What is the probability that the stock market closes higher on any given day?

The punch line: The probability that the stock market closes higher on any given day is (only) 53.7%. That's it. Better than flipping a coin, but not by much. The rest of the time it finishes lower (45.2% of the time) or unchanged (1.1%). Yet, because of compounding, this is all that it takes to produce a trend -- and a strong uptrend -- over time.*

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On any given day will the stock market rise or fall? I used daily adjusted closing price data from Yahoo! Finance for SPY, the S&P 500 ETF to find out. The data span 01/29/1993 to 12/11/2014. Here is a bar chart with results grouped by year:

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The bar chart is not zeroed on the y-axis and is scaled to make the differences apparent. The probability of up days spans a range of 47.4% (in 2002) to 59.2% (in 2014). On any given day, the stock market will rise 53.7% of the time (and fall or remain even 46.3% of the time). Your odds of making money are roughly 27:23, or even more roughly, 6:5. That's it. Don't bet the farm. For such a short period as a day, you're essentially tossing a coin.

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*  I'm almost certain that this phenomenon is similar to why a tiny preference by people for some attribute leads to a clustering of those attributes around a geographic area over time. In other words, what we expect to be a random distribution of attributes over geographic area instead exhibits a clustering effect. Likewise, for us, what we expect to be a random distribution of stock prices over time, instead behaves -- when there's a slight increase in chance -- as a strong trend of gradually rising prices.

How have the biggest losing stocks of 2013 fared so far

The punch line: The accepted wisdom, really theory, is that big losers of one year become big winners the next year. Buy the losers in December. This theory is invalid -- or at least should be modified as far as it pertains to all stocks. The theory may have validity for the huge companies of the Dow, where companies do tend to come back and companies rarely fail. With most other stocks, however, total failure is a genuine possibility. Big losers of one year can become even bigger losers the next year because they have systemic troubles. In general, stay away from companies with systemic troubles. They can dissolve into nothingness. If a preliminary pass to avoid such stocks is made, returns improve.

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Method: I took a random list of big stocks that were losers in 2013, "Fortune 500: Worst-performing stocks of 2013," http://money.cnn.com/gallery/investing/2013/12/19/fortune-500-worst-stocks/, and calculated how they have performed YTD in 2014. I just read off the returns from Yahoo! Finance. Thus things like bad data, dividends (potentially), and reorganizations are not considered.

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Results: A portfolio of the fifteen worst stocks of 2013 has returned -10% so far this year, underperforming the +10% return of the index. However, it gets more interesting when the group is broken down into two constituents: (a) companies with long-term troubles; and (b) the rest. The stocks in group (a), indicated by a comment in the last column below, have returned -37%. When you have that many coal stocks and one bankruptcy (or close to it, NIHD lost 97% and now trades on the pink sheets as NIHDQ -- I've used -100% in the table) that is bound to happen. The gold miner may not be in long-term trouble but gold has done poorly over the long term. The stocks in group (b) have returned a more respectable +13%, ahead of the market by 3 percentage points. Here is the breakdown:

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Conclusion: You have to be careful buying losers, as far as it pertains to most stocks. The best bet is to avoid those with systemic troubles. You need to do a preliminary pass and weed out such stocks. If this is done, buying the remaining losers (as a group) can work though you have to be careful and pretty patient.