Over the last number of years, digital currencies such as Bitcoin have become increasingly topical as investors question their potential role within a portfolio. The monograph below, produced by Dr. Jason Fink, attempts to address this question while providing additional context into Bitcoin’s history, potential value and ultimately, the type of asset category Bitcoin likely falls within.

Additionally, Charles Schwab provides a high-level FAQ guide to Bitcoin which may be of use for those interested. Link: Bitcoin FAQ_Schwab

Introduction

The purpose of this monograph is to consider what, if any, role Bitcoin may have to play in client portfolios moving forward. Bitcoin has been proposed in both financial publications and the popular press to have value for several reasons: as a speculative investment, as a store of value, and as a hedging mechanism – either directly or as a convenient asset for diversification. Here, we will first entertain a brief history of monetary regimes in the United States, and how Bitcoin functions from both a technical and economic level. From there, we will discuss the viability of Bitcoin as a currency and the implications of a Bitcoin-denominated money supply. In light of these discussions, we will examine the various proposed reasons Bitcoin may retain value in the future.

How Does Bitcoin Work?

Bitcoin is designed to work as a peer-to-peer version of electronic “cash.” The technical specifications of Bitcoin were published in a 2008 white paper by an author using the pseudonym Nakamoto.

One of the great difficulties with currencies, quite naturally, is legitimacy. A currency is only valuable if it is widely recognized and desired, and difficult to replicate. Historically, gold became the de facto currency for numerous nations because it was easily recognizable, difficult to mine, difficult to counterfeit, and ultimately available in sufficient but limited quantities¹.  It further had the ancillary benefit of making attractive jewelry (and further benefits still – it doesn’t oxidize like iron, and it isn’t radioactive like uranium).

Prior to 1973, all U.S. dollars were backed by gold². In that year, President Nixon permanently removed the U.S. tie to gold that he had temporarily severed in 1971, creating the U.S. dollar as a true “fiat currency.” The primary driver of this decision was that the U.S. was running out of gold to back all of the dollars in circulation. An efficiently functioning economy requires a money supply to grow roughly in proportion with economic production, or the price level will swing wildly and likely lead to deflation. One substantial drawback to gold is that its rate of growth is only somewhat related to economic growth. As a result, the standard deviation of U.S. dollar inflation has dropped from 6.03% in the post-WWI gold standard era of 1914 – 1972, to 3.01% in the fiat-money era since 1973. Inflation has been slightly higher under fiat money (3.9% since 1973, compared to 2.7% before), but it has been much more stable³. This stability is to a large extent the result of the U.S. Federal Reserve intervention in bond markets, modifying the amount of fiat currency available to suit economic conditions.

For decades, the field of computer science has gradually put forth the fundamental ideas of completely electronic currencies. Notable contributions to this literature include Chaum (1983) and Chaum and Brand (1997) which developed encrypted signatures for exchange and Back (2002) that developed the notion of solving complex mathematical problems as a decentralized method of authentication.

Nakamoto (2008) built on this prior work in developing what has become known as “blockchain” technology. The key breakthrough in this paper was the development of a system by which currency transactions can be verified within a decentralized network, so long as the “honest” nodes of the network are never exceeded by potentially “hostile” network nodes trying to disrupt the system. Further, the network is constructed in such a way as to incentivize participants to work within the system rather than trying to disrupt it. Payments are (more or less) immediately final, irreversible, untraceable and not reliant on a centralized authority such as a bank. In these ways, Bitcoin is intended to serve a role similar to that of gold, but with many characteristics of a fiat currency such as the U.S. dollar. Further, the convenience of electronic payment reduces many of the transactions costs of storing and transporting cash (and obviously is much improved over these same considerations for gold).

Bitcoin transactions are verified through a series of “hashes” or one-way functions that are only replicable by the “owner” of the bitcoin. The creation of these functions and their solutions is computationally expensive. Computer nodes on the peer network provide the computing power for these functions and are rewarded for doing so by the granting of new bitcoins. This is why there now exist large computer farms that exist solely for the purpose of verifying transactions – they are “mining” for new Bitcoins. The number of new Bitcoins permitted to be created is a time-dependent function, with decreasing numbers of coins provided through time. Currently about 18.8 million Bitcoins are in existence, and a maximum of 21 million Bitcoins can ever be produced. This maximum is part of the original Bitcoin software. Because the number of Bitcoins produced through time is declining, it is expected that the last Bitcoin will be minted around 2140, if the system is still in existence at that time. Bitcoin miners are actually compensated for verifying transactions with both new Bitcoins and transaction fees. The greater the demands on the system, the higher the fees. Once all coins are mined, they will only be compensated with transaction fees. Current transaction fees are around $2.30 per transaction, but they fluctuate significantly, with a peak in April 2020 over $62 ⁴.

The cap on the number of Bitcoins built into the Bitcoin system is a more extreme form of the limitation that gold has as a basis of the currency system of a modern economy – in a growing economy, Bitcoin is destined to exhibit deflation.

Bitcoin as a Currency

At first glance, the notion of Bitcoin as a speculative investment appears inextricably tied up with the longevity of Bitcoin as a major currency⁵. If Bitcoin is eventually adopted as a mainstream unit of trade or store of value, the demand for Bitcoin will be very high and will no doubt result in a substantial price. The M2 money supply of the U.S. dollar is currently about $19.9 trillion⁶. At the time of this writing (August 2021) one Bitcoin is worth approximately $45,650. With about 18.8 million bitcoins in existence, that indicates a worldwide value of bitcoins of about $858 billion⁷. Were Bitcoin to supplant the M2 money supply tomorrow, that would imply a Bitcoin value of $1.058 million per coin. It is reasonable to consider this the most optimistic scenario for the coin.

Armstrong (2021) argues that for the purposes of understanding the current valuation, Bitcoin may be thought of as a call option on a company with an unproven technology. This is an insightful take, but what is the business of this “company with an unproven technology?” How do we correctly characterize the underlying asset of the hypothetical call option? This is important, because thinking of Bitcoin as a call- like asset in some ways permits sloppy thinking – we can focus on the call-like assets, note that options are driven largely by volatility, and move on. But this abstract “company” with unproven technology could potentially derive value in several ways. Again, the most straightforward initial consideration is the possibility that it could become a viable currency. Bitcoin is currently not a currency in that it is neither a widely used medium of exchange, nor a reliable store of value. But it could conceivably become so. If Bitcoin became a widely used currency, the payoff to early adopters Bitcoins could be substantial.

So from a speculative perspective, due diligence requires some understanding of the likelihood of the adoption of Bitcoin as a widespread currency. One of the biggest obstacles to long term Bitcoin adoption is the existence of the 21 million Bitcoin cap⁸. While we briefly discussed the implications of that cap, we can investigate in a bit more detail by appealing to the money supply equation

MV = PQ

where M is the supply of money, V is the velocity of money, P is the aggregate price level and Q is real GDP. This equation is often considered when discussing national currencies. If Bitcoin were to be adopted as a national currency, the equation would be expected to apply. This equation can be written as percentage changes with perhaps more intuition, and approximated by

∆M% + ∆V% = ∆P% + ∆Q%.

If we assume the velocity of money to be constant (implying ∆V% = 0) for simplicity, then the percentage change in the money supply will equal the percentage change in the price level plus the percentage change in real GDP⁹. When Bitcoin has been fully mined, the money supply will no longer be changing, and so ∆M% = 0. This will imply ∆P% = −∆Q%. So if real GDP increases 2%, it will be matched by a decline in the price level of 2%. Deflation is a built in characteristic of Bitcoin if it were a national currency.

It seems unlikely that Bitcoin would ever be adopted as a national currency for a major nation – the instability of deflation alone would likely be enough to keep public servants from concluding that its adoption would in the national interest. One could imagine a cryptocurrency with a built-in Taylor Rule or something similar that could potentially be more viable, but Bitcoin does not possess this feature.

Further, it is conceivable that some developing countries may adopt Bitcoin as legal tender. While the variability of Bitcoin is a great negative for these countries, it may be preferable to local unstable currencies, or as a political alternative to dependence on the U.S. dollar. For example, recently El Salvador (which has a national GDP lower than any individual U.S. state) has announced their intention to adopt bitcoin alongside the U.S. dollar as legal tender¹⁰. Early adoptions such as these are as likely to be political stunts as serious economic initiatives (The U.S. recently pulled aid from the government of El Salvador for ousting their Attorney General and many top judges). But for small nations largely dependent upon remittances from the United States, legal tender that is easily transferred without a “middle man” may be of value.

It is important to note that suggesting that Bitcoin is unlikely to ever become a major currency is different from suggesting that no cryptocurrency could emerge to form the basis of a national currency. There are thousands of “cryptocurrencies” in existence, many of which employ a similar blockchain technology to Bitcoin. Infinite possibilities of future cryptocurrencies still exist, including the likely possibility that they may be created by national governments. For example, the case of El Salvador above may demonstrate the benefit that the U.S. government may reap by creating a digital version of the U.S. dollar that isn’t dependent upon banks for international transfers.

Crucially, the blockchain technology was published via an internet-distributed white paper in Nakamoto (2008), as discussed earlier. An important economic byproduct of that publication is that Bitcoin does not have a monopoly on the underlying technology that powers it. There are mechanisms in place that do give Bitcoin some market power. It had a distinct “first mover” advantage and is the clear cryptocurrency leader in terms of name recognition. This “branding” can indeed convey market power, but it is tenuous. Myspace had a similar first mover advantage over Facebook. Netscape had first-mover advantage in the browser market. Since everything that makes Bitcoin what it is can be replicated (save its name), there is a key phrase that needs to be added when describing Bitcoin as a call option on a company with an unproven technology. Bitcoin is better thought of as a call option on a company built on an unproven technology with network effects that’s network is broadly replicable by others. Because of this, it is quite possible that some future (or even present) cryptocurrency utilizing the blockchain technology could become a major currency. Speculation on which ones or their possible success is well beyond the scope of this monograph, but the mere fact that an infinite number of these alternatives exist should put an upward limit on the value of Bitcoin in the long run. And limits on value in the long run should put limits on its value in the present.

If Bitcoin is Unlikely To Become a Currency – What Is It? What Could it Be?

While Bitcoin seems unlikely to become a currency for a major economy, it conceivably could develop one of the characteristics of a currency – that of a store of value. In this sense, rather than serving as a replacement for the Dollar or the Euro, it would be an alternative to gold or silver. This is an extremely difficult outcome in which to determine the value of Bitcoin. Unlike gold or silver, there is no “intrinsic” value to Bitcoin. It isn’t aesthetically attractive, it can’t be used to make jewelry, and it doesn’t have any industrial uses. Further, there is no long history of value to the asset that gives a worth around which psychology may coalesce. In the end, Bitcoin will only be a store of value if enough people believe it is a store of value.

So if not for intrinsic reasons, what would lead individuals to believe Bitcoin has staying power as a store of value? Perhaps the world of collectibles provides the most reasonable parallels. Collections of art, wine, stamps, baseball cards, even musical instruments have long been argued to be viable alternatives to classic investable assets. These arguments have been addressed with increasing frequency in the academic literature over the past several decades¹¹. All of these classes of collectibles have retained value over long-term horizons, and even provided reasonable holding period rates of return.

An excellent discussion of what drives the value of collectibles is provided in Dimson and Spaenjers (2014). Ultimately, the value of such assets to individuals, and therefore to aggregate markets, is likely to be (as they suggest) driven by a combination of financial and emotional considerations. However, that both financial and emotional considerations combine to affect the value of such items is likely to imply that their returns are less than comparably risky investment assets. For a simple example of this, consider the Capital Asset Pricing Equation (CAPM) of Sharpe (1964):

E(ri) − rf = β(E(rm) − rf), or
E(ri) = rf + β(E(rm) − rf).

Here, E(ri) and E(rm) are the expected financial return to asset i and the overall market respectively, rf is the risk free rate, and β is a parameter that measures the association between the asset and the market. This classic equation demonstrates that the expected  return to an asset is dictated by the risk free rate, plus a function of its correlation with the overall market. High-beta assets have high expected returns in excess of the risk free rate, while low-beta assets have lower such expected returns.

Now consider how this equation is augmented if an investor values both a financial and an emotional return. The expected financial return now augmented by an emotional return to the investor, α. The resulting equation is

E(ri) + α = rf + β(E(rm) − rf), or
E(ri) = rf + β(E(rm) − rf) − α.

The expected return to the asset is reduced by parameter α, the emotional return to investors from the asset. The greater the emotional return to investors, the lower the financial return. While they do not derive this CAPM equation explicitly, these results can be seen in the empirical experiments of Renneboog and Spaenjers (2013) in which they find that “art has appreciated in value by a moderate 3.97% per year, in real U.S. dollar terms, between 1957 and 2007. This is a performance similar to that of corporate bonds – at much higher risk.” Further, they find in that work that art returns are driven to a significant extent by market sentiment and high-income consumer confidence.

Naturally, simple equations such as the CAPM and/or our extension of it are unable to fully capture market dynamics, but they give us a basis by which we can understand the forces at play. In the case of collectibles, the expected returns on assets are reduced by the degree of investor emotional attachment. While Bitcoin does not exactly fit the mold of a “collectible”, it does have many similar traits, including that of emotional attachment by investors. To this end, Abraham et al (2018) found that they were able to forecast Bitcoin price changes through simple measurement of the quantity of Tweets while Ahn and Kim (2021) find that emotion affects the total return variation process of cryptocurrencies ¹². This is reminiscent of Penasse et al (2014) who find that sentiment predicts short-term art prices.

Can Bitcoin Be An Effective Portfolio Diversifier?

Collectibles have been demonstrated to be effective portfolio diversifiers, although perhaps inefficient ones. Graddy and Margolis (2011) find that the real return to fine violins has a negative correlation with both the S&P 500 and U.S. Treasury bonds. They further find art to have a correlation with the S&P 500 that is close to zero and a negative correlation with Treasury bonds.

To get a sense of the diversifying benefits of Bitcoin, let’s first examine its standard deviation and correlation with other major asset classes.

Correlation

AGGBitcoinBCOMS&P 500
AGG1
Bitcoin0.0791
BCOM-0.1100.1571
S&P 500-0.0150.2240.5011

Standard Deviation

AGGBitcoinBCOMS&P 500
0.0080.6030.0410.039

Note: Data is monthly from Jan 2014 to Dec. 2020.

This correlation table is constructed from monthly data from January 2014 – Dec 2020. There is a clear argument that Bitcoin could potentially provide diversification benefits. The correlation between Bitcoin and the S&P 500 return is about 0.22. While this provides less diversification than corporate bonds (proxied by the Bloomberg-Barclay’s Aggregate Bond index), it provides a greater diversification benefit than the broad commodity index (proxied by the Bloomberg Commodities Index). It is still a low correlation that would likely yield diversification rewards, provided expected returns were somewhat stable. It is this latter assertion that is at issue given the current maturity of Bitcoin. The standard deviation of Bitcoin returns are enormous, at 0.60. This is 15 times more variable than equity and commodity returns and 75 times more variable than corporate bond returns.

Nonetheless, these results suggest that Bitcoin could be valuable as a diversifier in the long run if it could be trusted to retain value. It will retain value in the long run if the pool of investors with an emotional interest in the asset remains large and stable. Of course, the stronger the emotional interest (the α above) the lower the expected return to the asset. Finally Bitcoin, like other emotional assets is likely to be dependent upon sentiment and therefore will always have the potential of price collapses. That likely limits its value as a diversification tool.

Conclusion

The purpose of this monograph is to address the question of whether there is a useful role for Bitcoin in client portfolios. Is there such a role? At the moment, it doesn’t appear that Bitcoin features in a responsible asset management plan. With a standard deviation of returns 15 times that of equities, the stability of the asset is still very much in question. Bitcoin appears to behave as an emotional asset similar to collectibles, but this gives rise to the risk that the emotional appeal of the asset is currently elevated, given its relatively recent appearance and massive recent returns. That said, Bitcoin’s volatility could provide some appeal as a limited speculative investment.

This role as an emotional asset indicates that Bitcoin could have a future role in asset management, with some of the same benefits as other collectibles such as violins or baseball cards. Chief among these benefits is a relatively low correlation between the asset and mainstream asset classes such as equities and bonds. That low correlation is achieved at a relatively high volatility cost however, and so the benefits of Bitcoin as a diversifier are likely limited unless Bitcoin returns stabilize as the asset matures (which seems likely, if it survives that long). In the event of such a maturation, theory provides an indication that expected returns are likely to be lower than conventional asset classes, since the emotional attachment of many investors to the asset provides an upward pressure on the price of the asset that must be paid to acquire it. But given the current state of the market, the Bitcoin trade appears to currently be more a gambling mechanism than an investment strategy.

Footnotes

¹ If you were to collect all of the world’s gold and put it in one place, the result would be a roughly 68’ cube, though there is some substantial disagreement about this. See this for an interesting discussion.

² Prior to 1933, dollars had been exchangeable for gold. Between 1933 and 1973, the U.S. held a fixed amount of gold per dollar, though holders of dollars could not change them for gold with the Federal Reserve.

³ The benefits of leaving the gold standard have been even greater since 1982. Over the 40 years since then, inflation has averaged 2.72% with a standard deviation of 1.41%.

⁴ See: https://bitinfocharts.com/comparison/bitcoin-transactionfees.html

⁵ We are working here with the common definition of currency as an item that serves both as a store of value and as a medium of exchange.

⁶ See https://www.federalreserve.gov/releases/h6/current/default.htm

⁷ See https://www.blockchain.com/charts/total-bitcoins

⁸ Interestingly, this is often touted by advocates as one of the great advantages of Bitcoin.

⁹ It is important to recognize that money velocity is not constant. Nonetheless, this simplifying assumption allows us the opportunity to think through some implications here.

¹⁰ See https://www.bbc.com/news/world-latin-america-57373058

¹¹ See for example Goetzmann Renneboog & Spaenjers (2011), Graddy and Margolis (2011) and Renneboog & Spaenjers (2013).

¹² Anecdotally, Mark Cuban recently referred to Bitcoin as “a store of value…that is more religion than solution to any problem.” (see https://www.cnbc.com/2020/12/17/mark-cuban-bitcoin-is-a-store-of-value-that-is-more- religion.html) Bitcoin dropped more than 3% when Elon Musk Tweeted a breakup emoji about Bitcoin (https://www.cnbc.com/2021/06/04/bitcoin-falls-after-elon-musk-tweets-breakup-meme.html).

References

Abraham, J., Higdon, D., Nelson, J. and Ibarra, J. (2018) “Cryptocurrency Price Prediction Using Volumes and Sentiment Analysis.” SMU Data Science Review, 1, p. 1 – 21.

Ahn, Y. and Kim, D. (2021) “Emotional Trading in the Cryptocurrency Market” Finance Research Letters, forthcoming.

Armstrong, Robert. “Bitcoin as a Call Option.” Unhedged, Financial Times, May 26, 2021.

Back, A. (2002) “Hashcash – A Denial of Service Counter-Measure.” Working paper.

Chaum D. (1983) “Blind Signatures for Untraceable Payments.” Advances in Cryptology. p 199 – 203.

Chaum, D. and Brands, S. (1997) “’Minting’ Electronic Cash.” IEEE Spectrum 34, 30 – 34.

Dimson, E. and Spaenjers, C. (2014) “Investing in Emotional Assets.” Financial Analysts Journal 70, p. 20– 25.

Georges, Alexander and Korenchan, James “The Patent Landscape of Cryptocurrency and Blockchain” Intelligence – Snippets, MBHB, https://www.mbhb.com/intelligence/snippets/the-patent-landscape-of-cryptocurrency-and-blockchain  Accessed 5/27/2021.

Goetzmann, W., Renneboog, L., and Spaenjers, C. (2011) “Art and Money.” American Economic Review 101, p 222 – 226.

Graddy, K. and Margolis, P. (2011) “Fiddling with Value: Violins as an Investment?” Economic Inquiry 49, p 1083 – 1097.

Nakamoto, S. (2008) “Bitcoin: A Peer-to-Peer Electronic Cash System.” Working Paper.

Penasse,J., Renneboog, L., and Spaenjers, C. (2014) “Sentiment and Art Prices” Economics Letters 122, p 432 – 434.

Renneboog, L. and Spaenjers, C. (2013) “Buying Beauty: On Prices and Returns in the Art Market” Management Science 59, p 36 – 53.

Sharpe, W. (1964) “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” Journal of Finance 19. p 425 – 442.