# DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen.

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DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen Wageningen University, The Netherlands 8EWEPA Oviedo 24-26 September 2003

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

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

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

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

Elementary DEA-model Returns as outputs, no inputs

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

Stochastic Dominance (SD) Approach Return is an i.i.d. 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.

Stochastic Dominance as a criterion of Risk

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. z R

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

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

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

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

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

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

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

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

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 Do environmentally responsible mutual funds differ from traditional large blend funds in their portfolio efficiency?

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%

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

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

Return distributions: 8 green funds

Dominating distribution

Conclusions Stochastic Dominance criteria applicable for measuring portfolio efficiency and finding efficient diversification strategies. Direct analogy with DEA Elementary DEA can be enhanced by accounting for permutations composing dominating portfolios directly from stocks rather than peer funds

Further details... The theory and the LP efficiency measures available in working paper Efficient Diversification According to Stochastic Dominance Criteria. A DEA oriented paper with an application to environmentally responsible mutual funds is still work in progress. Send an e-mail to Timo.Kuosmanen@wur.nl Or navigate to my homepage: http://www.sls.wau.nl/enr/staff/kuosmanen

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