Sharpe (Ratio) Thinking about the Investment Opportunity Set and CAPM Relationship | Zendy

Valeriy Zakamulin | Zendy

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

Author(s) -

Valeriy Zakamulin

Publication year - 2011

Publication title -

economics research international

Language(s) - English

Resource type - Journals

eISSN - 2090-2123

pISSN - 2090-2131

DOI - 10.1155/2011/781760

Subject(s) - sharpe ratio , portfolio , capital asset pricing model , investment (military) , economics , modern portfolio theory , investment strategy , set (abstract data type) , portfolio optimization , econometrics , investment performance , expected return , asset allocation , financial economics , asset (computer security) , actuarial science , return on investment , microeconomics , computer science , profit (economics) , programming language , computer security , production (economics) , politics , political science , law

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 set in the investment practice. The Sharpe ratio thinking also motivates reconsidering the CAPM relationship and adjusting Jensen's alpha in order to properly measure abnormal portfolio performance

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