Question

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 2020 returns?

Answer 1

Given about Australian All ordinaries index,

Average return u = 10.50%

standard deviation s = 18.50%

For a prediction interval of 95%, approximate value of Z = -2 to +2

So, range of return is from (u-Z*s) to (u+Z*s) = (10.50 - 2*18.5) to (10.5 + 2*18.5)

Range = -26.50% to 47.5%

But exact value of Z used for this range is 1.96

So, using Z = 1.96, we get range = -25.76% to 46.76%

Please use answer (-26.5% to 47.5%) if you use approximate Z value. or use answer (-25.76% to 46.76%) if you use exact Z values in calculations.