The Value of Bitcoin in Enhancing the Efficiency of an Investor’s Portfolio

Journal of Financial Planning: September 2014


Chen (Ken) Y. Wu, Ph.D., is an assistant professor of finance at the University of Texas at Tyler. He received a bachelor’s and a master’s degree in engineering from the University of California, Berkeley. He also holds a master’s degree and a doctorate degree in finance from Carnegie Mellon University and Arizona State University, respectively.

Vivek K. Pandey, DBA, CFA, FRM, is a professor of finance at the University of Texas at Tyler. He received a doctorate of business administration from Mississippi State University.

Executive Summary

  • During recent years, bitcoin has emerged as the best-known and most widely used digital currency. With limited supply and a lack of central authority for its creation, its proponents laud its usefulness as an alternative currency that is free from the inflationary influence of stimulative monetary policy. 
  • This study examines bitcoin’s role as a currency and its usefulness as an investment asset.
  • Results suggest that while bitcoin may be less useful as a currency, it can play an important role in enhancing the efficiency of an investor’s portfolio.

Bitcoin is a digital currency devised by a programmer or a group of programmers under the pseudonym of Satoshi Nakamoto. Nakamoto guided bitcoin’s development until 2010. This monetary asset differs from other virtual currencies used online, such as Second Life’s Linden dollars, in that it isn’t controlled by a single organization that also serves as a clearinghouse for all of its transactions, nor is it pegged to any real world currency such as the U.S. dollar.1 Unlike most virtual currencies, bitcoin can be exchanged for real-life goods and services on a limited basis.2 

Bitcoin has emerged as the most widely used digital currency, with proponents lauding its usefulness as an alternative currency. But how useful is bitcoin as a currency, and what role might bitcoin play in enhancing the efficiency of an investor’s portfolio? This paper attempts to answer these questions. But first, it’s important to understand the fundamentals of this digital currency. 

Bitcoins are created at a steady but diminishing rate until an arbitrary limit of 21 million has been reached (Grinberg 2011). To date, about 12.4 million bitcoins have been “mined” (created using the prescribed algorithm) and as of early March 2014 with an exchange rate of roughly $600, the total value of bitcoins in circulation was just over $7.2 billion.3

This limit to the creation of bitcoins is very appealing to those wary of high inflation resulting from the extremely stimulative monetary policies of major western central banks, particularly the U.S. Federal Reserve, Bank of Japan, the European Central Bank, and the Bank of England. For the same reason, bitcoin is also appealing to proponents of a return to the gold standard. These individuals see bitcoin as analogous to a naturally occurring mineral with a limited and exhaustible supply.4

The most common way to purchase bitcoins is through an account with a bitcoin exchange, such as,,, and (Roose 2013). These exchanges also post current exchange rates between one bitcoin and major currencies, including the U.S. dollar and the euro. After an account has been created, one can directly transfer money from a financial intermediary, including banks and Paypal. Once the transfer has been cleared, one can use the funds to purchase (if applicable, fractional) bitcoins from the exchange for a fee (as an example, charges 0.0006 bitcoin per sale while purchases are free) at the prevailing rate and hold the asset in the account holder’s bitcoin wallet. At this point, the bitcoins are ready to be sold back to the exchange or used for purchases.5 To speed up this process, which can take several days because of increasingly strict measures against money laundering, physical ATMs began to appear in several locations in late 2013 that allow users to buy and sell bitcoins for cash in a matter of seconds (Rick 2014).

Tax Guidance Emerges

Confusion reigns in the tax treatment of bitcoins for citizens of many countries. However, as virtual currencies become more popular, tax authorities in a handful of countries have started to provide guidance on how virtual currency transactions must be treated.

On March 25, 2014, the U.S. Internal Revenue Service issued its guidance on virtual currencies via IR-2014-36. According to the IRS, virtual currencies (including bitcoins) are treated as property for taxation purposes. As such, wages and payments to independent contractors paid in the form of bitcoins are taxable using applicable income tax rates. Gains and losses from the sale and exchange of virtual currencies are subject to capital gains rates if the virtual currency is a capital asset in a taxpayer’s portfolio. A detailed explanation regarding this guidance from the IRS is presented in IRS Notice 2014-21, also posted by the IRS on March 25, 2014. Therefore, regardless of the treatment of bitcoin transactions for tax purposes (ordinary income or capital gains), it is necessary for taxpayers to keep track of a bitcoin’s cost basis in order to compute taxable income and capital gains or losses.

Wins and Losses

In keeping with the growing fascination with bitcoin as its price skyrocketed in 2013, popular media began to report stories of individuals becoming rich with well-timed bitcoin investments and more disturbingly, instances of individuals losing large sums as a result of technical issues or plunges in bitcoin prices. One such story involved Kristoffer Koch, a Norwegian man who reportedly purchased 5,000 bitcoins with 150 Norwegian kroner (then worth about $27), which has since increased nearly 10,000 fold in value (Gibbs 2013). On the other hand, a British man named James Howells lost 7,500 bitcoins purchased for a trivial amount in 2009 when he threw away the laptop containing the private key to his bitcoin wallet (Hern 2013). The unregulated, decentralized, and anonymous nature of bitcoins means in cases like this, there is no protection for either consumers or investors. It is estimated that nearly 4 percent of all bitcoins outstanding have been permanently lost because of issues such as hard-disk failure, hacking, fraud, or outright theft (Williams 2014).

More recently, the bankruptcy of the leading bitcoin exchange, known as Mt. Gox, led to protests by angry customers who feared they’d lose the nearly 750,000 bitcoins they owned (about 6 percent of the 12.4 million bitcoins outstanding) worth about $420 million (at roughly $560 per bitcoin) as a result of a security breach (Villar, Knight, and Wolf 2014). In addition, Mt. Gox revealed it had lost 100,000 of its own bitcoins and that the theft of bitcoins has been going on for years (O’Brien 2014). The volatile price history of bitcoins can also rapidly expose investors to losses. The Winklevoss twins, who became famous because of their lawsuit against Mark Zuckerberg over the alleged theft of their idea of a social network by the founder of Facebook, were reported to have lost as much as $11 million from their investment in bitcoin in April 2013 when the asset’s price temporarily crashed by 60 percent before resuming its upward trajectory (Popper and Lattman 2013).

Supply and Demand

Bitcoin is not pegged to any “real” currency and its value is determined by supply and demand. The supply of bitcoins is limited by the amount of electricity and computer CPU time needed to mine it. There is no central clearinghouse, nor are any financial institutions such as banks involved in facilitating transactions, which are both faster and cheaper than transactions involving traditional means of payment. The bitcoin user community performs the function of maintaining the block chain, a public and distributed ledger, to keep track of transactions between anonymous accounts on a peer-to-peer network. Without such a ledger, the same bitcoin could be exchanged for cash, products, or services more than once. This is known as the double spending problem.

Members of the bitcoin community, known as “miners,” solve increasingly complicated mathematical problems that verify transactions in the block chain so bitcoins do not suffer the double spending problem (Brito and Castillo 2013). In technical terms, verifying transactions involves the generation of “blocks” for which “miners” are rewarded with bitcoins, and if the block is used to verify a transaction, miners receive additional bitcoins. Finally, the number of bitcoins generated per block is set to fall according to a rule that will result in a maximum of 21 million bitcoins in circulation by 2040, according to the European Central Bank. 

Thus, the supply of bitcoins is independent of any central bank policy. This is also the most powerful reason why many of its backers and users prefer bitcoin to fiat currencies.

Pros and Cons

The 2012 European Central Bank (ECB) report, “Virtual Currency Schemes,” offers a synopsis of the basic technical features of the bitcoin system, as well as a discussion of the monetary aspect of bitcoins. The report states that many in the bitcoin community believe bitcoin has the ability to end central banks’ monopoly on currency creation without any reference to a commodity (typically gold) and the concomitant manipulation of the money supply through the existence of a fractional reserve banking system. If true, this will avoid both inflation and business cycles that they believe are products of manipulation of the money supply. Instead, bitcoin may suffer from a deflationary spiral in which its owners postpone consumption in anticipation of falling prices of goods and services when denominated in bitcoin. However, this is a distant prospect at the moment because the number of bitcoins in circulation is far below the 21 million limit, according to the ECB report. In addition, bitcoin is not the legal tender of any country or currency union. As such, bitcoins are only linked to the supply of goods and services provided by merchants that accept bitcoins. Therefore, the possibility exists that merchants may choose to reduce the supply of goods and services denominated in bitcoin to avoid such a deflationary spiral.

The ECB report also mentions the many drawbacks of bitcoin as a currency. Bitcoin is also vulnerable to theft since bitcoin owners need a public and private key to use it. If the file that contains this information is altered or lost, say as a result of a hard disk failure, a computer virus, or hacking, the bitcoin associated with the keys is lost. This has been reported by several users, according to the report. Cyber-attacks have even targeted exchanges that serve to facilitate bitcoin transactions, causing the value of bitcoins to plunge. On another level, bitcoin has no intrinsic value and can be seen as an example of a Ponzi scheme because early users and owners can only receive fiat currency for bitcoin they own if new users enter the community and are willing to buy bitcoin using a fiat currency.

From a law enforcement perspective, the anonymity of bitcoin accounts makes it ideal for money laundering, tax evasion, and black market trading of contraband goods (Brustein 2013; Goldberg 2012).

Literature Review

To date, there has been very little academic research on the economic aspects of bitcoin. Four reasons help explain the paucity of research. One is the relative obscurity of bitcoin to those outside of the computing and cryptography community (Lee 2013). Another is that the number and value of bitcoins created so far have been quite small in relation to the size of the global economy (Velde 2013). Bitcoin is also difficult to use for the payment of goods and services in the physical world, and, as per records available from the website, in 2013 the number of daily transactions has only once exceeded 100,000.

Finally, many bitcoin enthusiasts and active members of the community that govern the mining of bitcoins and maintain the records of their transactions are extremely skeptical of central banks entrusted with the management of fiat currencies. Instead, they prefer “hard” currencies that cannot be created at will by central banks, such as currencies tied to a commodity such as gold (Grinberg 2011). Mainstream economists generally have little respect for these views and may have, by extension, ignored something favored by these groups (Lee 2013).

However, the sharp spike in bitcoin price in 2013 attracted attention from the popular press. In line with the mining of additional bitcoins and their rapidly rising value, the number of daily transactions has mushroomed to tens of thousands. Even the U.S. Treasury’s Financial Crimes Enforcement Network (FinCEN) has become interested in bitcoins because their anonymity can facilitate illegal activities. In late March 2013, FinCEN announced steps to extend monitoring of money laundering activities to include companies that deal in bitcoins. These firms must keep more detailed records of bitcoin transactions and report high volume transactions (Satter 2013).

Grinberg (2011) examined the economic aspects of bitcoin and pointed out that bitcoin has a competitive advantage in micropayments because it is divisible to eight decimal places. In addition, it is competitive in the online gaming world because it is not tied to any one particular issuer such as Facebook credits, Linden dollars, and World of Warcraft (WoW) gold, which are controlled by Facebook, Second Life, and Blizzard Entertainment, respectively. However, bitcoin is also vulnerable to the emergence of a competing virtual currency because barriers to entry and start-up costs are extremely low or a crisis of confidence caused by abuse of discretionary authority by the leaders of the bitcoin community (Grinberg 2011).6 Another threat is possible government regulation that is motivated by the desire to make it more difficult for bitcoin to be used for illegal purposes or to hold on to the monopoly of currency issuance.

Jacobs (2011) explored the issue of bitcoin’s legality and concluded that the appeal of bitcoins to consumers and commercial entities could be enhanced by providing more clarity on regulatory issues, both in the United States and the European Union. Currently, the 2009 electronic money directive of the European Union does not offer such clarity because bitcoin may qualify to be exempt from the regulation (Jacobs 2011). However, it appears that legislators are moving toward introducing regulations that would make bitcoin transactions more secure and transparent even though the use of bitcoins for economic transactions is extremely limited, especially if illegal activities are excluded. Velde (2013), in his capacity as senior economist of the Chicago Federal Reserve, concluded his discussion of bitcoins with an intriguing possible scenario that bitcoins could eventually form the basis of a new monetary system. In a throwback to the gold standard era, money will not be based on a fiat currency and central banks will have only limited flexibility in its creation. However, the quantity of money would not be affected by the geological and political uncertainties associated with physical gold.

This paper examines bitcoin’s ability to function as a currency and its nature as a financial asset. In particular, this study examines whether bitcoin has the three main attributes of a currency: (1) medium of exchange; (2) unit of account; and (3) store of value. This paper also investigates the value of bitcoin as an investable financial asset by incorporating it in portfolios that include major world currencies, U.S. stocks, U.S. bonds, U.S. real estate, commodities, and the U.S. equity volatility index. This study assesses whether the inclusion of bitcoins in such an investment portfolio enhances its efficiency.

Methodology and Data

Daily closing prices and trading volume of bitcoins was taken from, and daily exchange rate data for the euro, yen, pound, Australian dollar, and Canadian dollar were downloaded from

Gold is often considered a good hedge and a safe haven currency during times of extreme financial distress (Bauer and Lucey 2010). Hence, in addition to major world currencies, we also compared bitcoin price returns to gold price returns. We obtained daily price quotes for gold from the Bloomberg Professional database.

To assess portfolio performance of bitcoins when this asset is included in a diversified portfolio with major asset classes, we needed proxy portfolios of various asset classes. For this part of the study, we included major indexes representing each asset class. Major world currencies were represented by the Bloomberg Dollar Spot Index (BBDXY). This index evaluates the U.S. dollar against a basket of the 10 most actively traded world currencies. Stocks were represented by the S&P 500 Index (SPX). Bonds were represented by the Bloomberg USD Investment Grade Composite Bond Index (BIG). The U.S. real estate market was represented by the FTSE NAREIT total return index (FNARTR), while the commodities markets were represented by the S&P CME spot commodities index (SPGSCI). Additionally, we obtained values of the S&P 500 Volatility Index (VIX), as it has become available as a major tool to manage portfolio volatility.

For the final part of the analysis, we needed investable assets representing these asset classes in order to capture market capitalization data. Exchange traded funds (ETFs) provided the solution. We also obtained daily values and market capitalization data for the SPDR S&P 500 Index ETF (SPY), the iShares iBoxx $ Investment Grade Corporate Bond ETF (LQD), the iShares U.S. Real Estate ETF (IYR), and the Global Commodity Equity ETF (CRBQ). Daily values for these indices and ETFs were obtained from the Bloomberg Professional database.

Data Analysis

In an attempt to examine if bitcoin behaves like a currency, we examined the distributional properties of its returns along with those of other major currencies and gold. Then, to gain a preliminary insight into the investment property of bitcoin, we examined the correlation of daily returns with the returns of major currencies, stocks, bonds, real estate, commodities, and the VIX Index, which measures the implied volatility of S&P 500 Index options, often referred to as the “fear index.”

Another objective of the analysis presented here was to examine whether bitcoins can serve to enhance portfolio performance metrics. As mentioned earlier, we examined portfolios formed with indices representing currencies, stocks, bonds, real estate, commodities, and the fear index with and without the addition of bitcoins to these portfolios. Optimum portfolios were examined after a simulation of 1,000 trials in which random weights for each asset class were drawn in each trial; then the portfolio that optimized each examined measure was selected for illustration. Consistent with most investor preferences, we chose to examine long-only portfolios. At first, we examined portfolios that minimized the total variance. This objective was defined as:

Where, σp is the standard deviation of portfolio returns over the sample period. The optimization of asset weights (wpi) in each portfolio (p) was conducted subject to the constraints that the portfolio is fully invested (all asset weights sum up to 1) and that each asset weight is greater than or equal to zero (long-only portfolios). We examined two versions of the minimum variance portfolio: one minimizing total variance and another minimizing the downside semi-variance. The latter optimization procedure minimized the negative variance of long-only portfolios under the assumption that investors choose to ignore positive deviation and are only concerned about minimizing the negative deviation in portfolio returns.
We also measured portfolio efficiency with the Sharpe ratio and the Sortino ratio. These measures maximize risk- adjusted excess returns. The optimization process may be defined as:

Here, µp is the mean portfolio return over the sample period, and RFR is the average risk-free rate over the sample period. The Sharpe ratio seeks to maximize the ratio of an asset’s risk premium proportional to its total risk measured by its standard deviation. Hence, σp in the pevious expression defining the optimization process refers to the total standard deviation of the asset’s returns. On the other hand, the Sortino measure seeks to maximize the ratio of the portfolio’s excess returns (over a specified target) and its downside risk. Here, σp represents the downside risk defined as the lower partial standard deviation of returns deficient of the target. We used the risk-free rate (RFR) as the target return in the optimization process.

Next, following post-modern portfolio theory, we examined the portfolios that maximize the measured Omega ratio. The Omega ratio is based on the proportional distribution of returns above and below a specified target. Among its many advantages (see Shadwick and Keating 2002), the one that pertains most to an investor is that it minimizes the potential for extreme losses. In the portfolio optimization process using the Omega ratio, we used zero as the target to differentiate positive from negative returns. The optimization process can be defined as:

Where, F(x)dx represents the respective cumulative distribution functions. As mentioned earlier, 1,000 trials were conducted for each portfolio over the sample period in order to select the optimal portfolio weights. To assess the risk of the portfolio, we observed the optimal portfolio’s standard deviation, as well as its probability of loss. The probability of loss is simply the relative frequency with which a negative return is observed in the 1,000 trials.

The final part of the analysis used the Black-Litterman approach to examine whether bitcoins remain in an investment portfolio even after incorporating various pessimistic views regarding the performance of bitcoins.7 The Black-Litterman model allows investors to quantify forecasts (views) and apply these to portfolio construction. Data enters the Black-Litterman model from two sources: historical and forecasted views. Historical returns and co-variances were used to produce baseline forecasts that were supplemented with quantified views. A vector of revised expectations, conditioned on these views, was then entered into the model to produce optimum portfolio weights. To begin with, one must start with a neutral portfolio. Black and Litterman (1992) suggested starting with the equilibrium market capitalization weighted portfolio. We used ETFs rather than indices for this part of the analysis. Also, lacking a suitable ETF to represent the value of the U.S. dollar with regard to other major currencies, we did not include currencies as an asset class in this part of the analysis. Starting with the neutral market capitalization weighted portfolio, we employed the Black-Litterman approach to tilt the portfolios reflecting various pessimistic views regarding bitcoin returns over the next period. We focused on these pessimistic views regarding bitcoins because we were interested in observing whether bitcoins are still a consequential part of an optimal portfolio after model expectations have been revised to incorporate these pessimistic outcomes.


The limited number of daily bitcoin transactions, although growing rapidly, suggests that this asset fails in serving as a medium of exchange capable of being traded for a wide variety of goods and services. Nor are bitcoins used much as a unit of account. In fact, even merchants that accept bitcoins still price their goods and services in sovereign fiat currencies, such as the U.S. dollar. Bitcoin’s high price volatility also suggests it is a poor store of value and is quite risky. So, bitcoin does not have the key attributes of a currency and instead should be regarded as a very illiquid financial asset.

It’s possible to see in Table 1 that in the sample period examined (July 2010 through December 2013), bitcoin returns were uniquely large in magnitude, garnering over 1 percent average daily returns. All other examined currencies, as well as gold, provided U.S. dollar denominated returns of a much smaller magnitude. The Japanese yen is unique in its negative average daily return, attributable to the weakness of the Japanese currency relative to the U.S. dollar during the sample period. The large daily returns for bitcoin were also accompanied by larger risk, as evidenced by its standard deviation, which was the highest of all currencies examined, as well as that of gold. While bitcoin returns do not suffer from skewness, it is highly leptokurtic, indicating a fat tailed distribution. This underscores the risk inherent in bitcoins, which was not evidenced in most of the examined currencies, except for the Swiss franc. Gold returns also demonstrate high kurtosis. However, given that gold returns have a much smaller standard deviation, bitcoin was the most risky currency (or pseudo currency) examined. 

The correlation of daily returns between bitcoins and other assets are shown in Tables 2A and 2B. From Table 2A, it is worth noting that daily bitcoin returns have very low or insignificant correlations with other world currencies. Correlations among the other currencies examined were quite large and statistically significant. Returns from the Japanese yen had the lowest correlation with other currencies, but these correlations were still larger than those of bitcoins and all were statistically significant. As shown in Table 2B, bitcoin returns also had a very low correlation with gold returns. These results reinforce the conclusion that bitcoin does not behave much like a currency.

Table 2B also demonstrates that bitcoin had low or insignificant correlations with major investable asset classes, such as stocks, bonds, real estate, commodities, and the fear index. It is remarkable that almost all of the daily returns of major currencies and various asset classes in Tables 2A and 2B had a negligible impact on the daily returns of bitcoins. This indicates that bitcoins could serve as a potent diversifier for an investment portfolio. 

Table 3A shows the metrics of optimal portfolios formed with major asset classes, excluding bitcoins. Table 3B shows optimal portfolios formed with the inclusion of bitcoins. To minimize daily noise, we examined weekly portfolio returns over the sample period (July 2010 to December 2013). One thing that is startling to note is that the remarkable run-up of bitcoin values in the short sample period caused the optimal portfolios (those with maximum Sharpe and Sortino ratios) in Table 3B to be comprised entirely of bitcoins. Table 3A demonstrates a similar trend with stocks when portfolios were formed without bitcoins. Together, optimization of the Sharpe and Sortino ratios are heavily influenced by high returns. However, these portfolios come with considerably higher risk, as measured by portfolio standard deviation, when compared to optimal portfolios that minimize risk and/or maximize the Omega ratio. Both Tables 3A and 3B demonstrate that the probability of loss is minimal with portfolios that maximize Omega.

Comparing Tables 3A and 3B also demonstrates that portfolio returns are higher, and the risk (probability) of incurring a loss is much lower, when bitcoins are added to an investment portfolio with every portfolio optimization measure examined. Hence, the analysis demonstrates that adding bitcoins to an investor’s portfolio does enhance efficiency.

Figure 1 provides a visual depiction of portfolios that maximize the Omega ratio on a quarterly basis. For this analysis, we used daily returns in order to obtain enough observations during each quarter. The short sample period yielded 14 quarters of results (third quarter 2010 until fourth quarter 2013). As illustrated, bitcoin was an integral part of an optimal (Omega maximizing) portfolio in virtually every quarter with just a couple of exceptions. This observation further underscores the importance of bitcoins in enhancing an investment portfolio’s efficiency metrics.

Finally, we employed the Black-Litterman approach to incorporate some pessimistic views regarding bitcoins in an investment portfolio.8 Table 4 displays the optimum portfolios formed by employing the Black-Litterman approach. As suggested by Black and Litterman (1992), the neutral portfolio has a market capitalization weighted portfolio comprising bitcoins, stocks, bonds, real estate, and commodities. Given the relative market capitalization, bitcoins account for less than 3 percent of the neutral portfolio. When pessimistic views were incorporated in absolute terms—based on the assumption that one expects bitcoins to lose 50 percent of their value over the next period—the composition of bitcoins in the optimal portfolio dropped by nearly 60 percent (down to 1.71 percent from the original 2.83 percent). However, bitcoins remained in the optimal portfolio even with the revised expectation. The remaining columns in Table 4 display optimal portfolios under pessimistic views regarding bitcoins, but in relative terms. The remaining columns of Table 4 show optimal portfolios under the views that bitcoins will underperform stocks by 50 percent, bonds by 50 percent, real estate by 50 percent, and commodities by 50 percent, respectively. Once again, the Black-Litterman algorithm continued to provide positive allocations to bitcoins in the optimal portfolio. Results presented in Table 4 demonstrate that bitcoins have the potential to enhance portfolio performance even under pessimistic views.


In conclusion, the analysis reveals that, as a currency, bitcoins are in their infancy. Currently, limited acceptability makes bitcoins a poor medium of exchange, while high volatility makes this asset a poor store of value. This could change over time. However, even now, bitcoins do provide the potential to enhance the performance of an investor’s portfolio. Therefore, it can be useful to hold bitcoins as a component within a diversified investment portfolio.

Trading and investing in a virtual currency, such as bitcoins, is readily accessible to individual investors. Uncertainty regarding taxation of bitcoin transactions has been ameliorated with new IRS tax guidance (IR-2014-36). Additionally, competing exchanges have brought down the costs of trading bitcoins to a minimal level.

Given these observations, and the conclusions from the empirical analysis, individual investors can benefit from holding a small amount of bitcoins in a diversified portfolio.

Financial planners can open bitcoin trading accounts (or digital wallets) for their clients at a number of digital currency exchanges, such as,,, and offers only a bitcoin digital wallet while the others facilitate trading in multiple virtual currencies. While recommending virtual currencies as an investment asset, it is important to underscore the risk involved with investing in these assets. Bitcoins should only be held as a minor component of a well-diversified portfolio, such as in a market-weighted basket of major asset classes.


  1.  See the following from The Economist: “Bits and Bob,” posted June 13, 2011 ( and “The Bursting of the Bitcoin Bubble,” posted October 21, 2011 (
  2. See from The Economist: “Monetarists Anonymous,” posted September 27, 2012 (
  3. Source:, a website for the bitcoin community devoted to statistics and charts relating to bitcoin.
  4. See from The Economist: “Bits and Bob,” posted June 13, 2011 (
  5. For more information, see a primer (Brito and Castillo 2013) on bitcoin that is non-technical and well-suited to bitcoin novices.
  6. An example of the latter is the March 2013 decision to support blocks generated by version 0.7 of bitcoin software when blocks generated by version 0.8 did not get reciprocal treatment by users running version 0.7 resulting in “losses” to those who generated the version 0.8 blocks (Lee 2013). This immediately sent the price of bitcoin sharply lower.
  7. Details regarding the methodology and algorithms to implement the approach are available at
  8. Black and Litterman (1992) suggested a simplistic approach to incorporating currencies in a global portfolio. Their approach relates a currency’s capitalization to the equity and bond market capitalization of the representative country. However, the portfolio we examined was not global and the asset class currencies, as in the earlier analysis, were represented by an index that weights the U.S. dollar against 10 other major currencies. Therefore, currencies were left out of the analysis.


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