Lecture12-2004

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

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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 Ω = 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 = = Ω 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 Ω μ 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 [ ] ( ) ( ) = - μ ρ σ 2 2 max ' ' x x x x x μ ρ- Ω 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...
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Lecture12-2004 - The Farm Portfolio Problem The Farm...

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