Chapter 2 Calculating Expected Utility Theory

Discussion in 'CM2' started by Bill SD, May 6, 2022.

  1. Bill SD

    Bill SD Keen member

    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
     
    Last edited: May 6, 2022
  2. Busy_Bee4422

    Busy_Bee4422 Ton up Member

    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.
     
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  3. Bill SD

    Bill SD Keen member

    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?
     
  4. Steve Hales

    Steve Hales ActEd Tutor Staff Member

    The "1/15" is the pdf of the uniform distribution U(0,15)
    This comes from the standard result that the variance of the sum of two random variables is equal to the sum of their individual variances plus twice the covariance between them. There's more on this on pages 8 & 9 of Chapter 6
     
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