This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Derivation of the Expected Value-Variance Frontier with a Risk-Free Asset: Lecture XXII Charles B. Moss October 14, 2010 I. Introduction of a Risk-free Asset A. If a risk-free asset is introduced into the portfolio, the ecient set of portfolios becomes a straight line between the risk-free asset and a tangency on the ES frontier as depicted in Figure 1. B. Mechanics 1. Setting up the portfolio problem min w 1 2 w w s . t . ( z R 1) w = R (1) 2. Forming the Lagrangian L = 1 2 w w ( R ( z R 1) w ) w L = w ( z R 1) = 0 w = 1 ( z R 1) (2) with w = 1 1 w defined as the amount of wealth invested in the risk-free asset if w > 0 or borrowed if w < 0. 3. Substituting this result into the constraint yields ( z R 1) 1 ( z R 1) = R z 1 z R z 1 1 R 1 1 z R 2 1 1 a = R (3) 1 AEB 6182 Agricultural Risk Analysis and Decision Making...
View Full Document
- Fall '08