Crypto Pricing with Hidden Factors

Matthew Brigida

REVIEW 4 major objections 5 minor 10 references

Crypto Pricing with Hidden Factors

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Cryptocurrency expected returns carry significant risk premia tied to hidden technology and profitability factors, evidence that crypto is partially integrated with equity markets.

desk verdict A legitimate but preliminary Giglio-Xiu application to crypto with new sentiment factors; the integration claim doesn't survive multiple-testing scrutiny. read the letter →

arxiv 2601.07664 v3 pith:36IQNOSB submitted 2026-01-12 q-fin.PR econ.EMq-fin.GN

Matthew Brigida This is my paper · ORCID

classification q-fin.PRecon.EMq-fin.GN

keywords cryptocurrencyriskpremialatentfactorsfactorpricingcross-sectionofreturnsassetmarketintegrationsentiment

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether cryptocurrency returns are priced only by crypto-specific risks or also by traditional equity risks. Using a three-pass estimator that extracts unobserved (hidden) factors from the cross-section of 253 large coins, it finds that expected crypto returns carry positive premia on the Software equity industry portfolio, on broad stock market returns, and on a stock profitability factor, alongside strong crypto market and size premia. The same factors estimated with a conventional two-pass regression give materially different—often smaller—premia, which the author takes as evidence that omitting latent risks distorts crypto asset pricing. The results matter because they suggest crypto is becoming partially integrated with equity markets rather than remaining a fully segmented asset class, and because they point to sentiment (Fear & Greed) as a priced state variable.

What carries the argument

The load-bearing tool is a three-pass latent-factor estimator. Pass one estimates K=7 latent common factors from the covariance of the weekly return panel, iteratively filling missing returns under a K-factor structure before applying principal component analysis. Pass two regresses the observed factors (crypto and stock factors plus non-tradable state variables) on the latent factors to obtain a mapping Λ. Pass three estimates latent risk prices γ via a cross-sectional regression, then maps them into observed-factor premia via λ=Λγ. Inference uses a moving-block bootstrap with block length 8 and 1000 resamples.

What would settle it

Re-estimate the three-pass model on the same data with K=6 and K=8, and with alternative missing-data fill-in rules; if the Software, RMW, and Fear & Greed premia change sign or lose significance, the result is an artifact of the factor count. A sharper test: simulate returns from a known factor structure with missing observations and check whether the EM/PCA procedure recovers the true factors—if it does not, the mapped premia inherit that bias.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a latent-factor asset-pricing model for weekly cryptocurrency returns over 2023–2024 assigns statistically significant risk premia to equity factors: the Software industry portfolio (0.071% per week), aggregate stock market returns (0.064%), and the stock profitability factor RMW (−0.033%), alongside the crypto market (0.471%) and a strongly negative crypto size premium (−1.345%). Shocks to the Fear & Greed sentiment index also carry a negative premium (−0.051%). The paper interprets these as evidence that crypto and traditional equity markets are increasingly integrated, and that unobserved common factors must be controlled for when es

Load-bearing premise

The latent factors recovered by iteratively filling missing weekly returns under a seven-factor model must faithfully represent the true unobserved risks; if the fill-in is inconsistent or the number of factors is wrong, every mapped risk premium in the paper is biased.

Editorial extensions

If this is right

If the positive Software, stock-market, and profitability premia are real, crypto is partially integrated with equity markets; portfolios of cryptocurrencies incorporate technology and profitability risk.
The large negative small-minus-big premium implies investors demand a premium for holding large-cap crypto, or equivalently a strong preference for larger cryptocurrencies.
The substantial gap between latent-factor and conventional premia (e.g., crypto market 0.471% vs 0.112% weekly) means omitting hidden factors can badly misstate the price of risk.
Priced Fear & Greed shocks suggest sentiment variables belong in crypto asset-pricing models alongside tradeable factors.
TVL's lack of a distinct premium after latent-factor control confirms it is spanned by broader crypto risk rather than an independent priced factor.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The sample is a short (104-week), mostly rising crypto market; the premia, especially the extreme negative size premium, may be specific to that regime and could dissipate in a longer or bear-market sample.
The three-pass mapping cannot cleanly separate a 'Software' equity factor from a broader technology or risk-on latent factor, so the software premium may be a proxy for a general tech-market channel rather than a distinct industry risk.
A natural out-of-sample check would extend the panel into 2025 (including the post-sample Bybit hack episode) and re-estimate with several alternative latent-factor counts K to test whether the software, profitability, and Fear & Greed premia survive.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The paper is a straight application of Giglio-Xiu to crypto with a fresh sample (2023–2024) and some genuinely new non-tradeable factors: Fear&Greed, Altseason, and hacked value scaled by market cap. That is a real contribution. The authors are transparent about the preliminary status, use a recognized estimator, and make a good-faith effort to avoid survivorship bias. The TVL result—spanned by latent factors rather than carrying an independent premium—sits nicely with Brigida (2025).

But the stress-test note is right, and it lands on the load-bearing claim. The abstract and conclusion highlight Softw, RS, and RMW as evidence of equity-market integration. All three are significant only at 10% in the G-X column, and in a 22-factor table six p-values below 0.10 is roughly what you'd expect under a global null. Applying Benjamini-Hochberg at q=0.10, no G-X factor survives—the smallest p-value is 0.008 against a critical value of 0.00455. The FM column rescues only Softw (p=0.003); RS is insignificant and RMW marginal. So the integration story is not yet established.

There are also internal inconsistencies that need cleaning up. The text says the FM crypto-market premium is 0.164% weekly; Table 5 reports 0.112. More concerning, the SMB_C factor has a sample mean of -10.04% per week while its FM risk premium is -0.083%—a 120-fold gap the paper never explains. For a traded factor, the cross-sectional premium should be close to the average return; if it isn't, the reader needs to know why. The EM fill-in for the unbalanced panel also lacks a convergence criterion and any robustness check on K. Since the entire second and third passes depend on those latent factors, that is a weak link.

These are fixable. Report FDR-adjusted p-values or at least acknowledge the multiplicity. Reconcile the RC numbers and explain the SMB_C discrepancy. Add sensitivity around K and the block size. The paper deserves a serious referee—the method is appropriate, the data are new, and the core questions are worth asking. But as it stands, the central claim is conditional, and the revision should be substantial.

For the reading group, it's a decent case study in how multiple testing can sink a headline result, but I wouldn't cite it as evidence yet.

Referee Report

4 major / 5 minor

Summary. The paper estimates risk premia in the cross-section of cryptocurrency returns using the Giglio–Xiu (2021) three-pass latent-factor estimator on a weekly sample of 253 large cryptocurrencies from January 2023 through December 2024. It considers observed factors that include crypto market, size, momentum, and TVL factors; standard Fama–French equity factors and industry portfolios; and three non-tradeable state variables (Fear & Greed, Altcoin Season Index, and hacked value). Results are compared with Fama–MacBeth estimates. The central claim is that crypto expected returns load on both crypto-specific factors and selected equity-industry factors—especially the Software portfolio, the aggregate stock market, and profitability—consistent with partial integration between crypto and equity markets.

Significance. If the central claim survives scrutiny, the paper would provide timely evidence on the evolving integration of cryptocurrency markets with traditional equity markets, an area with mixed prior findings. The use of the Giglio–Xiu latent-factor framework to handle omitted factors in crypto pricing is appropriate and potentially valuable, as is the inclusion of new non-tradeable factors. The paper also makes a useful methodological contribution by applying the three-pass estimator to an unbalanced panel and by using a block bootstrap for inference. However, the strength of the evidence is currently undermined by several internal inconsistencies and by the fragility of the headline results to multiple-testing corrections. The reported Fama–MacBeth comparison appears to contain an error, and the robustness of the latent-factor estimates to the unbalanced-panel imputation is not established. These issues are fixable, but they must be addressed before the empirical conclusions can be considered reliable.

major comments (4)

[Section 2.1, Table 5] The text states that the Fama–MacBeth estimate of the crypto market risk premium is 0.164% per week (8.5% annualized), but Table 5 reports a Fama–MacBeth RC premium of 0.112. The discrepancy is material: 0.112 weekly annualizes to approximately 5.8%, not 8.5%. Since the paper's contribution includes the claim that the latent-factor approach yields 'materially different premia' relative to Fama–MacBeth, the table and text must be reconciled. If the table is correct, the reported comparison is overstated.
[Table 1 vs. Table 5, SMB_C] Table 1 reports that the crypto small-minus-big factor SMB_C has a sample mean of -10.04% per week, while Table 5 reports a Fama–MacBeth risk premium of -0.083% per week for the same factor. For a traded long-short factor, the Fama–MacBeth risk premium should be close to the factor's sample mean. A 120-fold gap is implausible and suggests an error in factor construction, in the Fama–MacBeth implementation, or in the reported statistics. This undermines confidence in the Fama–MacBeth column and in the comparison between the two methodologies.
[Table 5, multiple testing] The paper's headline results—Softw (p=0.056), RS (p=0.066), and RMW (p=0.068)—are each significant only at the 10% level in a table of 22 G-X factors. Under the global null of zero premia, about 2.2 p-values below 0.10 are expected; the table contains six. Applying Benjamini-Hochberg at q=0.10 gives a first critical value of 0.1/22=0.00455; the smallest G-X p-value is 0.008, so no G-X factor survives. At q=0.20, only the crypto SMB_C survives. Thus the evidence that equity-industry factors are priced in crypto returns is indistinguishable from chance once multiplicity is accounted for. The authors should report FDR-adjusted p-values or otherwise justify why a multiple-testing correction is unnecessary.
[Section 2, unbalanced-panel estimation] The paper states that latent factors are estimated on an unbalanced panel by 'repeatedly filling in missing weekly returns with values implied by a K-factor structure' until the filled-in matrix stabilizes, and then applying PCA. No convergence criterion, simulation validation, or robustness to the number of latent factors K is reported. Because the Pass 3 risk premia λ_g = Λγ are linear functions of the estimated latent factors, any inconsistency in the imputed factors or in the choice of K can bias all reported G-X premia. The authors should provide either a Monte Carlo validation of their EM-PCA procedure or, at minimum, sensitivity analyses over K (e.g., K=6,8) and over different convergence tolerances. Without this, the latent-factor results are not yet credible.

minor comments (5)

[Section 1.1] The sentence listing industry factors has a typographical error: 'Banks, Insur, and F inindustries' should read 'Banks, Insur, and Fin industries.'
[Table 4] The Hacks factor is reported with mean and standard deviation 0.00, although the maximum is 0.02. More decimals are needed to convey the scale; the AR(1) residualization may make the units even more opaque.
[Conclusion and Table 5] The profitability factor is labeled 'RMWS' in Table 5 but spelled 'Robust Minus Weak (RM WS)' in the conclusion; the standard abbreviation is RMW. Please use consistent notation throughout.
[Table 5] Only p-values are reported, not standard errors or confidence intervals. Given that the bootstrap procedure is nonstandard (recentered statistic), reporting percentile or bootstrap-t intervals would improve interpretability.
[Section 2] The choice of K=7 is justified only by 'the Bai-Ng Information Criteria.' Please specify which variant of the Bai-Ng criteria was used and how it was implemented on an unbalanced panel with EM imputation, since the standard Bai-Ng theory assumes a balanced panel.

Circularity Check

0 steps flagged · score 2.0 of 10

No definitional circularity; central Giglio-Xiu premia are estimated, not assumed. Only peripheral self-citation in TVL orthogonalization.

full rationale

The paper's derivation chain is the Giglio-Xiu three-pass estimator: latent factors u-hat are estimated by PCA on the return panel (Eq. 1), observed factors are projected onto the latent factors (Eq. 2, g_t = a + Lambda u-hat_t + e_t), and observed-factor risk premia are formed as lambda_g = Lambda gamma (Eq. 3). No equation is defined in terms of its own output, and no fitted parameter is relabeled as a prediction: the Software, RS, RMW, and Fear&Greed premia are point estimates from cross-sectional regressions, not constraints imposed by the model. The only self-citation, Brigida 2025, is used to justify orthogonalizing the TVL factor ('Given evidence that TVL factor returns are spanned by the crypto market portfolio (Brigida 2025), we orthogonalize TVL with respect to crypto market returns.'). That step is peripheral to the abstract's central integration claim, and the later TVL conclusion is framed as complementary rather than derived from the citation. The unbalanced-panel EM fill-in and the multiplicity of the 22-factor significance table are legitimate validity concerns, but they are not circularity: they concern robustness and inference, not equations reducing to their inputs. Accordingly, the central derivation is self-contained, with only a minor non-load-bearing self-citation.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The estimation rests on four data-driven choices (K=7, block size 8, EM fill-in, AR(1) residualization) plus the author's own prior TVL-spanning result used to orthogonalize TVL. These choices are not parameter-free; they are fitted or selected on the same sample that produces the risk premia. The observable factors themselves are standard FF portfolios and public crypto indices, so no invented entities appear.

free parameters (6)

Number of latent factors K = 7
K=7 chosen via Bai-Ng information criteria on the EM-filled unbalanced panel; all risk premia depend on this choice.
Bootstrap block size = 8
Moving-block bootstrap uses block size b=8 with 1000 repetitions; no justification or sensitivity analysis is given.
AR(1) residualization of non-tradeable factors = Estimated AR(1) coefficients for Hacks, Altseason, Fear&Greed, CVX
Each non-tradeable factor is converted to an AR(1) residual, so the priced object is a model-defined 'shock' whose AR parameter is estimated on the same sample.
TVL orthogonalization = OLS projection of TVL factor on crypto market returns
TVL is orthogonalized to the crypto market based on the author's prior result (Brigida 2025), changing the TVL risk-premium estimate.
EM fill-in convergence = Iteration until 'stabilizes'
Missing returns are filled with values implied by a K-factor structure until the matrix stabilizes; no convergence threshold is specified.
Portfolio breakpoints = Top/bottom 25%
Crypto factors use 25% breakpoints following Fama-French convention; the choice is standard but not independently motivated for crypto.

assumptions (7)

standard math Giglio-Xiu three-pass estimator consistently estimates risk premia under their assumptions (linear factor model, strong factors, no-arbitrage).
Invoked in Section 2; the paper applies the estimator without re-deriving or verifying the regularity conditions on this specific unbalanced panel.
domain assumption The panel of crypto returns follows a K-factor structure with K=7.
Section 2: '7 latent factors chosen via the Bai-Ng Information Criteria'; if the true number differs, pass-1 PCA and all risk premia are inconsistent.
ad hoc to paper The EM-style fill-in of missing returns preserves the true factor structure and does not introduce spurious common variation.
Section 2: 'repeatedly filling in missing weekly returns with values implied by a K-factor structure...'; no convergence criterion or simulation evidence is given.
ad hoc to paper Observed non-tradeable state variables are priced through their AR(1) residuals.
Section 1.1: 'We then convert each non-tradeable factor into its residual component via an AR(1) model'; the AR(1) parameter is estimated on the same sample.
domain assumption CoinMarketCap, DeFiLlama, CVX, and Ken French data are accurate and free of material errors.
Section 1 relies on these external data sources for prices, hacked value, volatility, and equity factors.
domain assumption The moving-block bootstrap with block length 8 and 1000 replications provides valid inference for the risk premia.
Section 2: 'moving block bootstrap with 1000 repetitions and a block size of 8'; no sensitivity to block length is reported.
domain assumption The top-100-at-any-point universe selected over the sample period is representative and does not introduce look-ahead bias beyond the acknowledged survivorship-bias fix.
Section 1: 'any non-stablecoin cryptocurrency that was in the top 100 cryptocurrencies by market cap at any point in our sample period'; selecting on full-sample membership can induce look-ahead relative to early weeks.

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Cite this review

Pith. "Pith review of Crypto Pricing with Hidden Factors." pith.science (2026). https://pith.science/paper/36IQNOSB

@misc{pith2026260107664,
  author       = {Pith},
  title        = {Pith review of: Crypto Pricing with Hidden Factors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/36IQNOSB}},
  note         = {Machine review of arXiv:2601.07664}
}

read the original abstract

We estimate risk premia in the cross-section of cryptocurrency returns using the Giglio-Xiu (2021) three-pass approach, allowing for omitted latent factors alongside observed stock-market and crypto-market factors. Using weekly data on a broad universe of large cryptocurrencies, we find that crypto expected returns load on both crypto-specific factors and selected equity-industry factors associated with technology and profitability, consistent with increased integration between crypto and traditional markets. In addition, we study non-tradable state variables capturing investor sentiment (Fear and Greed), speculative rotation (Altcoin Season Index), and security shocks (hacked value scaled by market capitalization), which are new to the literature. Relative to conventional Fama-MacBeth estimates, the latent-factor approach yields materially different premia for key factors, highlighting the importance of controlling for unobserved risks in crypto asset pricing.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

10 extracted references · 4 canonical work pages

[1]

Risk Premia in the Bitcoin Market

Almeida, Caio et al. (2024). “Risk Premia in the Bitcoin Market”. In:arXiv preprint arXiv:2410.15195(cit. on p. 2)

arXiv 2024
[2]

Crypto Risk Premia

Borri, Nicola et al. (2022). “Crypto Risk Premia”. In:SSRN Electronic Jour- nal.issn: 1556-5068.doi:10.2139/ssrn.4154627.url:http://dx. doi.org/10.2139/ssrn.4154627(cit. on pp. 2, 8)

work page doi:10.2139/ssrn.4154627.url:http://dx 2022
[3]

The surprising irrelevance of total-value-locked on cryptocurrency returns

Brigida, Matthew (2025). “The surprising irrelevance of total-value-locked on cryptocurrency returns”. In:Economics Letters257, p. 112673.issn: 0165-1765.doi:https://doi.org/10.1016/j.econlet.2025.112673. url:https : / / www . sciencedirect . com / science / article / pii / S0165176525005105(cit. on pp. 4, 9)

arXiv 2025
[4]

(2005).Asset Pricing: Revised Edition

Cochrane, John H. (2005).Asset Pricing: Revised Edition. Princeton, NJ: Princeton University Press, pp. xi, 533.isbn: 978-0691121376 (cit. on p. 8)

2005
[5]

Common risk factors in the returns on stocks and bonds

Fama, Eugene F and Kenneth R French (1993). “Common risk factors in the returns on stocks and bonds”. In:Journal of financial economics33.1, pp. 3–56 (cit. on p. 3)

1993
[6]

Risk, Return, and Equilibrium: Empirical Tests

Fama, Eugene F. and James D. MacBeth (May 1973). “Risk, Return, and Equilibrium: Empirical Tests”. In:Journal of Political Economy81.3, 607–636.issn: 1537-534X.doi:10.1086/260061.url:http://dx.doi. org/10.1086/260061(cit. on p. 8). Foley,Seanetal.(2022).“WhatistheexpectedreturnonBitcoin?Extracting the term structure of returns from options prices”. In:Eco...

work page doi:10.1086/260061.url:http://dx.doi 1973
[7]

Asset Pricing with Omitted Factors

Giglio, Stefano and Dacheng Xiu (July 2021). “Asset Pricing with Omitted Factors”. In:Journal of Political Economy129.7, 1947–1990.issn: 1537- 534X.doi:10 . 1086 / 714090.url:http : / / dx . doi . org / 10 . 1086 / 714090(cit. on pp. 2, 5, 8, 9)

2021
[8]

Risks and Returns of Cryp- tocurrency

Liu, Yukun and Aleh Tsyvinski (Sept. 2020). “Risks and Returns of Cryp- tocurrency”. In:The Review of Financial Studies34.6. Ed. by Itay Gold- stein, 2689–2727.issn: 1465-7368.doi:10 . 1093 / rfs / hhaa113.url: http://dx.doi.org/10.1093/rfs/hhaa113(cit. on p. 2)

work page doi:10.1093/rfs/hhaa113(cit 2020

Show all 10 references

[9]

Common risk factors in cryptocurrency

Liu, Yukun, Aleh Tsyvinski, and Xi Wu (2022). “Common risk factors in cryptocurrency”. In:The Journal of Finance77.2, pp. 1133–1177 (cit. on p. 2)

2022
[10]

On the Estimation of Beta-Pricing Models

Shanken, Jay (Jan. 1992). “On the Estimation of Beta-Pricing Models”. In: Review of Financial Studies5.1, 1–33.issn: 1465-7368.doi:10.1093/ rfs/5.1.1.url:http://dx.doi.org/10.1093/rfs/5.1.1(cit. on p. 8). 12

1992 doi

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [1]

Risk Premia in the Bitcoin Market

Almeida, Caio et al. (2024). “Risk Premia in the Bitcoin Market”. In:arXiv preprint arXiv:2410.15195(cit. on p. 2)

arXiv 2024

[2] [2]

Crypto Risk Premia

Borri, Nicola et al. (2022). “Crypto Risk Premia”. In:SSRN Electronic Jour- nal.issn: 1556-5068.doi:10.2139/ssrn.4154627.url:http://dx. doi.org/10.2139/ssrn.4154627(cit. on pp. 2, 8)

work page doi:10.2139/ssrn.4154627.url:http://dx 2022

[3] [3]

The surprising irrelevance of total-value-locked on cryptocurrency returns

Brigida, Matthew (2025). “The surprising irrelevance of total-value-locked on cryptocurrency returns”. In:Economics Letters257, p. 112673.issn: 0165-1765.doi:https://doi.org/10.1016/j.econlet.2025.112673. url:https : / / www . sciencedirect . com / science / article / pii / S0165176525005105(cit. on pp. 4, 9)

arXiv 2025

[4] [4]

(2005).Asset Pricing: Revised Edition

Cochrane, John H. (2005).Asset Pricing: Revised Edition. Princeton, NJ: Princeton University Press, pp. xi, 533.isbn: 978-0691121376 (cit. on p. 8)

2005

[5] [5]

Common risk factors in the returns on stocks and bonds

Fama, Eugene F and Kenneth R French (1993). “Common risk factors in the returns on stocks and bonds”. In:Journal of financial economics33.1, pp. 3–56 (cit. on p. 3)

1993

[6] [6]

Risk, Return, and Equilibrium: Empirical Tests

Fama, Eugene F. and James D. MacBeth (May 1973). “Risk, Return, and Equilibrium: Empirical Tests”. In:Journal of Political Economy81.3, 607–636.issn: 1537-534X.doi:10.1086/260061.url:http://dx.doi. org/10.1086/260061(cit. on p. 8). Foley,Seanetal.(2022).“WhatistheexpectedreturnonBitcoin?Extracting the term structure of returns from options prices”. In:Eco...

work page doi:10.1086/260061.url:http://dx.doi 1973

[7] [7]

Asset Pricing with Omitted Factors

Giglio, Stefano and Dacheng Xiu (July 2021). “Asset Pricing with Omitted Factors”. In:Journal of Political Economy129.7, 1947–1990.issn: 1537- 534X.doi:10 . 1086 / 714090.url:http : / / dx . doi . org / 10 . 1086 / 714090(cit. on pp. 2, 5, 8, 9)

2021

[8] [8]

Risks and Returns of Cryp- tocurrency

Liu, Yukun and Aleh Tsyvinski (Sept. 2020). “Risks and Returns of Cryp- tocurrency”. In:The Review of Financial Studies34.6. Ed. by Itay Gold- stein, 2689–2727.issn: 1465-7368.doi:10 . 1093 / rfs / hhaa113.url: http://dx.doi.org/10.1093/rfs/hhaa113(cit. on p. 2)

work page doi:10.1093/rfs/hhaa113(cit 2020