This sure would be a coincidence.
While the number might look on its face to be sort of random and convenient, the firm insisted in a note to clients that it actually represents a halfway point between two proprietary models it uses to determine market valuation:
The 2014 target reflects our expectation that the stock market will have opportunity to move higher over the course of next year, and turn in yet another double-digit increase—albeit around half the size of this year's rally to date. Our price target is set using the mid-point between our dividend discount model and a price/earnings model.
(Read more: Short sellers see big chance—if they can survive)
Indeed, the P/E model puts the price target at 2,060 while the dividend-discount model prices the index at 1,967. With the actual average 2,013.5—well, why not round up?
Oppenheimer chief market strategist John Stoltzfus also noted that the firm has increased its 2013 price target from 1,730, which the index blew past in mid-October, to 1,812—less than 1 percent higher from current levels.
The projections are part of a clearly bullish market outlook:
We expect these valuation projections to be supported by improving fundamentals. We continue to believe that US economic growth has in effect been "primed" by the Federal Reserve's Quantitative Easing (QE) programs. Recent improvements in the tone of US economic data suggest to us that prospects are good for investors to see a continuation of the economic recovery that could drive earnings higher in the year ahead.
If that outlook fails, though, look out for S&P 2,015 in 2015.
(Read more: Huge change could be coming in 2014: Schwab CIO)
—By CNBC's Jeff Cox. Follow him on Twitter @JeffCoxCNBCcom.