Lecture12-2004 - The Farm Portfolio Problem Part I Lecture...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
The Farm Portfolio Problem: Part I Lecture XII I. Deriving the EV Frontier A. The discussion over the past two weeks has touched on the equivalence between the mean-variance approach and direct utility maximization. Now, I want to further develop the EV approach. B. Let us begin with the traditional portfolio model. Assume that we want to minimize the variance associated with attaining a given level of income. To specify this problem we assume a variance matrix: Ω = 924 41 458 52 202 22 135 22 458 52 76129 452 99 72 55 202 22 452 99 49011 109 09 135 22 72 25 109 09 284 17 . . . . . . . . . . . . . . . . and a constraint matrix which depicts (1) the income constraint and (2) the portfolio constraint Ax b x x x x x x x x x x x x = = + + + = + + + = 8119 11366 6 298 8 014 10 10 10 10 7 0 10 8119 11366 6 298 8 014 7 000 1000 1 2 3 4 1 2 3 4 1 2 3 4 . . . . . . . . . . . . . . . . . The portfolio choice problem can then be stated as max ( ) ' x f x x x st Ax b = = . C. In this initial formulation we find that the optimum solution is x = . . . . 11613 10666 39508 59546 which yields a variance of 228.25. II. A Diversion into Computer Usage GAMS Program sets icrops crops /1*4/ consts constraints /income,portf/; alias(icrops,jcrops);
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
AEB 6182– Agricultural Risk Analysis and Decision Making Fall 2004 Professor Charles Moss 2 table var(icrops,jcrops) variance covariance matrix 1 2 3 4 1 924.41 458.52 202.22 135.22 2 458.52 761.29 452.99 72.55 3 202.22 452.99 490.11 109.09 4 135.22 72.55 109.09 284.17 table line(icrops,const) constraints income portf 1 8.119 1.0 2 11.366 1.0 3 6.298 1.0 4 8.014 1.0 parameter b(const) /income 7.00, portf 1.00/; variables x(icrops) level of each crop rhs(consts) level of each right hand side risk; positive variables x; equations vari variance lconst linear constraints; vari.. sum((icrops,jcrops),var(icrops,jcrops)*x(icrops)*x(jcrops)) =e= risk; lconst(consts).. sum(icrops,line(icrops,consts)*x(icrops)) =e= b(consts); model risk1 using /all/; solve risk1 using nlp minimizing risk; III. Starting with the basic model of portfolio choice: min ' ' * x x x st x Y µ > Freund showed that the expected utility of a normally distributed gamble given negative exponential preferences could be written as [ ] E U x x x [ ] ( ) ( ) = µ ρ σ 2 2 Extending this formulation to vector form, the problem can be expressed as: max ' ' x x x x x µ ρ .
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern