Question: QUESTION THREE a) b) d) Can you be certain that a rational investor with the utility function nix) = '3 x2 + 45 x will

QUESTION THREE a) b) d) Can you be certain that a rational investor with the utility function nix) = '3 x2 + 45 x will prefer mean-variance efficient portfolios? Explain. (8 marks) If you did NOT know an investor's utility function, what other conditions will be required so that we are certain that a rational investor will prefer mean-variance efficient portfolios? (8 marks) The correlation between the returns on risky assets A and B is zero. Can we combine A and B to create a risk free portfolio? Explain. (10 marks) Can two distinct risky assets A and B be combined to create a risk free portfolio that comprises A and B only? Explain. (12 marks) Define the efficient frontier of risky assets, mathematically, where there is no risk free asset but short sales on risky assets are allowed. (12 marks)

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