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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.

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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

8EWEPAOviedo24-26September 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


  • 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 RA=(1,4), RB=(3.5,1.6), RC=(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 Gj and Gk.

  • Portfolio j dominates portfolio kbyFSD (SSD, TSD) if and only if




    with strict inequality for some z.


Problem of diversification

1. Diversification

(time series)

2. Sorting / Ranking


3. SD

(distribution function)

FSD dominating set

  • Kuosmanen (2001)

    Consider R0 = (1,4).

FSD dominating set

SSD dominating set

  • Kuosmanen (2001)

    R0 = (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 R0 is FSD efficient if and only if

SSD efficiency measure

Return profile R0 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





Green Century0.48


Results: Traditional funds

Fund% p.a.Fund% p.a.














Return distributions: 8 green funds

Dominating distribution


  • 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 [email protected]

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