The authors calculated the confidence intervals that would have reduced
the incidence of surprises to 20%. The results were striking. To maintain the
rate of surprises at the desired level, the CFOs should have said, year after
year, ”There is an 80% chance that the S&P return next year’ will be between
-10% and +30%.” The confidence interval that properly reflects the CFOs’
knowledge (more precisely, their ignorance) is more than 4 times wider
than the intervals they actually stated.