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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


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 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

    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 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

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 [email protected]

  • Or navigate to my homepage:

    http://www.sls.wau.nl/enr/staff/kuosmanen


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