The average annual return over the period 1926-2009 for the S&P 500 is 12.0%, and the standard deviation of returns is 21.3%. Based on these numbers, what is a 95% confidence interval for 2010 returns? A) -1.5%, 21.8% B) -10.7%, 32.8% C) -30.6%, 54.6% D) -30.6%, 76.4%

To calculate a 95% confidence interval for the S&P 500 returns, we can use the concept of a normal distribution and standard deviation. A 95% confidence interval can be calculated by using the average return (mean) and the standard deviation of the returns, along with a Z-score that corresponds to the desired confidence level. For a 95% confidence interval, the Z-score is typically 1.96, which means that the interval will extend from 1.96 standard deviations below the mean to 1.96 standard deviations above the mean.

Let's use the given average annual return and the standard deviation to calculate the confidence interval:

Mean (average annual return) = 12.0% Standard deviation = 21.3%

Lower End of 95% Confidence Interval = Mean - (Z-score * Standard Deviation) = 12.0% - (1.96 * 21.3%) = 12.0% - 41.748% = -29.748%

Upper End of 95% Confidence Interval = Mean + (Z-score * Standard Deviation) = 12.0% + (1.96 * 21.3%) = 12.0% + 41.748% = 53.748%

Rounding the results to one decimal place: Lower end = -29.7% Upper end = 53.7%

Therefore, the closest answer to our calculated 95% confidence interval for 2010 returns is C) -30.6%, 54.6%. Note that the range provided in the multiple-choice answers doesn't exactly match our calculated result, but option C is the closest approximation to the interval we calculated.