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A 2022 paper authored by mid- and senior-level employees at the investment behemoth BlackRock is causing quite a lot of upheaval in the crypto-focused circles of social media currently, given its phenomenally positive implications for Bitcoin. While the core thesis of the paper is quite likely to have been priced in already, the wild buzz that it is only now generating merits a thorough understanding of the underlying assumptions, limitations, and conclusions.
Bitcoin Twitter is freaking out about a @BlackRock research paper that apparently suggests an optimal portfolio allocation of 84.9% to #Bitcoin.
How do they come this conclusion and what are the underlying assumptions?
Let's find out 👇🧵 pic.twitter.com/HsshAbRcJV
— André Dragosch | Bitcoin & Macro ⚡ (@Andre_Dragosch) July 26, 2023
The paper, titled “Asset Allocation with Crypto: Application of Preferences for Positive Skewness,” has been authored by BlackRock’s head of factor investing strategies, Andrew Kang, quantitative hedge fund portfolio manager, Tom Morris, and BlackRock’s head of systematic investing, Raffaele Savi.
The paper was authored in February 2022 and is likely to have been circulated internally at BlackRock, given the involvement of the investment titan’s upper echelons of management. In fact, as speculated by Deutsche Bank’s André Dragosch here, the paper might have been instrumental in spurring BlackRock to try to win approval from the SEC for a spot Bitcoin ETF.
Before going over the paper’s conclusions, it might be a more helpful exercise to examine its underlying assumptions. The authors assume that Bitcoin’s returns have a normal mixture distribution. A mixture distribution is a mixture of two or more probability distributions. Here the authors assume that Bitcoin’s returns have fat positive tails, which connects with their assumption that the cryptocurrency has an extremely positive return skewness – where the probability of extremely positive returns is quite high as compared to the bell-shaped normal distribution of returns.
Next, the authors divide Bitcoin’s returns into two distinct regimes: normal and bliss. In a normal regime, Bitcoin offers low average returns and high volatility. In a bliss regime, Bitcoin offers high average returns with lower volatility. As per the authors’ tabulation, Bitcoin has been in its bliss phase only 3.6 percent of the time.
Finally, the paper’s authors assume that two behavioral theories dictate how investors make their financial decisions: Constant Relative Risk Aversion (CRRA) and Cumulative Prospect Theory (CPT). The CRRA tries to quantify how much risk people are willing to take to acquire a bit more of something (in this case, Bitcoin). The CPT assumes that people feel the impact of losses much more severely than that from equivalent gains. It also assumes that sequential constant gains entail a declining level of excitement.
The Paper’s Conclusions: Add Bitcoin to Your Portfolio
18/ Assuming CRRA/power utility-like investors 🧮
One can deduce the theoretical risk aversion parameter within the utility function that leads to a 60/40 allocation.
By holding that risk aversion parameter constant and adding #Bitcoin to the range of possible assets, one can… pic.twitter.com/SpsDNkcN5o
— André Dragosch | Bitcoin & Macro ⚡ (@Andre_Dragosch) July 26, 2023
Let’s now go over the paper’s findings. For the CRRA, the authors first deduce the level of risk aversion that leads to a classic 60/40 portfolio (60 percent of investments in stocks and 40 percent in bonds). Then, they hold this level of risk aversion constant and start adding Bitcoin to a range of different portfolio combinations. Assuming standard risk aversion in a 60/40 portfolio, optimal Bitcoin allocation stands at 84.9 percent. In the case of high risk aversion, where 80 percent of a portfolio is in bonds and just 20 percent in stocks, optimal Bitcoin allocation stands at 12.5 percent.
20/ The authors change the probability of the bliss market regime in order to get realistic results to 0.1% instead of 3.6% (empirically) and also change the mean return in the normal market regime to -90% (assuming a significant loss in the 'normal' market regime).
Still:… pic.twitter.com/kU7opUegiB
— André Dragosch | Bitcoin & Macro ⚡ (@Andre_Dragosch) July 26, 2023
When considering the CPT model, a standard portfolio consists of 28 percent stocks and 72 percent bonds. Here too, assuming the very slim probability of a bliss market, optimal Bitcoin allocation stands at 9.5 percent.
While the paper bodes well for Bitcoin’s prospects, readers should note that investors usually do not make deliberate investment decisions based on the CRRA or CPT. That said, the paper’s optimal Bitcoin allocation level of 12.5 percent for a risk-averse portfolio (as should be the case for most managed funds) does appear quite reasonable. Hence, its well-earned buzz currently.
About the author: Writing is my one incontrovertible passion. Over the past six years, he has authored over 2,200 distinct articles on financial and tech-related topics, spanning nearly 1 million words. And he has been a member of Wcctech mobile team since 2025. As an alumnus of the University of Toronto, Rotman Commerce Program, I bring nuance, in-depth knowledge, and a unique perspective to every topic that I cover. When I'm not writing, I'm traveling the world, exploring hidden confectionaries and restaurants as an aspiring food connoisseur.
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