The mathematical case for cryptocurrency investment
Digital assets don't need to go to the moon – they just need to be themselves, and maths does the rest.
The "efficient frontier" (pictured) is the mathematically best return on investment according to the principles of modern portfolio theory. It's the theoretically ideal blend of risk and return, incorporating diversification as measured by the price correlation between different asset classes.
This means that the invention of an entirely new asset class, such as cryptocurrency, stands to move the efficient frontier and set a new benchmark for the theoretically optimal investment portfolio. This is especially true if that new asset class has very little price correlation with existing asset classes, such as cryptocurrency does.
This is because diversification isn't black and white. An investment portfolio isn't just diverse or not, but can instead achieve different levels of diversity, in a full spectrum of shades of grey.
The Digital Currency Institute's Grayscale investment fund might not have had this in mind when choosing a name, but its A New Frontier research paper by Matthew Beck clearly establishes how important these shades of grey can be.
The momentous increases in crypto value in late 2017 mean most hypotheticals have it play an outsized role on portfolio performance, but this doesn't always do justice to the diversification benefits of cryptocurrency as an asset class that moves very differently to others, and the benefits that a small allocation can theoretically bring.
The question is not whether a portfolio is diverse, so much as how diverse it is as measured by the correlation between each investment or asset type within a portfolio. For example, "diverse" investments in real estate, building material commodities and shares in construction companies might be very closely correlated, despite being different asset types.
The problem is that almost everything is connected in some way, and unexpected circumstances can have unpredictable ripple effects across a wide range of industries and asset types. In the interconnected real world, there are generally no asset types with zero correlation to others, so a wide range of asset types is key to minimising correlation and creating a safer portfolio.
Purely by virtue of being a new asset class, the research paper argues, serious investors should be giving serious consideration to cryptocurrency as a way of further diversifying portfolios beyond what was previously possible.
Go a step beyond that though, and the argument's much more compelling.
Being in the right place at the right time
Beyond simply being a new field to diversify into, Beck notes that cryptocurrency movements tend to have almost no correlation with other asset types, while decentralised systems can be theoretically entirely detached from previously inescapable risks. For diversification alone, cryptocurrency is difficult, if not impossible, to beat.
Grayscale compared the price correlation between different asset types, and within crypto, based on rolling one month returns over a year and a half, and unsurprisingly found that cryptocurrencies correlated strongly with each other, but had much less to do with other market movements.
As an added bonus, despite the similar movements among crypto prices there's still an extraordinary amount of diversity within the digital asset field itself, including currencies like bitcoin, application platforms like Ethereum, deflationary business products like Ripple XRP, and an extraordinary range of tokenised assets ranging from fractionalised exotic cars to CGI rendering power and much more. In short, adding crypto to a portfolio can introduce more safety in the form of more diversity, and within that crypto chunk someone can also diversify for the same benefits.
Conventional wisdom also suggests that cryptocurrencies and digital assets are in the right place at the right time to grow further.
"Digital assets are squarely at the intersection of some of the most significant trends reshaping the global economy," Beck says.
These trends include the following:
- An environment of slow economic growth, low interest rates and divergent central bank policies
- Rapid technological shifts which are altering traditional financial industry economics, making it possible to move and settle almost anything digitally, at the speed of information
- Ongoing regulatory shifts that are constantly increasing the cost of compliance and operations in traditional financial services
- Demographic shifts driven by the next generation of investors entering their prime earning years, and boomers entering retirement and tapping into underfunded pension plans
By the numbers
The paper suggests that even the most conservative interpretations have digital assets looking like a sensible addition to a diverse portfolio in line with Modern Portfolio Theory.
But the less conservative takes, factoring in the unique features and benefits of cryptocurrencies and other digital assets, have Grayscale suggesting that they're a whole lot more, and that with the addition of digital assets "the optimal beta portfolio lies somewhere higher than what was previously believed to be the efficient frontier."
Grayscale's take on the benefits of diversification is fairly clear. In general, the risk reductions associated with diversification are dependent on the number of different asset types in a portfolio, and how closely correlated each of them is.
Mathematically, more diversification is a lot like free money in the form of reduced risk without an anticipated loss of investment returns.
For example, if you assume that each asset in a portfolio carries an identical risk/reward ratio, and that each asset has zero correlation with the other, then a portfolio of four assets would be 50% less risky than a single asset. On paper, that means higher returns without any real downside.
By the numbers, as long as the risk-to-reward ratio of each asset type in a portfolio remains the same, more diversification (in the form of less correlation between asset types in a portfolio) will always be preferable and lead to statistically higher expected returns.
Because cryptocurrencies and digital assets are a new asset class, and because they have less correlation to other asset types than other asset types have to each other, Beck notes, they're just an inherently smart addition to most portfolios, assuming they carry an equivalent risk/reward ratio.
On risk/reward ratios
The Sharpe Ratio is the most widely used system for calculating risk-adjusted returns. In other words, it boils down the risk/reward ratio to a single number. A higher Sharpe Ratio means lower risk and higher reward, and a negative Sharpe Ratio would mean an investment is expected to return less money than a "zero risk" benchmark like the US dollar.
Interestingly, all asset types tend to have a similar Sharpe Ratio in the long run, Beck notes, averaging 0.3. Traders simply demand higher returns for higher risks, and expect lower returns for lower risks, regardless of how an investment is categorised. Volatility varies widely between asset classes, but the overall return on investment demanded by speculators tends to remain similar across the board.
Of course, cryptocurrencies have previously bucked the trend, and any analysis that uses the last five years of bitcoin prices as a benchmark will leave crypto smelling like roses. But because different asset types come together at an average 0.3 Sharpe Ratio regardless of volatility, it's reasonable to assume that the cryptocurrency asset class will end up broadly similar, assuming that the intense gains of the last couple of years are a one-off.
So even if cryptocurrencies don't go to the moon, or have already been there and are now coming back down to Earth, buying might still be a mathematically smart move due to the diversification benefits.
With the "past performance is no guarantee of future returns" mantra in mind, Grayscale assembled a more useful set of assumptions based on a 0.3 Sharpe Ratio and some educated guesses.
"We think it is reasonable to assume that digital assets will continue to be the most volatile asset class for quite some time," Beck predicts. "However, we assume that the equilibrium volatility will dampen to around 35%. In this scenario, we’d expect digital assets to have an annualised excess return of approximately 10.5%, based on a Sharpe ratio of 0.3.
"Although the average correlation of digital assets to other asset classes appears to be around zero today, we think that correlations could increase as more managers allocate to digital assets over time. Our basis for this is that managers must often make decisions about how they allocate between cash and risk assets, particularly in a liquidity crisis. Since digital assets clearly fit into the "risk" bucket, this relationship could drive their correlations to other risk assets higher. Still, we continue to believe that a high proportion of the returns for the digital asset class will be driven by idiosyncratic factors. For this reason, we assume an equilibrium correlation of 0.2."
Digital asset expected returns
With these hypotheticals established, Grayscale ran the numbers on different scenarios. The most detailed was probably a 5% digital asset allocation on top of a Global 60/40. with $100,000 initial investment and $18,500 year on year after that.
"The Global 60/40 (95%) + Digital Assets (5%) hypothetical simulated portfolio would generate roughly 30 bps of additional return on an annualized basis when compared to the Global 60/40, at the same level of risk. While this might seem small, the effect of compound returns can make this meaningful over time," the paper says.
Even in the worst case scenario, assuming the value of digital assets drops to $0 in year 1 when the impact on compounding returns is greatest, the maximum shortfall across a 40-year period is only 1.2% less than the dollar value of the Global 60/40 alone. Meanwhile, Grayscale's expected digital asset performance sees the same simulated portfolio up almost 8% after 40 years, compared to the Global 60/40 alone.
So assuming cryptocurrencies work much like any other asset class and bring similar returns, they still have the ability to move more independently of other asset classes. Grayscale found a median net positive outcome from a 5% crypto allocation over 40 years.
So even under these quite conservative assumptions a small crypto allocation makes sense. It's not as exciting as lamborghinis on the moon, but it does look like a sane addition to a healthy portfolio.
"Although we believe this analysis is relatively conservative, we encourage investors to use this framework and test their own set of assumptions," Grayscale says.
There's a reason the OTC crypto market is still booming, and why institutions are pouring money into digital assets, even as prices slump. They've formulated their own expectations and models for digital assets, run the numbers, and realised that even the most conservative expectations make a very compelling case for getting into crypto.
The tipping point for institutional interest in cryptocurrency wasn't when bitcoin hit $20,000 bitcoin. If anything, the price spike just fuelled the idea that crypto was a temporary speculative bubble to be avoided, rather than a potential long-term investment to work with.
The real tipping point was interest in the technology itself and the realisation that it's here to stay. That's when institutional investors stopped asking "should we buy?" and started asking "how do we buy?"
Disclosure: At the time of writing, the author holds ETH, IOTA, ICX, VET, XLM, BTC and NANO.
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