Pervasive Seasonal Relative Weakness Cycles?

Is there a flip side of cyclic relative weakness to the cyclic relative strength described in “Pervasive 12-Month (and 5-Day) Relative Strength Cycles?”? In their October 2018 paper entitled “Seasonal Reversals in Expected Stock Returns”, Matti Keloharju,Juhani Linnainmaa and Peter Nyberg test whether cyclic weakness (seasonal reversal) balances the cyclic strength (seasonality) effect. For example, if a stock is seasonally strong in March, it may be seasonally weak across other months. They test this hypothesis using actual monthly U.S. stock returns and simulated returns calibrated to actual returns. Specifically, they compute correlations between average historical returns for a stock during one month and the sum of its historical average returns during other months. In robustness tests, they repeat this test for 10-year subperiods and for daily U.S. stock returns, monthly non-U.S. stock returns, monthly country stock indexes, monthly country government bond indexes and monthly commodity returns. Finally, they construct the following three factors for U.S. stocks by first each month sorting stocks into two size groups (small and big market capitalizations) and then:

1. Seasonality factor – Sorting each size group into three average same-calendar-month past return portfolios. The factor return is the difference in value-weighted returns between the two highest-average portfolios and the two lowest-average portfolios.
2. Seasonal reversal factor – Sorting each size group into three average other-calendar-month past return portfolios within each size group. The factor return is the difference in value-weighted returns between the two lowest-average and the two highest-average portfolios.
3. Annual-minus-non-annual factor – Sorting each size group into three portfolios based on the difference between the average same-calendar-month and other-calendar-month returns. The factor return is the difference in value-weighted returns between the two largest-difference and the two smallest-difference portfolios.

Using U.S. monthly and daily stock returns since 1963 and monthly returns for country stocks and stock market indexes, country government bond indexes and commodities since the end of 1974, all through 2016, they find that:

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