1 / 20

Stochastic Dominance Portfolio Analysis of Forestry Assets

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 ,.

indra
Download Presentation

Stochastic Dominance Portfolio Analysis of Forestry Assets

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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 ,

  2. Empirical motivation • Heikkinen (1999): Cutting Rules for Final Fellings: A Mean-Variance Portfolio Analysis, J. Forest Econ. • 4 harvestable mixed stands of borealis forest • Stock market (index) represents investment alternatives • Mean-Variance efficient frontier used for assessing portfolio composition (i.e., which stands to harvest and to what extent).

  3. Overview of the 4 forest stands

  4. r = - 0.016

  5. 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.

  6. Empirical fit of Normal distribution: Stand 165 r = 0.442

  7. Stochastic Dominance as a criterion of Risk

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

  9. 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.

  10. Illustration of the problem 1. Diversification (time series) 2. Sorting / Ranking (irreversibility) 3. SD (distribution function)

  11. Solution • Preserve the time series structure of the data to keep track of the diversification possibilities, i.e. work with Y instead of X. • Instead, re-express the SD criteria in terms of time-series. Definition: The set , l = 1,2, is the lorder dominating set of the evaluated portfolio y0. Lemma: Portfolio y0 is l order SD efficient, l = 1,2, if and only if the l order dominating set of y0 does not include any feasible portfolio, i.e.

  12. FSD case • Theorem: where P denotes a permutation matrix. Example: Let y0 = (1,4). FSD dominating set

  13. SSD case • Theorem: Where W denotes a doubly stochastic matrix. Example:

  14. SSD test Portfolio y0 is SSD efficient in if and only if

  15. Results • The original forest portfolio proved inefficient both in terms of SSD and MV. • SSD points towards Stand #163 as the source of problem: In numerous trials, we find portfolio inefficient whenever an infinitesimal fraction of S163 is present, and efficient whenever it is fully harvested.

  16. Challenges for Future Research • We can now simply test whether a given portfolio is efficient or not, we still cannot characterize the entire efficient set. • SD is sensitive to errors/noise in the data, especially in the left tail of the distribution. • Sampling error: ”Catastrophic” events tend to be under/over-represented in the data.

  17. Further details... • The short version available on the conference proceedings and the homepage. • Earlier papers on SD diversification analysis: Send e-mail to Timo.Kuosmanen@alg.shhk.wau.nl • Overall info of the research program from the homepage: http://www.sls.wau.nl/enr/staff/kuosmanen/program1/

More Related