Sharpe Ratios, Target Ratios, and Return Goals

Abstract

Some form of success estimation is present in virtually all decision-making processes. In most cases, estimations are implicit and judgmental. However, in certain data-rich areas, success prospects can be sharpened into probabilities. Although funds may settle for an expected return that equals some fixed target return, that match results in only a 50% probability of success. However, important goals may require a higher success probability, such as 60%. In this article, the authors present an approach that facilitates calculation of success probabilities for many common investment situations. The key success factor turns out to be the target ratio (T-ratio), a generalization of the standard Sharpe ratio. In addition to fixed return targets, the T-ratio can be applied to a wide range of market-dependent targets such as policy portfolios, benchmark indexes, and/or peer group percentiles. Moreover, within the typically relevant range, a simple approximation can directly map T-ratio values into success probabilities. The structure of the T-ratio underscores the importance of more tightly integrating risk control considerations and success probabilities into the return-seeking process.

TOPICS: Performance measurement, risk management, volatility measures

Key Findings

• • The common practice of matching the expected portfolio return to some fixed target return may prove insufficient for critically important goals that require a higher than 50% probability of success.

• • To obtain a success probability above 50%, a fund’s risk–return structure must provide a sufficiently high T-ratio, a generalization of the Sharpe ratio. A simple formula, based on this T-ratio, can be applied to estimate success probability.

• • To preserve a fund’s return advantage and desired probability of success, the fund also must achieve a level of risk control that results in the T-ratio value associated with that probability.