If you rank the countries of the world in terms of the academic performance of their schoolchildren, the U.S. is just below average, half a standard deviation below a clump of relatively high-performing countries like Canada and Belgium.

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Once you know the average return, the standard deviation of each index and the correlation coefficient between each pair of indexes, the rest is math.

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The gray area around the average line shows the two standard deviation range of the data.

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It is also more than one standard deviation below the historical average of 30%, making this an unusually low reading.

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Nonetheless, optimism remains more than one standard deviation above its historic average of 39%-a sign that it remains at high levels.

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Pessimism not only stayed at its lowest level since December 23, 2010, it also remained at a reading that is more than one standard deviation below the historical average of 30%.

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For example, two of eight American League clubs in 1927 posted winning percentages below .400, leading to a league-wide standard deviation of .123 percentage points above and below the average .500 record.

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Bearish sentiment has been at or above 41% during three out of the last four weeks, equaling or exceeding one standard deviation above the average.

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Table 3 below provides a summary of the annualized standard deviation and returns for each asset class, the weighted average risk and return and the total portfolio risk and return from January 1979 through December 2009.

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