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Applying Modern Portfolio Theory to Bitcoin and Bitcoin Mining Stocks

Applying Modern Portfolio Theory to Bitcoin and Bitcoin Mining Stocks

It’s not every day that a new asset class is born. In the years since Satoshi’s white paper, Bitcoin has evolved from a shadowy proof of concept to a fully-fledged investable asset. Its returns have been astronomical but naturally very risky. It’s no secret that when compared to more mature asset classes, Bitcoin, and its associated equities, have exhibited significantly higher volatility and more extreme drawdowns. With this in mind, how does a diversified investor allocate to Bitcoin accordingly? What about its associated equities such as Bitcoin mining stocks? Applying Modern Portfolio Theory can offer insight into the most optimal allocation.

The Efficient Frontier is the cornerstone of Modern Portfolio Theory. The Efficient Frontier is formed on the outermost “northwest” region of a scatterplot mapping various portfolio allocation combinations. It represents the most “efficient” portfolio allocation at every given level of assumed risk. The scatter plot shown below maps various allocation combinations of ordinary investment assets that we will refer to as the “traditional” universe. This universe consists of US stocks (SPY), international stocks (EFA), US bonds (AGG), treasuries (TLT), real estate (IYR), and gold (GLD).

The two “corner” portfolios highlighted are the minimum variance portfolio, and the maximum Sharpe portfolio. The minimum variance portfolio is the combination of assets that would result in the minimum level of risk possible given the universe of investment options. The maximum Sharpe portfolio is the most optimal portfolio that sits along the Efficient Frontier. It maximizes the ratio of expected return to risk given the universe of investment options.

But what happens when Bitcoin is introduced? The “traditional + BTC” scatterplot, shaded in blue, elongates as additional risk enters the universe, but more importantly the Efficient Frontier shifts “northwest”, meaning the efficient portfolio at every level of risk is improved with an allocation to Bitcoin!

We can expand this new universe one step further by adding Bitcoin’s most closely related equities, Bitcoin mining stocks, as represented by the Hashrate Index Crypto Mining Stock Index. The scatterplot of the final “traditional + BTC + mining stocks” universe, shaded in green, again improves at almost all levels of assumed risk as the addition of Bitcoin mining stocks further enhances the opportunity set.

One of the most common criticisms surrounding Bitcoin mining stocks is that, given their obvious business exposure to the price of Bitcoin, they are nothing more than Bitcoin proxies trading on the stock exchange. As demonstrated in this analysis, the reality is much more complex. While it is true that Bitcoin mining stocks have a very strong correlation to the price of Bitcoin, they can offer more utility to an investor than simply serving as a proxy. Their additional diversity of risk and return drivers can enhance portfolios. The maximum Sharpe portfolio calls for an allocation to Bitcoin mining stocks, even when to universe includes Bitcoin itself!


· Daily, total returns observed is 6/30/2020 – 5/31/2022 to match the inception of the Hashrate Index Crypto Mining Stock Index

· Each Efficient Frontier is estimated by trialing 10,000 random portfolio weights. The minimum variance portfolio and maximum Sharpe ratio portfolios were optimized with Excel solver