Thus, a reading above 50% for bullish sentiment would be one standard deviation above average and a reading of 41% for bearish sentiment would be one standard deviation above the average.
Bullish sentiment is just slightly above one standard deviation from the historical average and bearish sentiment is within one standard deviation.
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Placing asset categories on the efficient frontier requires knowing their historical average return and standard deviation.
Bearish sentiment is back to being more than one standard deviation above average, making it unusually high, but not extraordinarily so.
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There have been just 50 occasions since 1973 when this ratio was greater than one standard deviation from that average, as it is now.
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.
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.
First, at least 33 percent by volume of the sales to an allegedly targeted group must be at prices that are less than one standard deviation below the average price to all other groups.
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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.
The gray area around the average line shows the two standard deviation range of the data.
In statistical terms, optimism is more than one standard deviation above the historical average.
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Pessimism is more than one standard deviation above its historical average, which makes it unusual, but not extraordinary.
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Optimism is currently more than one standard deviation beyond its historical average, meaning that this is an unusually high reading.
Rather it is just one standard deviation away from its average, making the current reading atypical, but not an outlier.
It is also more than one standard deviation below the historical average of 30%, making this an unusually low reading.
Nonetheless, optimism remains more than one standard deviation above its historic average of 39%-a sign that it remains at high levels.
Bullish sentiment is now more than one standard deviation above its historical average, placing it above the typical range that has been registered over the course of the survey.
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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%.
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.
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.
The 500 stocks that make money consistently each of the last four quarters are weighted based on their daily standard deviation over the last 180 trading days, compared to their average.
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