This paper extends the Treynor performance ratio for a single index to the case of multiple indexes. The new measure, called the Generalized Treynor Ratio, preserves the same key geometric and analytical properties of the original Treynor Ratio. The Generalized Treynor Ratio is defined as the abnormal return of a portfolio per unit of premium-weighted average systematic risk, normalized by the premium-weighted averagesystematic risk of the benchmark. Numerical simulations reveal that the portfolio rankings produced with this measure are more precise and more stable than the ones provided by Jensen's alpha and the Information Ratio.

Using an international database featuring 1624 mutual funds over 15years, this paper analyses the joint abilities of performance measures to predict subsequent fund failure. We examine the probability of disappearance over a time window, and expected fund survival time, and study the circumstances of a fund’s disappearance, its currency and domicile. By combining relevant measures, fund failure appears to a significant extent predictable, more than with single classical measures. Survivorship predictability has significant economic value. Such evidence suggests that past performance does not only influence investors’ perception of fund quality, but also reflects managers’ ability to sustain performance.

Factor performance is highly sensitive to the number of stocks composing its long and short basis portfolios. We examine three methodological choices that have an impact on portfolio diversification: the (in)dependence and the (a)symmetry of the stock sorting procedure and the sorting breakpoints. We show that these methodological choices have to be considered jointly and that a dependent (D) sort that starts with the control variables with whole sample or “name” (N) breakpoints and that performs a symmetric (S) sort on characteristics minimizes the biases from unpriced risks. This paper also demonstrates that the biases introduced by currently popular sorting methodologies can become very severe under specific market conditions and are not driven by small capitalizations. This alternative framework generates much stronger “turn-of-the-year” size and “through-the-year” book-to-market effects than what is conventionally documented.

This paper analyzes the implications of the advanced measurement approach (AMA) for the assessment of operational risk. Through a clinical case study on a matrix of two selected business lines and two event types of a large financial institution, we develop a procedure that addresses the major issues faced by banks in the implementation of the AMA. For each cell, we calibrate two truncated distributions functions, one for “normal” losses and the other for the “extreme” losses. In addition, we propose a method to include external data in the framework. We then estimate the impact of operational risk management on bank profitability, through an adapted measure of RAROC. The results suggest that substantial savings can be achieved through active management techniques.