Day of the Month Matters
Seasonality is tricky.
Certain seasonality biases clearly persist (ex. returns around the turn of the month), but the topic too often includes other events that are by their nature uncommon and subject to data mining (ex. returns around a given holiday).
I think the focus of this post, day-of-the-month seasonality, is the former: a real, persistent bias. The question is whether that bias is strong enough to actually influence your trading.
The graph above shows a simple walk-forward test, trading the S&P 500 from 1950 to present. By walking the test forward we ensure that the test only has visibility to the data available at that moment in history.
1. All months were fit to a standard 21 trading days. Months with less than 21 days were stretched, and those with more were compressed (1).
2. At the end of each month, I calculated the (geometric) average daily return for each of our 21 trading days over the previous 20 years (as of that point in time).
3. For the following month, I assumed we were long just those days that had (as of the previous month) performed better (red) or worse (grey) than the median trading day over the previous 20 years.
Results ignore transaction costs, slippage, return on cash, and dividends.
The test clearly shows that trading the days of the month that have been strong historically, consistently leads to stronger returns in the future. That’s as true today as it was in 1950.
I’ve intentionally made this test as KISS as possible. The only parameter I’ve set is the 20 year lookback, and similar results are achieved using any lookback from ~10 years up.
Some of this observation’s effectiveness is simply a result of the strategy picking up on the “turn of the month” (i.e. days near the beginning and end of the month) which have been bullish over the period tested.
But that doesn’t explain all of the observation’s effectiveness. Even days “inside” the month (ex. days 4 to 18) have been consistently stronger when part of the “best half” than when part of the “worst half”.
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As mentioned, I intentionally made this test as KISS as possible, and I would encourage readers to reproduce these results using more sophisticated measures of what days qualify as the best and worst parts of the month.
The more interesting question now is how this observation might influence actual trading.
First off, being one of the best days of the month (red) clearly doesn’t by itself justify going long. There are still lots of ugly days in that red equity curve.
And being one of the worst days of the month (grey) doesn’t justify going short. Returns have been middling, but not necessarily bearish.
So while I think this simple walk-forward clearly demonstrates that day-of-the-month seasonality exists, its only practical use is as an input into some other more predictive strategy. The observation isn’t strong enough to stand on its own, but I think it could do a fine job helping to fine tune the trade.
(1) How I normalized months to 21 days: (a) number the trading days of the month from 1 to X (X being the last trading day of the month), (b) divide each trading day by X and multiply by 21, and (c) round the resulting value to the nearest integer.
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Filed under: Time-based, Trading Strategies | 22 Comments