Performance with Restricted Borrowing: A Generalization of Usual Measures
Posted: 22 Jun 2001
Date Written: January 2001
Traditional measures of performance may become somehow misleading when borrowing is either limited or forbidden. This paper is an attempt at generalizing the measures of Sharpe, Treynor and Jensen to the case of an imperfect market for loans. We consider the portfolios combining an investment in one managed fund and lending or borrowing the riskless asset. We then define a partial ordering relation, called dominance, on these portfolios which, in its turn, induces a relation on the managed funds. The ex post efficient frontier consists in the set of the undominated portfolios. Absolute performance is the distance to the frontier whereas relative performance is the ratio of the measure of Sharpe of the fund under review to that of the undominated portfolio exhibiting the same risk. We also generalize Treynor's and Jensen's measures in a very similar manner considering, alternatively, a unique factor of risk and a multifactor risk relation. Performance is then analogous to the concept of efficiency by Debreu (1951) and Farell (1957) in industrial economics.
Keywords: Performance Measurement, Asset Pricing Models, Efficiency.
JEL Classification: G12
Suggested Citation: Suggested Citation