Hi everyone, In the course material, Chapter 5 -Question 5.4 and Question 5.5. It says that proportion 'a' is invested in Equity A and the rest in non-interest security but in the answer nowhere (1-a) comes in to picture as it was done in Question 5.4 and 5.5. Also won't the E(U(w)) in question 5.5 be "0.5*log(100a -18a) + 0.5*log(100a+20a) " since 'a' proportion of her wealth(100) is 100a and return on '-18%' will be '100a * (-.18)' . Therefore total wealth will be '100a-18a' not '100-18a', similarly for the other part.
I'm not sure what question you are referring to in your first query, but I'm pretty sure Q5.5 is correct. When you invest a proportion a into the risky asset, you still also have (1-a) in the risk-free asset. So in one year's time you will either have: 100(1-a) + 100a x 0.82 = 100 - 18a or 100(1-a) + 100a x 1.20 = 100 + 20a, so the answer in the notes is right. You do always have to include the (1-a) bit as it is part of your total wealth, it's just the expression usually simplifies so that it's not there explicitly.
