DEEMA RIZK THA #4 BSB123
Take Home Assignment 4
Continuous Probability Distributions
Before we can use the Z tables, we have to standardise the normal variable (X) first, i.e. converting X into Z
score. THA 4 will assess you on your ability of applying the standardisation formula and using the Z and
inverse Z tables.
Stock Returns
Stock returns are often assumed to be normally distributed. This means that the full probability distribution
of returns can be explained by the mean and variance of returns, i.e. we can calculate probabilities by
knowing the mean and variance.
Assume that a stock has a mean annual return of 10% and an annual standard deviation of returns of 20%,
(a)
What is the probability that you will return between 5% and 15% in any given year?
(2 marks)
When X = 5% Z = (0.05-0.10) /0.2 = 0.25
When X = 15% Z= (0.15-0.10) / 0.2= 0.25
P(5< X < 15)
= P(0.25 < Z < 0.25)
= P(0.0987 < Z < 0.0987
=- 0.0987-0.0987
= 19.74%
5%
10%
15%
The probability that I will return between 5 and 15 percent in any given year is
19.74%
Probability of returns between
5 % and 15%