What’s so special about time series momentum?

We find that the buy-and-hold (B&H) strategy for the S&P 500 index (^GSPC) for January 1950–April 2019 had a significantly higher return than that produced by time series momentum (TSM). However, TSM was superior in terms of the Sharpe ratio due to its lower volatility. The statistics for all ten- and twenty-year periods within the range January 1950–April 2019 show that the simple moving average (SMA) strategy outperformed TSM in the past, but since the late 1990s the performance of the two strategies has become very close. The profitability of B&H and the trend-following trading strategies TSM and SMA may be due to the fact that the optimal autoregressive moving average model of the monthly ^GSPC returns for January 1950–April 2019 has a positive mean.