Analysis of the Effects of Including Bitcoin in Investment Portfolios

The Bank of Russia in its Financial Stability Review last year ^{[3, p. 40]} noted with reference to CoinMarketCap ^[8] that during 2021 there was a rapid increase in the total capitalization of the global digital currency market: in early November 2020, this indicator was about 440 billion US dollars, in early November 2021 – 2.9 trillion US dollars (the capitalization of digital currencies increased 6.6 times over the year), which is higher than the market capitalization of such major companies as Apple and Microsoft. In the autumn of 2021, the Bank of Russia has already pointed out the risks of investing in cryptocurrencies, fearing that the population will transfer part of their savings into poorly predictable and highly volatile assets.

It can be said that the concerns of the Central Bank of the Russian Federation were not unfounded, so as of the end of September 2022, the total market capitalization of cryptocurrencies amounted to $ 942 billion, which indicates that the market has lost 2/3 of its value in less than a year (Fig. 1).

Fig. 1. Total market capitalization of cryptocurrencies August 2017-September 2022. (Source: CoinMarketCap, ^[8])

According to the estimates of the Bank of England ^[5], 95% of currently existing crypto assets are unsecured. This conclusion is based on the fact that "they have no intrinsic value, that is, there are no assets or goods behind them: the value of crypto assets is determined solely by the price that the buyer is willing to pay at any given moment. As a result, their value is very unstable."

The concern of financial regulators about the rapidly developing cryptocurrency market is explained by the fact that transactions are made in a poorly regulated space with high price volatility. In addition to the obvious investment risks associated with investing in cryptocurrency assets, high attention to cryptocurrencies is attracted by the possibility of using them to make calculations related to transactions carried out on the border of the legal field or beyond. And this is, in many ways, a more serious challenge for any state system than the factor of insecurity, which, we believe, is exaggerated compared to the fiat money we are already familiar with. Appealing to gold and foreign exchange reserves, the government, the army and taxes as factors of the security of national currencies, in fact, leads to a scientific discussion, since the government cannot dictate the value of its currency, because the state determines only its supply, and already the market evaluates the strength of monetary properties.

D. Goldberg in his article ^[4], devoted to the well-known myths associated with fiat money, emphasizes that in 1971, after the decision of US President Richard Nixon to separate the US dollar from gold, a system of national fiat currencies that have no internal and use value is used worldwide. They have value only because the people who use them as a medium of exchange agree with their value. They believe it will be accepted by merchants and other people.

You can see the similarity between cryptocurrencies and fiat money by the criterion of their unsecurity. But the real concern on the part of national states is their lack of influence on the mechanisms of emission or other types of direct or indirect control of cryptocurrencies, which mainly explains the restrictions imposed on transactions with cryptocurrencies in various jurisdictions.

In the UK, there is a ban on transactions with derivatives related to digital currencies. In China, activities related to digital currencies, in particular issuance, exchange, trading, mining, as well as the provision of intermediary services and so on, are illegal. At the same time, in 2021, bitcoin was officially recognized as legal tender in El Salvador. A number of countries are introducing requirements regarding licensing/registration of digital currency exchanges. As a rule, licensed digital currency exchanges are required to comply with the requirements of AML/CFT (countering money laundering and terrorist financing), as well as the requirements for the identification of participants in transactions with digital currencies and some others that guarantee the rights of their customers.

In Russia, there is still an official ban on the use of digital currency as a means of payment, but in the conditions of anti-Russian sanctions pressure, full-fledged legalization of cryptocurrency as a settlement tool would neutralize the negative consequences of disconnecting Russian banks from SWIFT and the withdrawal of Visa and Mastercard payment systems from the country.

The world's economic institutions have not previously functioned in the reality of a new kind of money, and we may not be aware of the possible negative aspects of their use. We should not forget about climate risks, given the high energy intensity of generating certain types of digital currencies. Today, cryptocurrencies are not yet full–fledged money, but it is already possible to draw a clear analogy with investments in art objects: the subjectivity of demand, the fashion factor, the presence of the same AML/CFT requirements.

Cryptocurrencies are a modern investment tool, interest in them is constantly growing. The most popular among cryptocurrencies today is still bitcoin, which in 2008 began its history and the history of cryptocurrencies, when a person or group of persons under the pseudonym Satoshi Nakamoto published the source code and a description of the principles of the Bitcoin network. As N.A. Stefanova notes ^{[1, pp. 81-84]}, the possibility of obtaining colossal incomes attracted the attention of many investors and led to an urgent and still controversial issue related to the justification of the hype for this type of investment.

As a digital currency and payment system, the term Bitcoin was first mentioned in Forbes magazine in 2011 ^{[1, pp. 119-122]}. Currently, the leading cryptocurrency exchanges for bitcoin trading are Binance, BTCEX, OKX, Bybit and Deepcoin.

The largest capitalization of bitcoin was in November 2021 (1.2 trillion US dollars, 43% of the cryptocurrency market) ^[8]. In September 2022, the capitalization of bitcoin decreased to 366 billion US dollars, but it is still not only the very first, but also an expensive cryptocurrency with a share of 39% of the entire global cryptocurrency market (Fig. 2).

Fig. 2. The share of the market capitalization of cryptocurrencies May 2013-September 2022. (Source: CoinMarketCap, ^[8])

It is worth agreeing with D. Li, L. Guo and Yu.Wang ^{[3, pp. 16-40]} is convinced that the popularity of bitcoin from more than a thousand types of cryptocurrencies is due to a number of advantages, which include:

1. Decentralization, expressed in the fact that access to the currency is realized via the Internet without regulatory authorities.

2. Flexibility, which consists in setting up bitcoin wallets without fees, rules, and also without the need to link to a location.

3.      Transparency, when each owner has the opportunity to verify transactions, thanks to blockchain technology.

4. Speed of transactions (the speed of the transaction is estimated at a few seconds, and its verification is about 10 minutes).

5. Low transaction fees. No transaction fee is required.

A new milestone in the development of bitcoin can be considered October 2021 after the U.S. Securities and Exchange Commission (SEC) approved the first Bitcoin futures ETFs: ProShares Bitcoin Strategy ETF (listed on the NYSE) and Valkyrie Bitcoin Strategy ETF (listed on NASDAQ). Despite the fact that in November 2021, the SEC rejected the offer of the asset management company VanEck to launch a spot exchange-traded fund based on Bitcoin, the very presence of cryptocurrency ETFs traded on two of the largest stock exchanges in the world suggests that now the technical threshold of entry for investing in Bitcoin is no different from what it will face an investor who wants to invest in shares of a public company in the USA. It is also worth noting that several Bitcoin and Ethereum ETFs, including spot ones, have already been approved and are operating in Canada.

The role that cryptocurrencies began to play in the global financial system not so long ago is becoming difficult to ignore. The existing gaps in the legal regulation of their turnover are gradually being filled, and institutional investors are increasingly investing in their purchase.

In this regard, we have attempted to analyze some of the effects of including bitcoin (Bitcoin), as the most popular cryptocurrency, in the structure of investment portfolios consisting of assets of various classes. Taking into account the factor of globalization and the current high speed of changes in the global financial system, we hope that the materials of our research will be of interest to Russian investors who want to critically assess the nature and consequences of events in international financial markets developing within the framework of modern trends.

We were able to find the statistics of prices and yields of financial instruments necessary for our research on the resource Investing.com . The data analysis was carried out over an interval of 10 years – from October 2011 to October 2021.

The first thing we found when preparing the initial data was a high degree of mutual correlation between the dynamics of the bitcoin price and the S&P 500 index, which was a discovery for us and caused our serious surprise.  When analyzing this dependence, our attention was attracted by the fact that historically the price of bitcoin has increased with a pattern close to that which can be described by an exponential function. To bring the series to comparable values, we used the natural logarithm function for the bitcoin price as the inverse of the exponential. This transformation even allowed us to graphically see the existing synchronicity in the dynamics of the two instruments (Fig. 3). To assess the dynamics of the S&P 500 index, we used the quotes of the SPDR S&P 500 Trust ETF, the world's largest exchange-traded fund, which has been traded on the New York Stock Exchange (NYSE) since January 1993, designed to to track the S&P 500 stock market index.

Weekly measurement intervals were used for both series. The obtained results allowed us to construct a regression equation (Fig. 4) for the dependence of bitcoin prices (logarithmic scale) on the value of the SPDR S&P 500 Trust ETF (logarithmic scale). The value of the coefficient of determination R2 gives reason to believe that the dynamics of the S&P 500 index by 92.25% describes fluctuations in the price of bitcoin, which is due, apparently, to the natural flow of investments from the stock market to the new and tempting cryptocurrency market.

Fig. 3. Bitcoin price dynamics (logarithmic scale) and SPDR S&P 500 Trust ETF

Fig. 4. Regression equation for the dependence of Bitcoin prices (logarithmic scale) on the value of the SPDR S&P 500 Trust ETF (logarithmic scale)

The high earnings of investors on stock trading formed the need to search for new high-yield financial assets as an investment object when closing positions, and gradually bitcoin began to fulfill such a functional role. At the same time, during periods of losses in the stock market, if there was no outflow of investments from bitcoin, then at the moment the demand for cryptocurrency significantly weakened, which became a factor in the decline in bitcoin quotes. Due to significant differences in the volumes of the stock market and the bitcoin market, the functional form of the relationship between the bitcoin price and the S&P 500 index found by our study is logarithmic, not linear.

The results obtained formed the basis of a hypothesis suggesting the possibility of effectively replacing bitcoin investments in the stock market of American companies, given the unidirectional and synchronous change in their quotes. The apparent weakness of this assumption may mistakenly appeal to the incomprehensible nature of cryptocurrencies, but, on the other hand, many researchers consider the same stock market to be overvalued at certain intervals of its development. In this regard, the risk of the formation of financial bubbles is of an identical nature for cryptocurrencies and for any other asset whose value is determined more by investors' faith in it than by some rational and practical content and objective utility. When the stock prices of highly unprofitable companies included in the S&P 500 index break quotation records, investments in cryptocurrency no longer look so radical.

To assess the effects of including bitcoin in the investment portfolio, we used the portfolio theory of G. Markowitz ^[7], which is based on the optimal choice of assets based on the required risk/return ratio.

In this model, to calculate the expected return of the portfolio, use:

where R _p is the profitability of the portfolio;

R _i – profitability of the i-th asset;

w _i - weight of the i-th asset (that is, the share of asset i in the portfolio).

The variance of portfolio returns is calculated:

where s _i and s _j are the standard deviation of the profitability of the i–th and j-th asset;

r _ij is the correlation coefficient between the profitability of the i-th and j-th assets.

Portfolio yield volatility (standard deviation):

We have included the following financial instruments in our basic portfolio:

1) SPY - SPDR S&P 500 Trust ETF (S&P 500 Index);

2) BTC/USD – Bitcoin price;

3) US10YT=X – index of 10-year US government bonds;

4) US1YT=X – index of 1-year US government bonds;

5) ZG – Gold futures;

6) Brent – United States Brent Oil Fund, LP (BNO) (oil prices);

7) Wheat – Teucrium Wheat (WEAT) (wheat prices);

8) DXY – futures on the US dollar index.

Table 1 shows the parameters of profitability and risk for various financial instruments on the investment horizon of 1, 3 and 5 years. The probability of loss was calculated based on the indicators of the average return of the asset and its standard deviation.

With an increase in the investment horizon, the average return on shares remains approximately at the same level of 12-14%, but the standard deviation level decreases from 11% (1 year) to 4% (already in 3 years). The estimated probability of receiving a loss at the 1-year horizon is 12%, and already in the 3-year interval it decreases to almost zero values.

 Bitcoin looks outstanding both in terms of profitability and in terms of volatility expressed in terms of standard deviation, promising an average of 30-fold enrichment in 5 years. However, its coefficient of variation (the ratio of the standard deviation to the average yield), although decreasing from 2.2 with a 1-year horizon to 1.5 with 5 years of investment, indicates a risk significantly higher than we encounter on the stock market. For example, for the S&P 500 index, the coefficient of variation in comparable horizons is only 0.8 and 0.3. That is, if we conditionally compare two portfolios: one consisting of 100% shares of S&P 500 index companies and the second consisting entirely of bitcoin, we will see that from the point of view of the premium for risk, the first portfolio is balanced an order of magnitude better. The Sharpe ratio when investing in stocks will increase with the growth of the horizon from 1.2 (1 year) to 3.5 (5 years), and in the case of bitcoin – from 0.5 to 0.7, without even reaching 1. The estimated probability of a loss for bitcoin is reduced from 33% to 25% after 5 years of holding, which does not make it a direct alternative to stocks.

Table 1. Profitability and risk parameters for various financial instruments on the investment horizon of 1, 3 and 5 years

However, commodity classes (commodities) look like outsiders in terms of profitability parameters in the analyzed decade: wheat and oil. With an increase in the investment horizon, the average loss of oil increases from -2% to -7-8%. For operations on the wheat market, this indicator remains unchanged at the level of 11-12%, regardless of the investment period. At the same time, the decrease in the standard deviation from 38% to 7% for oil and from 16% to 4% for wheat practically emphasizes the increase in the evidence of losses in these classes, which is confirmed by the estimated probability of losses increasing by 5 years from 52 to 86% for oil and from 77 to 100% for wheat.

Gold and the US dollar look similar assets in terms of characteristics: the average yield does not depend on the investment horizon and is 2-3% per annum. At the same time, there is a decrease in the standard deviation with an increase in the term of investments: gold – from 13 to 5%, the US dollar from 4 to 2%. Nevertheless, due to the low average yield, the record holders of low volatility on the horizon of 1 and 3 years demonstrate a higher probability of losses than bitcoin, and only with a 5-year term, investments in the dollar are predicted with a lower probability of losses than bitcoin. Therefore, it is difficult to formulate an unambiguous judgment regarding the degree of riskiness of investments in them.

Government bonds do not seem to be a "safe haven" for investors in the last decade. For 10-year-olds, the average yield, sliding into a negative range (from 6 to -1% by 5 years), determines the probability of losses in more than half of the cases, more than 2 times exceeding bitcoin by this indicator. At the same time, the standard deviation for bitcoin is ten times higher than this indicator for 10-year government bonds.

The average yield of short-term 1-year government bonds increases from 36 to 179% (5 years). Volatility increases from 93 to 178%, but decreases in relative terms, as evidenced by a decrease in the probability of losses from 35 to 16% by 5 years of the investment horizon.  

The matrix of paired correlations of returns of financial instruments on the investment horizon of 1.3 and 5 years (Table 2) indicates the possibility of obtaining interesting portfolio diversification effects due to the presence of strong negative and positive relationships for different asset classes.

Table 2. Matrix of paired correlations of returns of financial instruments on investment horizons of 1, 3 and 5 years

Minimization of the standard deviation at the specified levels of profitability was used as an objective function in solving the problem of optimizing the portfolio structure. The maximum effect of the inclusion of bitcoin is fixed after the specified level of portfolio profitability exceeds 15% per annum (Fig. 5).

Fig. 5. The effect of reducing the risk (standard deviation) of the portfolio when bitcoin is included in its composition on the investment horizons of 1, 3 and 5 years

At the same time, the use of bitcoin allows you to increase the profitability of the portfolio over 36.1% on a 1-year horizon without a significant increase in risks. For example, the maximum standard deviation of 93% was achieved in a portfolio without bitcoin with a yield of 36.1%, and the inclusion of bitcoin increases the profitability of the portfolio by 2 times for this level of risk. 

The probability of a portfolio loss (Fig. 6) is also significantly lower for the scenario with bitcoin in the composition. The theoretical minimum probability of loss is achieved for a portfolio with a target yield of 10%. As the targeted level of portfolio profitability increases, bitcoin also gives the portfolio the effect of reducing the probability of losses.

Fig. 6. The effect of reducing the risk (probability of losses with normal distribution) of the portfolio when bitcoin is included in its composition on the investment horizons of 1, 3 and 5 years

For portfolios without the inclusion of bitcoin, the main effect of diversification on the horizon of 1 year is achieved through a combination of the S&P500 index and 1-year US government bonds (Table 4) after a yield of 15%. In this situation, the leading role is played by a negative correlation coefficient between assets -0.39, as well as a higher average yield of short-term bonds. At the same time, for portfolios with a target yield of up to 15%, the main risk reduction effect is provided by gold and the US dollar.

Adding bitcoin to the portfolio increases the portfolio's profitability to 100% and above (Table 3). Its share in the one-year portfolio is recommended to 14.6%, and balances the portfolio at the expense of 85.4% of 1-year government bonds.  With a target portfolio yield of 20% on the horizon of 1 year, the share of the S&P 500 index in the portfolio structure occupies a dominant place (86.7%), gradually decreasing with an increase in total profitability – up to 2.9% with a portfolio yield of 85%. The place of stocks in the portfolio is occupied by bonds and bitcoin in a limited amount.

Table 3. Structure of the optimal portfolio with risk minimization (standard deviation) using bitcoin on the investment horizon: 1, 3 and 5 years