Title:
|
Measuring of second–order stochastic dominance portfolio efficiency (English) |
Author:
|
Kopa, Miloš |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 |
Volume:
|
46 |
Issue:
|
3 |
Year:
|
2010 |
Pages:
|
488-500 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
In this paper, we deal with second-order stochastic dominance (SSD) portfolio efficiency with respect to all portfolios that can be created from a considered set of assets. Assuming scenario approach for distribution of returns several SSD portfolio efficiency tests were proposed. We introduce a $\delta$-SSD portfolio efficiency approach and we analyze the stability of SSD portfolio efficiency and $\delta$-SSD portfolio efficiency classification with respect to changes in scenarios of returns. We propose new SSD and $\delta$-SSD portfolio efficiency measures as measures of the stability. We derive a non-linear and mixed-integer non-linear programs for evaluating these measures. Contrary to all existing SSD portfolio inefficiency measures, these new measures allow us to compare any two $\delta$-SSD efficient or SSD efficient portfolios. Finally, using historical US stock market data, we compute $\delta$-SSD and SSD portfolio efficiency measures of several SSD efficient portfolios. (English) |
Keyword:
|
stochastic dominance |
Keyword:
|
stability |
Keyword:
|
SSD portfolio efficiency measure |
MSC:
|
60E15 |
MSC:
|
91B28 |
MSC:
|
91B30 |
MSC:
|
91G10 |
idZBL:
|
Zbl 1193.91140 |
idMR:
|
MR2676085 |
. |
Date available:
|
2010-09-13T17:00:13Z |
Last updated:
|
2013-09-21 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140763 |
. |
Reference:
|
[1] Dentcheva, D., Henrion, R., Ruszczyński, A.: Stability and sensitivity of optimization problems with first order stochastic dominance constraints.SIAM J. Optim. 18 (2007), 322–333. MR 2299687, 10.1137/060650118 |
Reference:
|
[2] Dentcheva, D., Ruszczyński, A.: Optimization with stochastic dominance constraints.SIAM J. Optim. 14 (2003), 548–566. MR 2048155, 10.1137/S1052623402420528 |
Reference:
|
[3] Dentcheva, D., Ruszczyński, A.: Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints.Math. Programming 99 (2004), 329–350. MR 2039044, 10.1007/s10107-003-0453-z |
Reference:
|
[4] Dentcheva, D., Ruszczyński, A.: Portfolio optimization with stochastic dominance constraints.J. Banking and Finance 30 (2006), 2, 433–451. 10.1016/j.jbankfin.2005.04.024 |
Reference:
|
[5] Rudolf, G., Ruszczyński, A.: Optimization problems with second order stochastic dominance constraints: duality, compact formulations, and cut generation methods.SIAM J. Optim. 19 (2008), 3, 1326–1343. MR 2460744, 10.1137/070702473 |
Reference:
|
[6] Hadar, J., Russell, W. R.: Rules for ordering uncertain prospects.Amer. Econom. Rev. 59 (1969), 1, 25–34. |
Reference:
|
[7] Hanoch, G., Levy, H.: The efficiency analysis of choices involving risk.Rev. Econom. Stud. 36 (1969), 335–346. Zbl 0184.45202, 10.2307/2296431 |
Reference:
|
[8] Hardy, G. H., Littlewood, J. E., Polya, G.: Inequalities.Cambridge University Press, Cambridge 1934. Zbl 0634.26008 |
Reference:
|
[9] Kopa, M., Chovanec, P.: A second-order stochastic dominance portfolio efficiency measure.Kybernetika 44 (2008), 2, 243–258. Zbl 1154.91456, MR 2428222 |
Reference:
|
[10] Kopa, M., Post, T.: A portfolio optimality test based on the first-order stochastic dominance criterion.J. Financial and Quantitative Analysis 44 (2009), 5, 1103–1124. 10.1017/S0022109009990251 |
Reference:
|
[11] Kopa, M.: An efficient LP test for SSD portfolio efficiency.Working paper, available at: http://ssrn.com/abstract=1340863. |
Reference:
|
[12] Kuosmanen, T.: Efficient diversification according to stochastic dominance criteria.Management Sci. 50 (2004), 10, 1390–1406. 10.1287/mnsc.1040.0284 |
Reference:
|
[13] Levy, H.: Stochastic Dominance: Investment Decision Making Under Uncertainty.Second edition. Springer Science, New York 2006. Zbl 1109.91037, MR 2239375 |
Reference:
|
[14] Luedtke, J.: New formulations for optimization under stochastic dominance constraints.SIAM J. Optim. 19 (2008), 3, 1433–1450. Zbl 1180.90215, MR 2466178, 10.1137/070707956 |
Reference:
|
[15] Ogryczak, W., Ruszczyński, A.: Dual stochastic dominance and related mean-risk models.SIAM J. Optim. 13 (2002), 60–78. MR 1922754, 10.1137/S1052623400375075 |
Reference:
|
[16] Pflug, G. Ch.: Some remarks on the value-at-risk and the conditional value-at-risk.In: Probabilistic Constrained Optimization: Methodology and Applications (S. Uryasev, ed.), Kluwer Academic Publishers, Norwell MA 2000, pp. 278–287. Zbl 0994.91031, MR 1819417 |
Reference:
|
[17] Post, T.: Empirical tests for stochastic dominance efficiency.J. Finance 58 (2003), 1905–1932. 10.1111/1540-6261.00592 |
Reference:
|
[18] Roman, D., Darby-Dowman, K., Mitra, G.: Portfolio construction based on stochastic dominance and target return distributions.Math. Programming, Series B 108 (2006), 541–569. Zbl 1138.91476, MR 2238714, 10.1007/s10107-006-0722-8 |
Reference:
|
[19] Römisch, W.: Stability of stochastic programming problems.In: Stochastic Programming. Handbooks in Operations Research and Management Science 10 (A. Ruszczyński and A. Shapiro, eds.), Elsevier, Amsterdam 2003, pp. 483–554. MR 2052760 |
Reference:
|
[20] Rothschild, M., Stiglitz, J. E.: Rules for ordering uncertain prospects.J. Economic Theory 2 (1969), 225–243. |
Reference:
|
[21] Ruszczyński, A., Vanderbei, R. J.: Frontiers of stochastically nondominated portfolios.Econometrica 71 (2003), 4, 1287–1297. MR 1995832, 10.1111/1468-0262.t01-1-00448 |
Reference:
|
[22] Uryasev, S., Rockafellar, R. T.: Conditional value-at-risk for general loss distributions.J. Banking and Finance 26 (2002), 1443–1471. 10.1016/S0378-4266(02)00271-6 |
Reference:
|
[23] Whitmore, G. A.: Third degree stochastic dominance.Amer. Econom. Rev. 60 (1970), 457–459. |
. |