10-month vs. 40-week vs. 200-day SMA

A reader requested: "I would love to see a backtest pitting a 10-month simple moving average (SMA) against a 200-day SMA for SPDR S&P 500 (SPY). I assume trading costs would go through the roof on the latter, but do performance gains offset additional costs?" Others asked about a 40-week SMA. To investigate, we use the three SMAs to time SPY since its inception and compare results. Specifically, we buy (sell) SPY at the close as it crosses above (below) the SMA, anticipating crossing signals such that trades occur at the close on the signal day (assuming calculations can occur just before the close). The baseline SMA calculation series is dividend-adjusted, but we also check use of unadjusted prices and underlying S&P 500 Index levels. We assume return on cash is the 3-month U.S. Treasury bill (T-bill) yield (ignoring settlement delays). We use a baseline 0.1% one-way SPY-cash switching frictions and test sensitivity to frictions ranging from 0.0% to 0.5% (but assume dividend reinvestment is frictionless). We ignore tax implications of trading. Using daily dividend-adjusted and unadjusted closes for SPY, daily closes of the S&P 500 Index and daily T-bill yield from the end of January 1993 through mid-April 2023, we find that: