Transcript SD Istanbul

Efficient Portfolio Diversification according to
Stochastic Dominance Criteria: Applications
to Mixed-Asset Forest Portfolio Management
and Environmentally Responsible Mutual
Funds
Timo Kuosmanen
Wageningen University, The Netherlands
Ympäristö ja luonnovarataloustietee kollokvia, Helsinki 15.10.2003
The presentation is based on 3 papers:



Kuosmanen, T. (2001): ”Stochastic Dominance Efficient
Diversification ”, Helsinki School of Economics Working
Paper W-232?
Heikkinen, V.-P., and T. Kuosmanen (2003): ”Stochastic
Dominance Portfolio Analysis of Forestry Assets”,
chapter 12 in Wesseler et al. (Eds.): Risk and
Uncertainty in Environmental and Resource Economics,
Edward Elgar.
Kuosmanen (2003): ”DEA and Stochhastic Dominance
Portfolio Analysis: Do Environmentally Responsible
Mutual Funds Diversify Efficiently?, paper presented at
the 8EWEPA, Oviedo, Spain, 24-26 Sept. 2003.
Stochastic Dominance as a Criterion of Risk
1
0 ,8
0 ,6
0 ,4
0 ,2
0
- 1 0 ,0 0 %
- 5 ,0 0 %
0 ,0 0 %
5 ,0 0 %
1 0 ,0 0 %
1 5 ,0 0 %
2 0 ,0 0 %
Stochastic Dominance as a Criterion of Risk
1
A
0 .8
B
0 .6
0 .4
0 .2
0
- 1 0 .0 0 %
- 5 .0 0 %
0 .0 0 %
5 .0 0 %
1 0 .0 0 %
1 5 .0 0 %
2 0 .0 0 %
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:
Gk ( z )  G j ( z )  0
z
SSD:
TSD:
 G (t )  G (t ) dt  0
k
j

z u
  G (t )  G (t ) dtdu  0
k
j
 
with strict inequality for some z.
zR
Economic interpretation of SD


Consider the Expected Utility Theory of von Neumann &
Morgenstern.
If portfolio j dominates portfolio k by FSD (SSD, TSD), then
portfolio j is preferred to portfolio k by all investors who are
FSD: non-satiated (u’(x)0).
SSD: non-satiated and risk averse (u’(x)0, u’’(x)0).
TSD: non-satiated and risk averse with decreasing absolute
risk aversion (u’(x)0, u’’(x)0, u’’’(x)0).
Second-order Stochastic Dominance (SSD)
1
0 .8
HE X
S T3
0 .6
0 .4
0 .2
0
- 3 0 .0 0 %
- 2 0 .0 0 %
- 1 0 .0 0 %
0 .0 0 %
1 0 .0 0 %
2 0 .0 0 %
3 0 .0 0 %
Setting






N assets
T different states of nature (time periods)
R(j,t) = rate of return of asset j in state t
j = portfolio weight of asset j
N
Rate of return of portfolio in state t is  j R ( j , t )
j 1
Portfolio can be characterized equivalently in
terms of the return vector R in the state space
(primal) or the portfolio weights  (dual).
Stochastic Dominance (SD) Approach




Return is an i.i.d. random variable drawn from an
unknown distribution. Returns in different states
are a sample drawn from that distribution.
State independence: investor indifferent between
return profiles (x,y) and (y,x).
Empirical distribution function gives a
nonparametric minimum variance unbiased
estimator of the underlying distribution function.
SD criteria applied to the empirical distributions.
Problem of diversification
20.00%
1. Diversification
15.00%
10.00%
(states / time series)
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%
HEX
PineLog
2. Sorting / Ranking
-20.00%
1
(irreversibility)
0.8
HEX
ST3
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 R0 = (1,4).
7
6
5
FSD dominating set
4
(1,4)
(4,4)
3
2
1
(4,1)
0
0
1
2
3
4
5
6
7
8
SSD dominating set

Kuosmanen (2001)
8
R0 = (1,4).
7
6
5
SSD dominating set
4
(1,4)
(4,4)
3
2
1
(4,1)
0
0
1
2
3
4
5
6
7
8
SD efficiency
Definition: Portfolio k is FSD (SSD) inefficient if the portfolio set
includes another feasible portfolio that dominates k by FSD
(SSD).
Otherwise k is FSD (SSD) efficient.
Typical approach is to apply the basic pairwise comparisons to
a sample of assets/portfolios using the standard crossing
algorithms.
However, there are infinite numbers of alternative diversified
portfolios! Therefore, even though it is possible to falsify
efficiency by pairwise comparisons, it is not possible to verify
it.
Testing for SD efficiency: FSD

Is fund A FSD efficient?
R2
5
FSD dominating set
4
A
3
2
C
B
1
0
0
1
2
3
4
5
R1
Testing for SD efficiency: SSD

Is fund A SSD efficient?
R2
5
4
SSD dominating set
A
3
2
C
B
1
0
0
1
2
3
4
5
R1
Measuring efficiency

How much higher return should be obtained in
all periods to make A efficient?
R2
5
4
A
3
2
C
B
1
0
0
1
2
3
4
5
R1
FSD efficiency measure
Return profile R0 is FSD efficient if and only if 1 ( R0 )  0
T
1 ( R0 )  max  st / T
 ,P
t 1
s.t.
N
T
 R( j, t )   P R(0, i)  s =0
j
j 1
T
i 1
T
P  P
i 1
ti
t 1
ti
ti
 1 t , i  1,..., T
Pti  0,1 t , i  1,..., T
 
t
t  1,..., T
SSD efficiency measure
Return profile R0 is SSD efficient only if  2 ( R0 )  0
T
1 ( R0 )  max  st / T
 ,P
t 1
s.t.
N
T
 R( j, t )  W R(0, i)  s =0
j
j 1
T
i 1
T
W  W
i 1
ti
t 1
ti
ti
 1 t , i  1,..., T
Wti   0,1 t , i  1,..., T
 
t
t  1,..., T
Stochastic Dominance Portfolio Analysis
of Forestry Assets
Veli-Pekka Heikkinen (Varma-Sampo Mutual Pension Insurance
Company, Helsinki, Finland)
Timo Kuosmanen (Wageningen University, The Netherlands)
Risk and Uncertainty in Environmental and Resource Economics, June 5-7, 2002 ,
Empirical motivation

Heikkinen (1999): Cutting Rules for Final Fellings: A
Mean-Variance Portfolio Analysis, J. Forest Econ.

The Faustmann rule can determine the optimal timing of
harvest, but the targeting harvest to specific stands can
be used for hedging portfolio risk of the land-owner.
5 assets:




4 harvestable mixed stands of borealis forest
Stock market (index) represents investment alternatives
Forest stands offer physical growth (assumed certain)
but involve a risk in stumpage prices. The composition of
species and thickness influences the price risk.
Research questions

Are the current portfolio weights of stands and the stocks
SD efficient?

Does risk aversion (FSD vs SSD) play a role?

Do additional constraints on acquiring additional growing
stock with characteristic similar to existing stands
influence the result?
Overview of the 4 forest stands
Pine sawlogs
Spruce sawlogs
Birch sawlogs
Pine pulpwood
Spruce pulpwood
Birch pulpwood
Total
Growth (%)
Value (FIM)
Portfolio weight
Area (ha)
Stand
#162
Stand
#163
Stand
#165
17 m3
67 m3
16 m3
1 m3
9 m3
2 m3
3 m3
16 m3
31 m3
4.1
5589
0.05
0.5
47 m3
4.1
7106
0.07
0.6
25 m3
92 m3
3.2
16904
0.16
0.7
Stand
#173
Total
267 m3
191 m3
14 m3
485 m3
3.7
78675
0.72
2.2
628 m3
108273
4
Prices
FIM/m3
1996:12
248.1
206.1
98.1
123.8
246.9
94.2
P ric e v ola tility
2 0 .0 0 %
r = - 0.016
1 5 .0 0 %
1 0 .0 0 %
5 .0 0 %
0 .0 0 %
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101 106 111 116 121 126 131
-5 .0 0 %
-1 0 .0 0 %
-1 5 .0 0 %
-2 0 .0 0 %
HE X
P in e L o g
The MV assumptions

All asset Returns are normally distributed


the higher moments of the distribution (skewness, etc)
equal to zero.
OR
Forest owners expected utility function is of
quadratic form, U(x) = a + bx + cx2

the higher moments do not matter.
S T3
Empirical fit of Normal distribution: Stand
1
165
r = 0.442
ST3
0 .8
0 .6
0 .4
0 .2
0
- 1 0 .0 0 %
- 5 .0 0 %
0 .0 0 %
5 .0 0 %
1 0 .0 0 %
1 5 .0 0 %
2 0 .0 0 %
Empirical fit of Normal distribution: Stand
1
165
r = 0.442
S T3
S T3 No rm
0 .8
0 .6
0 .4
0 .2
0
- 1 0 .0 0 %
- 5 .0 0 %
0 .0 0 %
5 .0 0 %
1 0 .0 0 %
1 5 .0 0 %
2 0 .0 0 %
Results
1
1) Unconstrained case
2) Constrained case
0.0008
0.0000

n
2
0.0008
0.0000
Conclusions




Original portfolio slightly inefficient (0.08 %
points p.a. inefficiency premium).
Risk preferences did not play a role.
If new identical timber stock cannot be acquired,
the current portfolio is actually efficient.
The MV model suggests very similar reference
portfolios. Offers 1.8 percent decrease in
portfolio variance in the constrained case.
Stochastic Dominance Efficiency Analysis of
Investment Portfolios:
Do Evironmentally Responsible Mutual Funds
Diversify Efficiently?
Timo Kuosmanen
Wageningen University, The Netherlands
Lunch presentation 6 October 2003
Environmentally responsible mutual funds

Part of Socially Responsive Investing (SRI) or
Ethical Investing

”Green” funds with special focus on the
environment

Most ethical/religious funds also have
environmental criteria in their investment
strategy
Methods of SRI funds

screening of corporate securities
positive screens (invest in clean firms)
 negative (avoid polluting firms)


shareholder advocacy

community investing
Screening of corporate securities

Common screens
Alcohol
 Tobacco
 Gambling
 Weapons/Defence
 Animal testing
 Human Rights
 Labor relations
 Equal opportunities
 Environment

Shareholder advocacy


Influence the CEOs and the board of directors as
shareholder
Proxy voting in annual general meetings of the
companies


Present resolutions
Vote to resolutions presented by other shareholders in
accordance with the values of the fund
Community investing

Support development initiatives in low-income
communities and get responsible businesses get
started. Help people who may not be able to
obtain financing through traditional lenders.

Channeled through:

Community Banks,
Community Credit Unions,
Community Loan Funds

Microenterprise lenders


Are ”green” funds efficient?

Constraints on fund managers => cannot
hedge risk as efficiently as normal funds
=> higher risk/lower return.

Focus on best practice within each
industry. If environmental performance is
correlated with profitability (Porter
hypothesis), environmental indicators
contain useful information => higher
return/lower risk
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%
Shapiro-Wilks normality test
SRI funds
Securities
[DJSI &
SP500]
Reject normality at significance level
1%
5%
10%
0
1
1
13
17
22
Total
8
175
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
Dominating distribution
1,0
0,9
0,8
0,7
cum
0,6
0,5
0,4
0,3
0,2
0,1
0,0
-5
-4
-3
-2
-1
0
return
1
2
3
4
Dominating distribution
1.0
0.9
0.8
0.7
cum
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-5
-4
-3
-2
-1
0
return
1
2
3
4
Conclusions



Stochastic Dominance criteria applicable for
measuring portfolio efficiency and finding
efficient diversification strategies.
Dominating reference portfolios can be
composed directly from stocks rather than peer
funds
No notable differences in the efficiency
distribution of green funds and traditional funds
Questions & comments

The first two papers are available by request, the third
one is work in progress.

Coordinates:
 E-mail: [email protected]
 homepage: http://www.sls.wau.nl/enr/staff/kuosmanen/