Do the high market valuations of cryptocurrencies reflect their fundamental value or speculation? Is their volatility caused by irrational investors? In ‘Equilibrium Bitcoin Pricing’, forthcoming in The Journal of Finance, TSE researchers Christophe Bisière, Matthieu Bouvard, Catherine Casamatta along with TSE Associate Bruno Biais, and their coauthor Albert J. Menkveld, investigate the impact of transactional costs and benefits, as well as extrinsic volatility, on cryptocurrency prices.
What are the costs and benefits of cryptocurrencies?
A cryptocurrency (such as bitcoin) can provide transactional benefits that standard money (such as a dollar) cannot. For example, citizens of Venezuela or Zimbabwe can use bitcoins to conduct transactions even when their national currencies and banking systems are in disarray. Cryptocurrencies can also be used for cross-border transfers when high costs or government controls hinder transfers via traditional financial institutions.
The costs of cryptocurrencies include limited convertibility into traditional currencies, transaction costs on exchanges, fees that agents must pay to the miners who validate transactions, and risk of a crash. As cryptocurrency ownership is defined outside the legal system, it is also more vulnerable to theft by hackers.
How do cryptocurrencies compare to stocks?
In our model, investors rationally choose their demand for cryptocurrency based on their beliefs about future prices and net transactional benefits. So when it becomes more likely that a cryptocurrency will facilitate transactions, its price should go up. This is consistent with the rise in bitcoin price, for example, following announcements that firms such as Paypal, MasterCard or Visa would integrate bitcoin in their payment architecture.
This highlights that transactional benefits are to cryptocurrencies what dividends are to stocks. There is, however, a major difference. In perfect markets, dividends do not depend on stock prices and provide a real anchor for valuation. In contrast, the transactional benefits provided by a cryptocurrency depend on its price: The higher the price of the cryptocurrency, the stronger its purchasing power relative to the standard currency, and consequently the higher the transactional benefits it delivers.
What does your model reveal about price volatility?
Economists use the term "sunspots" to refer to exogenous variables that reflect something other than the basic fundamentals of an economy, such as investors’ emotions and expectations. Because cryptocurrency prices reflect beliefs about future prices rather than real variables independent of prices, this suggests that sunspots may have an important impact on cryptocurrency volatility.
Our paper offers a new characterization of two classes of equilibria. First, we consider “constant price equilibria” in which, at each period, there can be a sunspot leading to a crash in which the cryptocurrency price permanently drops to zero, while the standard currency price remains positive. Before and after the crash, however, prices of both currencies are constant. Second, we characterize “volatile price equilibria,” in which sunspots can trigger price changes at each period. The different crash probabilities determine the state of the sunspot at that time – including whether a crash occurred, and the belief about a crash occurring in the current period – and the corresponding equilibrium price. We can then obtain the equilibrium cryptocurrency prices at all previous periods.
Our model shows that cryptocurrency volatility can be increased by extrinsic volatility unrelated to fundamentals.
Which data do you use to test your model?
We construct a time series of bitcoin prices from July 2010 to December 2018. We then collect the transaction fees paid by bitcoin users to miners. These fees are high when the trading is large, leading to congestion in the blockchain. Thus, high transaction fees are not only costly by themselves but also signal costs associated with congestion.
Next, we collect information on events likely to affect bitcoin’s transactional costs (such as the shutdown of a large platform) and benefits (such as when bitcoin becomes tradable against a new currency or accepted by merchants). We also collect data about bitcoin thefts and hacks: On average, during the whole sample period, the fraction of bitcoins lost per week is about 0.04%.
We calibrate our model using these data. For simplicity, we assume that investors are risk-neutral.
Were you surprised by your findings?
Using our proxies of transactional costs and benefits, we show that these fundamentals account for part of bitcoin returns. Calibrated required bitcoin weekly returns start very high (above 10% per week), but then decline, to 2% at the end of the sample period.
Crash risk accounts for around 11 percentage points of the required return at the beginning of the sample period, before falling close to zero. The costs associated with mining fees and congestion are negligible, except for 2017. Difficulty in exchanging bitcoin for standard currency initially adds almost 10 percentage points to the required return. Within a year, however, its contribution drops to remain at around eight percentage points.
Against these costs, the calibrated transactional benefit starts around zero but hovers around 8% from 2015 onwards. Although this may be implausibly high, it is useful to compare this with cross-border transfer costs, which cryptocurrencies can help to avoid. For example, World Bank data suggests that remittance costs are around 6%.
Consistent with our theoretical predictions, our calibration also shows that changes in net transactional benefits only explain a small share (around 5%) of the variance of bitcoin returns. This implies that a large part of the fluctuation in bitcoin prices reflects extrinsic volatility unrelated to fundamentals.
Where might this research path lead to next?
Reflecting the very large realized bitcoin returns, our calibrated transactional costs and benefits are very large, and arguably implausible. This calls for extensions of our framework that could better rationalize observed returns. Richer specifications, possibly allowing for differences in beliefs, or keeping the probability of a crash high even after a long period without crash, could help match the data with more plausible parameters.
Article published in TSE Reflect, April 2022
