Question

Question3 An investor has utility function U(w) n(w) and initial wealth 100. The investor has the choice of investing in a safe asset or a risky asset. $1 invested in the safe asset returns $1 with certainty. $1 invested in the risky asset returns $1.25 when the market state is "good" and returns $0.8 when the market state is "bad". The good state occurs with probability 2/3 and the bad state occurs with probability 1/3. Let x be the amount of money this investor allocates to the risky asset. (a) What is the investor's final wealth in each state? (10 marks) (b) What is the optimal investment in the risky asset and safe asset? (10 marks)

Answer 1

Here, The investor has a choice of investing in a safe and risky asset.

Q-1

If an investor invests in safe asset then he won't get any return because $1 invested in safe asset returns only $1

while, if he invests in risky asset then in the best case scenario he will get 25% return and in the worst case -20%

The possibility of the best case scenario is 66.66% and worst case scenario is 33.33%

Hence the expected return should be

1.25*2/3 + 0.8*1/3 = 1.09 = 9%