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 2016 returns?
A)-10%, 10%
B)-18.5%, 18.5%
C)-26.5%, 47.5%
D)-37%, 37%

Question

Quizplus · Accepted Answer

To calculate the 95% prediction interval, we need to use the formula: 
Prediction interval = (mean return +- z-score x standard deviation)

The z-score for a 95% confidence level is 1.96. 
Mean return = 10.5%
Standard deviation = 18.5%

Substituting these values into the formula, we get: 
Prediction interval = (10.5% +- 1.96 x 18.5%) 
Prediction interval = (10.5% +- 36.26%)

Therefore, the 95% prediction interval for 2016 returns is (10.5% - 36.26%) to (10.5% + 36.26%), or -26.76% to 47.76%. 
The closest answer choice to this range is C, -26.5% to 47.5%.

Assume That the Average Annual Historical Return for Shares That