Lecture12-2004 - The Farm Portfolio Problem: The Farm...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The Farm Portfolio Problem: The Farm Portfolio Problem: Part I Part I Lecture XII Fall 2004 2 Farm Portfolio Problem I An Empirical Model of Mean- An Empirical Model of Mean- Variance Variance Deriving the EV Frontier 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: Fall 2004 3 Farm Portfolio Problem I = 924 41 45852 202 22 13522 45852 76129 452 99 72 55 202 22 452 99 49011 109 09 13522 72 25 109 09 28417 . . . . . . . . . . . . . . . . max ( ) ' x f x x x st Ax b = = Fall 2004 4 Farm Portfolio Problem I Ax b x x x x x x x x x x x x = = + + + = + + + = 8119 11366 6298 8014 10 10 10 10 7 0 10 8119 11366 6298 8014 7 000 1000 1 2 3 4 1 2 3 4 1 2 3 4 . . . . . . . . . . . . . . . . Fall 2004 5 Farm Portfolio Problem I In this initial formulation we find that the optimum solution is x which yields a variance of 228.25. x =- . . . . 11613 10666 39508 59546 Fall 2004 6 Farm Portfolio Problem I Parts of the GAMS Program Parts of the GAMS Program GAMS Program Sets Tables Parameters Variables Equations Model Setup Fall 2004 7 Farm Portfolio Problem I Starting with the basic model of portfolio choice: min ' ' * x x x st x Y Fall 2004 8 Farm Portfolio Problem I Freund showed that the expected utility of a normally distributed gamble given negative exponential preferences could be written as [ ] E U x x x [ ] ( ) ( ) = - 2 2 max ' ' x x x x x - Fall 2004 9 Farm Portfolio Problem I January- June 1.199 1.382 2.776 .000 60.0 July- December .000 1.382 2.776 .482 60.0 Production Capital Period 1 1.064 .484 .038 .000 24.0 Period 2-2.064 .020 .107 .229 12.0 Period 3-2.064-1.504-1.145--1.229 0.0 Fall 2004 10 Farm Portfolio Problem I...
View Full Document

Page1 / 29

Lecture12-2004 - The Farm Portfolio Problem: The Farm...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online