Chapter 2 Calculating Expected Utility Theory

Hi,

The first question on pg 5 (Chap 2 course notes) asks to calculate the expected next-period utility when there's only a proportion, 'a' of wealth, w, invested in Equity A.

Realise its a basic point but dont understand how to calculate the answer. Why is it 0.25*(log(1-.04a)w) + 0.75*log(1+.08a)w rather than:
0.25*(log(.96a)w) + 0.75*log(1.08a)w?

Sim. unclear how to calculate the given answer for Q(iii) at the bottom of that page/top of next

 

Hi Bill

Firstly, congrats on beginning studies so early.

You invest your wealth with proportion a in equity and 1 - a non-interest bearing account.

At the end of the period, you have 1 - a in the non-interest bearing account and either 0.96a or 1.08a for the equity.

This gives total wealth as
either
1 -a + 0.96a = 1 - 0.04a
or of
1 - a +1.08a = 1 + 0.08a

Then you compute the expected utility.

 

thanks allot for your helpful answer.
I have two additional but separate questions on this Chapter:

1) Pg 31 of Acted notes (section 7.2 -Finding the maximum premium) quotes the Core Reading that: "the individual's expected utility is:
E[U(a-X)] = int(0,15): sqrt(15-x) dx/ 15"

Where does this formula come from, and presume specific to the uniform distribution?

2) The solution to the Chap 2 practice question 2.1 (on pg 41) states:
"Vp=x_A^2 + x_B^2+ 2*x_A*x_B*sigmaA*sigmaB*rhoAB"

Where does this formula come from?