Performance Glossary

We briefly present below the definitions of some of the most important performance measures (and related concepts) developed by the literature. For every definition, you will also find a link to a related paper.

  • Alexander and Baptista (2003)

    Strongly inspired by Dowd (2000), Alexander and Baptista (2003) proposes to add the risk-free rate at the denominator of the original Dowd (2000) Reward-to-Value-at-Risk ratio.

    Alexander, G. and Baptista, A. (2003) Portfolio performance evaluation using value-at-risk. Journal of Portfolio Management 29(4):93–102.
    Description / Abstract / Where to find it
  • Aftalion-Poncet (1991)

    The Aftalion and Poncet (1991) index compares the expected return of the investor’s portfolio in excess of the expected return of its reference portfolio, to the return that should have been reached according to the total risk of the managed portfolio.

    Aftalion, F. and Poncet, P. (1991) Les mesures de performance des OPCVM. La revue banque, 517: 582-588.
    Description / Abstract / Where to find it
  • Ang and Chua (1979)

    The Ang-Chua Excess Return gives the excess return obtained by the manager which is not explained by his/her current risk positions (supposing, this time, that there are two stable risk factors: the market factor and the excess volatility of the market factor).

    Ang, J.S. and Chua, J.H. (1979) Composite Measures for the Evaluation of Investment Performance. Journal of Financial and Quantitative Analysis, 14: 361-384.
    Abstract / Where to find it
  • Billio, Jannin, Maillet and Pelizzon (2016)

    Billio et al. (2016) introduce a new flexible Generalized Utility-based N-moment measure (GUN), relying both on a characterization of the whole distribution and on preferences of the investor, which is adapted to analyze the performance of hedge funds.

    Billio, M., G. Jannin, B. Maillet and L. Pelizzon (2016) A New Generalized Utility-based N-moment Measure of Performance. Working Paper 77 pages.
    Description / Abstract / Where to find it
  • Black (1972)

    Black (1972) proposes the “zero-beta CAPM” by exploring the nature of capital market equilibrium under two restrictive assumptions. First, he assumes the absence of a riskless asset, but considers different risk-free borrowing and lending. Secondly, he supposes the existence of a riskless asset and the possibility to only take long positions on it (short positions are not allowed). In both cases, the investor can take unlimited long or short positions in risky assets.

    Black, F. (1972) Capital market equilibrium with restricted borrowing. Journal of Business 45(3):444–455.
    Description / Abstract / Where to find it
  • Brown, Kang, In and Lee (2010)

    The Doubt Ratio is based on differences between MPPM when considering two risk aversion coefficients. Beyond a certain degree of manipulation of portfolio returns, values of MPPMs will tend to be (almost) equal, for any risk aversion coefficients, i.e. whatever the type of investor risk profiles.

    Brown, S., Kang, M., In, F. and Lee G (2010) Resisting the manipulation of performance metrics: An empirical analysis of the manipulation-proof performance measure. Finance and Corporate Governance Conference 59 pages
    Description / Abstract / Where to find it
  • Connor and Korajczyk (1986)

    The Connor-Korajczyk Residual gives the excess return obtained by the manager which is not explained by his/her current risk positions. It generalizes the Jensen’s alpha in a multifactorial framework.

    Connor, G. and Korajczyk, R.A. (1986) Performance Measurement with the Arbitrage Pricing Theory: A New Framework for Analysis. Journal of Financial Economics 15:373-394.
    Description / Abstract / Where to find it
  • Dowd (2000)

    Based on a quantile model, Dowd (2000) introduces a performance measure that adjusts the expected excess return of the investor’s portfolio by the α-Value-at-Risk (α-VaR) of the portfolio return distributions.

    Dowd, K. (2000) Adjusting for Risk: An improved Sharpe Ratio. International Review of Economics and Finance, 9(3):209–222.
    Description / Abstract / Where to find it
  • Fama (1972)

    The Fama's Index gives the excess return obtained by the manager that cannot have been obtained investing in the market portfolio. It compares the extra return obtained by the portfolio manager with a specific risk and the extra return that could have been obtained with the same amount of systematic risk.

    Fama, E. (1972) Components of Investment Performance. Journal of Finance 27: 551-567.
    Description / Abstract / Where to find it
  • Ferson and Schadt (1996)

    The Ferson-Schadt Measure gives the excess return obtained by the manager which is not explained by his/her current risk positions (supposing, this time, that risk factors are truly variable).

    Ferson, W.E. and Schadt, R.W. (1996) Measuring Fund Strategy and Performance in Changing Economic Conditions. Journal of Finance 51: 425-461.
    Description / Abstract / Where to find it
  • Graham and Harvey (1997)

    Graham and Harvey (1997) build two performance measures based on market timing advice, provided by investment newsletters, which recommend increasing investments in risky assets before market appreciation and decrease before market shocks.

    Graham J, Harvey C (1997) Grading the performance of market-timing newsletters. Financial Analysts Journal 53(6): 54–66.
    Description / Abstract / Where to find it
  • Henriksson and Merton (1981)

    The Merton-Henriksson Measure gives the excess return obtained by the manager that can not be replicated by a mix of options and market portfolio. That represents the excess return that have been economized by the manager because of its market timing ability.

    Henriksson, R.D. and Merton, R.C. (1981) On Market Timing and Investment Performance. II. Statistical Procedures for Evaluating Forecasting Skills. Journal of Business 54: 513-533.
    Description / Abstract / Where to find it
  • Israëlsen (2005) Information Ratio

    Israëlsen (2005) suggests a corrected version of the Information Ratio that takes into account those cases when the estimated expected excess return of the investor's portfolio is negative.

    Israëlsen, C. (2005) A Refinement to the Sharpe Ratio and Information Ratio. Journal of Asset Management 5(6):423-427.
    Description / Abstract / Where to find it
  • Israëlsen (2005) Ratio

    This measure belongs to the family of relative performance measures and is a corrected Sharpe ratio. It also measures the compensation earned by the portfolio manager per unit of portfolio total risk, but differs from it when expected returns are negative (the higher, the better).

    Israëlsen, C. (2005) A Refinement to the Sharpe Ratio and Information Ratio. Journal of Asset Management 5(6):423-427.
    Description / Abstract / Where to find it
  • Ingersoll, Goetzmann, Spiegel, and Welch (2007)

    Ingersoll et al. (2007) develop an “ungamable” performance measure, named “Manipulation-Proof Performance Measure” (MPPM for short), to gauge the performance of an active manager.

    Ingersoll, J., Goetzmann, W., Spiegel, M. and Welch, I. (2007) Portfolio Performance Manipulation and Manipulation-proof Performance Measures. Review of Financial Studies 20(5):1503-1546.
    Description / Abstract / Where to find it
  • Jensen (1968)

    The Jensen’s Alpha gives the excess return obtained when deviating from the benchmark.

    Jensen, M.C. (1968) The Performance of Mutual Funds in the Period 1945-1964. Journal of Finance 23: 389-416.
    Description / Abstract / Where to find it
  • Keating and Shadwick (2002)

    This performance measure incorporates all of the higher moments of a return distribution, not just the mean and variance. Omega is easily calculated, is not dependent on an assumed utility function, and incorporates the impact of gains and losses relative to any specified return threshold.

    Keating C., Shadwick W. (2002) A Universal Performance Measure. Journal of Performance Measurement 6(3):59–84.
    Description / Abstract / Where to find it
  • Kestner (1996)

    The Sterling’s ratio of Kestner (1996) is a relative measure of performance. It is defined as the annualized return of the fund, deducted the yield of an investment without risk, divided by a scaled average annual maximum draw-down on a given period.

    Kestner, L. (1996) Getting a Handle on True Performance. Futures, 25:44-46.
    Description / Abstract / Where to find it
  • Morningstar Risk Adjusted Ratio (MRAR)

    The Morningstar Risk Adjusted Ratio (MRAR) is defined as the expected value of the certainty equivalent annualized geometric return on a given horizon. It is built on the Expected Utility theory and considers a Power Utility function.

    Caporin, M., Jannin, G., Lisi, F. and Maillet, B. (2014) A Survey on the Four Families of Performance Measures. Journal of Economic Surveys 28(5):917-942.
    Description / Abstract / Where to find it
  • Moses, Cheyney and Veit (1987)

    The Moses-Cheyney-Veit Measure gives the excess return obtained by the manager normalized by the return obtained for a specific risk level equal to those of the fund.

    Moses, E.A., Cheyney, J.M. and Veit, E.T. (1987) A New and More Complete Performance Measure. Journal of Portfolio Management 13: 24-33.
    Description / Abstract / Where to find it
  • Scholz and Wilkens (2005a)

    Scholz and Wilkens (2005a) propose performance measure similar to the RAP measure, named the “Market Risk-Adjusted Performance” by considering the systematic risk sensitivity of the managed portfolio returns instead of its total risk.

    Scholz, H. and Wilkens, M. (2005) A Jigsaw Puzzle of Basic Risk-adjusted Performance Measures. Journal of Performance Measurement 9: 57-64.
    Description / Abstract / Where to find it
  • Sharpe (1994) Information Ratio

    Since the reference to competitors is a crucial topic in the management industry, Sharpe (1994) proposes a second performance measure, named “Information Ratio” (IR), which takes into account the Tracking Error volatility of an actively managed portfolio.

    Sharpe, W. (1994) The Sharpe Ratio. Journal of Portfolio Management 21(1):49-58.
    Description / Abstract / Where to find it
  • Sharpe (1966)

    The Sharpe’s Ratio is a relative measure of performance. It allows to compare the returns to a specific measure of risk: in this case the standard deviation. It is designed to evaluate the potential returns in light of the underlying risk.

    Sharpe, W.F. (1966) Mutual Fund Performance. Journal of Business 39: 119-138.
    Description / Abstract / Where to find it
  • Sortino and van der Meer (1991)

    The Sortino’s Ratio compares the returns to a specific measure of risk: in this case the downside risk. It is designed to evaluate the potential returns in light of the underlying risk measured during the negative price phases.

    Sortino, F.A. and van der Meer, R. (1991) Downside Risk. Journal of Portfolio Management 17: 27-31.
    Description / Abstract / Where to find it
  • Treynor (1965)

    The Treynor’s Measure compares returns to a specific measure of risk: in this case the beta. It is designed to evaluate the potential returns in light of the underlying risk.

    Treynor, J.L. (1965) How to Rate Management of Invested Funds. Harvard Business Review 43: 63-75.
    Description / Abstract
  • Treynor and Black (1973)

    The Treynor-Black Measure gives the excess return obtained when deviating from the benchmark when taking into account the systematic risk of the portfolio. It allows to correct the Jensen’s alpha in the sense that it is a relative performance measure. The magnitude of the Treynor-Black Measure depends on two key variables: the return of the benchmark and the beta.

    Treynor, J.L. and Black, F. (1973) How to Use Security Analysis to Improve Portfolio Selection. Journal of Business 46: 66-86.
    Description / Abstract / Where to find it
  • Watanabe (2006) Extended Sharpe Ratio

    Watanabe (2006) proposes an extension of the original Sharpe (1966) dealing with higher-moments. This measure is the Sharpe ratio multiplied by ratio of the skewness and the kurtosis of the investor’s portfolio return distribution.

    Watanabe, Y. (2006) Is sharpe ratio still effective? Journal of Performance Measurement 11(1): 55–66.
    Description / Abstract / Where to find it
  • Watanabe (2006) Extended Sortino Ratio

    Watanabe (2006) proposes an extension of the Sortino-Meer (1991) dealing with higher-moments. This measure is the Sharpe ratio multiplied by ratio of the skewness and the kurtosis of the investor’s portfolio return distribution.

    Watanabe, Y. (2006) Is sharpe ratio still effective? Journal of Performance Measurement 11(1): 55–66.
    Description / Abstract / Where to find it
  • Treynor and Mazuy (1966)

    The Treynor-Mazuy Measure gives the excess return obtained by the manager which is not explained by his/her current risk positions (supposing, this time, that he/she changes risk positions according to the market portfolio return expectations).

    Treynor, J.L. and Mazuy, K.K. (1966) Can Mutual Funds Outguess the Market? Harvard Business Review 44: 131-136.
    Description / Abstract
  • Yitzhaki (1982)

    Yitzhaki (1982) suggests an alternative method to the Mean-Variance approach for comparing uncertain prospects based on the Gini coefficient.

    Yitzhaki, S. (1982) Stochastic dominance, mean variance, and gini’s mean difference. American Economic Review 72(1): 178–85.
    Description / Abstract / Where to find it
  • Young (1991)

    The Calmar’s ratio is conceived to provide information about the mean return obtained by the portfolio manager put in perspective with the potential maximum loss supported by the investor.

    Young, T.W. (1991) Calmar Ratio: A Smoother Tool. Futures 20: 40.
    Description / Abstract
  • Ziemba (2005)

    A further case is the “Downside Risk Sharpe ratio” suggested by Ziemba (2005) (see also Gergaud and Ziemba, 2012), which is obtained by considering the square root of an LPM of the second order and multiplied by two in the denominator of The Sortino-Satchell (2001) Reward-to-Lower Partial Moment Ratio (RLPM).

    Ziemba W (2005) The symmetric downside-risk sharpe ratio. Journal of Portfolio Management 32(1): 108–122.
    Description / Abstract / Where to find it