Factor Performance

This page presents performance results for the optimal factor specification identified by cross-sectional pricing tests using Liu et al. (2022) test portfolios:

Liu, Tsyvinski & Wu (2022) — VW, 2×3 double sort, sharp-year calendar

This configuration achieved the highest GRS p-value (best cross-sectional pricing) across 288 tested parameter combinations.

Sample: 2013-04-30 to 2026-02-19 (667 weeks)

Cumulative Returns

Cumulative log returns of the three crypto risk factors. Sample starts Jul 2014 (n > 30 coins). CMKT is the value-weighted market excess return, CSMB is the small-minus-big size factor, and CMOM is the winner-minus-loser momentum factor, constructed following Liu, Tsyvinski & Wu (2022).

Summary Statistics

Weekly factor return summary statistics. Sharpe ratio annualised (×√52). t-statistic tests H₀: mean = 0.

Factor	Mean (%)	Median (%)	SD (%)	Skewness	Kurtosis	Sharpe (ann.)	t-stat	Min (%)	Max (%)	N
Market (CMKT)	1.385	0.530	11.234	1.43	14.62	0.89	3.18	-38.24	104.50	667
Momentum (CMOM)	0.219	-0.397	16.027	1.05	40.55	0.10	0.35	-159.92	168.06	662
Size (CSMB)	0.982	-0.429	16.335	7.68	111.01	0.43	1.55	-103.20	246.45	667

Factor Correlations

Pairwise correlations between weekly factor returns.

Factor	Market (CMKT)	Size (CSMB)	Momentum (CMOM)
Market (CMKT)	1.000	-0.046	0.134
Size (CSMB)	-0.046	1.000	-0.023
Momentum (CMOM)	0.134	-0.023	1.000

Return Distributions

Weekly return distributions for each factor. Vertical dashed lines indicate the mean.

Rolling Performance

52-week rolling annualised Sharpe ratio for each factor.

Test Portfolio Performance

Size-Sorted Portfolios (Decile)

Decile portfolios sorted by market capitalisation (D1 = smallest). Weekly, VW.

Portfolio	Mean (%)	SD (%)	t-stat	Sharpe
D1	0.905	18.763	1.25	0.35
D2	0.560	18.384	0.79	0.22
D3	1.007	24.191	1.08	0.30
D4	0.852	17.932	1.23	0.34
D5	0.545	17.629	0.80	0.22
D6	0.893	16.855	1.36	0.38
D7	0.657	15.581	1.08	0.30
D8	1.074	15.977	1.71	0.48
D9	0.708	16.062	1.12	0.32
D10	1.095	10.204	2.71	0.77
10-1 Spread	0.332	15.297	0.55	0.16

Momentum-Sorted Portfolios (Decile)

Decile portfolios sorted by 4-week momentum (D1 = losers, D10 = winners). Weekly, VW.

Portfolio	Mean (%)	SD (%)	t-stat	Sharpe
D1	-0.089	24.261	-0.09	-0.03
D2	-0.080	14.316	-0.14	-0.04
D3	0.898	14.746	1.57	0.44
D4	0.682	15.425	1.14	0.32
D5	2.101	21.434	2.52	0.71
D6	1.148	15.046	1.95	0.55
D7	1.335	14.590	2.34	0.66
D8	2.899	22.314	3.30	0.94
D9	2.737	22.132	3.13	0.89
D10	0.500	25.806	0.49	0.14
10-1 Spread	0.581	27.622	0.53	0.15

Cumulative Portfolio Returns

Cumulative log returns for extreme size decile portfolios (D1 = smallest, D10 = largest) and the long-short spread. Sample starts Jul 2014.

Cumulative log returns for extreme momentum decile portfolios (D1 = losers, D10 = winners) and the long-short spread. Sample starts Jul 2014.

Specification Details

This page displays results for the optimal factor specification selected via GRS cross-sectional pricing tests (details). The parameters are:

Parameter	Value	Rationale
Weighting	Value-weighted	Best GRS p-value with Liu et al. test assets
Size breakpoints	Quintile (5)	Finer than median, less noisy than decile
Momentum lookback	4 weeks	Strongest cross-sectional pricing power
Calendar	Monday-Monday	Slightly outperforms Liu et al. sharp-year
Exclusions	Stablecoins only	Wrapped/derivative exclusion has marginal impact
Delisting returns	Off	Synthetic -100% adds noise without improving pricing

All other parameter configurations are available for download on the Download Data page.