Let R 1 and R 2 be the random gross returns on two assets. Assume that these are independent and follow an identical distribution function. Show that an expected utility maximiser with wealth w will divide w between both assets provided she is risk-averse; and will invest all her wealth in one of the assets if she is risk-neutral.

[Hint: the wealth of the investor when putting a fraction in the first asset is R 1 + (1 )R 2.]