U.S. Equity Turn-of-the-Month as a Diversifying Portfolio

Is the U.S. equity turn-of-the-month (TOTM) effect exploitable as a diversifier of other assets? In their October 2018 paper entitled “A Seasonality Factor in Asset Allocation”, Frank McGroarty, Emmanouil Platanakis, Athanasios Sakkas and Andrew Urquhart test U.S. asset allocation strategies that include a TOTM portfolio as an asset. The TOTM portfolio buys each stock at the open on the last trading day of each month and sells at the close on the third trading day of the following month, earning zero return the rest of the time. They consider four asset universes with and without the TOTM portfolio:

1. A conventional stocks-bonds mix.
2. The equity market portfolio.
3. The equity market portfolio, a small size portfolio and a value portfolio.
4. The equity market portfolio, a small size portfolio, a value portfolio and a momentum winners portfolio.

They consider six sophisticated asset allocation methods:

1. Mean-variance optimization.
2. Optimization with higher moments and Constant Relative Risk Aversion.
3. Bayes-Stein shrinkage of estimated returns.
4. Bayesian diffuse-prior.
5. Black-Litterman.
6. A combination of allocation methods.

They consider three risk aversion settings and either a 60-month or a 120-month lookback interval for input parameter measurement. To assess exploitability, they set trading frictions at 0.50% of traded value for equities and 0.17% for bonds. Using monthly data as specified above during July 1961 through December 2015, they find that:

• Over the full sample period, average annualized gross returns (volatilities) for individual assets are 13.5% (15.4%) for the small size portfolio, 12.4% (15.2%) for the value portfolio, 12.4% (15.4%) for the momentum winners portfolio, 10.6% (15.4%) for the market portfolio, 9.7% (7.1%) for the TOTM portfolio and 6.8% (6.1%) for bonds.
• Over the full sample period, correlations between TOTM portfolio gross returns and those of other assets range from 0.03 for bonds to 0.40 for the market portfolio. 20-year rolling correlations between TOTM portfolio gross returns and market portfolio returns rarely exceed 0.60.
• Across all strategy methods, risk aversion settings and parameter measurement lookback intervals (based on gross returns):
  • TOTM portfolio allocations range from 28% to 93%. In other words, the TOTM portfolio is a relatively attractive asset in strategic context.
  • Average annualized gross Certainty Equivalent Return (CER), the excess performance required of the asset mix to compensate for excluding the ToM portfolio, is 2.6%.
• Out-of-sample benefits survive accounting for the assumed level of trading frictions. For example, across all strategy methods and risk aversion settings for the 120-month parameter measurement lookback interval, average annualized net CER is 2.4%.

In summary, evidence indicates that investors may be able to exploit the TOTM effect in the U.S. equity market as a formal diversifier of other assets.

Cautions regarding findings include:

• Testing four asset class universes, six allocation strategies, three levels of risk aversion and two parameter estimation lookback intervals introduces material data snooping bias, such that best-performing strategies overstate expectations.
• Per “Managing Stock Portfolio Trading Frictions” and “Trading Frictions Over the Long Run”, the assumed level of trading frictions for asset portfolio maintenance and asset class rebalancing are unreasonably low for equities over much of the sample period, especially if the TOTM portfolio is equal-weighted (unclear in the paper).
• Moreover, it seems that trading frictions should have much larger effects on CERs than reported. For example, monthly buying and selling of the ToM portfolio incurs costs of 0.5% + 0.5% = 1% per month, which would (more than) eliminate profitability of the portfolio. There would also be internal maintenance frictions for other component portfolios and overall rebalancing costs of the portfolio of portfolios. The authors did not respond to inquiries on this point.

For additional perspective, see:

• “Turn-of-the-Month Effect Persistence and Robustness”
• “Does the Turn-of-the-Month Effect Work for Sectors?”
• “Does the Turn-of-the-Month Effect Work for Asset Classes?”