Slides21-2010

# Slides21-2010 - Derivation of the Expected Value-Variance...

This preview shows pages 1–6. Sign up to view the full content.

Derivation of the Expected Value-Variance Frontier without a Risk-free Asset : Lecture XXI Charles B. Moss October 12, 2010 Charles B. Moss () Eﬃcient Frontier without Risk-free Asset October 12, 2010 1 / 20

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

View Full Document
1 Expected Value-Variance Versus Direct Utility Maximization Comparing Specifcations Numerically 2 Mathematical derivation without a Risk-Free asset Lagrange ±ormulation Gradients oF the Variance Matrix Stock PortFolio Example Charles B. Moss () Eﬃcient Frontier without Risk-free Asset October 12, 2010 2 / 20
Expected Value-Variance Versus Direct Utility Maximization Due to various fnancial economic models such as the Capital Asset Pricing Model that we will discuss in our discussion oF market models, the fnance literature relies on the use oF mean-variance decision rules rather than direct utility maximization. There is a practical aspect For stock-brokers who may want to give clients alternatives between eﬃcient portFolios rather than attempting to directly elicit each individuals utility Function. Kroll, Levy, and Markowitz examines the acceptability oF the Mean-Variance procedure whether the expected utility maximizing choice is contained in the Mean-Variance eﬃcient set. We assume that the decision maker is Faced with allocating a stock portFolio between various investments. Charles B. Moss () Eﬃcient Frontier without Risk-free Asset October 12, 2010 3 / 20

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

View Full Document
Comparing Specifcations Numerically Two approaches for making this problem are to choose between the set of investments to maximize expected utility max x E [ U ( x )] s . t . n X i =1 x i =1 x i 0 (1) The second alternative is to map out the eﬃcient Mean-Variance space by solving max x c 0 x s . t . x 0 Ω x t x i 0 (2) Charles B. Moss () Eﬃcient Frontier without Risk-free Asset October 12, 2010 4 / 20
A better formulation of the problem is max x c 0 x ρ 2 x 0 Ω x s . t . x i 0 (3) where ρ is the Arrow-Pratt absolute risk aversion coeﬃcient. Table 1 presents the optimal shares of the portfolio based on direct

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

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

{[ snackBarMessage ]}

### Page1 / 20

Slides21-2010 - Derivation of the Expected Value-Variance...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online