A Survey on the Four Families of Performance Measures Massimiliano - PowerPoint PPT Presentation

“A Survey on the Four Families of Performance Measures” Massimiliano Caporin 1 Grégory M. Jannin 2 Francesco Lisi 3 Bertrand B. Maillet 4 1 Department of Economics and Management 2 A.A.Advisors-QCG (ABN AMRO), Variances and “Marco Fanno”, University of Padova University of Paris-1 (PRISM) massimiliano.caporin@unipd.it gregory.jannin@univ-paris1.fr 3 Department of Statistical Sciences, 4 A.A.Advisors-QCG (ABN AMRO), Variances University of Padova and University of Orléans (LEO/CNRS and EIF) lisif@stat.unipd.it bertrand.maillet@univ-orleans.fr 30 th International French FInance Association Conference - EM Lyon, May 2013 - The fourth author thanks the Europlace Institute of Finance for financial support. This presentation engages only its authors and does not necessarily reflect the opinions of their employers. The usual disclaimers apply.

Agenda A Survey on the Motivation Four Families of Performance Measures M. Caporin Aim of the Article G. Jannin F. Lisi B. Maillet Literature The Four Families of Performance Measures Preliminary Conclusions Extensions 2 / 35

Motivation (1/8) 160 A Survey on the Four Families of Performance 140 Fund W (Good) Measures 120 100 Fund Z (Bad) 80 60 5 40 12/08 03/09 06/09 09/09 12/09 03/10 06/10 09/10 12/10 03/11 06/11 09/11 12/11 Source: simulations by the author. Fund W is preferred => higher performance and no obvious risk 3 / 35

Motivation (2/8) 160 A Survey on the Four Families Fund X (Good) of Performance 140 Measures 120 Fund Y (Bad) 100 80 60 5 40 12/08 03/09 06/09 09/09 12/09 03/10 06/10 09/10 12/10 03/11 06/11 09/11 12/11 Source: simulations by the author. Fund X is preferred => higher performance but more risky sometimes 4 / 35

Motivation (3/8) A Survey on the Four Families of Performance 300 Measures Fund A 250 Fund B D.J. Index DJI Fund A (Good) 200 150 100 Fund B (Bad) 50 0 01/99 01/00 01/01 01/02 01/03 01/04 01/05 01/06 01/07 01/08 01/09 01/10 01/11 Source: USD Daily quotes, from 01/01/1999 to 05/13/2011. We compare in this illustration the performance of the Fund A and the Fund B – the uninformed agent – to their benchmark which is the DJI. Fund A corresponds to the informed investor who is characterized by an alpha set to .01% and a sensitivity of his portfolio to the benchmark equals to .39, while the Fund B, namely the uninformed investor, has respectively an alpha -.01% sets to and a beta equals to 1.10. We use an Ordinary Least Square method to calculate these data. Computations by the authors. Fund A is preferred => higher performance 5 / 35

Motivation (4/8) Net Asset Values of Fund A, Fund B and the D.J. Index on A Survey on the the last period Four Families of Performance 2 nd Shock 1 st Shock Measures 150 140 Fund A 130 Performance 120 110 100 90 Fund B DJI 80 70 01/01 01/02 01/03 01/04 01/05 01/06 01/07 01/08 01/09 01/10 01/11 01/12 Dates Source: Illustration of Net Asset Values of Fund A (thin grey line) and Fund B (bold black line) over a one-year period. Grey areas represent market shocks. The x-axis corresponds to dates whilst the y-axis shows the performance of the two funds. Computations by the authors. Fund A or Fund B ? Performance and/or Risk ? 6 / 35

Motivation (5/8) Statistics of Fund A and Fund B on the last period Fund A Fund B Ranking A Survey on the MPPM ( � = 2) 12.69% 13.31% B Four Families MPPM ( � = 3) 11.50% 11.58% B of Performance Ann. Performance 15.20% 16.47% B Measures Ann. Volatility 15.79% 18.09% A Skewness 2.12 -2.44 A According to the Kurtosis 9.86 16.06 A Max Drawdown -10.00% -20.00% A main criteria, Fund Value-at-Risk 95% -1.06% -1.68% A A is preferred Value-at-Risk 99% -1.54% -4.09% A Sharpe 1.04 1.01 A Omega 5.99 5.78 A Sortino 3.35 1.92 A Kappa 3 2.46 1.13 A Fund B is however Calmar 1.63 0.92 A preferred by some Burke .44 .32 A Sharpe-Omega .13 .12 A performance Treynor .34 .23 A Treynor-Black .26 .15 A measures (MPPM) Graham-Harvey .09 .08 A Sterling .83 .62 A Cornell 11.94% 10.94 A Israëlsen 1.04 1.05 A Jensen-Alpha 11.23% 10.30% A RAP 20.18% 19.57% A MRAP 34.09% 23.20% A SRAP 9.55% 8.94% A Ulcer 2.01 1.65 A 7 / 35 Ziemba 1.70 .61 A

Motivation (6/8) Iso -MPPM Frontiers displaying the Quantity of Over-volatility required A Survey on the for a Given Over-performance for reversing the MPPM Ranking Four Families of Performance 1 Measures 2.00 ρ =7 ρ =6 ρ =8 ρ =9 ρ =10 ρ =5 Sharpe Ratio performance ρ =4 Over-performance 1.00 ρ =3 Fund B .50 ρ =2 5 .00 1.00 .00 .50 1.00 1.50 2.00 Over-volatility 6 risk Source: Illustration of over-performance (the y-axis) and over-volatility (the x-axis), both expressed in %, of returns in Fund B (symbolized by the blue star), compared to Fund A, and ranking frontiers (solid lines) computed from the Manipulation-Proof Performance Measure (see, Ingersoll et al. , 2007) when varying the risk aversion coefficient from 2 to 10 (is equal to 3 in the original paper). Computations by the authors. 8 / 35

Motivation (7/8) A Survey on the Four Families of Performance Performance depends on the investor’s preferences and risk profiles Measures Strong link between performance and inflows/outflows in funds Performance measures published in the academic literature are based on different dimensions (total risk, systematic risk sensitivity, drawdowns, return density, VaR, CAPM, APT, utility function, etc. ) More than 100 ways to measure portfolio performance… 9/ 35

Motivation (8/8) A Survey on the THE TAXONOMY TABLE OF PERFORMANCE MEASURES Four Families of Performance Measures 1 st Family: Relative Performance Measures 3 1966 4 2005 4 2001 5 2009 7 2009 5 2006 3 1994 4 2005 3 1965 4 1965 2008 1994 N 2005 Parameter Publication S IS1 DS ASSR ASKSR W1 IR IS2 T T2 BA SE GT Number Date Zakamouline- Zakamouline- Srivastava- Sharpe Israëlsen Morey-Vinod Watanabe Sharpe Israëlsen Treynor Treynor Bacon Hübner Koekebakker Koekebakker Essayyad SHORT NAME 3 2000 2003 3 2002 3 2003 3 1998 3 1982 2 2009 3 1991 3 2011 3 2001 3 1991 2006 3 2004 4 2005 3 1989 3 1994 3 1991 1996 κ RVAR AB RMVAR RCVAR YO YI L KY ERR RLPM SM W2 DRS UIP B C K Martin-Rachev- Darolles-Gouriéroux- Author(s) Dowd Alexander-Baptista Favre-Galeano Young Yitzhaki Konno-Yamazaki Caporin-Lisi Sortino-Stachell Sortino-Meer Watanabe Kaplan-Knowles Ziemba Martin-McCann Burke Young Kestner Siboulet Jasiak 2 nd Family: Absolute Performance Measures 4 1968 5 1972 4 1999 5 2000 1998 2007 2009 4 1972 8 1970 6 1966 6 1981 1986 6 1973 1973 6 1979 8 1993 10 1997 1993 7 1998 4 1999 5 1991 N 1996 α J α ZB α B α TM α HM α CK α McD α PSR α AC α FF α C α EGDH α HS α LB α AP α FS NS RE / RC RE CM OE BK Briec-Kerstens- Pogue-Solnik- Elton-Gruber-Das- Jensen Fama Morey-Morey Cantaluppi-Hug Chauveau-Maillet Briec-Kerstens Black Brennan Treynor-Mazuy Henriksson-Merton Connor-Korajczyk McDonald Ang-Chua Fama-French Carhart Hwang-Satchell Leland Aftalion-Poncet Ferson-Schadt Jokung Rousselin Hlavka 5 1987 5 2001 6 2002 3 1989 1979 4 1997 2005 3 1997 3 1997 5 1999 2 1981 MCV CAP SHARAD PPW C RAP MRAP GH1 GH2 SRAP HM Modigliani- Moses-Cheyney-Veit Muralidhar Muralidhar Grinblatt-Titman Cornell Scholtz-Wilkens Graham-Harvey Graham-Harvey Lobosco Henriksson-Merton Modigliani 5 3 rd Family: Density-based Performance Measures 2 2000 2 2002 3 2006 3 2006 4 1999 4 2008 3 2004 6 2004 2010 2010 � GL LAP S LAP H U-P FT RR GRR RADD RMDD Gemmill-Hwang- Gemmill-Hwang- Sortino-Meer- Biglova-Ortobelli- Biglova-Ortobelli- Ortobelli-Rachev- Ortobelli-Rachev- Bernardo-Ledoit Keating-Shadwick Farinelli-Tibiletti Salmon Salmon Plantinga Rachev-Stoyanov Rachev-Stoyanov Biglova-Stoyanov Biglova-Stoyanov 4 th Family: Utility-based Performance Measures 2 2002 3 2000 4 2005 4 2007 2 2010 MRAR PI � � DR Ingersoll-Spiegel- Morningstar Stutzer Kaplan Brown-Kang-Lee Goetzmann-Welch 10/ 35 Legend: See Caporin M., G. Jannin, F. Lisi and B. Maillet, (2012), "A Survey on the Four Families of Performance Measures", 29 pages. The Main Performance Measure Other Performance Measures directly based on the Main One Alternative Performance Measures

Aim of the Article A Survey on the Four Families of Performance 1 Measures Definition of the four main families of measures M. Caporin G. Jannin F. Lisi General expressions for each family B. Maillet Identification and explicit formulations for the more representative measures (and their close variants in Appendix) Intuition for each measure with some short criticisms Codes (MatLab, R,…) available soon on: www.performance-metrics.eu 11 / 35