Abstract
This paper analytically determines the conditions under which four commonly utilized portfolio measures (the Sharpe index, the Treynor index, the Jensen alpha, and the Adjusted Jensen's alpha) will be similar and different. If the single index CAP M model is appropriate, we prove theoretically that well-diversified portfolios must have similar rankings for the Treynor, Sharpe indices, and Adjusted Jensen's alpha ranking. The Jensen alpha rankings will coincide if and only if the portfolios have similar betas. For multi-index CAPM models, however, the Jensen alpha will not give the same ranking as the Treynor index even for portfolios of large size and similar betas. Furthermore, the adjusted Jensen's alpha ranking will not be identical to the Treynor index ranking.
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