Scandinavian Working Papers in Business Administration

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2007/12: Simplifying and generalizing some efficient frontier and CAPM related results

Steinar Ekern ()
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Steinar Ekern: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway

Abstract: This paper simplifies, generalizes, extends, surveys and unifies results related to the efficient frontier in portfolio analysis and to asset pricing formulations of the Capital Asset Pricing Model (CAPM) type. It derives the composition and properties of many central portfolios in portfolio analysis. It also discusses and provides several CAPM type formulations involving different portfolios. In particular, it states the tangency portfolio in an instructive and very simple way, focusing on similarities in going from the global minimum variance portfolio via a null index portfolio whose zero beta portfolio has a zero expected return. The Non-frontier zero beta, the Null index and the Augmented frontier CAPM versions supplement standard CAPM formulations. More importantly, the GMVP and the Benchmark versions of the CAPM do not rely on a zero beta portfolio, but require two betas.

Keywords: CAPM types; Roll's approach; tangency portfolio; GMVP; benchmark

JEL-codes: G10; G11; G12

27 pages, March 27, 2007

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