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Using Stochastic Dominance criteria in Data Envelopment Analysis of mutual funds

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. DEA and Mutual Fund Performance. Murthi, Choi, Desai (1997), EJOR. transaction costs.

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Using Stochastic Dominance criteria in Data Envelopment Analysis of mutual funds

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  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 RA=(1,4), RB=(3.5,1.6), RC=(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 Gj and Gk. • Portfolio j dominates portfolio kbyFSD (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 R0 = (1,4). FSD dominating set

  13. SSD dominating set • Kuosmanen (2001) R0 = (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 R0 is FSD efficient if and only if

  18. SSD efficiency measure Return profile R0 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 A 0.35 Calvert C 0.36 Women's 0.36 Neuberger 0.43 Devcap 0.43 Advocacy 0.45 Green Century 0.48 Domini 0.51

  22. Results: Traditional funds Fund % p.a. Fund % p.a. NPPAX 0.00 AFEAX 0.44 ASECX 0.28 EVSBX 0.45 SSLGX 0.32 HFFYX 0.45 WFDMX 0.39 HIGCX 0.45 MMLAX 0.39 HGRZX 0.45 MDLRX 0.40 FGIBX 0.46 OTRYX 0.40 FBLVX 0.46 STVDX 0.42 PWSPX 0.47 PRFMX 0.43 FLCIX 0.49 PRACX 0.43 WCEBX 0.50 GESPX 0.43 FRMVX 0.50 ACQAX 0.43 IGSCX 0.51 IBCCX 0.44 EGRCX 0.51

  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

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