Tesseract Thoughts: Value of Cryptocurrencies in a Diversified Portfolio

January 2021


In this article of Tesseract Thoughts, our Portfolio Manager Juuso Ahlroos summarises some of his thoughts about the value of cryptocurrencies in a diversified portfolio.

Diversification is the way to earn the best risk-adjusted returns. Cryptocurrencies, an asset that is hard to be grouped under any traditional asset classes and does not have a high correlation with anything, could allow investors to increase their risk-adjusted return and the current research agrees with that.  Because of that, investors should start adding cryptocurrencies to the list of assets to consider when making allocation decisions.

1.   Cryptocurrencies in general

On October 31st  2008, Satoshi Nakamoto published his white paper on bitcoin: “Bitcoin: A Peer-to-Peer Electronic Cash System”. His idea was to create a trustless, irreversible payment system to protect both buyers and sellers. He proposed bitcoin as a peer-to-peer version of electronic cash, allowing for transactions to go directly to another party without going through financial institutions.

Bitcoin has come a long way from the initial whitepaper and currently, bitcoin’s market capitalisation is $360 billion, and the entire cryptocurrency market is worth around $580 billion according to coinmarketcap.com. As cryptocurrencies have reached a wider adoption, they have also moved far from the initial idea of being used just as electronic cash. Bitcoin has been compared to gold as an alternative way to store wealth by J.P. Morgan (2020). Baur, Hong and Lee (2018) also found that bitcoin is not used as an alternative currency or medium of exchange but a speculative asset.

Recently some technology companies have also started using cryptocurrencies, usually bitcoin, as a treasury asset. On October 7th, 2020, Square announced it had invested $50 million or around 1% of its assets in bitcoin. Square wanted to “expand their largely USD-denominated balance sheet” because of the “unprecedented uncertainty from a macroeconomic and currency regime perspective”. They received approximately 4709 bitcoins with an average price of around $10 600. As of 3.12.2020 bitcoin price has reached $19 414, leading to paper profits of 83% in under 2 months. Cryptocurrencies are indeed quite hard to fit into the framework of traditional assets, which makes them an interesting opportunity for those willing to take it.

2.   Diversified portfolio

Markowitz (1952) states that selecting a portfolio is done in two stages: the first stage is creating beliefs of future performance for available assets and the second stage is forming a portfolio based on those expectations. He also states that investors are risk-averse and if portfolios have the same expected return, investors will choose the less risky one. Based on that he shows how to create a mean-variance optimal portfolio. The underlying assumption in this is that not all available assets are fully correlated and therefore offer diversification benefits on just selecting a single asset.

Markowitz’s way to optimise a portfolio has been criticised by many and for example, DeMiguel, Garlappi and Uppal (2007) found that naively weighting all portfolio parts equally outperforms mean-variance models in terms of Sharpe ratio. However, Kritzman, Page and Turkington (2010) argue the opposite and say that taking longer samples for estimation and adding simple assumptions makes the optimised portfolios outperform the 1/N portfolios. No criticism is given to the benefits of diversification and that is agreed as being a “free lunch” of sorts.

3.   Role of bitcoin in diversified portfolio

In their study, Kritzman et al. used domestic equity, foreign equity, government bonds, corporate bonds, REITs, commodities, and cash as assets classes. Because portfolio optimisation is done by choosing the best combination of assets from the universe of available assets, increasing the available set cannot make the optimisation result worse. Because of this, adding newly available assets to portfolio optimisation can only make the portfolio better. For the new asset to make the optimised portfolio better, it cannot comove with the currently included assets too much or the effect from it will already be spanned by the current selection.

The longest time series between cryptocurrencies and traditional asset classes are available online from 2013 for example by Coinmetrics. The correlations between bitcoin and S&P 500 have been between -0.1 to 0.3, bitcoin and gold between -0.12 to 0.25 and bitcoin and USD between 0.2 to -0.25. This would preliminarily suggest that bitcoin could provide diversification benefits in traditional portfolios.

Kajtazi and Moro (2019) find that adding bitcoin in the portfolio of US, European and Chinese assets generates higher risk-adjusted returns. The addition of bitcoin increased both risk and return, but the return was proportionally significantly higher than the risk. Briere, Oosterlinck and Szafarz (2015) had similar results in the period from 2010 to 2013 with adding bitcoin in the portfolio of worldwide stocks, bonds, currencies commodities, hedge funds, and real estate. They found that allocation of 6% in bitcoin would increase annual yield 19 percentage points from 13.1% to 32.5%. The results over that period are hard to apply today because of the bull market between 2010-2013. In May 2010, 10 000 bitcoins were used to buy 2 pizzas and in late 2013 price of a single bitcoin was over $1000 which explains why the addition of bitcoin improved returns so much.

Gasser, Eisl and Weinmayer (2015) found that the optimisation approach with conditional value-at-risk approach leads to bitcoin being added with weights ranging from 1.65% to 7.69%. with data from 2010 to 2015. CVaR was used because bitcoin returns are not normally distributed. Gasser et al. (2019) used the same method again on data from 2010-2018 and found similar results.

Some criticism can be given for these studies for the choice of the sample period. The longer period usually provides a better sample, but bitcoin was worth practically nothing in 2010, which makes the returns astonishing. Another thing to note is that since the start of 2020 the correlation between bitcoin and S&P 500 has been rapidly increasing. This could be a sign of bitcoin becoming more mature this would mean the trend could continue according to cointelegraph.com

4.   Other cryptocurrencies

Although bitcoin is the largest cryptocurrency, there are also other significant players like Ethereum and Ripple. According to the correlation table at cryptowat.ch, cryptocurrencies are heavily correlated with each other. Still, adding cryptocurrencies other than just bitcoin might provide further diversification. Brauneis and Mestel (2019) indeed find that including more than just one cryptocurrency in an optimised portfolio significantly reduces the risk. Liu and Weiyi (2019) also find diversification benefits across different cryptocurrencies. Borri (2019) finds that although cryptocurrencies are highly exposed to tail-risk inside crypto markets, they are not exposed to tail-risk of U.S. equity or gold. Because of this, cryptocurrencies could also work as a hedge in the portfolio. He offers a counterargument that the liquidity of cryptocurrencies is relatively low and therefore the share in the optimal portfolio is small.

5.   Utilising this information in investing

According to studies cryptocurrencies indeed do provide increased diversification benefits for an investor who is already well diversified on traditional asset classes. For them, adding a cryptocurrency investment of 1% to 7% depending on the risk appetite would increase their risk-adjusted return. Optimally, they would spread their cryptocurrency investment across different currencies and optimise the allocation in their preferred way.

Depending on the investment mandate and the sophistication of the investor there are multiple ways to add exposure to cryptocurrencies.

For a technologically capable investor or someone with the resources to be one, buying the cryptocurrencies themselves from for example Coinbase and storing them inside a personal wallet would be a good idea. That takes away the need for an intermediary to hold your tokens and allows the investor to minimise counterparty risk. The whole process is not really a difficult one and I would suggest doing it this way. It also allows the investor to diversify their cryptocurrency investments without limitations as trusts for example rarely include other than the most popular cryptocurrencies. For someone who does not want to go through the hassle of setting up the storage, Coinbase provides a wallet where you can store the tokens.

For an investor with strict guidelines on what they can do, investing in cryptocurrencies through a trust could be a suitable option. As cryptocurrency ETFs are still under consideration by SEC and are not available yet, different investment vehicles like trusts would have to do. For example, Grayscale provides a bitcoin trust. Grayscale is audited and their bitcoin reserves are confirmed, so there is little risk counterparty risk. To note is that Grayscale bitcoin trust trades at a premium, which some might want to avoid to not take anything else than bitcoin price risk.

For an investor who wants to speculate with cryptocurrencies, which is a bit out of scope for this paper, they could use futures. For example, Binance provides an option to trade futures on multiple different cryptocurrencies.

For an investor who is not yet confident in the prospect of cryptocurrencies, the asset class is something to investigate more. There is a lot of potential benefits in including cryptocurrencies in the investment portfolio and that should not be skipped just because of the lack of knowledge.

Juuso Ahlroos, Portfolio Manager

6. Sources


Baur, D.G., Hong, K. and Lee, A.D., 2018. Bitcoin: Medium of exchange or speculative assets?. Journal of International Financial Markets, Institutions and Money, 54, pp.177-189.

Borri, N., 2019. Conditional tail-risk in cryptocurrency markets. Journal of Empirical Finance, 50, pp.1-19.

Brauneis, A. and Mestel, R., 2019. Cryptocurrency-portfolios in a mean-variance framework. Finance Research Letters, 28, pp.259-264.

Briere, M., Oosterlinck, K. and Szafarz, A., 2015. Virtual currency, tangible return: Portfolio diversification with bitcoin. Journal of Asset Management, 16(6), pp.365-373.

DeMiguel, V., Garlappi, L. and Uppal, R., 2009. How inefficient are simple asset allocation strategies. Review of Financial Studies, 22(5), pp.1915-1953.

Gasser, S., Eisl, A. and Weinmayer, K., 2015. Caveat emptor: Does Bitcoin improve portfolio diversification?. Available at SSRN 2408997.

Gasser, S., Eisl, A. and Weinmayer, K., 2019. Bitcoin and Investment Portfolios. In Business Transformation through Blockchain (pp. 171-195). Palgrave Macmillan, Cham.

Kajtazi, A. and Moro, A., 2019. The role of bitcoin in well diversified portfolios: A comparative global study. International Review of Financial Analysis, 61, pp.143-157.

Kritzman, M., Page, S. and Turkington, D., 2010. In defense of optimization: the fallacy of 1/N. Financial Analysts Journal, 66(2), pp.31-39.

Liu, Weiyi. “Portfolio diversification across cryptocurrencies.” Finance Research Letters 29 (2019): 200-205.

Markowitz, H.M., 1952. Portfolio selection. The Journal of Finance, 7, pp. 77-91


Madeira A., Correlation Between Bitcoin Price and Stocks Reaches a New All-Time High, cointelegraph.com (2020), referenced 4.12.2020 (https://cointelegraph.com/news/correlation-between-bitcoin-price-and-stocks-reaches-a-new-all-time-high)

J.P. Morgan, Flows & Liquidity, Bitcoin’s competition with gold (2020), referenced 3.12.2020 (https://markets.jpmorgan.com/research/email/-3oic3k5/j6T0uF3hzOPIuNailF_FUA/GPS-3532729-0)

Square, Inc. Bitcoin Investment Whitepaper (2020), referenced 3.12.2020 (https://images.ctfassets.net/2d5q1td6cyxq/5sXNrlEh2mEnTvvhgtYOm2/737bcfdc15e2a1c3cbd9b9451710ce54/Square_Inc._Bitcoin_Investment_Whitepaper.pdf)