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.

b) Calculate the variance and standard deviation of the return on Bobs portfolio.

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.