Efficient Portfolios with no short-sale restriction ch. 11
MGT 4850
Spring 2007
University of Lethbridge

Overview
• CAPM and the risk-free asset
– CAPM with risk free asset
– Black’s (1972) zero beta CAPM
• The objective is to learn how to calculate:
– Efficient Portfolios
– Efficient Frontier

Notation
• Weights – a column vector Γ (Nx1); it’s transpose Γ T is a row vector (1xN)
• Returns - column vector E (Nx1); it’s transpose E T is a row vector (1xN)
• Portfolio return E T Γ or Γ T E
• 25 stocks portfolio variance Γ T S Γ
Γ T (1x 25 )*S( 25 x25)* Γ(25x1)
• To calculate portfolio variance we need the variance/covariance matrix S .

Simultaneous Equations
• Solve simultaneously for x and y: x + y=10 x − y=2

Calculating the efficient frontier
• Only four risky assets

Find efficient portfolios
• Minimum Variance
• Market portfolio
• You can not establish the frontier from only two efficient portfolios when there are no short sale restrictions
• CML
• SML