1 INTRODUCTION↩︎

This survey establishes ten key empirical regularities of cryptocurrencies motivated by the view that cryptocurrency is an asset and thus can and should be analyzed from the asset-pricing point of view and, more specifically, from the cryptocurrency asset pricing view. Although the literature is relatively young—cryptocurrencies trace back to [1]’s short paper on Bitcoin—it is now at the point of maturity where it is useful to establish a core of stylized facts in cryptocurrency markets that can be used for both empirical and theoretical work. This common set of facts also provides emerging evidence that cryptocurrency is becoming an investable asset class.

Money has long been a central topic in economics—for example, see classic contributions of [2] and [3] to more recent advances. A large literature studied why money exists and how it functions—the role of money in economies with spatially separated agents ([4]), the coexistence of different types of money under different institutional restrictions ([5]), search-based models [6]–[9], mechanism-design approaches [10], the “money-as-memory” view [11], commodity and token money [12], [13], competing currencies [14], and the money-like safe assets ([15], [16]).

When the paper of [1] introduced a permissionless blockchain that provides public record-keeping without a central authority, financed and governed by a native token, the canonical literature on money had reached a degree of maturity. Permissionless ledgers can be viewed as technologies that supply public memory, with token systems financing and governing that record—keeping, and providing histories, communication, and enforcement mechanisms that are required for credit. With the rise of cryptocurrencies, these new ideas began to emerge primarily from practice more than theory and reopened classic monetary questions—record-keeping, commitment, enforcement—but now viewed from the point of view of blockchain economics.

When practice advances faster than theory, it is natural to start asking empirical questions that can themselves later be used to shape theory. The paper of [17] is the first comprehensive analysis of cryptocurrency through the lens of empirical finance and asset pricing. A sizable literature uses an asset pricing lens to study risk exposures, cross-sectional return patterns, cash-flow-like primitives, market microstructure, and limits to arbitrage (see, for example, [18], [19], [20], [21], [22], [23]).

Many have viewed cryptocurrencies—and, not unjustifiably, many still view them—as hype, speculation, or fraud. When cryptocurrency first appeared it was easy to dismiss it: money engineered by an unknown author and operating outside of the traditional financial system.² It is worth noting that several important financial innovations, such as the limited-liability company and mortgage-backed securities, were also initially met with distrust before becoming part of standard finance (see, for example, [26] and [27]), as institutions and legal frameworks evolved to manage their risks and as research deepened understanding of these innovations.

Since then research has evolved toward a much broader agenda that increasingly resembles research on any other asset class—the market structure ([28], [29], [30], [31], [32], [33], [34], [35]), regulation ([36],[37], [38]), digital asset pricing and valuation ([39], [40], [41]), transaction costs ([42], [43], [44]), central bank money ([45], [46], [47]), securitization ([48], [21], [49], [50]), safe assets ([51]), international capital flow ([22]), blockchain technologies and the traditional financial system ([52]) and market microstructure ([53]).

We synthesize the rapidly growing empirical finance of cryptocurrencies into a set of ten stylized empirical regularities that show how cryptocurrencies behave as assets, how their markets function, and what distinguishes them from traditional asset classes. These empirical facts are also useful to evaluate and revisit both the classic and the new theories of money. Ten Facts in Cryptocurrency Asset Pricing and Empirical Finance. Facts 1 and 2 overview the core asset-pricing characteristics of cryptocurrency markets—the risk-return trade-off and the diversification benefits. Facts 3 and 4 discuss the structure of returns in cryptocurrency—factors, or “smart-beta”, which explain the cross-section of returns and optimal portfolio shares. Fact 5 shows the importance of large, discrete price movements—jumps—and the importance of extreme events for understanding cryptocurrency risk and valuation. Fact 6 shows that the higher-order terms of a parsimonious four-factor model account for a large fraction of the cross-section of returns and provide a “glass box” alternative to the “black box” neural net models with interpretable economic factor structure. Fact 7 shows the importance of the blockchain structure and network economy phenomena for cryptocurrency prices—on-chain user adoption influences cryptocurrency returns. Facts 8 documents large and persistent market inefficiencies due to frictions that limit arbitrage, and discuss risks for arbitrageurs. Fact 9 is about the cryptocurrency futures market and funding premia, and their evolution. Finally, Fact 10 is about the importance of regulation, disclosure, and transparency. In sum, these ten facts can be viewed as providing evidence that cryptocurrency, and more broadly, digital assets are coming of age as an emerging investable asset class.

2 DATA↩︎

The empirical analysis is based on the most recent data aggregated from multiple sources.

First, we collect comprehensive price data on all cryptocurrencies from CoinGecko.com, covering both active and inactive coins between December 31, 2013, and September 6, 2025. The sample includes 18,622 coins listed on CoinGecko at the end of the period, as well as 29,230 inactive coins that have since been delisted but for which historical data are available. Including inactive coins allows us to avoid survivorship bias. We exclude stablecoins because they are designed to track the value of a currency, a basket of fiat currencies, or another reference asset. We also exclude wrapped tokens (such as Wrapped Ether) as they are essentially replicas of existing coins on different blockchains. Furthermore, we drop daily observations with missing or non-positive values for price, market capitalization, or trading volume. We also exclude all coins with fewer than 30 daily observations. The final dataset comprises 16,468 unique coins and approximately 9.5 million records.

Second, for the construction of the crypto carry strategy of [54], we collect perpetual futures prices, funding rates and spot index prices for Bitcoin at the 8-hour frequency from Binance for the period August 1, 2020 to May 31, 2025. The data on new addresses are from [55]. Moreover, for the construction of the crypto arbitrage strategy of [56], we collect Bitcoin prices against 510 pairs from 165 different centralized exchanges quoted against 49 fiat currencies from CryptoCompare.com for the period December 31, 2013 to January 30, 2025. Furthermore, for estimation of jumps in cryptocurrency we collect tick-level transaction data for Bitcoin and Ethereum from Kraken.com and measures of realized variance constructed from tick-level data for the components of the Dow Jones Industrial Average Index from the CaPiRe dataset, for the period January 1, 2015 to March 31, 2025.³

Unless otherwise noted, we aggregate daily closing prices to construct weekly coin returns. Each year is divided into 52 weeks: the first week contains the year’s first seven days, the next 50 weeks consist of seven days each, and the final week contains the remaining days of the year. For the construction of weekly returns, we exclude coins with a market capitalization below $1 million at the formation date and winsorize returns at the 0.0025% level in both tails. We construct a cryptocurrency market return as the value-weighted return of all underlying coins. The cryptocurrency excess market return is constructed as the difference between the cryptocurrency market return and the risk-free rate measured as the 1-month T-bill rate at the weekly frequency, which we obtain from the Federal Reserve Bank of St. Louis.

Figure 1 summarizes the time-series evolution of cryptocurrency prices and market capitalization. A one-dollar investment at the start of the sample grows to about $160 in Bitcoin and $80 in the overall market. There is substantial variation over time. Market capitalization reaches nearly $4 trillion, with Bitcoin and Ethereum accounting for approximately 58% and 12% of the total at the end of the sample.

3 THE TEN FACTS OF CRYPTOCURRENCY↩︎

We organize the main discussions of this review into the ten key stylized empirical facts on cryptocurrency markets.

3.1 Fact 1: High return, high volatility—normal Sharpe ratio↩︎

Fact 1: The cryptocurrency market has an order of magnitude higher returns and volatility than equities, but a broadly similar Sharpe ratio.

Popular discussion of cryptocurrencies tends to focus either on their dramatic average returns or on dramatic volatility. From the classic finance point of view, the relevant measure is, however, risk-adjusted performance—the Sharpe ratio, i.e., mean excess return per unit of volatility ([57]).

[17] establish that the aggregate cryptocurrency market exhibits returns and volatilities an order of magnitude higher than those of the aggregate stock market, but Sharpe ratios remain broadly comparable. Fact 1 revisits and confirms this finding in a longer and larger dataset up to September 2025.

Table [tab:tab195sumstats], Panel A, reports summary statistics for the sample beginning in 2014 and ending in September 2025, as well as for the samples pre-2020 and post-2020. We compare returns on the aggregate coin market, a large-cap index of the top 100 cryptocurrencies (Coin 100), Bitcoin, and the aggregate U.S. stock market. The average returns and volatilities of all cryptocurrency return series are an order of magnitude greater than those of the stock market across all sample periods. For instance, average weekly returns exceed 1% for all cryptocurrency indices, compared with less than 0.3% for the aggregate stock market. However, the weekly Sharpe ratios are similar across cryptocurrencies and equities. This, confirms that the Sharpe ratio calculated by [17] holds in the most recent sample.

Table [tab:tab195sumstats], Panel A, reports maximum drawdowns and run-ups for the four return indices. Drawdowns are important as they provide a measure of tail-risk not fully reflected by standard deviation. Drawdowns and run-ups are substantially larger for cryptocurrencies than for equities. Importantly, for all three cryptocurrency indices, maximum drawdowns and run-ups are smaller in magnitude in the post-2020 sample than in the pre-2020 sample, while the reverse holds for equities. This pattern can also be observed in the standard deviations of returns—they decline for cryptocurrencies and rise for equities in the more recent period.

3.2 Fact 2: Cryptocurrency is a distinct asset: it moves largely on its own—but increasingly with equities, gold and commodities↩︎

Fact 2: The aggregate cryptocurrency market remains largely uncorrelated with most traditional asset classes, but its correlation with U.S. equities has increased sharply—from 2% before 2020 to 37% after 2020.

How cryptocurrencies co-move with traditional asset classes is a first-order question for asset pricing and portfolio choice (e.g., [58]). Correlations are an important determinant of diversification benefits and show whether cryptocurrency risk is distinct to that market or simply represent familiar risks from other markets. We revisit the cryptocurrency aggregate correlation structure using updated data, contrasting the pre-2020 and post-2020 return correlation.

One of the main results of [17] is that aggregate cryptocurrency returns have insignificant exposures to the returns of traditional asset classes, such as equities, bonds, commodities, and foreign exchanges. In other words, the correlation between the aggregate cryptocurrency returns and those of traditional asset classes are low. Fact 2 revisits this finding. We show that there is a rising correlation with the U.S. stock market.

Table [tab:tab195sumstats], Panel B, reports correlations of aggregate cryptocurrency returns with those of major asset classes. In the pre-2020 sample, correlations with equities, corporate bonds, government bonds, commodities, gold, and the dollar are all statistically insignificant, confirming the earlier findings of [17]. In contrast, in the post-2020 sample, aggregate cryptocurrency returns become significantly correlated with equities (37%), commodities (27%), gold (18%), and corporate bonds (13%) at the 5% level. The correlation with the dollar index is negative (-10%) and significant at the 10% level. Government bonds remain the only asset class with no significant link.

The most striking change is the correlation with the U.S. stock market, which rises from only 2% before 2020 to 37% afterwards. This substantial increase is an important indicator that cryptocurrencies have become more integrated with equity markets. We also document a significant post-2020 correlation with changes in expected inflation (31%), measured as the first difference in the yield differential between nominal and inflation-indexed U.S. Treasury bonds with 10-year maturity. Since this measure incorporates an inflation risk premium, the result may reflect the same underlying risk component that drives the stronger comovement between cryptocurrencies and equities in recent years. In our view, this link with expected inflation is important, as it provides empirical evidence on the original motivation of cryptocurrencies as assets designed to hedge against the inflationary risks of government printing money.

The increase in correlation between the cryptocurrency market and traditional asset classes has been documented in recent studies, for example, [59] and [60]. Several mechanisms are proposed to explain this phenomenon, including monetary policy, retail investor trading, and financialization. The literature has yet to reach a consensus on the cause of this important shift in the return dynamics of the cryptocurrency market.

3.3 Fact 3: Significant diversification benefits from adding small amount of cryptocurrencies in investment portfolios↩︎

Fact 3: Cryptocurrency idiosyncratic risk can be significantly reduced by constructing optimal mean-variance asset portfolios that include cryptocurrencies—the inclusion of cryptocurrencies enlarges the mean-variance frontier. Optimal portfolio allocates 3.1% cryptocurrency for retail investors and 5.5% for institutional investors.

Modern finance theory, starting from [58], emphasizes the central insight of diversification: an asset’s covariance with the investor’s portfolio matters more than its volatility. Low correlations push the efficient frontier outward, and volatile assets can add value if their expected returns compensate for marginal risk. Since Fact 1 establishes that cryptocurrencies have low correlations with stocks and bonds, they can be effective risk diversifiers under standard portfolio-theory frameworks.

[17] show that cryptocurrencies can improve portfolio efficiency because of their historically low correlations with traditional asset classes and comparatively high expected returns. Using the Black–Litterman portfolio allocation model ([61]) to incorporate investor views, [17] estimate that a representative investor would optimally allocate between 1% and 6% of wealth to cryptocurrencies, depending on the strength of those views. A complementary view comes from Bayesian portfolio theory. [62] obtain similar optimal weights in the 1%–5% range. [63] find much larger optimal weights when investors have a preference for positive skewness, such as under constant relative risk aversion.

Because the optimal crypto weight is sensitive to the joint return distribution—especially the correlation between cryptocurrencies and traditional assets—and because this correlation structure shifted after 2020 (see Fact 2), we re-estimate the theoretical optimal allocations using post-2020 data under the same Black–Litterman framework.

Moreover, we extend the analysis to two representative investor classes: a retail investor and an institutional investor. In calculating the theoretical optimal crypto portfolio shares for them, we differ only in their investable options. This simplification abstracts from practical complications, such as liquidity, custody, and regulatory constraints, to make the exercise tractable.

For a retail investor, we start with a baseline portfolio that is 50–50 between financial assets and real estate, with the financial portion 60–40 stocks–bonds. Based on the model, if we add an allocation to the cryptocurrency market, we would raise the portfolio’s Sharpe ratio from 0.39 to 0.52, with an optimal crypto weight of 3.1% of total wealth. As a historical counterfactual, we also compute the theoretical optimal portfolio using only pre-2020 data; the optimal crypto share is 1.4%. Mapping this to per-capita U.S.net wealth in 2019, a 1.4% allocation implies an investment of about $3,500; held from 2020 to the end of our sample, this position would have grown by roughly $52,000 (about 1,462%). This is a back-of-the-envelope, buy-and-hold calculation that assumes no rebalancing.

For an institutional investor, we consider a broader investable universe—equities, government and corporate bonds, commodities, and real estate—with baseline weights proportional to each asset class’s market capitalization. Solving for the optimal portfolio and assuming slightly greater confidence in views on cryptocurrencies than in the retail case, the model implies an increase in the portfolio’s Sharpe ratio from 0.69 to 0.95, with an optimal share of 5.5% in the cryptocurrency market.

These results show that—even with the post-2020 increase in comovement with equities—optimal allocations to cryptocurrency are sizable and in the 3–5% range, with larger weights for institutional portfolios. It is important to note that the estimations in this section are back-of-the-envelope and rely on the properties of returns that may not persist and abstract from important issues related to liquidity, custody, and regulatory risk, and therefore should be viewed as theoretical upper bounds on the potential diversification benefits of this emerging investable asset class, not as actual investment recommendations. For context, CalPERS, one of the largest U.S.pension funds, reports portfolio shares of comparable magnitude in emerging-market debt (5.3%), high-yield bonds (5.3%), private debt (3.8%), and mortgage-backed securities (5.8%) as of June 2025, indicating that the model-implied weights of cryptocurrencies are within a realistic range.

3.4 Fact 4: How to be “smart” in crypto—crypto-size, crypto-momentum and crypto-value↩︎

Fact 4: A small number of smart beta strategies—based on crypto-size, crypto-momentum, and crypto-value—span the cross-section of cryptocurrency returns.

A central question in asset pricing is whether systematic variation in expected returns can be explained by a parsimonious set of factors. In equities, substantial academic endeavor—most prominently by Eugene Fama and Kenneth French (e.g., [64])—established this approach, and factor models play a core role in modern finance practice and theory from risk management of large banks to niche hedge fund strategies. For cryptocurrencies, [19] establish that a three factor model consisting of the aggregate cryptocurrency market, size, and momentum (C-3 factor model), captures a large fraction of the cross-section of expected returns. [55] show that adding a value factor (C-4 factor model) further strengthens the explanatory power. We revisit this evidence using our updated sample and show that a small number of predictors drive the cross-section of cryptocurrency returns over the longer sample and post-2020.

We construct smart beta strategies by sorting coins into quintile portfolios based on three established significant predictors: market capitalization (CSIZE), past two-week returns (CMOM), and the price-to-new-address ratio (CVALUE).⁴ The return to each predictor is measured as the long-short spread between the highest and lowest quintiles (Portfolio 5 minus Portfolio 1).

Table [tab:portfolio95strategies95main], Panels A and B, report average excess returns to the quintile portfolios and the corresponding long-short strategies for the full sample and the post-2020 subsample. All three predictors generate statistically significant long-short returns in the full sample. The average long-short returns based on size and value are significantly negative and the average long-short return based on momentum is significantly positive, consistent with [19]. Cryptocurrency value is the weekly quintile portfolio of each bracket based on the price-to-new address ratio. High bracket is the low-value coins and low bracket is the high-value coins. The sorting is done in week \(t\) and the returns are the value-weighted average in the following week.

Importantly, these results remain robust in the post-2020 sample, the core set of smart beta strategies in the C-3 factor model and C-4 factor model continues to explain variation in cryptocurrency returns even in the more recent period.

The C-4 structure of the crypto-market thus parallels the equity market, where a small number of equity-market factors—most notably size, value, momentum, and profitability—dominate the cross-section of expected returns. For example, [68] present evidence of value and momentum in equities, bonds, currencies, and commodities. The C-4 factor model of [19] and [55] is the cryptocurrency counterpart of the classic 4-factor model of [64] and [69] for equities. It is important to note that the predictors in cryptocurrency markets are only partly analogous to those in equity markets. CSIZE and CMOM closely resemble their equity counterparts, although crypto momentum is measured over a much shorter horizon (previous two weeks, versus the standard 12-to-2 months in equities). In contrast, there is no direct analogue to book value ([70]) in cryptocurrencies, so we follow [55] and proxy CVALUE with the price-to-new-address ratio.⁵

Establishing the small factor structure of the cryptocurrency returns, in our view, is not only important from purely the empirical asset pricing point of view but also since it provides a set of stylized low dimensional features that capture the main insights of several important theoretical models of cryptocurrency ([40], [21], [71]).

A related important point is that in addition to determining which betas are smart, it is equally as important to establish which betas from the factor zoo are not “smart”. Specifically, [19] and [55] show that—besides crypto-specific size, momentum, and value—most of the smart beta strategies from the canonical factor zoo in the equity market ([72]) either do not generate significant hedged long-short strategy returns or are subsumed by the C-4 factor model. In Table [tab:portfolio95strategies95not95work], we study long-short strategies based on these signals post–2020. These strategies include portfolios based on long-horizon momentum, volatility, volume, and beta. We find that these long-short strategies continue not to generate significant average returns in the recent sample.⁶ These results give evidence that the cross-section of cryptocurrency returns can be summarized by a small number of factors.

3.5 Fact 5: Mind the Jumps—large, sudden price moves and “common disasters”↩︎

Fact 5: Jumps are frequent and account for a large share of variation of cryptocurrency returns, far more than in equities. Thus, disasters are not rare but common.

Leibniz wrote that natura non facit saltus—nature makes no jumps. In economics and finance, this often means that most changes occur gradually, with only occasional discontinuities. Indeed, jumps are rare in many asset classes, and this key insight leads [74], in their celebrated option pricing paper, to model prices as Brownian motions.⁷ Rare disasters are also used as a central ingredient to explain risk-premia (e.g., [76], [77]). Cryptocurrencies are different: jumps, and hence disasters, are not “rare disasters” but are “common disasters.” Specifically, [67] show that 12.8% of Bitcoin’s daily variability can be attributed to jumps—large, sudden price moves—and that higher-order moments such as skewness and kurtosis explain the risk premium on Bitcoin.⁸ Fact 5 revisits and extend this finding, documenting the frequency and size of jumps in cryptocurrency and showing that those are far more relevant than for the U.S. stock market.

Table [tab:crypto95jumps] reports the frequency and magnitude of jumps in Bitcoin and Ethereum—the two largest cryptocurrencies by market capitalization—compared with U.S. stocks. Jumps are identified as the difference between the daily realized variance of [79] and the bi-power variation of [80], a jump-robust measure of integrated variance. The two realized measures are constructed from tick-level data aggregated at the 5-minute frequency. For U.S.equities, the same procedure is applied, and values represent cross-sectional averages across the constituents of the Dow Jones Industrial Average. Only jumps that are statistically significant at the 0.1% confidence level according to the BNS test of [80] are retained. For Bitcoin and Ethereum, the probability of a significant jump on a given day is around 40 percent in the pre–2020 sample and 15–20 percent in the post–2020 period. In sharp contrast, the probability of a daily jump in U.S. stocks is below 10 percent before 2020 and falls to about 3 percent thereafter. Thus, jumps are far more frequent in cryptocurrencies than in equities. Conditional on a jump occurring, however, the share of total return variation explained by the jump is broadly similar across asset classes, particularly in the post–2020 period. This shows that what sets cryptocurrencies apart is the high frequency of jumps—contrary to Leibniz’s dictum that natura non facit saltus, cryptocurrencies are markets where saltus sunt regula (jumps are the rule), rather than the exception.

These results show that higher-order moments are central to understanding cryptocurrency risk. Equity and bond markets follow relatively smooth dynamics with only rare discontinuities. Cryptocurrency markets are characterized by frequent and sizable jumps that are a defining feature of their return distribution. This prevalence of jumps, and the corresponding role of higher-order moments, means significant challenges for risk management and portfolio allocation (see, e.g., [81]). The implication is that we need empirical asset-pricing strategies that explicitly accommodate higher-order moments and nonlinearities (see, e.g., [82], [83], [84]).

3.6 Fact 6: Few factors, higher orders—rather than machine learning: why less is more↩︎

Fact 6: In cryptocurrency, higher-order terms of the C-4 model accounts for approximately 25% of the cross-section of returns and captures most of the insights of machine learning methods.

A growing literature in finance uses machine learning methods, such as neural networks, to investigate the cross-section of returns (see, for example, [85], [86], [87]). Neural networks have become extremely successful in many prediction problems and moreover have the universal approximation property ([88], [89])—a sufficiently large neural network can approximate any continuous function—and thus, in principle, capture any features of the data. These ideas have been present in the machine learning literature for several decades, but only recently have they become dramatically successful, as computational advances enabled the estimation of very large models, essentially aligning with the core idea of the universal approximation theorem. This has led finance and economics, as well as many other fields, to develop models with a very large number of parameters. The main shortcoming of neural networks for finance is that they are “black box” models. Once millions and sometimes hundred of millions of “factors” are run through often rather complicated and delicate gradient descent-like algorithms, it is difficult to see what features are economically important, how exactly the model produces results, and if an environment changes, whether the model still continues to perform.

One alternative to neural nets is the Kolmogorov–Arnold representation theorem ([90], [91]) introduced in finance by [92].⁹ Kolmogorov–Arnold remarkably shows that any nonlinear function can be written exactly as a combination of a finite sum of univariate functions composed with a link function. This formulation is thus a representation, not an approximation. Importantly, the early machine learning literature showed how to use in theory this representation to construct a shallower and smaller network ([93], [94], [95]). This network can be thought of as a much lower dimensional neural network where the activation functions of each neuron are being trained and adapt to the data. While theoretically this result is remarkable,¹⁰ it is not clear whether this approach would work on actual data because of the complexity that the theory requires for the representation of any function, and in particular, on finance data, which is both relatively small and has a very low signal-to-noise ratio. [92] is the first paper that shows the practical implementation and effectiveness of the Kolmogorov–Arnold architecture on actual data. Specifically, they show that this methodology enables construction of a single non-linear factor (KA factor) that captures a significant part of the variation in expected returns.¹¹ The main advantage of this approach is that the KA-factor can be thought of as a simple representation of a much more complicated and larger neural network and, in principle, captures all such networks, without having to consider a variety of neural networks specifications and the optimization algorithms.

Another alternative to neural networks follows the traditional finance toolbox—approximate and estimate the stochastic discount factor via a Taylor expansion. However, the Taylor approximation to the higher order generates a very large set of factors, due to the need to account for all of the interactions of the higher-order terms in the Taylor expansion. [84] develop the properties of a forward-selection Fama–MacBeth (FS-FMB) method for selecting the higher-order factors and their interactions that are most important for the cross-section of returns. The method proceeds sequentially, adding one factor or interaction to the selected set at a time and, at each step, choosing the term that maximizes the Fama–MacBeth (FMB) second-step cross-sectional R-squared. The main advantage of this approach is that it is a fully “glass box” model both in terms of determining the important factors and in the process to select them that allows to map features of the data to the economic factors and their higher order interactions.¹²

Table 1, Panel A, reports second-step FMB results for the crypto-CAPM, or C-1, model and for the C-4 model of [55]. The test assets are the set of 50 portfolios formed using the smart beta strategies described in Fact 4 (see Tables [tab:portfolio95strategies95main] and [tab:portfolio95strategies95not95work]), and the CARB strategy described in Fact 8 (see Table [tab:portfolio95strategies95arb], Panel B). As with the classic CAPM, the C-1 model cannot account for the cross-section of average returns. By contrast, the C-4 model explains 47.3% of the cross-sectional variation, and satisfies the restriction of a zero intercept.

Table 1, Panel B, reports the result of a specification which augments the C-4 model with the single KA-factor based on the Kolmogorov-Arnold architecture of [92]. One can think of this factor as a stand-in that captures a variety of different neural nets. The cross-sectional R-squared increases by approximately 25 pp, and the intercept is not statistically different from zero at standard levels.

Table 1, Panel C, reports the results from the estimation of the FS-FMB ([84]). At each step, we augment the C-4 by one additional higher-order factor (\(h_{j}\)) which maximizes the adjusted cross-sectional R-squared. Higher-order factors include the squared and cubed of the factors in the C-4 model, as well their pair-wise interactions up to order three. The procedure selects three higher-order factors. The first is CMOM cubed, resulting in an increase of the cross-sectional R-squared of approximately 15 pp. The importance of this factor is that it relates to the frequent and large jumps which are the distinct feature of cryptocurrency of Fact 5. The second and third selected factors are CMKT squared and the interaction between CMKT and CSIZE. [84] show that the equity counterparts of these factors are important for the cross-section of equity returns. The cross-sectional R-squared of the FS-FMB procedure is 70%, a value very similar to that of the model including the KA-factor. In all models, the estimate of the intercept is not statistically different from zero.

These results show that the FS–FMB procedure recovers essentially the same nonlinear structure as the KA single factor. Moreover, since KA can represent any neural net, FS–FMB provides a simple, transparent, “open box” alternative to black-box models that is directly connected to the economic structure of the model and to observables characteristics.¹³ In short, rather than estimating a neural network (or studying a particular variant of the multitude of neural networks), one can estimate the FS–FMB specification and capture the relevant nonlinearities in a parsimonious and interpretable way without relying on millions of parameters.

3.7 Fact 7: In crypto, the (block)chain drives the gain↩︎

Fact 6: Blockchain economics and information significantly affects cryptocurrency prices, on-chain user adoption accounts for about 8% of the variation in cryptocurrency returns.

Network externalities are a fundamental concept in economics because they shape markets and influence competition, regulation and technology adoption. Classic work has analyzed how networks form and evolve ([104]), how pricing and competition operate on networked platforms ([105]), and how shocks propagate through financial networks ([106]). A central question common in this work is information diffusion and learning in a network ([107], [108]).

One of the defining features of blockchain and one of the important innovations that it delivers is that blockchains create a continuously updated, public, and verifiable record of economic activity. Blockchains provide an observable, real-time map of user adoption and economic interactions. This makes them particularly useful for studying how information absorption affects asset values. As Metcalfe’s law put it, “the value of a network grows as the square of the number of its users.”

Empirically, [55] show that on-chain user adoption—measured as new user growth—has a statistically and economically significant effect on cryptocurrency prices. Importantly, this single on-chain variable accounts for about 8% of the variation in cryptocurrency returns. In time-series tests for the largest coins, on-chain user adoption alone can account for more than 10% of the variation in their returns.

[55] also examine how markets absorb this information and what conditions amplify its relevance. Event-time evidence shows a sharp price reaction when weekly adoption information is realized, with muted pre-announcement behavior and no post-announcement drift—in contrast to equities. The result gives evidence that investors fully incorporate the information at the weekly frequency.

Lastly, [55] show that the crypto value measure, constructed as the price-to-new-address ratio, negatively predicts cryptocurrency returns—a result we discuss in Fact 4.

3.8 Fact 8: Young cryptocurrency markets, old inefficiencies.↩︎

Fact 8: The young cryptocurrency markets are still inefficient. But the origins are canonical: market segmentation and restrictions on capital flows. Cross-exchange cryptocurrency “arbitrage” is no free lunch.

A central concept in finance is the law of one price—identical securities should sell for identical prices. The law of one price, and the related concept of absence of arbitrage, is important for the existence of a discount factor ([109], [110]). Deviations from the law of one price have been presented as proof of irrational investor behavior ([111]), limits to arbitrage and market segmentation ([112]), or previously overlooked risks ([113]).

One of the main features of cryptocurrency is that it is possible to trade coins simultaneously on multiple exchanges and against a number of fiat and crypto pairs. For example, an investor could buy Bitcoin on Binance or Kraken, two prominent centralized exchanges, against fiat currencies such as the U.S. dollar or the euro, or even against another cryptocurrency such as Ethereum or Tether, a stablecoin. [18] and [114] document sizable, persistent deviations in the dollar price of Bitcoin across exchanges and across fiat- and crypto-quoted pairs. We revisit this evidence on updated data for 510 BTC–fiat pairs traded on 165 centralized exchanges in 49 currencies. Bitcoin price discounts are computed each week relative to the dollar price on Kraken (the benchmark exchange). All quotes are converted to U.S. dollars using daily spot FX rates. In the 2014–2025 sample, the 10th and 90th percentiles of Bitcoin price discounts are –1.8% and 3.7%, respectively. These figures remain virtually unchanged in the post-2020 period (–2.1% and 3.5%). Moreover, discounts are highly persistent, with a half-life of roughly 1.1 weeks in both samples. These deviations—classic examples of market inefficiency and violations of the law of one price—are results of market segmentation induced by capital controls and idiosyncratic domestic shocks that prevent arbitrage.¹⁴

Table [tab:portfolio95strategies95arb], Panel A, reports the properties of an “arbitrage” (CARB) strategy that attempts to exploit these price discrepancies. Each week, we sort BTC–fiat pairs by their discount and form five portfolios. The CARB return for a given pair is defined by buying Bitcoin on Kraken in week \(t\) and selling it on the target pair in week \(t{+}1\); portfolio returns are the simple average across constituent pairs. Using weekly formation and holding periods substantially alleviates execution and timing concerns. In practice, capital controls, withdrawal limits, transaction costs, settlement latency, and venue-specific frictions prevent the cross-market trades needed to enforce the law of one price. Not surprisingly, the mean excess returns are implausibly high—on the order of 68.5% per week over 2014–2025, rising to 95% per week from 2020 onward—precisely because the required arbitrage trades are blocked or prohibitively costly. Specifically, [56] shows that this seemingly exceptional performance is concentrated in the extreme portfolio that holds pairs with the highest Bitcoin price relative to the benchmark quote, where segmentation and frictions are most severe. That is, the cryptocurrency market inefficiencies reflect the classic market segmentation and trading frictions as in [112].

As Sophocles writes in Antigone, “Nothing vast enters the life of mortals without a curse.” Early cryptocurrency investors often told a different story: that outsized returns came from cross-exchange “arbitrage.” Public interviews with Sam Bankman-Fried—the founder of the now-defunct exchange FTX—describe how Alameda Research, a hedge fund he helped run, allegedly began by focusing on such trades.¹⁵ However, [56] show that implementability is limited to a narrow set of highly liquid pairs on reputable cryptocurrency exchanges without binding capital controls.

We revisit the analysis in [56] and construct the CARB strategy for 226 Bitcoin pairs, traded on 96 exchanges against 11 fiat currencies (Australian dollar, Canadian dollar, Danish krone, euro, Hong Kong dollar, Israeli shekel, Japanese yen, Polish łoty, Swiss franc, British pound, and U.S. dollar). These are the pairs that are realistically investable. Table [tab:portfolio95strategies95arb], Panel B, documents that excess returns remain statistically significant but are orders of magnitude smaller: the long–short weekly return declines from about \(0.68\) to roughly \(0.038\) in the full sample, and measures around \(0.041\) in the post-2020 sample. In other words, where the strategy is actually implementable, the apparent “free lunch” largely vanishes. These returns are not pure arbitrage—they are compensation for risk. [56] show that the expensive pairs (those priced above the benchmark) are systematically riskier—they depreciate more in bad times for crypto-investors, when aggregate liquidity and sentiment are low.

The collapse of Alameda Research and the failure of FTX in November 2022—only a few months after the demise of the synthetic stablecoin ecosystem Terra–Luna described in [117], is the most visible manifestation of the results described in this fact.

3.9 Fact 9: When the funding dries up, we finally learn the worth of futures↩︎

Fact 9: Cryptocurrency carry trade, the defining characteristics of the futures market, used to be highly profitable, but profitability has compressed sharply since 2024.

Derivatives are a cornerstone of modern markets, enabling hedging, leverage, and price discovery across equities, interest rates, and commodities ([74], [118], [119]).

There is widespread usage of derivatives in the cryptocurrency market, albeit with novel designs. Among all derivatives, perpetual futures are the most common derivative contract in cryptocurrency markets. For example, [54] document that perpetual futures account for more than 98% of the Bitcoin futures volume in their sample. Perpetuals, inspired by [120], have no maturity; positions are marked to market (typically every 8 hours) and a funding rate—positive or negative by design—flows between longs and shorts to keep futures prices anchored to spot. [121] provides the theoretical foundations for the pricing of perpetual cryptocurrency futures. The crypto-carry trade strategy of [54] is short a perpetual futures contract and long a position in the corresponding spot market.

Figure 2 plots the evolution over time of one dollar invested in the crypto-carry strategy (black line, left y-axis) and in the spot Bitcoin market (red line, right y-axis). Over the full sample, which goes from 2020 to 2025, the annualized Sharpe ratio of the cryptocurrency carry is 6.45. Beginning in 2024, the Sharpe ratio falls to 4.06, and it turns negative in 2025. The profit from the cryptocurrency carry strategy is mostly driven by the funding rate, which in the full sample has a mean return of approximately 8% with a low volatility of 0.8%.

This shift in the profitability of the crypto-carry trade strategy has important implications for the crypto-industry. A growing set of crypto “yield” products—most prominently delta-neutral, funding-rate-harvesting structures (e.g., synthetic dollar projects that combine spot holdings with short perpetuals)—derive an important part of their returns from the funding rate. A prominent example is Ethena.fi, whose stablecoin uses a delta-neutral construction and relies on perpetual-funding payments. As of September 2025, Ethena’s stablecoin reached a market capitalization of about $14 billion, with its governance token ENA valued at around $4 billion. If funding premia compress or become more volatile, the economics of these strategies deteriorate and the expected yields decline. The lower profitability of the crypto-carry trade shows that funding-rate premia are neither guaranteed nor permanent and, even more importantly, raises difficult questions about the long-run sustainability of yield products built on them.

3.10 Fact 10: Growing up with supervision—regulation and oversight strengthen cryptocurrency markets↩︎

Fact 10: As the market matures, there is growing disclosure and transparency in cryptocurrencies.

A fundamental insight of information economics is that markets with asymmetric information can fail to allocate resources efficiently. When one party possesses superior information, such as inside information, prices may deviate from fundamentals, and capital may be misallocated (e.g., [122]). Accounting research builds directly on this and shows how disclosure, regulation, and intermediaries can reduce these frictions ([123], [124], [125], [126]). However, in the absence of regulation and supervision, managers may strategically disclose for private benefits ([126], [127]). Policymakers thus issue regulations to address these inefficiencies and to produce credible, comparable, and decision-useful information. Intermediaries, such as analysts and auditors, emerge to reduce information asymmetry by analyzing and validating information ([128]).

Information asymmetry remains pervasive in cryptocurrency markets, though regulation and disclosure have increased in recent years. On the corporate side, public firms with material cryptocurrency exposure are now required to disclose their cryptocurrency holdings and risks. Importantly, the introduction of Accounting Standards Update (ASU) 2023-08 by the Financial Accounting Standards Board provides a coherent framework for the accounting of crypto-assets, which formally requires fair-value accounting treatment ([129]). Recent accounting research emphasizes measurement reliability and disclosure consistency for digital assets ([130]).

On the cryptocurrency side, voluntary disclosures, such as whitepapers and social media announcements, have become increasingly common (e.g., [131], [132], [133]). [134] and [135] show the importance of voluntary disclosures in the initial coin offering stage. Studies also examine information intermediaries (e.g., analysts and auditors) and find that they play an important role in this market (e.g., [135], [136]).

In July 2025, Congress enacted the Guiding and Establishing National Innovation for U.S. Stablecoins Act (GENIUS Act), the first comprehensive federal framework for digital asset oversight in the United States. The Act focuses primarily on payment stablecoins, aiming to improve their transparency and stability. It mandates monthly public disclosures of reserve compositions of stablecoins, and explicitly prohibits stablecoin companies from making misleading claims that their tokens are backed by the U.S. government, federally insured, or legal tender.

The recent regulations and market developments show that greater transparency in the cryptocurrency space is not only increasingly required by the regulators but is also valued by the market. The cryptocurrency market is starting to increasingly implement and value more rigorous accounting principles and slowly converging to the accounting practices of traditional asset classes, for which reliable, comparable, and verifiable disclosure is a major and perhaps the most important determinant of investor confidence and growth of an asset class.

4 ADDITIONAL DISCUSSIONS↩︎

The ten facts summarize key developments in cryptocurrencies through the lens of empirical asset pricing. In this section, we provide additional discussions on emerging topics, including retail investor trading in the cryptocurrency market, the non-fungible token market, and studies on the dark side of cryptocurrency usage.

Recent research increasingly examines individual investor beliefs and behavior in cryptocurrency markets and compares and contrast them with those in traditional investments. [23] show that the trading behaviors of retail investors are drastically different between cryptocurrencies and traditional assets, such as stocks and gold. In particular, retail investors are contrarian in stocks and gold, but trend-chasing in cryptocurrencies. [23] conjecture that the trend-chasing behavior is due to cryptocurrency price changes affecting the likelihood of future widespread adoption, which leads retail investors to update their price expectations. [137] use data from a medium-sized cryptocurrency exchange and document that investor portfolios are typically small in value, highly concentrated in a few coins, and characterized by short holding periods. [138] complement this evidence using repeated large-scale surveys of U.S. households, showing that cryptocurrency investors differ systematically from other investors. [20] provide complementary evidence on the use of cryptocurrencies as a means of payment, using the case of El Salvador—where Bitcoin was made legal tender—and show that privacy and security concerns remain key barriers to adoption. [139] study how social interactions and sentiments affect retail investor trading in cryptocurrency markets. Finally, [140] incorporate individual-level survey data into a structural characteristics-based demand model where investors can hold cryptocurrencies. They find that individual beliefs of cryptocurrency are different and are critical in explaining cryptocurrency valuation.

The bulk of this review is about fungible tokens. A significant segment of the cryptocurrency market, however, is non-fungible tokens (NFTs). [141] is the first to construct repeated sales return indices of NFTs and examine their properties. [142] provide a comprehensive analysis of the NFT market. They highlight the importance of visual features in cryptocurrency valuation and how it leads to a conspicuous consumption effect in the market. Furthermore, [142] shows that, due to the high non-fungibility of NFTs, the market is highly segmented, which has implications for returns and investor behaviors in the market. [143] document that behavioral biases—such as selection neglect and extrapolative beliefs—play a significant role in NFT pricing. [144] document preference-driven herding in NFT primary market sales.

A stream of work examines the so-called dark side of cryptocurrencies, especially in the early years. [24] argue that in the early days, the majority of Bitcoin transactions were about illegal activities, but this is recently challenged by [145] that show the results of [24] are largely driven by double-counting. [25] analyze blockchain and market data to argue that Tether flows timed after market downturns are associated with large Bitcoin price increases during the 2017 boom, consistent with price manipulation. [146] show that abnormal spikes in on-chain transfers around major terrorist attacks carry predictive power for attack timing and highlight chokepoints visible in public ledgers, and [147] provide an anatomy of crypto-enabled crimes. [148] document pervasive cryptocurrency pump-and-dump episodes that generate brief surges in prices, volume, and volatility followed by rapid reversals, with pre-event run-ups consistent with insider gains at outsiders’ expense.

5 CONCLUSIONS↩︎

In the 16 years since Nakamoto, cryptocurrencies have reached a certain stage of maturity: they can now be studied using the same measurement, data quality, and research rigor applied to other asset classes. The market is now worth more than four trillion dollars. Major financial firms are using cryptocurrency in their businesses.

We show that there are important similarities between cryptocurrency markets and traditional asset markets—Sharpe ratios are broadly comparable, and a small number of factors and their higher orders summarize the cross-section of returns. On the other hand, cryptocurrency also has its own character—frequent jumps and blockchain information driving prices. The cryptocurrency market has become more mature and is emerging as an asset class with its own distinct characteristics that still, however, needs more data, research, supervision, enforcement, and a better legal and regulatory framework.

Given the maturation of cryptocurrency into an asset class, this review shows that cryptocurrency should be studied the same way we study any asset. The right way to understand it is exactly through traditional finance tools—empirical asset pricing. The ten facts we present summarize the key takeaways from this view.

DISCLOSURE STATEMENT↩︎

The authors are not aware of any affiliations, memberships, funding, or financial holdings that might be perceived as affecting the objectivity of this review. This review is for academic purposes only and should not be construed as investment or legal advice.

References↩︎