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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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Timo kuosmanen wageningen university the netherlands

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

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

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

Return possibilities frontier: 2-periods

  • Funds A, B, C; returns RA=(1,4), RB=(3.5,1.6), RC=(2,2).

Elementary dea model

Elementary DEA-model

  • Returns as outputs, no inputs

Properties elementary dea model

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

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

Stochastic Dominance as a criterion of Risk

Definition of sd

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

Problem of diversification

1. Diversification

(time series)

2. Sorting / Ranking


3. SD

(distribution function)

Fsd dominating set

FSD dominating set

  • Kuosmanen (2001)

    Consider R0 = (1,4).

FSD dominating set

Ssd dominating set

SSD dominating set

  • Kuosmanen (2001)

    R0 = (1,4).

SSD dominating set

Combining sd with dea

Combining SD with DEA

  • Is fund A FSD efficient?

FSD dominating set

Combining sd with dea1

Combining SD with DEA

  • Is fund A SSD efficient?

SSD dominating set

Measuring efficiency

Measuring efficiency

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

Fsd efficiency measure

FSD efficiency measure

Return profile R0 is FSD efficient if and only if

Ssd efficiency measure

SSD efficiency measure

Return profile R0 is SSD efficient only if

Efficiency of env resp mutual funds

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

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

Results: Green funds

  • SSD: Inefficiency premium (% per annum)

Fund% p.a.

Calvert A0.35

Calvert C0.36





Green Century0.48


Results traditional funds

Results: Traditional funds

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














Return distribution s 8 green funds

Return distributions: 8 green funds

Dominating distribution

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

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.

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