John is looking to invest 10000 and has no choice of purchasing 2 different financial assets, A&B. The annual return on A is known to follow a normal distribution with a mean of 8% and a standard deviation of 10%. The annual return on B is also known to follow a normal distribution with a mean of 6% and a standard deviation of 5%. The return on A is known to be independent of the return on B.a. What is the probability that A will have a return higher than 10%?b. Find the probability that each asset will make a loss.c. Suppose that each year, we know that A had a return of 5%. What is the probability that the return on B is lower than A in that year, but higher than 0%?d. Suppose john decides to invest 40% of his money in A and 60% in B. What is the expected return on his investment? What is the probability that the value of his portfolio will exceed 11000 at the end of the year?e. John tells you that while he would like a high expected return, the most important thing to him is to minimise the probability of making a loss. How would you advice he invests his money? Give reasons for your advice.

Worksheet 3 1. John is looking to invest $10000, and has choice of purchasing two different financial assets, A and B. The annual return on A is known to follow a normal distribution with a mean of 8% and a standard deviation of 10%. The annual return on B is also known to follow a normal distribution with a mean of 6% and a standard deviation of 5%. The return on A is known to be independent of the return on B. a) What is the probability that A will have a return higher than 10%? b) Find the probability that each asset will make a loss. C) Suppose that each year, we know that A had a return of 5%. What is the probability that the return on B is lower than A in that year, but higher than 0%? d) Suppose John decides to invest 40% of his money in A and 60% in B. What is the expected return on his investment? What is the probability that the value of his portfolio will exceed $11000 at the end of the year? e) John tells you that while he would like a high expected return, the most important thing to him is to minimise the probability of making a loss. How would you advise he invests his money? Give reasons for your advice