I thought I remembered reading in A Random Walk Down Wall Street that there's a statistically significant underperformance of the stock market in January, probably due to people making tax-related decisions. It's not enough of a difference to overcome extra trading costs to make money off of, though.
That would totally contradict the "as January goes, so does the rest of the year" theory.
I thought that this was an interesting allegation, so I did some back testing with S&P 500 data. I looked at the S&P 500 monthly opening numbers from January 1950 to January 2014. Additionally I'd like to note that these two ideas aren't mutually exclusive. January can be indicative of the entire year while still underperforming. That is January can have 1% annualized growth when there is 5% growth on the year, or January can have 5% negative growth when there is 1% negative growth on the year. Both of these cases demonstrate January underperforming the yearly return, but revealing the general direction of growth.
The annualized growth in the S&P 500 during January underperformed the growth during the entire year about 39% of the time. Restricting ourselves to 1990 or later, annualized growth during January underperformed growth during the entire year about 41.5% of the time. This reveals a general trend of January outperforming the year more often than in it underperforms on the year.
When the S&P 500 lost value during January, annualized January growth underperformed growth during the rest of the year about 84.5% of the time. About half of the time that the S&P 500 lost value during January it gained value during the entire year. From that information we can conclude that when the S&P 500 loses value both during January and during the entire year annualized January growth underperforms growth during the entire year about 69% of the time. For reference, annualized growth of the S&P 500 as of this afternoon is about -20%.
Interestingly, when the S&P 500 gained value in January, it gained value during the entire year about 92% of time.
From the above I would say that historically January growth generally has predicted positive returns on the year quite accurately, but it hasn't faired so well at predicting negative growth. Additionally, in years where negative growth in January has accurately predicted negative growth for the year, the annualized January return is generally more dire than the return for the entire year. So, stocks have faired worse in January than the rest of the year in years where stocks are down in January.
With a broader context in mind that the market has generally trended up and monthly returns are extremely volatile, these results aren't surprising. If you are to conclude anything from them (which is ill-advised), conclude that you should keep to the plan of investing as early and often as possible.