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

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, Sept

Stochastic Dominance as a Criterion of Risk

Definition of SD Risky portfolios j and k, return distributions G j and G k. Portfolio j dominates portfolio k by FSD (SSD, TSD) if and only if FSD: SSD: TSD: with strict inequality for some z.

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)

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 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).

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 1. Diversification (states / time series) 2. Sorting / Ranking (irreversibility) 3. SD (distribution function)

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

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

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? FSD dominating set

Testing for SD efficiency: SSD 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 R 0 is FSD efficient if and only if

SSD efficiency measure Return profile R 0 is SSD efficient only if

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

r =

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 + cx 2 the higher moments do not matter.

r = Empirical fit of Normal distribution: Stand 165

r = Empirical fit of Normal distribution: Stand 165

Results

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/ /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

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

Dominating distribution

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: homepage: