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
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Timo Kuosmanen Wageningen University, The Netherlands
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. - PowerPoint PPT Presentation
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Efficient Portfolio Diversification
according to Stochastic Dominance
Criteria: Applications to Mixed-Asset
Forest Portfolio Management and
Environmentally Responsible Mutual
FundsTimo 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.
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 Rate of return of portfolio in state t is Portfolio can be characterized equivalently in terms
of the return vector R in the state space (primal) or the portfolio weights (dual).
1
( , )N
jj
R j t
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 diversification1. Diversification(states / time series)
SD efficiencyDefinition: 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?
C
A
B
0
1
2
3
4
5
0 1 2 3 4 5 R1
R2
FSD dominating set
C
A
B
0
1
2
3
4
5
0 1 2 3 4 5 R1
R2
Testing for SD efficiency: SSD
Is fund A SSD efficient?
SSD dominating set
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?
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
SSD efficiency measure
Return profile R0 is SSD efficient only if 2 0( ) 0R
Timo Kuosmanen (Wageningen University, The Netherlands)
Risk and Uncertainty in Environmental and Resource Economics, June 5-7, 2002 ,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.
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?
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
Reject normality at significance level Total1% 5% 10%
SRI funds 0 1 1 8Securities[DJSI &SP500]
13 17 22 175
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