Assume that the average annual historical return for shares that comprise the Australian All Ordinaries index is 10.5%, and the standard deviation of returns is 18.5%. Based on these numbers what is a 95% prediction interval for 2012 returns?

Question

Quizplus · Accepted Answer

To calculate the prediction interval, we use the following formula:
Prediction interval = average return +/- (z-value x standard deviation)
where z-value is the critical value for the desired confidence level, which is 95% in this case.
From the standard normal distribution table, the z-value for 95% confidence level is 1.96.
So, the prediction interval for 2012 returns would be:
Prediction interval = 10.5 +/- (1.96 x 18.5)
= 10.5 +/- 36.26
= -25.76% to 46.76%
Therefore, the answer is D, which covers the correct range of returns.

Assume That the Average Annual Historical Return for Shares That