This is an update to a post that I first wrote last year, the last time that the S&P 500 had a big rise in the first month of the year.
When the S&P 500 has a good first month, it has statistically been followed by a really good year. The index has risen by more than 4% in January 18 times in its 56 year history. In those years it has averaged a 21.1% return for the full year, and it has been up double digits in every one of those years except for 1987 (which was a good year up until the October crash).
The S&P 500 has never been negative in a year with a big January, but it's worth noting that if a similar analysis is performed on the Dow, which has a 118 year history, there are five years (out of 28) that the index was up more than 4% in January and ended negative for the year. Many of those years were significantly negative too: the average loss was 18.4% and the list includes 1914, 1929 and 1930. The index ended those years down 30.7%, 17.2% and 33.8% after being up 5.1%, 5.8% and 7.5% in January respectively.
Weird eerie coincidence, the Dow has had a daily crash three times in its history: in 1914, 1929 and 1987. All three years had big Januaries.