTC /DGX 0.0994 0.0033 0.0013 0.3337 −0.2288

XNFT/BTC 0.8164 0.0077 0.0138 0.2894 −1.2718 LINK /BTC 1.1869 −0.0007 0.0044 0.7440 −0.7879

XNFT/ETH 0.6296 0.0082 0.0138 0.2947 −1.2736 LINK /ETH 0.9271 0.0001 0.0045 0.7732 −0.8190

XNFT /BNB 0.6217 0.0090 0.0134 0.2360 −1.2161 LINK /BNB 0.6001 0.0024 0.0034 0.4050 −0.3592

XNFT/FTT 0.2291 0.0086 0.0132 0.2149 −1.1796 LINK /FTT 0.2311 0.0016 0.0032 0.3591 −0.2971

XNFT/PAXG 2.6036 0.0104 0.0134 0.2149 −1.2044 LINK /PAXG 0.6682 0.0036 0.0030 0.0984 −0.1925

XNFT/XAUT 2.8130 0.0099 0.0134 0.2149 −1.2045 LINK /XAUT 0.5586 0.0036 0.0030 0.0761 −0.1880

XNFT/PMGT 0.0873 0.0099 0.0128 0.0096 −1.1087 LINK /PMGT 1.8474 0.0040 0.0033 0.3591 −0.3304

XNFT/DGX 0.0195 0.0100 0.0128 0.0235 −1.1092 LINK /DGX 0.1108 0.0037 0.0030 0.2388 −0.2244

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A systematic approach to predicting NFT prices using time series forecasting and macroeconomic factors in digital assets

Article

Full-text available

Feb 2025

Non-fungible tokens (NFTs) have gained mainstream attention in the fintech community, but there is little research on their statistical properties. This study investigates the long-memory characteristics of NFT returns and volatility, focusing on their potential for predicting price movements. As NFTs do not conform to traditional models, understanding their unique features is crucial for comprehending complex market dynamics. This study aims to reveal the impact of macroeconomic factors on NFT prices, understand their correlation and develop predictive models using autoregression and artificial intelligence (AI) technology. This research utilized datasets from the Centers for Disease Control and Prevention (CDC), U.S. Bureau of Labor Statistics, Bureau of Economic Analysis, Christie’s, Dune, and Google Trends. Correlation and p value tests revealed strong relationships between NFT prices and variables such as weekly volume, pandemics, inflation and security. The Baseline Model using autoregression with NFT volume, security and technology factors outperformed all other models demonstrating the speculative volatility of NFTs. The Transformer Model using transformers, an architecture used by ChatGPT, Gemini and Stable Diffusion, showed high accuracy with less feature selection and preprocessing efforts. This study provides a novelty using a systematic approach for researchers to perform financial forecasting and contributes to the scarce literature on NFTs. This research offers valuable insights to investors and private agents regarding the right economic conditions for NFT investments by reducing portfolio risks and making informed decisions. To the authors’ best knowledge, this is the first study to utilize time-series transformers for forecasting NFTs based on macroeconomic factors.

Systematic Analysis of Decentralized Finance

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Jan 2025
J GLOB INF MANAG

The purpose of this article is to study analysis the Decentralized Finance (DeFi) literature. By synthesizing the themes and theorical frameworks, we aim to identify knowledge gaps and potential areas for future research in the DeFi landscape. We conduct bibliometric and content analysis on a corpus of 275 articles extracted from the Web of Science and Scopus databases. We use the Bibliometrix package in R software to apply co-citation and bibliographic coupling. We find three research clusters (a) socioeconomic (b) technology and (c) financial with their conceptual structure, interactions and transformations. Applying both co-citation and bibliographic coupling network analysis yields a dynamic view of the field tracing thematic evolution from its inception to the present day, revealing a decline in academic interest in DeFi security vulnerabilities in contrast to the growing emphasis on social media's influence on DeFi prices.

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Dec 2024

This paper investigates the dependence structure between the crypto coins and the NFTs. We have taken data of 5 years from 2017 to 2022 and used crypto currency (Bitcoin, Ethereum & BNB). Through an analysis of price formation from the prices of various cryptocurrencies, the study offers fascinating insights into the possibility of NFT price prediction. The paper identifies the nature and strength of the dependence structure between NFTs and cryptocurrencies, revealing they exhibit positive dependence. Our findings reveal a positive dependence between NFTs and major cryptocurrencies (Bitcoin, Ethereum, and BNB), though with weak correlations. This suggests that while there is some level of interconnection, the dynamics of NFT markets may not directly mirror the movements of cryptocurrencies. However, the weak dependence still opens avenues for diversification in portfolios that contain both assets. Investors who are heavily exposed to the volatility of cryptocurrencies may consider NFTs as an alternative or complementary asset, especially given the potential for price prediction models based on cryptocurrency price movements.

The graphical fascination of NFT: Insights from tree-based methods

Preprint

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Oct 2024

Yunfei Zhao

Non-Fungible Tokens (NFTs) have garnered significant attentions as an emerging digital asset class with unique properties that cannot be replicated. In this paper, this study analyzes the graphical factors affecting the pricing of NFTs represented by CryptoPunks using decision trees, random forests and XGB regression methods. This study reveals that various image attributes of CryptoPunks exhibit significant variability and exert an influence on their prices. These finding provides valuable insights into the pricing dynamics of NFTs and shed light on the key attributes that impact their value in the market.

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Shi-Feng Shao

Quantile connectivity between cryptocurrency, commodities, gold and BRICS index: what is the best investment strategy?

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Oct 2024

Motivated by the concept of an investment portfolio, BRICS is an influential combination of emerging countries that have a say in global economic issues. In this context, the present study is designed to retrieve the most optimally effective portfolio strategy fit for hedging the BRICS stock indices via Bitcoin, gold, WTI, and Gas during crisis times. For this purpose, we consider applying the novel quantile connectivity approach, initially developed by Chatziantoniou, I., Gabauer, D., & Stenfors, A., Econ. Lett., 204, 109891, to investigate the study period ranging from January 2, 2016 to July 28, 2023, marked with the prevalence of various stress occurrences, particularly, the COVID-19 outbreak, the Russian-Ukrainian war, as well as the banking crisis. Our reached results clearly turn out to reveal the persistence of an unstable relationship binding the BRICS assets, bitcoin, gold, WTI, and gas, fluctuating following extremely stressful and unexpected event occurrences. The empirical findings also highlight the predominance of divergent responses in regard to the examined assets (as shocks receivers or transmitters), depending on the war or the pandemic intensity crises. Accordingly, portfolio managers are recommended to account for shock-emitting assets as diversifier properties, and shock-receiving assets as safe haven properties, while gold, bitcoin, and BSE30 turn out to stand as major shock transmitters throughout the recent banking crisis.

Dynamic spillover effects between cryptocurrencies and China’s financial Markets: New evidence from a TVP-VAR extended joint connectedness approach

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Assessing Bitcoin, gold and gold-backed cryptocurrencies as safe havens for energy and agricultural commodities: insights from COVID-19, Russia–Ukraine conflict and SVB collapse

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May 2024

Purpose: This paper aims to investigate the safe haven feature of Bitcoin, gold and two gold-backed cryptocurrencies (DGX and PAXG) against energy and agricultural commodities (crude oil, natural gas and wheat) during the COVID-19 pandemic, the Russia–Ukraine conflict and the Silicon Valley Bank (SVB) collapse. Design/methodology/approach: The authors use the threshold GARCH (T-GARCH)-asymmetric dynamic conditional correlation (ADCC) model to evaluate the asymmetric dynamic conditional correlation between the return series and compare the diversifying, hedging and safe-haven ability of Bitcoin, gold and the two gold-backed cryptocurrencies (DGX and PAXG) against financial swings in the commodity market during the COVID-19 outbreak, the Russian–Ukrainian military conflict and SVB collapse. The authors also calculate the hedging ratios (HR) and hedging effectiveness index (HE). The authors finally use the wavelet coherence (WC) approach to check our results’ robustness and further investigate the impact of the three crises on the relationship between Bitcoin, gold gold-backed cryptocurrencies and commodities. Findings: The results show that PAXG serves as a strong hedging instrument while gold, Bitcoin and DGX act as strong diversifiers during normal times. During crises, gold outperforms Bitcoin as a diversifier and a safe haven against commodities. Gold-backed cryptocurrencies also exhibit strong performance as diversifiers and safe havens. HR results indicate that Bitcoin and DGX are more cost-effective for commodities risk mitigation than gold and PAXG. In terms of hedging effectiveness, gold and PAXG emerge as the best hedging instruments for commodities, while DGX is considered the worst one. Bitcoin shows superior hedging against oil compared to wheat and gas risks. Moreover, the results of the WC approach confirm those of the T-GARCH-ADCC results in both the short and long run. Originality/value: This paper provides a comprehensive analysis of the diversification ability of gold, Bitcoin and gold-backed cryptocurrencies during different crises (the COVID-19 pandemic, the Russia–Ukraine conflict and the SVB collapse). By taking into consideration gold-backed cryptocurrencies, the authors expand the understanding of safe havens beyond conventional assets.

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Global Finance J

Are DeFi tokens a separate asset class from conventional cryptocurrencies?

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Jan 2023
ANN OPER RES

We test for the existence of bubbles in conventional and DeFi-focused cryptocurrencies, seeking to identify key driving forces that distinguish DeFi tokens from conventional cryptocurrencies. Utilising Generalized Supremum Augmented Dickey-Fuller tests, we identify the presence of significant bubbles across multiple markets, with relatively more stable price developments in DeFi-focused cryptocurrencies. Finally, DCC-GARCH and Diebold–Yilmaz spillover analyses of return and volatilities indicate that DeFi-focused cryptocurrencies possess stronger and more stable correlations with Ethereum than Bitcoin, and that neither cryptocurrency influenced a significant DeFi bubble formation that occurred during 2020. Results suggest that the DeFi market should be viewed as a separate asset class from conventional cryptocurrencies. Our findings provide important information for investors seeking additional diversification opportunities, as well as well as policymakers and regulatory authorities separating and better understanding these growing asset classes.

Modeling tail-dependence of crypto assets with extreme value theory: Perspectives of risk management in banks

Article

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Dec 2022

Cryptocurrencies show some properties that differ from typical financial instruments. For example, dynamic volatility, larger price jumps, and other market participants and their associated characteristics can be observed (Pardalos, Kotsireas, Guo, & Knottenbelt, 2020). Especially high tail risk (Sun, Dedahanov, Shin, & Li, 2021; Corbet, Meegan, Larkin, Lucey, & Yarovaya, 2018; Borri, 2019) leads to the question of whether the methods and procedures established in risk management are suitable for measuring the resulting market risks of cryptos appropriately. Therefore, we examine the risk measurement of Bitcoin, Ethereum, and Litecoin. In addition to the classic methods of market risk measurement, historical simulation, and the variance-covariance approach, we also use the extreme value theory to measure risk. Only the extreme value theory with the peaks-over-threshold method delivers satisfactory backtesting results at a confidence level of 99.9%. In the context of our analysis, the highly volatile market phase from January 2021 was crucial. In this, extreme deflections that have never been observed before in the time series have significantly influenced backtesting. Our paper underlines that critical market phases could not be sufficiently observed from the short time series, leading to adequate backtesting results under the standard market risk measurement. At the same time, the strength of the extreme value theory comes into play here and generates a preferable risk measurement.

Enhancing Portfolio Performance with Crypto Tokens: a Correlation Network Analysis

Conference Paper

Jul 2023

A network-based strategy of price correlations for optimal cryptocurrency portfolios

Article

Sep 2023
Finance Res Lett

Enhancing Portfolio Performance with Crypto Tokens: a Correlation Network Analysis

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Jan 2023

Volatility Spillovers and Other Dynamics Between Cryptocurrencies and the Energy and Bond Markets

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Jul 2023
Q Rev Econ Finance

Disentangling the impact of economic and health crises on financial markets

Article

Mar 2023
Res Int Bus Finance

This paper explores the impact of different crises on the informational efficiency of financial assets. The study covers stock markets indices (ASX200, DAX30, EuroStoxx50, S&P500 and Nikkei), commodities (gold and oil) and volatility (VIX). The study analyzes, using a rolling window method, the long memory profile and the multifractality of the time series by means of the DFA and generalized Hurst exponents. This dynamic analysis is important as it uncovers the time-varying behavior of retuns characteristics, affecting the investment decisions and trading strategies at different moments of time. The paper extends the current literature on informational efficiency, providing evidence of the distinct impact on the long memory and on the multifractality of the time series, depending on the nature of the crisis and the market. The results could be of interest for investors as well as for academics, regarding the hedging limits of the models during calm or turbulent times.

Forecasting and backtesting systemic risk in the cryptocurrency market

Article

Mar 2023
Finance Res Lett

Systemic risks in the cryptocurrency market: Evidence from the FTX collapse

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May 2023
Finance Res Lett

Stablecoins as a tool to mitigate the downside risk of cryptocurrency portfolios

Article

Jan 2023
N Am J Econ Finance

This paper empirically assesses the ability of three putative stablecoins (two dollar-backed, Tether and USD Coin; and one gold-backed, Digix Gold) to mitigate the risk of facing severe losses (downside risk) of a traditional cryptocurrency portfolio. There are institutional features that induce cryptoinvestors to use stablecoins as diversifiers instead of withdrawing dollars or adding assets traditionally considered as safe havens, such as gold, crude oil, etc. Stablecoins, however, are not as stable as their name and collateralized peg suggest. A monthly rebalance experiment is conducted over an out-of-sample period considering higher order conditional moments when dynamically measuring the tail risk of cryptocurrency portfolios. The empirical evidence shows that the low conditional correlations of dollar-backed stablecoins with cryptocurrency portfolios make them particularly suitable as a hedge for crypto investors. It also shows that all stablecoins considered have high diversification capacities by systematically reducing portfolio tail risk.

Dependence structure between NFT, DeFi and cryptocurrencies in turbulent times: An Archimax copula approach

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