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This article was first published in Traders Magazine. A huge thank you to them for publishing my article.

Intro

Over the past 6 months, there have been numerous discussions on how Bitcoin and crypto could fit into an overall investment portfolio. Much of this has stemmed from the growing narrative that Bitcoin is a hedge against global instability, as well as the uncorrelated nature of Bitcoin compared to equity and bond markets. However, with Bitcoin’s YTD average daily volatility of 4.11% and a drawdown of 84% peak-to-trough in 2018, the most common question asked is: what is the best way to size a Bitcoin position within a portfolio?

In this article, we apply Markowitz Modern Portfolio Theory where we use efficient frontiers and capital allocation lines to take a mathematical approach to size a Bitcoin position into a larger portfolio. This model will use a balanced 60/40 portfolio (60% stocks and 40% bonds) to observe the impact of a Bitcoin allocation to the portfolio.

Efficient Frontiers

An efficient frontier is a graphical representation of possible portfolios between two assets. The graph represents Portfolio Expected return (E(r)) on the Y-axis and Portfolio standard deviation (SD) on the X-axis. This graphical representation shows how a portfolio is impacted by adjusting the weight combinations of the two asset portfolio, allowing an investor to determine where they want to be positioned on a risk-reward spectrum.

Asset 1: 60/40 Portfolio

Asset 2: Bitcoin

60/40 Portfolio and Bitcoin Efficient Frontier

To get a better understanding of what each portfolio represents, we can look at the table below to see each portfolio’s corresponding weights, as well as expected returns and standard deviations.

By looking at the efficient frontier, we can interpret it in a few ways. Anything below the vertex of the curve can be considered an “inefficient” portfolio allocation. This is simply because the portfolio has a lower expected return with a higher level of risk associated with the portfolio (higher standard deviation). In addition, any portfolio above the vertex represents an “efficient” portfolio allocation with higher risk and higher expected returns the farther up the Efficient Frontier one goes.

Finding the Optimal Portfolio

There are two portfolios that we should consider when thinking about allocation based on the Efficient Frontier:

Minimum Variance Portfolio: The solid blue line at the vertex of the Efficient Frontier represents which portfolio has the lowest variance and therefore lowest expected risk.

This portfolio calls for a 9.56% allocation to Bitcoin, 90.44% allocation to 60/40 portfolio. This allocation would lead to an expected return of 9.19%, a standard deviation of 4.79% and an expected portfolio Sharpe ratio of 1.29. This portfolio on its own significantly outperforms a traditional 60/40 portfolio which has an average annual return of 7.8%.

Optimal Portfolio: The red dashed line on the graph, Portfolio O, represents where the Sharpe Ratio of a portfolio along the Efficient Frontier would be highest. In other words, it shows when the ratio between expected returns and standard deviation are highest.

The Optimal Portfolio calls for an allocation of 14.21% Bitcoin, 85.79% 60/40 portfolio. These weights would lead to an annual expected return of 13.25%, a standard deviation of 6.16%, and a Sharpe ratio of 1.66. This portfolio once again significantly outperforms the average annual returns of the 60/40 portfolio. The expected return of the Optimal Portfolio also outperforms the average annual returns of the S&P (9.8%). Perhaps most importantly, based on the growing instability throughout the world’s monetary policies and ongoing political unrest, both of which the Arca team has discussed previously, the Optimal Portfolio has a significantly lower standard deviation than the S&P average of 12.53%.

To conclude, it goes without saying that a 15% allocation into an incredibly new asset class is likely too large in a larger portfolio, and is the product of the model only taking into consideration a 60/40 portfolio. With the likely inclusion of real estate, private equity, and gold positions the projected allocation would likely decrease. However, the uncorrelated nature of Bitcoin still offers similar benefits in terms of increased expected returns and a decrease in overall risk in any portfolio with an allocation.

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