Lottery-like preferences and the MAX effect in the cryptocurrency market

Financial Innovation

Table 3 Returns on portfolios of cryptocurrencies sorted by multi-day MAX

Decile	N = 1	N = 2	N = 3	N = 4	N = 5
Panel A. Value-weighted returns on MAX(N) portfolios
Low MAX(N)	− 0.009	− 0.003	− 0.004	− 0.003	− 0.002
2	− 0.007	0.002	− 0.001	0.000	0.001
3	− 0.007	− 0.001	− 0.001	− 0.001	− 0.001
4	− 0.007	− 0.001	0.006	0.008	0.002
5	0.002	0.006	0.006	0.006	0.011
6	0.000	0.002	− 0.001	− 0.002	− 0.003
7	0.010	0.008	0.004	0.006	0.010
8	0.007	0.009	0.011	0.007	0.006
9	0.020	0.017	0.017	0.007	0.006
High MAX(N)	0.021	0.022	0.014	0.020	0.023
Return difference	0.030	0.026	0.018	0.023	0.025
	(4.102)***	(3.235)***	(3.040)***	(2.212)**	(2.447)***
Alpha difference	0.020	0.024	0.023	0.019	0.016
	(3.724)***	(3.525)***	(2.773)***	(2.431)***	(2.364)***

Decile	N = 1	N = 2	N = 3	N = 4	N = 5
Panel B. Equal-weighted returns on MAX(N) portfolios
Low MAX(N)	0.006	0.005	0.005	0.006	0.007
2	0.016	0.017	0.014	0.015	0.016
3	0.012	0.014	0.013	0.013	0.011
4	0.013	0.013	0.021	0.023	0.016
5	0.024	0.017	0.016	0.017	0.024
6	0.016	0.019	0.016	0.015	0.013
7	0.017	0.024	0.021	0.023	0.026
8	0.027	0.028	0.029	0.023	0.022
9	0.022	0.021	0.021	0.021	0.020
High MAX(N)	0.031	0.027	0.026	0.029	0.032
Return difference	0.025	0.022	0.021	0.023	0.025
	(3.217)***	(2.903)***	(2.857)***	(3.051)***	(3.176)***
Alpha difference	0.024	0.018	0.017	0.020	0.021
	(3.342)***	(2.543)***	(2.484)***	(2.795)***	(2.822)***

Decile portfolios are formed every week from January 2014 to September 2020 by sorting cryptocurrencies based on the average of N highest daily returns (MAX(N)) within the past month. Decile 1 (10) is the portfolio of cryptocurrencies with the lowest (highest) maximum multi-day returns over the previous month. Table presents the value-weighted (VW) (in Panel A) and equal-weighted (EW) (in Panel B) average weekly returns for N=1, 2, 3, 4, and 5. The bottom two rows report the differences in weekly returns and the differences in three-factor alphas between portfolios 10 and 1, and the corresponding t-statistics. Newey-West (1987) adjusted t-statistics are presented in parentheses
***, ** and * denote significance at 1%, 5% and 10%, respectively