Proof of Mean Variance Tautology

# Proof of Mean Variance Tautology - Mean-Variance Efficiency...

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

Unformatted text preview: Mean-Variance Efficiency and the Capital Asset Pricing Model Matthew Pollard 28th April 2008 Abstract I provide a simple proof of Roll’s (1977) result that mean-variance efficiency and the capital asset pricing model equation are mathematically equivalent. Proposition Let x p denote any mean-variance efficient portfolio with expected return E [ R p ], except for the minimum variance portfolio. For all assets i, the Capital Asset Pricing Model equation holds: E [ R i ]- E [ R zp ] = β i ( E [ R p ]- E [ R zp ]) where E [ R zp ] the unique mean-variance efficient portfolio satisfying Cov ( R p ,R zp ) = . Furthermore, any pair of portfolios ( x p ,x zp ) that satisfy the above conditions are necessarily both mean-variance efficient. Proof Let Σ = ( σ i,j ) N × N denote the matrix of asset covariances. Suppose x p is efficient; that is, it is the solution to the optimization problem x p = arg min 1 2 x T Σ x subject to x p = ER p , x T p 1 = 1 ....
View Full Document

## This note was uploaded on 04/28/2010 for the course ECON FINC3017 taught by Professor Xelloss during the Spring '10 term at University of St Andrews.

### Page1 / 3

Proof of Mean Variance Tautology - Mean-Variance Efficiency...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online