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A Note on the Leverage Effect on Portfolio Performance Measures

In a recent article, Modigliani and Pogue [2] raised the issue of “leverage bias” in portfolio performance measures. Specifically, they contended that the value of the Jensen's alpha (α) could be affected by borrowing or lending at the risk-free rate, while the Treynor index (TI) does not suffer from this shortcoming. They illustrated this effect through the use of a graphical example similar to the one in Exhibit I where A and B are two unlevered portfolios with the same α's but different TI's. Modigliani and Pogue argued that by leveraging, i.e., borrowing at Rf, the portfolio with the greater slope (TI), A, could attain a levered portfolio AL which clearly dominates portfolio B. In other L words, the line with the higher TI will dominate the line with a lower TI regardless of α values. This seems to imply that, in general, TI is a better measure of ex post portfolio performance, and that ranking based on TI's is consistent and invariant to the leverage effect, while ranking based on a's is not.