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).

R2

5 A 4 3 2 C B 1 0 0 1 2 3 4 5

R1

Elementary DEA-model  Returns as outputs, no inputs max   

R t j N

  1 

j



j

 0  1 

j N

  1 

j t

 1, 2,...,

T

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 1 A B 0.8

0.6

0.4

0.2

0 -10.00% -5.00% 0.00% 5.00% 10.00% 15.00% 20.00%

 Definition of SD Risky portfolios

j

and

k

, return distributions

G j

and

G k

.

 Portfolio only if

j

FSD:

k

dominates portfolio

k



j

 0 SSD: TSD:

z

   

G t k z

 

u

  

G t k

 

j j

 

dt

 0

dtdu

 0 by FSD (SSD, TSD) if and 

z

 R with strict inequality for some

z

.

Problem of diversification 1. Diversification (time series) 20.00% 15.00% 10.00% 5.00% 0.00% 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121 125 129 133 -5.00% -10.00% -15.00% -20.00% 2. Sorting / Ranking 1 (irreversibility) 0.8

HEX ST3 HEX PineLog 0.6

3. SD (distribution function) 0.4

0.2

0 -30.00% -20.00% -10.00% 0.00% 10.00% 20.00% 30.00%

 FSD dominating set Kuosmanen (2001) 8 Consider R 0 = (1,4).

7 6 5 4 3 2 1 0 0 (1,4) 1 2

FSD dominating set

(4,4) 3 (4,1) 4 5 6 7 8

SSD dominating set  Kuosmanen (2001) 8 R 0 = (1,4).

7 6 5 4 3 2 1 0 0 (1,4) 1 2

SSD dominating set

(4,4) 3 (4,1) 4 5 6 7 8

Combining SD with DEA  Is fund A FSD efficient?

R2

5

FSD dominating set

4 A 3 2 1 C B 0 0 1 2 3 4 5

R1

Combining SD with DEA  Is fund A SSD efficient?

R2

5 A 2 1 4 3 0 0 C 1 2

SSD dominating set

B 3 4 5

R1

Measuring efficiency  How much higher return should be obtained in 5 2 1 4 3 0 0 A C B 1 2 3 4 5

R1

FSD efficiency measure Return profile

R

0 is FSD efficient if and only if  1 (

R

0 )  0  1 (

R

0 )  max  ,

P t T

  1

s t

/

T j N

  1 

j



i T

  1

P ti R



i T

  1

P ti P ti

 

T



P t i t

   1 0,1

t

,

i

  1,...,

T



s t

=0

t

1,...,

T

1,...,

T

SSD efficiency measure Return profile

R

0 is SSD efficient only if  2 (

R

0 )  0  1 (

R

0 )  max  ,

P t T

  1

s t

/

T j N

  1 

j



i T

  1

W ti R i T

  1

W ti W ti

 

T



W t i

 

t

 1 0,1

t

,

i

   1,...,

T



s t

=0 1,...,

T

1,...,

T

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 Calvert A Calvert C Women's Neuberger Devcap Advocacy Green Century Domini % p.a.

0.35

0.36

0.36

0.43

0.43

0.45

0.48

0.51

Results: Traditional funds Fund NPPAX ASECX SSLGX WFDMX MMLAX MDLRX OTRYX STVDX PRFMX PRACX GESPX ACQAX IBCCX % p.a.

0.00

0.28

0.32

0.39

0.39

0.40

0.40

0.42

0.43

0.43

0.43

0.43

0.44

Fund AFEAX EVSBX HFFYX HIGCX HGRZX FGIBX FBLVX PWSPX FLCIX WCEBX FRMVX IGSCX EGRCX % p.a.

0.44

0.45

0.45

0.45

0.45

0.46

0.46

0.47

0.49

0.50

0.50

0.51

0.51

Return distributions: 8 green funds 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 -5 -4 -3 -2 -1 0 1 2

return

3 4

Dominating distribution 1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

-5 -4 -3 -2 -1

return

0 1 2 3 4

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