The classic Markowitz’s Mean-Variance model remains the standard technique of portfolio analysis. The Mean-Variance model requires the asset returns to be normally distributed or the decision-maker’s utility function to be of quadratic form. In many circumstances these assumptions appear questionable, not least in case of natural resource assets. A natural alternative to Mean-Variance approach is the Stochastic Dominance efficiency criterion (see e.g. Levy, 1992, for survey), which considers the entire probability distribution (not just the first two moments) and applies for the general classes of non-satiated and/or risk-aversive preference functions. Unfortunately, the Stochastic Dominance approach has had a serious shortcoming in dealing with diversified portfolios: While it is relatively simple to identify the Mean-Variance efficient set of portfolios, until now there has not been any method of testing whether a given portfolio is Stochastic Dominance efficient, let alone computing all Stochastic Dominance efficient portfolios. This also explains why theoretically appealing Stochastic Dominance criteria have attracted so little applications in Finance and related fields.
The ambitious aim of this project is to eliminate this handicap. In our studies (Kuosmanen, 2001a) we have found that the Stochastic Dominance efficient set exhibits a relatively simple polyhedral structure, which can be analyzed by standard techniques and algorithms. In fact, one can test for Stochastic Dominance efficiency by solving a simple Linear Programming problem, while Mean-Variance analysis requires more complex Quadratic Programming (see Kuosmanen, 2001a, for details). The Stochastic Dominance approach could be especially well-fit for portfolio analysis when natural resource assets (like forest) with non-normal return distributions are involved. For example, forestry risks include many "catastrophic" events such as fire, tornados, heavy snow, flood and pests, which shape the left tail of the return distribution. The objectives of the project also include adapting and extending the Stochastic Dominance approach to better deal with the catastrophic left-tail phenomena.
lllustration of the SSD dominating set of vector (1,4).
Dr. Timo Kuosmanen (Wageningen University, The Netherlands)
Dr. Veli-Pekka Heikkinen (Varma-Sampo Mutual Pension Insurance Company, Finland)
Mr. Pablo Benitez Ponce (Wageningen University, The Netherlands)
The project is performed in collaboration with Professor Thierry Post of Erasmus University Rotterdam. His research program can be found at
http://www.few.eur.nl/few/people/gtpost/stochastic_dominance.htm
Kuosmanen, T. (2001): "Stochastic Dominance Efficiency Tests under Diversification", Helsinki School of Economics and Business Administration, Working Paper W-283.
Kuosmanen, T. (2004): "Efficient Diversification according to Stochastic Dominance Criteria", Management Science, October.
Heikkinen, V.-P., and T. Kuosmanen (2003): "Stochastic Dominance Portfolio Analysis of Forestry Assets", in J. Wesseler, H.-P. Weikard, and R. Weaver (Eds.): Risk and Uncertainty in Environmental and Resource Economics, Edward Elgar.
Benítez, P.C., T. Kuosmanen, R. Olschewski, and G.C. van Kooten (2004): Conservation Payments under Risk: A Stochastic Dominance Approach, paper presented at the EAERE Annual Conference, Budapest, June 2004.