Sharpe (Ratio) Thinking About the Investment Opportunity Set and CAPM Relationship

Economics Research International, Vol. 2011

21 Pages Posted: 28 Sep 2009 Last revised: 6 Sep 2011

Valeriy Zakamulin

University of Agder - School of Business and Law

Date Written: May 6, 2011

Abstract

In the presence of a risk-free asset the investment opportunity set obtained via the Markowitz portfolio optimization procedure is usually characterized in terms of the vector of excess returns on individual risky assets and the variance-covariance matrix. We show that the investment opportunity set can alternatively be characterized in terms of the vector of Sharpe ratios of individual risky assets and the correlation matrix. This implies that the changes in the characteristics of individual risky assets that preserve the Sharpe ratios and the correlation matrix do not change the investment opportunity set. The alternative characterization makes it simple to perform a comparative static analysis that provides an answer to the question of what happens with the investment opportunity set when we change the risk-return characteristics of individual risky assets. We demonstrate the advantages of using the alternative characterization of the investment opportunity in the investment practice. The Sharpe ratio thinking also motivates to reconsider the CAPM relationship and adjust the Jensen's alpha in order to properly measure abnormal portfolio performance.

Keywords: investment analysis, optimal allocation, portfolio theory, investment opportunity set, CAPM, comparative static analysis, Sharpe ratio, Jensen's alpha

JEL Classification: G11

Suggested Citation

Zakamulin, Valeriy, Sharpe (Ratio) Thinking About the Investment Opportunity Set and CAPM Relationship (May 6, 2011). Economics Research International, Vol. 2011. Available at SSRN: https://ssrn.com/abstract=1479495

Valeriy Zakamulin (Contact Author)

University of Agder - School of Business and Law ( email )

Service Box 422
Kristiansand, N-4604
Norway
+47 38141039 (Phone)

HOME PAGE: http://vzakamulin.weebly.com/

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