Journal of
Risk and Financial
Management
Article
Bitcoin and Portfolio Diversification: A Portfolio
Optimization Approach
Walid Bakry
1,
*
,†
, Audil Rashid
2
, Somar Al-Mohamad
2
and Nasser El-Kanj
2
Citation: Bakry, Walid, Audil Rashid,
Somar Al-Mohamad, and Nasser
El-Kanj. 2021. Bitcoin and Portfolio
Diversification: A Portfolio
Optimization Approach. Journal of
Risk and Financial Management 14: 282.
https://doi.org/10.3390/jrfm
14070282
Academic Editor: Thanasis Stengos
Received: 7 May 2021
Accepted: 17 June 2021
Published: 22 June 2021
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1
School of Business, Western Sydney University, Sydney 2751, Australia
2
College of Business Administration, American University of the Middle East, Eqaila 54200, Kuwait;
audil.rashid@aum.edu.kw (A.R.); somar.al-mohamad@aum.edu.kw (S.A.-M.);
Nasser.El-Kanj@aum.edu.kw (N.E.-K.)
* Correspondence: wbakry@westernsydney.edu.au
† Current address: Locked Bag 1797, Penrith 2751, Australia.
Abstract:
This study investigates the performance of Bitcoin as a diversifier under different con-
straining portfolio optimization frameworks. The study employs different constraining optimization
frameworks that seek to maximize risk-adjusted returns (Sharpe ratio) of the portfolio by optimizing
allocations to each asset class (asset allocation). The performance attributes are evaluated by compar-
ing the portfolios both with and without Bitcoin under frameworks ranging from equal-weighted,
risk-parity, and semi-constrained to unconstrained. This study suggests that Bitcoin, due to its exotic
nature, unwavering appeal, and unknown set of drivers, could act as a diversifier in normal market
conditions, and it might also have some borderline hedge to safe haven properties. The results further
suggest that while Bitcoin may be a potential diversifier for a risk-seeking investor, the risk-averse
investor must exercise caution by limiting their exposure to Bitcoin in their portfolios, as unnecessary
exposure may increase the probability of losses in extreme market conditions.
Keywords: Bitcoin; cryptocurrencies; portfolio optimization; portfolio diversification
JEL Classification: G11; G15; C58
1. Introduction
One of the very disruptive and significant developments post-global financial crisis
(GFC) has been the emergence of cryptocurrencies, Bitcoin in particular. Bitcoin is a decen-
tralized, peer-to-peer electronic cash system designed by Satoshi Nakamoto (a pseudonym)
in 2008 that does not rely upon a trusted third-party or any central authority but uses
cryptography for transfers, control, and management (Nakamoto 2008). The global finan-
cial crisis (GFC) during 2008–2009 was classified as a period of severe distress to most
economies across the globe, the effects of which ranged from higher inflation, growing
budget and trade deficits, currency devaluations, and dwindling currency reserves. As the
GFC unfolded, investors discovered that they were less diversified than they originally
thought they were and therefore started looking for alternative investments that might
be considered safe havens, hedges, or diversifiers. It was in this context that Bitcoin rose
to prominence; by April 2018, Bitcoin (BTC) had a total market capitalization of more
than USD 116 billion (Yi et al. 2018), which rose to almost USD 700 billion by May 2021.
1
Nakamoto (2008) argued that due to its high transaction cost and the exclusion of a sub-
stantial portion of the world population from the formal financial system, fiat money is no
longer a proper medium of exchange. Therefore, by making BTC supply predetermined,
it has the potential to serve as a proper medium of transaction that is insulated against
inflation and as a reliable store of value (driven by precautionary motives) in the long run.
Cryptocurrencies, in general, have evolved by gradually shifting from being an im-
mature market to almost reaching maturity over the last decade. W ˛atorek et al. (2021)
J. Risk Financial Manag. 2021, 14, 282. https://doi.org/10.3390/jrfm14070282 https://www.mdpi.com/journal/jrfm
J. Risk Financial Manag. 2021, 14, 282 2 of 24
attributed this development to the growth of new trading platforms and exchanges as
well as to a substantial increase in trading volumes and frequency. They also argued
that although the exchange rates for most liquid cryptocurrency pairs resembled those of
the forex markets, developments in the cryptocurrency markets were still quite distinct
from the forex markets in terms of varying liquidity, different trading platforms, and the
existence of marginal arbitrage opportunities for less-liquid cryptocurrency pairs. While
the cryptocurrency market is still evolving and has yet to attain complete maturity, it would
be amiss to say that its popularity and acceptance are not gaining momentum within the
financial mainstream. Despite a huge leap in the acceptance of Bitcoin as a medium of
exchange, it has nonetheless failed to gain momentum in retail transactions, particularly
due to its exotic nature and its anti-regulatory, anti-environment, and fraudulent ‘feel’.
Moreover, Bitcoin has also failed to establish itself as an alternative asset, as it is believed
that the Bitcoin market is far from efficient due to the huge interest of young, inexperienced
individual investors and the subsequent absence of institutional investors and lack of
enough taxation and regulatory regulations by most countries (Tan and Low 2017; Bouri
et al. 2019). Opinions about the nature and characteristics of Bitcoin vary across a wide
spectrum; while some consider it an alternative to official fiat money and a step toward
the development of digital currencies (Bouri et al. 2017b), a large number of researchers
and practitioners consider Bitcoin simply another speculative asset (Glaser et al. 2014; Baek
and Elbeck 2015; Williamson 2018). On the other hand, some researchers have likened
Bitcoin to gold, often referring to it as ‘digital gold’ (Selmi et al. 2018), while Bouri et al.
(2017a)
considered Bitcoin a positive disruption and viewed it as an alternative to official
fiat currency.
Recent developments in the global financial and economic landscape have allowed
Bitcoin to gain some ground in terms of acceptance as a medium of transaction, but mostly
as an alternative asset that provides a hedge against domestic economic troubles and im-
prudent monetary policy actions. Amid the ongoing uncertainties regarding conventional
financial systems and the economic troubles faced by many countries, Bitcoin has gained
some ground in its popularity and ‘feel’ (Bouri et al. 2017a). Dyhrberg (2016a) believed that
global uncertainties in the wake of the global financial crisis abetted in and strengthened
the positive outlook and popularity of Bitcoin. Bitcoin, as it is often compared to gold
and exhibits some safe haven properties, has also gained prominence due to a loss of
faith in the stability of the conventional financial architecture. This is evident from the
chaos created by the much-hyped and politically motivated demonetization experiment
enforced by the Indian government and the Venezuelan government, restricting transaction
limits and the movement of capital in addition to hampering informal business operations
(Bouoiyour and Selmi 2017)
. The fact that Bitcoin is neither subject to a country’s political
and economic misadventures nor depends upon a central authority that could restrict
the movement of capital has led to the emergence of the notion that Bitcoin may provide
substantial diversification, hedge, and safe haven benefits in addition to being an effective
medium of transaction.
Since its inception, Bitcoin has attracted a lot of interest from the academic community
and practitioners alike. While the existing research has largely focused on the technological
and legal aspects of Bitcoin, scholars have recently taken up investigating the financial
and economic aspects of Bitcoin as well, particularly regarding its potential in portfolio
diversification. The fundamental objective of portfolio diversification is to construct a
portfolio of uncorrelated or mildly correlated assets to maximize risk-adjusted returns on
investment. Portfolio optimization is one of the techniques used by investment profession-
als to explore the potential of different assets in maximizing the risk-adjusted returns of
the portfolio by adjusting the weight of each asset using either simulations or constrained
scenarios. A significant amount of research has already been conducted in the area of
portfolio diversification, which helps investors devise their investment strategies and poli-
cies. Lately, cryptocurrencies in general and Bitcoin in particular have aroused significant
interest among investment professionals, policymakers, and regulators alike. Although
J. Risk Financial Manag. 2021, 14, 282 3 of 24
much research has primarily focused on the legal and technological aspects of Bitcoin, the
examination of other financial, diversification, hedge, and safe haven aspects of Bitcoin
has not progressed as far. To this end, the present study explores the potential of Bitcoin in
portfolio diversification using a portfolio optimization approach as well as establishing the
alternative asset characteristics (or otherwise) of Bitcoin.
The empirical literature on the nature of linkages between gold and other assets and
subsequently, the potential of gold as a diversifier, a hedge, or a safe haven has grown
remarkably. A vast literature discussing the different diversification-to-safe haven proper-
ties of gold has been well established (Ciner 2001; Kaul and Stephen 2006; Miyazaki and
Hamori 2014; Ciner et al. 2013; Reboredo 2013; Beckmann et al. 2015). Bitcoin, likewise,
demonstrates properties similar to gold in many ways; research has suggested that due to
the unique risk–return characteristics of Bitcoin and its uncorrelated nature with other as-
sets, Bitcoin might as well serve as a safe haven against global financial stress, commodities,
and energy (Bouri et al. 2017a, 2017c, 2018) as well as a hedge against equities, currencies,
commodities, and VIX (Bouri et al. 2017b, 2017c; Chan et al. 2019; Dyhrberg 2016a; Baur
et al. 2018).
This study is one of the very few studies exploring the diversification potential of
Bitcoin using a portfolio optimization approach. Earlier studies using a portfolio optimiza-
tion approach can be classified into four categories: The first category includes studies
that focus on portfolio optimization in general, Bitcoin not being a component of such
frameworks (Ehrgott et al. 2004; Krokhmal et al. 2002; Cai et al. 2000; DeMiguel et al. 2009;
Gaivoronski and Pflug 2005); the second category of studies have either focused on the US
markets (Brière et al. 2015; Carrick 2016; Wu and Pandey 2014) or local markets (Aggarwal
et al. 2018; Gangwal 2017; Kajtazi and Moro 2017); another strand of literature has generally
addressed cryptocurrencies and digital currencies (Boiko et al. 2021; Colombo et al. 2021;
Wang and Ngene 2020; Ma et al. 2020), and the fourth category of studies have evaluated
the diversification potential of Bitcoin with limited indices, assets, or variables (Platanakis
and Urquhart 2020; Garcia-Jorcano and Benito 2020; Pal and Mitra 2019; Eisl et al. 2015).
The current study contributes to the existing literature by using a wide range of variables
with the most recent data, thus bringing in new evidence regarding the potential for Bitcoin
in portfolio diversification using a portfolio optimization approach.
2. Literature Review
The literature on cryptocurrencies has evolved rapidly as they have gained prominence
and the attention of researchers amidst the ongoing economic and financial downturn. Sig-
nificant interest is also evolving among researchers wanting to learn how the characteristics,
price development, and volatility of cryptocurrencies and Bitcoin, in particular, will evolve
through the current downturn in financial markets. Dwyer (2015) investigated the return
volatility of Bitcoin and found that, on average, it was higher than other assets such as
gold. Blau (2017) conducted a dynamic analysis of Bitcoin price fluctuations and concluded
that the unusual volatility in Bitcoin prices was due mainly to speculation. Several other
studies have also explored the price determinants of cryptocurrencies (Brauneis and Mestel
2018; Ciaian et al. 2016; Garcia et al. 2014; Kristoufek 2015; Cheah and Fry 2015). For
instance, Ciaian et al. (2016) found that Bitcoin prices were mainly attributed to the supply
and demand generated mostly by investors departing from rationality (Bouri et al. 2019).
Similarly, Kristoufek (2015) and Garcia et al. (2014) confirmed the role of increased public
attention and Google trends in the development of Bitcoin prices. Kristoufek (2015) also
argued that Bitcoin markets were weakly related to stock markets due to different underly-
ing price determinants. Another strand of literature has investigated the financial maturity
of Bitcoin including the work of W ˛atorek et al. (2021), Dyhrberg et al. (2018), Koutmos
(2018)
, and Nadarajah and Chu (2017). It is argued in these studies that the cryptocurrency
market, and Bitcoin in particular, have reached a considerable level of maturity and can be
considered an alternative investment. With regard to liquidity and investability, only a few
J. Risk Financial Manag. 2021, 14, 282 4 of 24
academics have explored cryptocurrencies’ liquidity and investability (W ˛atorek et al. 2021;
Dyhrberg et al. 2018; Karalevicius et al. 2018; Wei 2018).
Boiko et al. (2021) and Wang and Ngene (2020) argued that while the inclusion of
different cryptocurrencies in a diversified portfolio under different portfolio optimization
strategies could lead to substantial enhancements in portfolio performance, Bitcoin was
still a dominant force in the cryptocurrency portfolio. Ma et al. (2020), on the other
hand, argued that the addition of multiple cryptocurrencies could lead to better portfolio
performance; however, Ethereum offered better diversification potential than Bitcoin. From
the standpoint of volatility spillover, Burnie (2018) and Guesmi et al. (2019) found that the
inclusion of Bitcoin could enhance portfolio diversification due to the lack of noticeable
spillover effects between Bitcoin and other financial assets. Conrad et al. (2018) showed
that the realized volatility of Bitcoin was negatively correlated with other assets, and that
the riskiness in US markets was negatively related to Bitcoin volatility. They also showed
that the volatility in Bitcoin decreased during financial distress or flight-to-safety periods,
thereby demonstrating the ability of Bitcoin to offer potential in portfolio diversification.
W ˛atorek et al. (2021) found that the most liquid cryptocurrencies, e.g., BTC and ETH, were
uncorrelated to traditional financial instruments, on average, and therefore might facilitate
portfolio diversification. Ozturk (2020) suggested that Bitcoin might not provide sufficient
contributions to portfolio diversification in the short and medium term, particularly due
to the volatile nature of Bitcoin; however, due to limited connectedness between Bitcoin
and other assets in the long run (gold and crude oil), it might offer potential gains from
diversification in the long run. Platanakis and Urquhart (2020) reported that Bitcoin might
generate substantial, risk-adjusted portfolio returns in a diversified stock–bond portfolio
under various asset allocation strategies considering different levels of risk tolerance. Bouri
et al. (2020) strongly supported Bitcoin as a potential diversification asset, with its benefits
surpassing that of gold and commodities. They also reported that Bitcoin resembled gold
in its safe haven properties and was, in fact, a superior safe haven for stocks over gold
and commodities. Shahzad et al. (2019), on the other hand, showed that Bitcoin had the
highest risk-return Sharpe ratio in contrast to gold, which had a much lower Sharpe ratio.
They found that although Bitcoin and gold had similar characteristics, gold was associated
with very few extreme losses compared to Bitcoin. Their results also revealed that Bitcoin
could at best offer potential for a weak safe haven similar to gold and commodities, but
not for all markets under study. They attributed the weak safe haven nature of Bitcoin to a
difference in the underlying determinants of price evolution in the two markets as well as
the differences in the pools of investors in the two markets. Pho et al. (2021) found that
while Bitcoin might act as a potential diversifier for risk-seeking investors, gold continued
to be a superior diversifier for risk-averse investors.
Jeribi and Fakhfekh (2021)
argued
that the contribution of Bitcoin to portfolio diversification might not be as substantial as
generally argued; their results suggested that to maximize risk-adjusted return, investors
must hold a larger proportion of conventional assets in their portfolio with a very small
exposure in cryptocurrencies. Similar results were reported by Bouri et al. (2019), Kristoufek
(2015), and Bouoiyour et al. (2016). Conrad et al. (2018), on the other hand, indicated
that the behavior of Bitcoin was considerably different than gold during high volatility
periods, and thus the comparisons to gold as a safe haven were questionable to some
degree. W ˛atorek et al. (2021) found that while the cryptocurrency market showed no
cross-correlation with traditional assets until recently, this relationship shifted during the
COVID-19 crisis, thereby undermining the potential of cryptocurrencies (BTC and ETH
being the most liquid) as safe havens.
Pal and Mitra (2019) showed that Bitcoin could provide a hedge against equity markets,
gold, and commodities. They also indicated that the hedging effectiveness of Bitcoin was
highest with gold; a long position in Bitcoin provided a hedge with a short position in
gold. Garcia-Jorcano and Benito (2020) found strong evidence in support of Bitcoin in
portfolio diversification; they also reported that Bitcoin might act as a hedge against all
international stock markets in normal market conditions, although such potential was
J. Risk Financial Manag. 2021, 14, 282 5 of 24
found to be stronger for the Hong Kong and Shanghai markets. Moreover, it was also
reported that during extreme market conditions, Bitcoin might fail to hedge the risk in
stock markets, though still acting as a diversifier. On the other hand, Baur et al. (2018)
tested the hedging capabilities of Bitcoin as compared to foreign exchange markets and
stock markets throughout different periods in a dynamic framework. They concluded
that Bitcoin should be considered a speculative asset rather than a transaction medium.
Ji et al. (2018)
tested the potential influence of changes in different assets’ prices on Bitcoin
and affirmed the idiosyncratic price movements of Bitcoin. More recently, Khaki et al.
(2020)
found that the value of Bitcoin was not closely correlated with capital markets or
the forex market. The uncorrelated nature of Bitcoin with other conventional assets might
indicate a potential diversification benefit when added to a well-diversified portfolio.
Mazanec (2021) argued that Bitcoin was leading the way for altcoins such as Binance Coin,
Cardano, Litecoin, and Ethereum to either replace or somehow supplement it as a potential
asset for portfolio diversification. To sum up, the majority of research has confirmed the
lack of interaction and spillover effects among Bitcoin and different groups of financial
assets. This, in turn, raises the question as to whether an optimal mix of Bitcoin and other
assets could enhance the risk–return tradeoff of a well-diversified portfolio and if so, what
implications this might have for investors’ investment strategies.
Research using the portfolio optimization approach has also attempted to gauge the
efficacy of adding Bitcoin to different portfolio frameworks including well-diversified port-
folios. Empirical evidence on the potential benefits of adding Bitcoin to a well-diversified
set of portfolios was provided by Brière et al. (2015). They employed the mean-variance
tests of Kandel and Stambaugh (1987) and Ferson et al. (2013) to investigate the impact of
Bitcoin inclusion on the risk–return trade-offs of three dissimilar, well-diversified portfolio
frameworks. They reported that the inclusion of Bitcoin in a well-diversified portfolio, even
in a small proportion, yielded superior mean-variance tradeoffs as compared to Bitcoin-free
portfolios. Similarly, Brière et al. (2015) and Eisl et al. (2015) utilized the conditional
value-at-risk approach to the four most widely used portfolio frameworks and provided
further evidence on the role of Bitcoin in enhancing expected returns as well as the levels of
risk of proposed portfolios; however, they claimed that Bitcoin’s contribution in leveraging
expected returns overweighed the additional risk. These results were supported by Gang-
wal (2017), who analyzed the effect of adding Bitcoin to a well-diversified portfolio under
various minimum holding constraints and including various asset classes. He found that
adding Bitcoin almost always improved the portfolio’s risk-adjusted return as measured
by the Sharpe ratio, especially when unconstrained short selling was allowed. In a similar
study, Symitsi and Chalvatzis (2019) employed daily data on multiple exchange rates, gold,
oil prices, and a pool of stocks to measure Bitcoin performance in different optimized port-
folios under different constraining scenarios. Their results confirmed the role of Bitcoin in
enhancing the Sharpe ratio with no statistically significant increase in portfolios’ variances,
especially for equally weighted and global optimal minimum variance portfolio strategies.
Bitcoin has also spurred interest in its potential contribution to portfolio diversification
and risk hedging. Bouri et al. (2017a) found that Bitcoin could be considered a good hedge,
as its prices tended to move against commodities prices. Similarly, Baumöhl (2019) affirmed
the importance of Bitcoin in portfolio diversification, as it exhibited a low correlation with
a variety of asset classes. Aggarwal et al. (2018) found that Bitcoin offered superior, risk-
adjusted return performance of portfolios under naïve and long-only frameworks across
the investment horizon as compared to a constrained portfolio framework. DeMiguel
et al. (2009) reported similar results and showed that the performance of a naïve portfolio
specification was as good as other constraining scenarios or sometimes even better.
Brière et al. (2015) showed that by adding Bitcoin to an already diversified portfolio of
US assets, the Sharpe ratio (Sharpe 1963) improved. Other studies have used other risk–
return measures such as the Omega ratio (Wu and Pandey 2014), value at risk (VaR), and
conditional value at risk (CVaR) (Eisl et al. 2015; Aggarwal et al. 2018; Selmi et al. 2018) to
evaluate the effectiveness of Bitcoin in portfolio diversification through optimization. More