Utility and Portfolio Choice

One period model 2 quadratic utility function or the

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: . © P. KOLM. 14 Portfolio Choice • Portfolio choice is dynamic and multi-period in nature, max E 0 (u(C 0,C 1,...,CT −1,WT )) , or ⎛T −1 ⎞ ⎜ u(C , t ) + u( ,T )⎟ ⎟ max E 0 ⎜∑ WT t ⎟ ⎜ t =0 ⎟ ⎝ ⎠ where C t denotes consumption in period t • For most applications the “full” problem is too difficult to solve for realistic portfolios so a number of simplifying assumptions are typically applied: 1. One period model 2. Quadratic utility function or the return distribution is jointly normally distributed → mean-variance optimization RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 15 1. The One Period Model max E (u(W )) {wi } where ⎛ ⎞ ⎜W − ∑ w ⎟(1 + r ) + ∑ w (1 + r ) W =⎜ 0 i⎟ f i i ⎟ ⎜ ⎝ ⎠ i i = W0 (1 + rf ) + ∑ wi (ri − rf ) i Necessary and sufficient conditions (For you: derive these) E ⎡⎢u ′(W )(ri − rf )⎤⎥ = 0 ⎣ ⎦ for all i E ⎡⎢u ′′(W )(ri − rf )2 ⎤⎥ < 0 ⎣ ⎦ for all i (Here we see that u ′ > 0 and u′′ < 0 m...
View Full Document

This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.

Ask a homework question - tutors are online