Bitcoin: The biggest financial innovation of fourth industrial revolution and a portfolio's efficiency booster

Since an extended period of time, innovations have largely been discussed for the ef f ects that they have on the economic growth and social change in a country (Schumpeter, 1934). There is no doubt that innovations bring with them, the potential for societal good and wel-fare. But at the same time, they also pose new risks and uncertainties.
During the last decade, there had been an explosion of f i nancial in-novations that were driven by the fourth industrial revolution (4IR), and whichsubsequently led towards the growing use of technology, introduction and implementation of machine learning and the in-creasing reliance on artif i cial intelligence in f i nancial markets. These innovations also serve the needs of society by making f i nancial products and investments accessible to each cadre, who is yearning to earn higher rate of returns (Pereira de Silva et al., 2019; Su et al., 2020a).

One such technologically engineered f i nancial product is the phenom-enon of cryptocurrency, which has received the attention of investors, f i nancial institutions, policy makers, regulators, media and the society alike. Moreover, the introduction of this particular technological innovation has also led to the intense scrutiny and criticism of the benef i ts and risks that cryptocurrencies have to of f er, for dynamic economic growth, f i nancial system's stability and the welfare of overall society (Ahluwalia et al., 2020; Qin et al., 2020). On one hand, cryp-tocurrencies hailed by many, as the biggest f i nancial innovation of the century, while on the other hand, they have been criticized by several as nothing but a libertarian exuberance.

By the end of February 2020, a total of 5300 cryptocurrencies were being traded in the f i nancial markets, with around US$250 billion worth of market capitalization value. The total market capitalization, excluding Bitcoin, was around US$90 billion, while Bitcoin alone held the largest market share at 64 percent, with a staggering total market capitalization of around US$140 billion.1With the support that was extended from big corporations like Starbucks, Microsoft, Dell and Quinn Emanuel in US; and also from countries like Japan and South Koreas, Bitcoin is also recognized as a legitimate legal mode of payment (Cooper et al., 2017) and (Young, 2017). Moreover, Bitcoin also joined the league of the legitimate asset classes in December 2017, when BitcoinbasedfuturescontractswerelaunchedintheChicago

Mercantile Exchange (CME) and the Chicago's Board Options Exchange (CBOE). Moreover, the CME received a regulatory approval, and laun-ched its new, Bitcoin futures Option in January 2020 as well. This pace of development of Bitcoin has resulted in new prospects opening up, which will grant an opportunity to examine the various unmapped aspects and potential of Bitcoin. Tapping into this potential may range from identifying the true nature of the role of this technological in-novation, in af f ecting the f i nancial markets, and hence, consequently the chances of maximizing the wealth in a society.
The initial studies conducted on cryptocurrencies were based on the assumption that cryptocurrencies were the new emerging currencies.

(Gervais et al., 2014) asserted that some researchers perceive Bitcoin as an illustrative of a real decentralized currency. In this regard, Karl Whelan claimed that Bitcoin indeed, has some similarities with the dollar, as both the dollar and bitcoin possess none, or a restricted in-trinsic value, and are utilized mainly as a medium of exchange (Su et al., 2020b; Whelan, 2013). However, (Yermack, 2015) pro-claimed that Bitcoin was unsuccessful in performing most of the basic roles that all the currencies around the globe innately undertake. There is a perception that the cryptocurrencies are justly supranational, de-volved and digital. They also have few features that are similar to gold, as asserted by (Bouri et al., 2018). The authors deduced that there exists a statistically signif i cant link between Bitcoin price and the gold prices, and both Bitcoin and the gold markets have some common character-istics; however, this link dif f ers between the short and long run.
The f i ndings of (Dyhrberg, 2016) uncovered that Bitcoin is decen-tralized, and has a limited market size. But, this does not imply that Bitcoin is less useful than other f i nancial assets that are available in the market. Moreover, Bitcoin binds some of the advantages of both the currencies and the commodities that are available in the market; and thus, the risk-averse investors can use them in instances when any ca-lamity or unfortunate f i nancial trouble befalls them. In addition to this, (Glaser et al., 2014) also postulated earlier, that the investors’ demands for a substitute investment vehicle, make the cryptocurrencies a unique class of assets. It was also ref l ected in the f i ndings of (Burniske and White, 2017), that many investment organizations are publicizing cryptocurrencies as a unique investment product. However, in this re-gard, (Baur et al., 2018) asserted that Bitcoin, and traditional asset classes are uncorrelated and are mainly utilized as a speculative tool.

While, (Islam et al., 2019) questioned the open, decentralized nature and ideology underlying Bitcoin.
It is also noteworthy that (White et al., 2020) conducted a com-prehensive research, in which they examined whether cryptocurrencies are actual currencies, or an asset-class. They also investigated whether cryptocurrencies are technology-based products, or f i nancial securities.
According to them, the behavior of Bitcoin resembles an asset-class, and a technology-based product, rather than a security or a currency. Bit-coin acts like a dicey evolving asset class, which has high determined associations that are utilized to derivative indices, and also an inverse association with the major currencies of the world. They further ob-served that there is a substantial improvement in the prof i le of return-for-risk once Bitcoin is taken into consideration, and proposed that bitcoin is a potential portfolio investment instrument.
In this study, we build upon the f i ndings of (White et al., 2020), and take bitcoin as an asset class. From thereon, we have then gone a step further, by constructing an optimal portfolio of traditional f i nancial assets with Bitcoin, in order to assess if an improvement is observed in the ef f i cient frontier, and the subsequent risk-return prof i le for the US investors.
In the recent years, only a few studies have made the ef f ort to assess the potential benef i ts of cryptocurrencies for investors, and the society.

In this regard, the role of the cryptocurrencies in terms of their cap-ability to hedge, diversify, and present themselves as a safe haven amidst uncertainties in f i nancial markets, has been analyzed. For in-stance, (Liu and Tsyvinski, 2019) concluded that the risk-return trade of f of dif f erent cryptocurrencies is dif f erent from that of stocks, metals, and currencies. Additionally, (Corbet et al., 2018) examined the dy-namic association between the cryptocurrencies and other f i nancial securities.w The f i ndings revealed that cryptocurrencies are a new class of investment, and they provide the benef i ts of diversif i cation for in-vestors. Similarly, (Phillip et al., 2018) studied 224 cryptocurrencies, and concluded that cryptocurrencies have various unique character-istics which include the leverage ef f ects, as well as the Student-t-error distributions. In their research, (Gil-Alana et al., 2020) investigated six of the foremost cryptocurrencies, and their associations with the stock market indices by utilizing the cointegration method. They concluded that the market of cryptocurrency of f ers diversif i cation option to the investors, due to the low level of association with the traditional asset class. In this regard, cryptocurrencies can be viewed as an independent f i nancial asset, and they serve as an attractive tool for the investors, as they constitute a little or no systematic risk. The f i ndings also revealed that there exist no linkages between the cryptocurrencies and the stock market indices, which suggests that the cryptocurrencies are dis-tinguished from the conventional f i nancial securities.
Although, these studies have reported the diversif i cation benef i ts of the cryptocurrencies, however, the characteristics of the optimal port-folio was not the focal point in these studies. In fact, there is actually a scarcity of literature, especially when it comes to constructing an ef f i -cient frontier for a sophisticated investor. In a recent systemic review of the empirical literature on cryptocurrencies by (Corbet et al., 2019), it highlighted that there were several gaps in the literature, and one such gap pertained to evaluating the benef i ts of the cryptocurrencies as an asset class, and part of a diversif i ed portfolio. In our study, we have aimed to f i ll the gap in the literature, and construct an ef f i cient frontier of a portfolio. We have also tried to keep the focus on portfolio opti-mization with Bitcoin as part of the portfolio of traditional asset classes for a US based investor. Furthermore, we have shown how Bitcoin contributes to an ef f i cient portfolio, by emphasizing on the evolving dynamics of the return-risk characteristics.
There exist a few studies, like those of (Wu and Pandey, 2014) and (Andrianto and Diputra, 2017), which documented the usefulness of Bitcoin, in enhancing the ef f i ciency of an investment portfolio. More-over, (Brière et al., 2015) also included Bitcoin within a diversif i ed portfolio of traditional and alternative assets. They concluded that Bitcoin had high diversif i cation benef i ts, as it had a low correlation with the other assets, and exhibited an exceptionally high average re-turn, as well as volatility, which added to these high returns. Likewise, (Eisl et al., 2015) propagated that adding a small portion of Bitcoin, in a well-diversif i ed portfolio, can improve the risk-return tradeof fsig-nif i cantly. However, all these studies suf f ered with the problem of limited sample periods, and were primarily focused on the initial years of the cryptocurrencies, and thus could not ref l ect the true performance of the portfolio in the long and the medium run.
There are, however, a few recent studies which have come closer to looking at the cryptocurrencies, and their ability to enhance the ef f i -ciency of the investment portfolio . For example, (Elendner et al., 2018) provided evidence of a limited, co-movement of the cryptocurrencies, with the traditional assets, and in turn the diversif i cation benef i ts. This task was undertaken by constructing the equally weighted and value-weighted broad portfolios that were made up of cryptocurrencies and the traditional assets. However, their study did not take into con-sideration the optimal portfolio construction. Similarly, (Brauneis and Mestel, 2019) developed a portfolio, which only consisted of the cryptocurrencies, and presented the evidence of the substantial reduc-tion in the risk factor. In another study, (Inci and Lagasse, 2019) ex-amined four major cryptocurrencies, and included each one of them in a portfolio of traditional asset classes; i.e., equity, bond, real estate and volatility. They also reported that the cryptocurrencies have a useful role in the optimal portfolio construction.

In our study, however, we set our focus on Bitcoin, as opposed to multiple cryptocurrencies. That is to say that, out of 5300 crypto currencies in circulation, Bitcoin is the oldest digital currency that was
created in the year 2008, and has been in trading since 2010. Bitcoin has been providing the opportunity to access the data set which has been spanning over almost a decade. Therefore, Bitcoin still holds the position of the market leader, with a market capitalization of around 160 billion US dollars, and a market share of around 64%. There hasn't been any other cryptocurrency which has been able to maintain a consistent market share of this magnitude, over the years. Moreover, it is only Bitcoin that has received the legitimacy of the derivative market, and entails the futures, and the options on the futures, that are based on it. Other than this, We include Bitcoin in a portfolio based on a range of asset classes that consist of equity, bonds and commodities; and con-struct ef f i cient frontiers, for a US based sophisticated investor. Though def i ned dif f erently by dif f erent countries and regulators, but broadly speaking, a sophisticated investor is an individual who has en-ough capital, experience, and net worth, so as to engage in more ad-vanced types of investment opportunities, and also the knowledge to evaluate their risks and merits.
In this regard, we employ the traditional mean-variance framework, as proposed by (Markowitz, 1952). Although, the alternatives to the mean-variance optimization have been proposed in the literature when returns are not normal; However, many seminal papers, such as (Levy and Markowitz, 1979) and (Kroll et al., 1984) demonstrate the equivalence of the mean-variance approach, with the expected utility maximization, under this non-normality. Moreover, our data also con-f i rms the normality trend in the returns of all asset classes, including Bitcoin. Other than this, we construct the ef f i cient frontiers, by con-sidering the risk-return trade-of f , for the portfolios that were com-prising of Bitcoin and the three asset classes. Two of these ef f i cient frontiers are based on no Bitcoin in the portfolios, while the two fron-tiers have been constructed with Bitcoin. We also develop frontiers with both long only and short selling strategies. The performance of each portfolio is evaluated by using the Sharpe ratio. Moreover, we show that out of all ef f i cient portfolios on the frontiers, there are still some portfolios with better reward to risk ratio, and so are the optimal ones.
Our results show that the inclusion of Bitcoin suggests a reasonable improvement in the Sharpe Ratios, and when added with the other asset classes, shifts the ef f i cient frontiers upward; providing a reasonable justif i cation of including Bitcoin in the investment universe of sophis-ticated investors. The optimal portfolio with the highest Sharpe ratio has a Bitcoin weight of 6.4% and 6.1%, without and with the short selling, respectively. Moreover, as we keep increasing our target risk and returns, our optimization procedure that is based on Mean-Variance framework suggests that there should be a continuous increase of weight in Bitcoin and thus the investors can be more f l exible in taking on positions that are tailored to their preferred level of risk and return.
The remainder of the paper is organized as follows. Section 2 ex-plains the data set, and shows some trends in the data. Followed by Section 3, which lays out the methodology of the paper. Then, Section 4 provides the descriptive statistics, and the risk-return characteristics of the asset classes. It also presents the results of ef f i cient portfolios and the frontiers, which further extends on to discuss the f i ndings. Lastly, Section 5 presents the conclusions.

1. Data For the purpose of this study, we use the daily price data of Bitcoin from Bloomberg, for the time period ranging from July 2010 to March 2020 and include Bitcoin in the portfolio of three asset classes: equity, f i xed income and commodities. It must also be noted, that we use Bitcoin only to represent cryptocurrencies as well as the technologically advanced f i nancial securities and investment classes. This is primarily because it is the oldest, and the most sophisticated cryptocurrency, providing the largest possible dataset. Moreover, it holds 64% of the global market share, along with the futures, and the options on the futures that are available on them. Additionally, we proxy the three asset classes by the indices that provide a broader coverage. Equity is proxied by the S & P 500 Index, Fixed Income by the S&P 500 Index Investment Grade Corporate Bond Index whereas the commodities are represented by the Thomson Reuters/Core Commodity CRB Index. The data on the three asset classes, and the risk-free rate, that have been proxied by the US 3-Months Treasury Bill Yield, has also been fetched from Bloomberg. Once we have the price data of all the assets, we calculate the continuously compounded daily returns of each asset class, by using: =r log( ) it p p it it1 ; where, ritis the return of the asset i at time t; pitis the closing price of the asset i at time t; andpit 1 is the closing price of the asset i at timet 1.
   Fig. 1 shows an interesting trend in the prices of the four asset classes. The price indices of commodities and f i xed income are reported on the primary axis, while equity and bitcoin prices have been reported on the secondary axis. The trends show that f i xed income and the equity prices have been steadily increasing, while there has been a consider-able amount of volatility in the prices of the commodities index and Bitcoin.
2. Methodology When taking into consideration the methodology, we use the tra-ditional mean-variance framework, proposed by (Markowitz, 1952), to evaluate how Bitcoin contributes to an ef f i cient portfolio, by empha-sizing on the evolving dynamics of the return-risk characteristics. Al-though, the alternatives to the mean-variance optimization have been proposed in the extant literature, when the returns are not normal;
   however,manyseminalpapers,suchasthoseof(Levyand Markowitz, 1979) and (Kroll et al., 1984) demonstrate the equivalence of the mean-variance approach with the expected utility maximization, under non-normality. Moreover, our data conf i rms the normality trend in the returns of all asset classes, including Bitcoin.
   We construct ef f i cient frontiers, by considering the risk-return trade-of f for the portfolios that are comprising of Bitcoin, and the three asset classes. In the context of Markowitz's framework, a portfolio is called ef f i cient’, if it of f ers the maximum return for a given level of risk, or of f ers the minimum risk, for a certain level of return; and an ef f i cient frontier consists of the set of ef f i cient portfolios. Specif i cally, we follow the Markowitz mean-variance theory, with the objective to maximize returns while minimizing the risk; which can be achieved with a single objective function, using the following Quadratic Program:

It must be noted that for λ > 0, the term λμTw pushes the μTw up-ward, in order to counterbalance the downward pull of the term w w T 1 2 . The upward push on μTw inreases as the λ increases.
Considering that end, we develop four ef f i cient frontiers. In Case 1, we perform the optimization as explained above, and construct the ef f i cient frontier without including Bitcoin in the portfolios of assets.
Moreover, in this case, we impose the long-only strategy, subject to =w wi e w for all i e0 ( . . , 0 ) and 1 i T ; and in this case, the short-selling is not allowed. In Case 2, we again construct an ef f i cient frontier without including Bitcoin in the set of portfolios. However, this time, we do not impose the long-only strategy which is subject to w ≥ 0;
rather we allow the short-selling which is typically subject to w ≥ 0;
only, and is interpreted as a situation where the investors can only borrow equal to the amount and the weight of their total investment. In the latter two cases, we construct ef f i cient frontiers and include Bitcoin as part of a portfolio, and assess how the ef f i ciency has improved or deteriorated with the insertion of Bitcoin. In Case 3, we perform the optimization and construct the ef f i cient frontier, including Bitcoin in the portfolios of assets. Moreover, in this case, we also impose the long-only strategy subject to =w wand e0 1 T , and short-selling is not allowed. In Case 4, we again construct an ef f i cient frontier, by including Bitcoin in the set of portfolios, but this time, we do not impose the long-only strategy, and allow the short-selling subject to =we 1 T , only. We also calculate the Sharpe ratio, which is a risk adjusted performance measure that is used to evaluate the performance of the set of portfolios that we def i ne. The Sharpe ratio also represents the excess reward per unit of the risk, with the risk measured as the standard deviation of the asset returns.

1. Results A descriptive performance analysis of Bitcoin with the other asset classes is provided inTable 2. Based on continuously compounded daily returns, Bitcoin shows that, it is indeed the riskiest asset class with a daily standard deviation of 6.54%, yet most rewarding as well, with an average daily return of 0.466%. However, in terms of the skewness and the fat tail risks associated, we don't f i nd Bitcoin any more risky as compared to the other asset classes. In fact, the f i xed income emerges as the riskiest asset class in terms of the skewness risk, and the equity in terms of the fat-tail (kurtosis) risk. Moreover, we don't f i nd the evidence for the non-normality of returns in any of the asset classes.
   One of the attractive characteristics of Bitcoin, as an investment is that it shows a low correlation with the other asset classes, and provides a high level of diversif i cation benef i ts. More importantly, we f i nd that all the pairwise correlations among these asset classes, fall within the range of −0.18 to 0.43, as shown in Table 3. This suggests a high magnitude of the diversif i cation ef f ects, in a risk-return framework.
   Thus, these results are consistent with the earlier studies, which report the high diversif i cation potential of Bitcoin in a portfolio of asset classes (Corbet et al., 2018), (Liu and Tsyvinski, 2019), (Gil-Alana et al., 2020).
   Based on the characteristics presented above, we also construct a simple risk return prof i le as illustrated in Fig. 2, in order to help in understanding the relative position of various risky asset classes. It is not surprising to see that Bitcoin proposes a high risk, high return combination; while Fixed Income, on the other side, with a blend of low risk, and low returns.
   4.1. Ef f i cient portfolios and frontiers under mean-variance framework In what must follow, we present the results of the ef f i cient frontiers constructed, by considering the risk-return trade-of f for the portfolios comprising of Bitcoin and the three asset classes.

Case 1. Optimization without Bitcoin – No Short Selling Allowed In this round of optimization, we construct 10 risky portfolios, from A to J, with a constraint imposed on the short selling thus restricting the weights allocated to each asset class to be Non-Negative.
The graphical representation of the weights clearly shows that as we move from portfolio A towards portfolio B, with a steady increase in the target risk, the returns spike up initially at a much faster rate. This increase in the returns causes the Sharpe ratio to go up quickly as well, as measured on the secondary axes in Fig. 3. However, any further increase in the target risk would not increase returns at the same rate, and the Sharpe ratio declines gradually. This happens despite the fact that all the portfolios from A to J are ef f i cient portfolios, with the highest possible Sharpe ratio with a given target risk. Another critical point of consideration is that the optimization procedures suggest in-clusion of commodities, only in portfolio A (minimum variance port-folio). This is primarily due to its negative correlation with the Fixed Income, which is the most prominent asset class in almost all the portfolios that are being taken into consideration. However, as we keep increasing our target risk and return, the optimization procedure sug-gests that there should be a continuous increase of the weight in Equity, and a decrease in the weight of Fixed Income, with zero allocation towards the commodities.
Case 2. Optimization without Bitcoin –Short Selling Allowed On the other hand, as indicated by Fig. 4, if we allow for Short selling, the results of the optimization procedure suggest that the weights for commodities should be negative, while the increased ex-posure is taken in both the Equity and the Fixed Income, as we move from portfolio (A) to portfolio (J).
Table 5 shows that portfolio (A) has a 6.4% allocation in com-modities, a 9.1% in equity, and a 84.5% in the f i xed income categories;
while portfolio (J) has a 125% allocation in the f i xed income, and a 83.9% in equity, whereas the commodities have a −109.4% allocation.

Portfolio (A) of f ers an average daily return of 0.016%, against the portfolio risk of 0.277%; whereas the risk-return combination of port-folio (J) is a 0.084% return, vs. a 1.10% risk. It must be noted that all the portfolios (A to J) are ef f i cient, as each portfolio of f ers the max-imum returns against the targeted standard deviation. However, the Sharpe ratio increases only up to the construction of portfolio C, after which it start to show a declining trend. Therefore, portfolio C is con-sidered to be an ef f i cient and optimal portfolio, with a portfolio return of 0.034%, a risk of 0.4%, and a Sharpe ratio of 0.0818.
Case 3. Optimization with Bitcoin – No Short Selling Allowed The optimization routine with Bitcoin included in our investment universe, and with the restrictions of short selling in place, would present a very interesting picture. It is clearly visible through Table 6 and Fig. 5, that as we move from a low risk (A), to a high target risk (J) portfolio, the optimization procedure suggests replacing the Equity with Bitcoin, with an almost constant allocation of around 84% in Fixed commodities. Portfolio (D) is the portfolio that provides the highest Sharpe ratio, and has a weight of 6.4% allocated to Bitcoin, and almost 9% to the Equity. The return of portfolio (D), with a 6.4% weight of Bitcoin, also provides the opportunity of greater returns of 0.048%, and a risk of 0.5%, with a Sharpe ratio of 0.09241.
Case 4. Optimization with Bitcoin –Short Selling Allowed However, as shown by Fig. 6, with the short selling allowed, the percentage allocation towards Bitcoin is lower than what it was in the absence of the short selling. Like Case 2, with no Bitcoin in the scenario, the optimization procedure suggests the negative weights be allocated, only for the Commodities. However, most of the extra exposure gen-erated through the Commodity short selling should largely be invested in Equity, with a minor additional allocation towards Fixed Income.
Most importantly, portfolio (E), which has the highest Sharpe ratio, suggest an allocation of around 6.1% in Bitcoin, 31.8% in Equity, −33.8% in Commodities, and a high allocation of almost 96% in fixed Income.
In summation, when pondering on the question whether Bitcoin improves the portfolio's ef f i ciency, our results, in Fig. 7, show that the inclusion of Bitcoin suggests a reasonable improvement in the Sharpe Ratios, when the Short Selling is restricted, as well as allowed. There-fore, this provides a reasonable justif i cation of including Bitcoin in the investment universe of sophisticated investors. Also noteworthy is the comparison that is made towards the individual asset classes, where the Equity of f ers a daily return of 0.034%, against a standard deviation of 1.065%. While the Fixed Income of f ers a daily return of 0.017%, against the standard deviation of 0.315%. Moreover, the portfolios with Bitcoin included, of f er a higher rate of return as well as the highest Sharpe ratios, as specif i cally seen with Portfolios (D) and (E).
Fig. 8 shows the four ef f i cient frontiers, constructed after estimating ef f i cient portfolios in all the four cases, where in the f i rst two cases, Bitcoin is excluded from the universe of risky assets, while in the latter two, Bitcoin is included. Interestingly, when Bitcoin is added with the other asset classes, it shifts the ef f i cient frontiers upwards and this rise is even more signif i cant when short selling is allowed. This ultimately indicates an increase in the reward to risk trade-of f , and the Sharpe ratio.

It must be noted that all these portfolios on the ef f i cient frontiers are indeed the ef f i cient ones, and the investors can choose any portfolio that is based on target risk. However, we also show that among all the ef f i cient portfolios, there are some portfolios which have outperformed the others in terms of the reward to risk ratio (Sharpe ratio) that they of f er and ref l ect. The optimal portfolios, with the highest Sharpe ratios (Portfolio (D) and Portfolio (E), in Case III and IV) have Bitcoin weights of 6.4% and 6.1%, without and with short selling respectively. These results are encouraging, as the earlier studies, which included crypto-currencies in a set of portfolios of risky assets, suggested relatively lower weights of Bitcoin. Moreover, our optimization procedure, based on Mean-Variance framework, suggests a continuous increase in the weight of Bitcoin, either with or without short selling. This is so be-cause, as we keep increasing our target risk and returns, the investors can be more f l exible in taking positions that are tailored to their pre-ferred level of risk and return.

1. Conclusion During the last decade, there has been an explosion of f i nancial innovations driven by the fourth industrial revolution (4IR). This in-dustrial revolution is characterized by the growing use of technology, the employment of machine learning algorithms and the reliance on artif i cial intelligence. These technological advancements are said to serve the demand of the society by making f i nancial producsts and investment accessible to each cadre of the society, who is yearning to earn higher rates of return (Pereira de Silva et al., 2019).
   Bitcoin is the oldest of the cryptocurrencies, and has received pro-found attention of the investors, f i nancial markets and institutions, regulators, policy makers and the media, over the years. Today, Bitcoin is recognized as a legal mode of payment (Cooper et al., 2017) and (Young, 2017). Moreover, it has also joined the league of legitimate asset classes, as of December 2017, when Bitcoin based futures con-tracts were launched in the Chicago Mercantile Exchange (CME), and the Chicago's Board of Options Exchange (CBOE).
   Earlier studies have reported the diversif i cation benef i ts of Bitcoin, however, the portfolio optimization was not the focus of most of them.

In fact, there is a scarcity of literature when it comes to constructing an ef f i cient frontier for a sophistical investor. In our study, we construct the ef f i cient frontiers of the portfolios of risky assets. Moreover, we focus on the portfolio optimization, with Bitcoin as part of the portfolio of traditional asset classes (Equity, Fixed Income and Commodities) for a US investor, who is generally known as ‘sophisticated investor’ for her possessing enough capital, experience, net worth to engage in more Fig. 2. Risk and Return Prof i le of Dif f erent Risky Asset Classes.
Note: Fig. 2 shows the risk-return prof i les of four asset classes. Mean returns are reported on the y-axis, and are shown in the form of percentage returns; and the standard deviation has been reported on the X-axis, and this is also denoted in the form of percentages. The sample period is from July 2010 to March 2020. advanced types of investment opportunities, as well as the knowledge to evaluate their risks and merits. We show how Bitcoin contributes to an ef f i cient portfolio of such investor, by emphasizing on the evolving dynamics of the return-risk characteristics.
To pursue our goal we employ the traditional mean-variance fra-mework, as proposed by (Markowitz, 1952), and our data fully supports the choice of this framework, as we don't f i nd the evidence for the non-normality of returns, in any of the asset classes (Equity, Fixed Income, Commodity and Bitcoin). In terms of the skewness and the fat tail risk, we don't f i nd Bitcoin to be as riskier as compared to the other asset classes, on average. We also f i nd that all the pairwise correlations among these asset classes fall within the range of −0.18 to 0.43, sug-gesting a considerable extent of diversif i cation ef f ects in a risk-return framework. is restricted and allowed. The optimal portfolio, with the highest Sharpe ratio has Bitcoin weight of 6.4% and 6.1%, without and with short selling, respectively. This provides a reasonable justif i cation of in-cluding Bitcoin in the investment universe of the sophisticated in-vestors. Interestingly, when Bitcoin is added with the other asset classes, it shifts the ef f i cient frontiers upward, and this shift is even bigger when the short selling is allowed. Moreover, as we keep in-creasing our target risk and return, the optimization procedure suggests that there should be a continuous increase in the weight of Bitcoin, either with or without short selling.
This study f i lls in the important gaps in the empirical literature on cryptocurrencies and the investment strategies. Out of the ten gaps identif i ed in the systemic survey by (Corbet et al., 2019), our study contributes in f i lling at least three out of those ten. First, this study uses the dataset spanning over a decade, from July 2010 to March 2020.
Second, we evaluate the benef i ts of Bitcoin separately, and do not combine the varying cryptocurrencies in our analysis. Third, we treat Bitcoin as an independent asset class, and make it part of a diversif i ed portfolio. In the future, however, this research can be expanded further, by including alternative asset classes in a portfolio, while also ex-panding the pool of individual cryptocurrencies. Moreover, it will be stimulating to observe the role of cryptocurrencies under normal, as well as turbulent time periods, separately.
When it comes to the question whether Bitcoin, as the biggest in-novation of Fourth Industrial Revolution, brings the potential for soci-etal good and welfare, this study aims to give a fair clarif i cation of the intricacies involved. It shows that Bitcoin provides an enhanced ef f i -cient frontier, and the opportunity for the f i nancial system and the society to earn higher returns than what the investors were earning before the inclusion of Bitcoin - and that too without assuming any additional risks. Moreover, our results are based on the data spanning over a decade, and during that time period, Bitcoin has experienced several ups and downs, showed its resilience and presence in the market, and maintained the position of a leader in the market for cryptocurrencies. Our f i ndings also provide a medium to long term perspective on the role of Bitcoin, which has not been the case with the earlier studies. Thus, this study provides some important implications for the investors, markets and the policy makers. On one hand, our f i ndings provide the conf i dence to the investors who can earn higher rates of return, by investing in Bitcoin; while, on the other hand, the markets and policy makers can observe that Bitcoin is as riskier as the other asset classes, such as commodities and equities. Moreover, Bitcoin has its own idiosyncratic risks; but it comes with the potential to pro-vide diversif i cation benef i ts to sophisticated investors Jing-Ping Li is a Professor and Vice Dean of School of Finance, Shanxi University of Finance and Economics, Taiyuan, China. Li's research and teaching includes International Finance, Exchange rate, Currency Derivatives and Risk Management, Corporate Finance and Budgeting, Security Valuation and Investments as well as investment portfolio, risk management. He has 10 years industry experience in f i nancial consultancy