The average annual return over the period 1886-2006 for stocks that comprise the S&P 500 is 10.5%,and the standard deviation of returns is 18.5%.Based on these numbers what is a 95% confidence interval for 2007 returns?

Question

Quizplus · Accepted Answer

To calculate a 95% confidence interval for the returns in 2007, we need to use the following formula:

CI = X ± Z * (σ / √n)

where X is the expected return, Z is the z-score for the desired confidence level (in this case 1.96 for a 95% confidence level), σ is the standard deviation, and n is the sample size (in this case, we don't have a sample size).

We don't know what the exact return for 2007 will be, but we can assume that it will be close to the long-term average of 10.5%. Therefore we can use 10.5% as our expected return (X).

Plugging in the numbers, we get:

CI = 10.5% ± 1.96 * (18.5 / √1)

Simplifying, we get:

CI = 10.5% ± 36.2%

Therefore, the confidence interval for 2007 returns is:

CI = (-25.7%, 46.7%)

The closest answer choice to this is C, which is (-26.5%, 47.5%). Therefore C is the best choice.

The Average Annual Return Over the Period 1886-2006 for Stocks