Bob is considering investing in three shares A, B and C. The expected returns over the next year for A, B and C are 8%, 7% and 5% respectively. The standard deviations for A, B and C are 10%, 7% and 5% respectively. The correlation between A and B is 0.3, the correlation between A and C is 0.2, and the correlation between B and C is -0.3. Bob is planning to invest 30% of his money in share A, 30% in share B, and 40% in share C.

a) Calculate the expected return on Bobs portfolio. [2 marks]

b) Calculate the variance and standard deviation of the return on Bobs portfolio. [4 marks]

c) What is the probability that Bobs planned portfolio will earn a negative return over the next year? Assume that shares A, B and C follow a multivariate normal distribution. [2 marks]

d) A friend of Bob has suggested that he should take the 40% of his money planned for share C and invest it in share D instead. Share D has the same expected return as share C, but is independent of shares A, B, and C. Should Bob follow his friends advice? Explain why or why not. [2 marks]