Corporate Social Responsibility CSR CSR CSR 1 2 ~ CSR 6 CSR 7 CSR 8 CSR 9 10 ~ CSR 14 CSR CSR 2013 A A 23.

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1 24 3 Vol. 24 No OPERATIONS RESEARCH AND MANAGEMENT SCIENCE Jun Markowitz 10 F A Improvement of Portfolio Models Research An Empirical Study of Corporate Social Responsibility QI Yue 1 2 LIN Long 2 1. China Academy of Corporate Governance Nankai University Tianjin China 2. Business School Nankai University Tianjin China Abstract In this paper we study corporate social responsibility CSR through the prism of investors in the process of portfolio. In order to study CSR we extend traditional portfolio model to five objectives portfolio selection model by adding CSR index as objective functions in Markowitz mean-variance. We extend traditional utility function and prove that the new function is efficient. We measure the typical corporate CSR performance by the mainstream evaluation criteria. The new model has five objectives which include expected returns variance the core stakeholders dormant stakeholders and edge stakeholders. We formulate portfolio by selecting 10 points on the surface of the minimum variance portfolio. The multi-objective formulation is tested by randomly choosing nondominated portfolios with out-of-sample data to testify efficiency. We find that part of portfolio returns are significantly higher than market returns in the same period. It shows that the formulation can not only help investors to control the CSR directly but also prove the advantage by actual data which can provide one method and an idea for investors who focus on CSR. Key words corporate social responsibility multi-objective portfolio selection multi-objective optimization portfolio model JJD YJC

2 Corporate Social Responsibility CSR CSR CSR 1 2 ~ CSR 6 CSR 7 CSR 8 CSR 9 10 ~ CSR 14 CSR CSR 2013 A A CSR 2 CSR 39 SEM CSR CSR 3 CSR 4 CSR 5 CSR CSR 6 CSR 7 CSR 8 CSR CSR Social Responsibility Investment SRI CSR CSR 9 CSR BJNY CSR 10 CSR CSR CSR 11

3 CSR 13 CSR 14 CSR 2 ~ CSR 6 CSR CSR CSR 2 max z 1 = f 1 x max z k = f k x s. t. x S x x R n k f 1 x f k x z = z 1 z k T z i S Z = z x S 1 1 z Z z Z z z z i z i i = 1 k z i < z i 2 1 z Z Z z z z z 3 1 x S z Z z Z x S 1

4 Z S S E Z N E N ε 1 f 1 x max f 1 x = z 1 s. t. f 2 x = ε 2 f k x = ε k x S ε 2 ε k i ε 1 x S ε 15 Markowitz 16 min z 1 max z 2 s. t. x S = var r = x T x = E r = μ T x r var E n n n μ n z 1 z 2 Huang and Litzenberger 17 max E u r s. t. x S u r r 4 u r = r qr2 q > 0 r 1 /q u r r Huang and Litzenberger Merton min z 1 max z 2 = x T x = μ T x 5 1 n 1 s. t. 1 T x = 1 Merton 18 ε 5 min z 1 = x T x s. t. μ T x = ε T x = 1

5 3 279 ε 2 6 ε Huang and Litzenberger 5 17 n n x R n x T x > z 1 = af - cc fz2 2-2cz 2 + a z 1 z 2 a = μ T -1 μ c = μ T -1 1 f = Markowitz Hirschberger Merton 5 Merton min z 1 = x T x max z 2 = μ T x max z 3 = c 1T x max z 4 = c 2T x max z 5 = c 3T x s. t. 1 T x = 1 μ z 1 z 2 3 c 1 c 2 c 3 n z 3 z 4 z 5 Markowitz - 24 Markowitz 3 4 8

6 u r = r qr2 + a 1 r c1 + a 2 r c2 + a 3 r c3 9 q > 0 r 1 /q u r r a 1 > 0 a 2 > 0 a 3 > 0 r r c1 r c2 r c3 r c1 r c2 r c3 c 1 c 2 c 3 E r c1 = c 1T x E r c2 = c 2T x E r c3 = c 3T x 10 r c2 r c3 1 r r c1 r c2 r c3 r r c1 = r qr2 + a 1 r c1 + a 2 r c2 + a 3 r c3 u r r r a 1 r c1 r c1 r c1 a 2 r c2 a 3 r c3 r c2 Hessian Matrix - q q > 0 - q < 0 r c2 r c3 4 max E s. t. 1 T x = = r qr2 + a 1 r c1 + a 2 r c2 + a 3 r c Steuer 25 u r r c Steuer ε- 8 min z 1 = x T x s. t. μ T x = ε 2

7 3 281 c 1T x = ε 3 c 2T x = ε 4 c 3T x = ε 5 1 T x = z 1 z 2 z 3 z 4 z 5 ε = ε 2 ε 3 ε 4 ε z 1 = ε T C T - 1 C - 1 ε 13 C = μc 1 c 2 c 3 1 n x = -1 C C T -1 C -1 ε Merton 18 CSR 12 8 ε - 12 c 1 c 2 c 3 CSR CSR Mahon and Wartick 27 Clarkson 28 Lanis and Richardson

8 P104 - P Global Industry Classification Standard GICS Wind RESSET Wind CSMAR CCER CSR CSR CSR 6 1 /6 10

9 CSR c 1 c c CSR CSR c 1 c 2 c CSR c 1 c 2 c μ

10 μ T ε x CSR 6 10 CSR 2007 ~ 2012 p1 p2 p3 p4 p5 p6 p7 p8 p9 p ε ε ε ε 3 ε 4 ε 5 CSR ε 3 ε 4 ε 5 p1

11 3 285 p2 p10 10 p1 p2 p10 p p ε ε t % p t p1 p2 p3 p4 p5 p6 p7 p8 p9 p t Stat P T < = t ε 3 7 t p4 p5 p6 p9 P p1 p2 p7 P t t p1 p2 p3 p4 p5 p6 p7 p8 p9 p t Stat P T < = t t 8 p2 p4 p5 p6 p9 P p1 p7 P CSR Markowitz Markowitz 10 6

12 CSR 2

13 J ISO26000 J J J J J J J BJNY J J J J J J J Markowitz H M. Portfolio selection J. The Journal of Finance Huang C Litzenberger R H. Foundations for financial economics M. Prentice Hall Englewood Cliffs New Jersey Merton R C. An analytical derivation of the efficient portfolio frontier J. Journal of Financial and Quantitative Analysis Brockwell P J Davis R A. Time series theory and methods M. 1st Edition. Springer Verlag New York J J Hischberger M Qi Y Steuer R E. Large - scale MV efficient frontier computation via a procedure of parametric quadratic programming J. European Journal of Operational Research M Markowitz H M. Foundations of portfolio selection J. The Journal of Finance Steuer R E Qi Y Hirschberger M. Suitable-portfolio investors non - dominated frontier sensitivity and the effect of multiple objectives on standard portfolio selection J. Annals of Operations Research M Mahon J Wartick S L. Corporate social performance profiling using multiple stakeholder perceptions to assess a corporate reputation J. Journal of Public Affairs Clarkson P M Li Y Richardson G D Vasvari F P. Revisiting the relation between environmental performance and environmental disclosure an empirical analysis J. Accounting Organizations and Society Lanis R Richardson G. Corporate social responsibility and tax aggressiveness an empirical analysis J. Accounting and Public Policy

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