Ran Duchin, David H Solomon, Jun Tu, and Xi Wang
Review of Finance, Volume 29, Issue 6, November 2025, Pages 1721–1767, https://doi.org/10.1093/rof/rfaf037
Finance academics, as a whole, tend to dislike giving normative advice. Like the Hippocratic Oath, if we can’t be sure our advice is correct, we can at least stop ourselves giving bad advice. But this reluctance often means our students sometimes have little guidance on some important questions. When it comes to cryptocurrency, the most common question is “Should I buy any?”. The finance literature gives little answer here.
We explore this question, while deferring to the enormous range of views that people have about what cryptocurrency is. Different beliefs about crypto can be expressed as priors over returns. We combine these in a Bayesian portfolio theory framework to develop conditional advice – essentially, “you tell me your beliefs about cryptocurrency, and we’ll tell you what allocations they imply”. Of possible beliefs and actions, some of the most interesting are the common combination in finance academia: the stated belief that cryptocurrency is a bubble with no fundamental value, and persistent zero weights (not having ever bought it, but also not having shorted it).
The headline result of the paper is that one can either think that crypto is a bubble going to zero (with negative expected returns), or one can have a weight of zero, but it is surprisingly hard to do both. An investor who had priors equivalent to ten years of returns before cryptocurrency began would have needed extremely pessimistic beliefs to justify never purchasing: -10.6% per month for Bitcoin, and -19.6% for an equal-weighted cryptocurrency portfolio. Anyone more optimistic than this would have bought by 2022. Meanwhile, even beliefs that are this pessimistic generally imply you should want to short cryptocurrency.
When we look at the optimal weight implied by a range of beliefs, they have four general properties. They are:
- Small
- Non-trivial (1-5% in magnitude)
- Frequently positive
- Smooth
The fact that cryptocurrency is volatile means that large weights are inadvisable, but most investors would have wanted at least a small weight in one direction or other.
The portfolio gains from access to cryptocurrency are considerable. For a range of priors, the benefits are equivalent to international diversification, access to commodities or equity anomaly portfolios, and portfolio mistakes like holding too few stocks or using the 1/N rule. In contrast to the informal view that purchasing cryptocurrency is a mistake, failing to trade cryptocurrencies appears to be costly enough to be on par with many frequently studied portfolio mistakes.
Adding realistic frictions or modeling complexities makes little difference to the answer. These include trading costs, different starting portfolios, model uncertainty, different utility functions, and return predictability. Zero weights are not impossible, however. They are most easily generated by very strong beliefs that cryptocurrency is a very slowly deflating bubble (i.e. it will earn slightly less than the risk-free rate)
Our analysis is far from the last word, but the general result that many prior beliefs can justify small positive weights in cryptocurrency is one that is surprisingly difficult to overturn.