Continuous Probability Distributions

You must draw diagram for each question and show all workings. Answers without clearly labelled diagrams and workings will not score full marks.

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.

Question 1 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 7.5% and an annual standard deviation of returns of 15%*,

a) What is the probability that you will return between 0% and 15% in any given year? (2 marks)

b) What is the probability that you will return exactly 7.5% in any given year? (2 marks)

c) What is the probability of losing money in any given year, i.e. getting a negative return? (2 marks)

d) To have a really good year, you would want returns to be in the top 5% of returns. What return must you earn to conclude that you have had a really good year? (2 marks)

e) Imagine that there was another stock with mean annual return of 10% but its standard deviation of returns was only 30%. In relation to your answer in (c), outline why you might prefer your old stock over this new stock if you were concerned about losing money (negative returns). (2 marks)