dea and stochastic dominance efficiency analysis of investment portfolios: do evironmentally...
TRANSCRIPT
![Page 1: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/1.jpg)
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
![Page 2: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/2.jpg)
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
![Page 3: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/3.jpg)
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
![Page 4: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/4.jpg)
Setting
N mutual funds T different time periods R(j,t) return for fund j in period t
![Page 5: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/5.jpg)
Return possibilities frontier: 2-periods
Funds A, B, C; returns RA=(1,4), RB=(3.5,1.6), RC=(2,2).
C
A
B
0
1
2
3
4
5
0 1 2 3 4 5 R1
R2
![Page 6: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/6.jpg)
Elementary DEA-model
1
1
max
. .
(0, ) ( , ) 1, 2,...,
1
0
N
jj
N
jj
j
s t
R t R j t t T
Returns as outputs, no inputs
![Page 7: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/7.jpg)
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
![Page 8: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/8.jpg)
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.
![Page 9: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/9.jpg)
Stochastic Dominance as a criterion of
Risk
0
0.2
0.4
0.6
0.8
1
-10.00% -5.00% 0.00% 5.00% 10.00% 15.00% 20.00%
A
B
![Page 10: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/10.jpg)
Definition of SD Risky portfolios j and k, return distributions Gj and Gk.
Portfolio j dominates portfolio k by FSD (SSD, TSD) if and only if
FSD:
SSD:
TSD:
with strict inequality for some z.
( ) ( ) 0k jG z G z
( ) ( ) 0z
k jG t G t dt
( ) ( ) 0z u
k jG t G t dtdu
zR
![Page 11: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/11.jpg)
Problem of diversification
1. Diversification(time series)
2. Sorting / Ranking(irreversibility)
3. SD(distribution function)
-20.00%
-15.00%
-10.00%
-5.00%
0.00%
5.00%
10.00%
15.00%
20.00%
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
HEX PineLog
0
0.2
0.4
0.6
0.8
1
-30.00% -20.00% -10.00% 0.00% 10.00% 20.00% 30.00%
HEX
ST3
![Page 12: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/12.jpg)
FSD dominating set Kuosmanen (2001)
Consider R0 = (1,4).
(4,1)
(4,4)(1,4)
0
1
2
3
4
5
6
7
8
0 1 2 3 4 5 6 7 8
FSD dominating set
![Page 13: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/13.jpg)
SSD dominating set Kuosmanen (2001)
R0 = (1,4).
(4,1)
(4,4)(1,4)
0
1
2
3
4
5
6
7
8
0 1 2 3 4 5 6 7 8
SSD dominating set
![Page 14: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/14.jpg)
Combining SD with DEA
Is fund A FSD efficient?
C
A
B
0
1
2
3
4
5
0 1 2 3 4 5 R1
R2
FSD dominating set
![Page 15: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/15.jpg)
C
A
B
0
1
2
3
4
5
0 1 2 3 4 5 R1
R2
Combining SD with DEA
Is fund A SSD efficient?
SSD dominating set
![Page 16: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/16.jpg)
C
A
B
0
1
2
3
4
5
0 1 2 3 4 5 R1
R2
Measuring efficiency
How much higher return should be obtained in all periods to make A efficient?
![Page 17: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/17.jpg)
FSD efficiency measure
Return profile R0 is FSD efficient if and only if
1 0,
1
1 1
1 1
( ) max /
. .
( , ) (0, ) =0 1,...,
1 , 1,...,
0,1 , 1,...,
ti
ti t
T
tP
t
N T
j tj i
T T
i
ti
i t
R s T
s t
R j t R i s t T
t i T
t
P
P
i T
P
P
1 0( ) 0R
![Page 18: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/18.jpg)
SSD efficiency measure
Return profile R0 is SSD efficient only if 2 0( ) 0R
1 0,
1
1 1
1 1
( ) max /
. .
( , ) (0, ) =0 1,...,
1 , 1,...,
0,1 , 1,...,
ti
ti t
T
tP
t
N T
j tj i
T T
i
ti
i t
R s T
s t
R j t R i s t T
t i T
t
W
W
i T
W
W
![Page 19: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/19.jpg)
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 advocacycommunity investing
Do environmentally responsible mutual funds differ from traditional large blend funds in their portfolio efficiency?
![Page 20: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/20.jpg)
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%
![Page 21: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/21.jpg)
Results: Green funds
SSD: Inefficiency premium (% per annum)Fund % p.a.Calvert A 0.35Calvert C 0.36Women's 0.36Neuberger 0.43Devcap 0.43Advocacy 0.45Green Century 0.48Domini 0.51
![Page 22: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/22.jpg)
Results: Traditional fundsFund % p.a. Fund % p.a.NPPAX 0.00 AFEAX 0.44ASECX 0.28 EVSBX 0.45SSLGX 0.32 HFFYX 0.45WFDMX 0.39 HIGCX 0.45MMLAX 0.39 HGRZX 0.45MDLRX 0.40 FGIBX 0.46OTRYX 0.40 FBLVX 0.46STVDX 0.42 PWSPX 0.47PRFMX 0.43 FLCIX 0.49PRACX 0.43 WCEBX 0.50GESPX 0.43 FRMVX 0.50ACQAX 0.43 IGSCX 0.51
IBCCX 0.44 EGRCX 0.51
![Page 23: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/23.jpg)
Return distributions: 8 green funds
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
-5 -4 -3 -2 -1 0 1 2 3 4return
cum
![Page 24: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/24.jpg)
Dominating distribution
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-5 -4 -3 -2 -1 0 1 2 3 4return
cum
![Page 25: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/25.jpg)
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
![Page 26: DEA and Stochastic Dominance Efficiency Analysis of Investment Portfolios: Do Evironmentally Responsible Mutual Funds Diversify Efficiently? Timo Kuosmanen](https://reader034.vdocument.in/reader034/viewer/2022051819/551493f6550346b2598b546a/html5/thumbnails/26.jpg)
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