Question

Assume a security has an expected return of .12 and a standard deviation of 0.08 a) What is the expected return two standard deviation above the mean and what is the probability of a return greater that this amount? B) What is the probability of a return greater than 0.04 for a given year.

Answer 1

Expected return of a security = μ = 0.12, standard deviation = σ = 0.08

A) Expected return two standard deviation above the mean = μ+2*σ = 0.12+(2*0.08) = 0.28

Answer -> 0.28

We will assume that the return on this security follows a normal distribution. We need to calculate that the expected return on this stock is greater than 0.28

Let X is the return on the security. So, we need to calculate P(X>0.28). Since the distribution of X follows a Normal Distribution, we can convert it to Standard Normal Distribution.

where Z= (X-μ)/σ is the standard normal distribution factor

From Standard Normal Distribution Table, P(Z<2) = 0.97725, we can also use excel function [=NORM.S.DIST(2,TRUE)]

Therefore, P(Z>2) = 1-P(Z<2) = 1-0.97725 = 0.52275 = 0.02275

Answer -> 0.02275

B) Similarly, we need to calculate P(X > 0.04)

So, P(Z > -1) = 1-P(Z < -1) = 1- 0.158655 = 0.841345 [From Z distribution Table, P(Z<-1)=0.158655 or Excel function =NORM.S.DIST(-1,TRUE)]

Answer -> 0.841345