1. Using Stochastic Dominance criteria in Data Envelopment Analysis of mutual funds Timo Kuosmanen Wageningen University, The Netherlands EURO / INFORMS joint meeting, Istanbul 6-10 July 2003

2. DEA and Mutual Fund Performance Murthi, Choi, Desai (1997), EJOR. transaction costs. Morey & Morey (1999), Omega. multiple investment horizons. Basso & Funari (2001), EJOR multiple risk measures, sub-period dominance Joro & Na (2001), w.p. skewness preferences

3. Stochastic Dominance portfolio analysis Kuosmanen (2001), w.p. SD efficiency tests and measures that account for portfolio diversification Post (2003), J. of Finance (to appear) dual approach, statistical properties, bootstrapping Heikkinen and Kuosmanen (2003), book chapter application to the management of a mixed asset forest portfolio

4. Setting N mutual funds T different time periods R(j,t) return for fund j in period t

5. Return possibilities frontier: 2-periods Funds A, B, C; returns R A =(1,4), R B =(3.5,1.6), R C =(2,2).

6. Elementary DEA-model Returns as outputs, no inputs

7. Properties - elementary DEA model The previous approach takes into account diversification opportunities risk: entire distribution of returns considered, not just the first moments (mean, variance). Can we do better? Preference information

8. Stochastic Dominance (SD) Approach Return is a random variable drawn from an unknown distribution. Returns in different time periods are a sample drawn from that distribution. State independence: timing of returns does not matter. Empirical distribution function gives a nonparametric minimum variance unbiased estimator of the underlying distribution function. SD criteria applied to the empirical distributions.

9. Stochastic Dominance as a criterion of Risk

10. Definition of SD Risky portfolios j and k, return distributions G j and G k. Portfolio j dominates portfolio k by FSD (SSD, TSD) if and only if FSD: SSD: TSD: with strict inequality for some z.

11. Problem of diversification 1. Diversification (time series) 2. Sorting / Ranking (irreversibility) 3. SD (distribution function)

12. FSD dominating set Kuosmanen (2001) Consider R 0 = (1,4). FSD dominating set

13. SSD dominating set Kuosmanen (2001) R 0 = (1,4). SSD dominating set

14. Combining SD with DEA Is fund A FSD efficient? FSD dominating set

15. Combining SD with DEA Is fund A SSD efficient? SSD dominating set

16. Measuring efficiency How much higher return should be obtained in all periods to make A efficient?

17. FSD efficiency measure Return profile R 0 is FSD efficient if and only if

18. SSD efficiency measure Return profile R 0 is SSD efficient only if

19. Efficiency of env. resp. mutual funds Part of Socially Responsive Investing (SRI) US SRI funds amounted to $2.34 trillion in 2001 Methods: screening (positive/negative) shareholder advocacy community investing Does portfolio efficiency of environmentally responsible mutual funds differ traditional large blend funds?

20. Return possibilities frontier 175 stocks traded in NYSE and included in the DJSI sustainability index Weekly returns for 26/11/2001 - 26/11/2002 Constraints on portfolio weights no shortsales weight of any single stock should not exceed 5.8% total weight of the US stocks at least 65%

21. Results: Green funds SSD: Inefficiency premium (% per annum) Fund% p.a. Calvert A0.35 Calvert C0.36 Women's0.36 Neuberger0.43 Devcap0.43 Advocacy0.45 Green Century0.48 Domini0.51

22. Results: Traditional funds Fund% p.a.Fund% p.a. NPPAX0.00AFEAX0.44 ASECX0.28EVSBX0.45 SSLGX0.32HFFYX0.45 WFDMX0.39HIGCX0.45 MMLAX0.39HGRZX0.45 MDLRX0.40FGIBX0.46 OTRYX0.40FBLVX0.46 STVDX0.42PWSPX0.47 PRFMX0.43FLCIX0.49 PRACX0.43WCEBX0.50 GESPX0.43FRMVX0.50 ACQAX0.43IGSCX0.51 IBCCX0.44EGRCX0.51

23. Dominating distribution

24. Further details... A full paper with an application to environmentally responsible mutual funds available soon. Send an e-mail to Timo.Kuosmanen@wur.nl The paper will be uploaded shortly on my homepage: http://www.sls.wau.nl/enr/staff/kuosmanen