Question

A hedge fund returns on average 26% per year with a standard deviation of 12%. Using the empirical rule, approximate the probability the fund returns over 50% next year. Multiple Choice 0.5% 1% 2.5% 5%

Answer 1

Answer: 0.125

Explanation:

The information given in the question can be depicted below as:

z(50%) = (50% - 26%) / 12% = 2

z (50/100) = (50/100 - 26/100)/12/100 = 2

z(0.5) = (0.5 - 0.26) / 0.12 = 2

z(0.5) = (0.24)/0.12 = 2

P(p > 0.5) = P(z > 2)

Based on the analysis done, we can note that 75% of the data will be found in 2 std of mean and this will bring about (25%/2) = 12.5% in each tail and we will then use Chebyshev's emperical rule which will give:

= (1.00 - 0.75)/2

= 0.25 / 2

= 0.125