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:

• For U.S. actual and simulated monthly stock returns:
  • The correlation with overall returns over other months is -0.06, consistent with other-month reversal of annual seasonality.
  • Average monthly gross returns for the three factors specified above are 0.61% for seasonality, 0.45% for seasonal reversal and 0.67% for annual-minus-non-annual. None of the factors has a negative average gross over any 10-year subperiod.
  • Regarding monthly correlations with other widely used stock return factors:
    • Seasonality relates positively to the market factor (0.18) and negatively to value (-0.23) and long-term reversion (-0.13) factors.
    • Seasonal reversal relates negatively to the market factor (-0.51) and positively to value (0.72) and long-term reversion (0.45) factors.
    • Due to offsetting correlations, annual-minus-non-annual is roughly uncorrelated with these other factors.
  • Annual-minus-non-annual generates monthly gross 3-factor (market, size, book-to-market) alpha 0.66% and monthly 4-factor alpha (plus momentum) 0.67%.
  • Over the full sample period, annualized gross Sharpe ratio of the market is 0.41. Optimal retrospective (perfect hindsight):
    • Addition of size, value, and momentum factors boosts annualized gross Sharpe ratio to 1.08.
    • Further addition of just seasonality (seasonality and seasonal reversal) boosts annualized gross Sharpe ratio to 1.69 (1.81). 
• Seasonality and seasonal reversal are also evident in daily U.S. stock returns, monthly international stock returns, monthly country stock and government bond index returns and monthly commodities returns.
• Evidence suggests that return seasonalities are due to temporary mispricings.

In summary, evidence indicates that assets exhibit seasonal reversals in returns that largely offsets return seasonality.

Cautions regarding findings include:

• Reported factor returns do not account for monthly portfolio reformation frictions, and turnovers for the described strategies are high. Shorting costs would further reduce returns, and shorting of some stocks as specified may not be feasible.
• Stock, bond and commodities indexes are not funds. Liquid tracking funds for these indexes would involve further frictions and fund manager fees.
• As noted, reported Sharpe ratios are optimal based on perfect foresight of returns.
• Exploitation is beyond the reach of most investors, who would bear fees for delegating to a fund manager.

See also “A 12-Month Cycle for Stock Returns?”.