| Breakpoint universe | Mean CSIZE (%/wk) | % of specs positive | Mean CMOM (%/wk) |
|---|---|---|---|
| All coins (Liu) | 1.57 | 100 | 0.29 |
| Investable ($100M floor) | 0.33 | 80 | 0.71 |
| Investable (top 100) | 0.33 | 77 | 0.67 |
The Investable Cross-Section
What survives when you can only hold what’s actually investable?
On the Methodology page we replicated the three factors (market CMKT, size CSIZE, momentum CMOM) of Liu et al. (2022). We then constructed these factors over a multiverse of defensible specification choices. The multiverse includes the data source (CoinMarketCap / CoinGecko), exclusions, the week-start calendar, weighting, breakpoints, momentum horizon, and the data-handling and universe rules described in the Methodology and can be downloaded from the Data page. Rather than report one “preferred” set of numbers, we report the distribution of results across all defensible specifications and ask a practitioner’s question: do the factors price the assets an investor can actually hold?
The central finding: the crypto size premium is an artifact of non-investable microcaps. Once breakpoints are computed on the investable universe — the standard NYSE-breakpoint discipline, which crypto needs even more than equities because it has no listing threshold — the size premium essentially vanishes, while short-horizon momentum survives and prices the cross-section.
2 · Only short-horizon momentum survives investability
| Characteristic | Mean L–S (%/wk) | % sig — full universe | % sig — investable universe |
|---|---|---|---|
| MAXDPRC | -1.85 | 100 | 0 |
| MCAP | -0.85 | 100 | 0 |
| PRC | -1.92 | 100 | 0 |
| r2,0 | 2.25 | 100 | 100 |
| r3,0 | 1.81 | 100 | 75 |
| r1,0 | 1.69 | 75 | 88 |
| r4,0 | 1.47 | 75 | 38 |
| r4,1 | 0.98 | 12 | 0 |
| PRCVOL | -0.40 | 0 | 0 |
| STDPRCVOL | -0.47 | 0 | 0 |
The table summarises the average long-short return for each characteristic across the multiverse of admissible specifications. For example, r2,0 = 2.25 indicates that, on average, a portfolio that buys the highest-momentum coins and shorts the lowest-momentum coins earns roughly 2.25% per week. The final two columns report the frequency with which the corresponding t-statistic exceeds 2 in absolute value under the full and investable universes, respectively. This is useful because it separates anomalies that are robust to realistic investability constraints from those that are only present in a broad, non-tradable universe.
MAXDPRC, MCAP, and PRC denote maximum daily price, market capitalisation, and current price. These are classic size- and price-type proxies, and they are precisely the variables that lose their predictive content once the sample is restricted to investable coins. The terms r1,0 to r4,1 correspond to momentum signals based on past return windows; the notation reflects both the return horizon and the lag structure used in the sort. Short-horizon momentum (r1,0, r2,0, r3,0) is therefore the economically relevant part of the momentum spectrum in this setting. PRCVOL and STDPRCVOL measure volatility-based characteristics, and neither delivers a robust relation to subsequent returns in the investable cross-section.
The pattern in the table is clear. In the full universe, the microcap and price proxies are significant in 100% of specifications, but they disappear entirely once the sample is restricted to investable assets. By contrast, short-horizon momentum remains economically meaningful and statistically reliable after the investability filter, whereas the volatility characteristics do not. This indicates that the apparent size and price premia are largely a by-product of the non-investable tail of the crypto universe, while short-horizon momentum is the one anomaly that survives under realistic trading constraints.
Size, price and maximum-price are significant in 100% of full-universe specifications but in 0% of investable ones — they are pure microcap artifacts. Short-horizon (1–3 week) momentum is the only anomaly that survives restriction to investable assets.
3 · A market + momentum model prices the investable cross-section
| World | Mean CSIZE | Mean CMOM | Cross-sec. adj R² | Momentum premium t (Shanken) |
|---|---|---|---|---|
| Investable | 0.33 | 0.71 | 0.51 | 2.76 |
| Liu (all / full) | 1.57 | 0.29 | 0.43 | 1.85 |
In Liu et al. (2022) all-coin specification the average size premium is large, while momentum is comparatively weak. Once the universe is restricted to investable assets, the average size premium falls sharply from 1.57 to 0.33, while the average momentum premium rises from 0.29 to 0.71 and the associated Shanken t-statistic increases from 1.85 to 2.76. The average cross-sectional adjusted R² also improves from 0.43 to 0.51, indicating that the investable specification prices the cross-section more successfully. This pattern is consistent with the view that the apparent size premium is largely a microcap artifact, whereas momentum remains the economically relevant signal once investability constraints are imposed.
4 · Calendar choice: dispersion without signal
The week-start convention (Monday … Sunday, or Liu’s calendar-year weeks) adds dispersion to the results but yields no robust effect — the best-pricing start-day is inconsistent across data source and universe, and is not Monday. Calendar choice is a non-standard-error dimension, not an exploitable phenomenon.
Replication data for every figure on this page is in the downloadable result tables. Factor construction is detailed in the Methodology.
References
Liu, Y., Tsyvinski, A., & Wu, X. (2022). Common risk factors in cryptocurrency. The Journal of Finance, 77(2), 1133–1177. https://doi.org/10.1111/jofi.13119