Question

Given the following past returns for a stock:

2013                + 15 %

2014                + 18 %

2015                + 30 %

2016                - 20 %

2017                + 10 %

Together, this stock’s expected return and stand alone risk measure mean:

a. there is a roughly 70% chance the actual return will be between - 8.02% and + 29.22%

b. there is a roughly 70% chance the actual return will be between + 8.02% and + 29.22%

c. there is a roughly 70% chance the actual return will be between - 3.41% and + 29.91%

d. there is a roughly 70% chance the actual return will be between + 3.41% and + 29.91%

e. there is a roughly 70% chance the actual return will be between - 8.62% and + 28.62%

this is all the info provided, it's using a nominal distribution

Answer 1

Therefore, Mean = 0.106 and Standard Deviation = 0.166565

Probability of 70% means z-score will be 1.036 and -1.036(reverse looking in normal distribution table)

Z = (x-Mean)/Standard Deviation

Therefore,

1.036 = (x-0.106)/0.166565

Therefore, x = (1.036*0.166565)+0.106 = 0.27856

-1.036 = (x-0.106)/0.166565

Therefore, x = (-1.036*0.166565)+0.106 = -0.06656

Accordingly, the MOST SUITABLE option is (c) Between -3.41% and +29.91%