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.
Zakamulin, V. (2011). Sharpe (Ratio) Thinking about the Investment Opportunity Set and CAPM Relationship. Economics Research International, 2011, 1–9. https://doi.org/10.1155/2011/781760