Adam is considering investing in three shares A, B and C. The returns of the shares over the next year are assumed to follow a multivariate normal distribution as below: (, , )~3(,) = (7%, 5%, 4%) = [ 0.0065 0.0024 0.0011

0.0024 0.0036 0.0011

0.0011 0.0011 0.0025 ]

Adam 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 Adams portfolio. [2 marks]

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

c) What is the probability that Adams planned portfolio will earn a negative return over the next year? [2 marks]

d) Chris has suggested that Adam should take the 30% of his money planned for share A and invest it in share D instead. Share D has the same expected return and standard deviation as share A, but is independent of shares A, B and C. Should Adam follow this advice? Explain why or why not.