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.

24 3 Vol. 24 No. 3 2015 6 OPERATIONS RESEARCH AND MANAGEMENT SCIENCE Jun. 2015 1 2 2 1. 300071 2. 300071 Markowitz 10 F830. 59 A 1007-3221 2015 03-0275-13 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 300071 China 2. Business School Nankai University Tianjin 300071 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 2014-01-24 71132001 14JJD630007 09YJC630133 1970-1977-

276 2015 24 0 2011 2012 2013 Corporate Social Responsibility CSR CSR CSR 1 2 ~ CSR 6 CSR 7 CSR 8 CSR 9 10 ~ CSR 14 CSR CSR 2013 A 2463 1522 941 A 23. 76 1 1 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

3 277 12 CSR 13 CSR 14 CSR 2 ~ CSR 6 CSR CSR 10 11 14 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

278 2015 24 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 - 1 2 qr2 q > 0 r 1 /q u r r Huang and Litzenberger 17 4 3 4 3 4 3 4 3 Merton 18 2 3 4 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 2 6 1 T x = 1

3 279 ε 2 6 ε 2 6 5 5 5 Huang and Litzenberger 5 17 n n x R n x T x > 0 19 6 1 z 1 = af - cc fz2 2-2cz 2 + a z 1 z 2 a = μ T -1 μ c = μ T -1 1 f = 1-1 1 18 Markowitz 16 20 21 Hirschberger 22 7 3 23 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

280 2015 24 8 u r = r - 1 2 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 - 1 2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 q > 0 - q < 0 r c2 r c3 4 max E s. t. 1 T x = 1 11 8 3 4 2 11 8 11 2 = r - 1 2 qr2 + a 1 r c1 + a 2 r c2 + a 3 r c3 13 8 Steuer 25 u r r c1 4 3 3 4 11 Steuer 25 11 8 8 8 2 6 ε- 8 min z 1 = x T x s. t. μ T x = ε 2

3 281 c 1T x = ε 3 c 2T x = ε 4 c 3T x = ε 5 1 T x = 1 12 12 26 1 2 3 26 8 z 1 z 2 z 3 z 4 z 5 ε = ε 2 ε 3 ε 4 ε 5 1 5 1 z 1 = ε T C T - 1 C - 1 ε 13 C = μc 1 c 2 c 3 1 n 5 13 7 7 13 26 12 x = -1 C C T -1 C -1 ε 14 4 8 Merton 18 CSR 12 8 ε - 12 c 1 c 2 c 3 CSR CSR Mahon and Wartick 27 Clarkson 28 Lanis and Richardson 29 2 5 23 3 4 23 2010 23 4. 1 23 3 9 36 100 31 10 6 146

282 2015 24 P104 - P142 1 1. 0. 502 2. 0. 258 3. 0. 241 1. 1 0. 202 1. 2 0. 145 1. 3 0. 155 2. 1 0. 047 2. 2 0. 105 2. 3 0. 061 2. 4 0. 045 3. 1 0. 133 3. 2 0. 108 2010 10 4. 2 Global Industry Classification Standard GICS 10 10 10 2 1010 000939 1510 000510 2010 600066 2520 000158 3020 600359 3520 600789 4010 600000 4520 000977 5010 600804 5510 000767 Wind 1 2 3 RESSET Wind CSMAR CCER 4 4. 3 2007 1 1 2012 12 30 2007 CSR CSR 1 4. 1 CSR 6 1 /6 10

3 283 3 CSR c 1 c 2 000939 0. 365 0. 183 0. 113 000510 0. 341 0. 169 0. 131 600066 0. 367 0. 185 0. 177 000158 0. 355 0. 161 0. 121 600359 0. 301 0. 184 0. 207 600789 0. 298 0. 158 0. 148 600000 0. 359 0. 195 0. 188 000977 0. 356 0. 167 0. 125 600804 0. 345 0. 163 0. 108 000767 0. 300 0. 183 0. 161 c 3 3 2 000939 000510 CSR CSR 000939 0. 365 0. 183 0. 113 c 1 c 2 c 2 8 5 CSR 8 13 14 12 13 3 c 1 c 2 c 3 4 5 10 μ 2007 1 1 2012 12 31 4 000939 000510 600066 000158 600359 600789 600000 000977 600804 000767 000939 0. 027 0. 020 0. 010 0. 020 0. 017 0. 016 0. 011 0. 017 0. 020 0. 019 000510 0. 020 0. 032 0. 012 0. 021 0. 022 0. 018 0. 012 0. 018 0. 020 0. 020 600066 0. 010 0. 012 0. 015 0. 009 0. 011 0. 009 0. 010 0. 009 0. 012 0. 009 000158 0. 020 0. 021 0. 009 0. 025 0. 019 0. 015 0. 012 0. 017 0. 019 0. 019 600359 0. 017 0. 022 0. 011 0. 019 0. 032 0. 018 0. 006 0. 015 0. 016 0. 015 600789 0. 016 0. 018 0. 009 0. 015 0. 018 0. 020 0. 007 0. 013 0. 014 0. 014 600000 0. 011 0. 012 0. 010 0. 012 0. 006 0. 007 0. 018 0. 008 0. 012 0. 010 000977 0. 017 0. 018 0. 009 0. 017 0. 015 0. 013 0. 008 0. 027 0. 018 0. 013 600804 0. 020 0. 020 0. 012 0. 019 0. 016 0. 014 0. 012 0. 018 0. 032 0. 016 000767 0. 019 0. 020 0. 009 0. 019 0. 015 0. 014 0. 010 0. 013 0. 016 0. 021

284 2015 24 5 μ T 000939 000510 600066 000158 600359 600789 600000 000977 600804 000767 0. 024 0. 027 0. 022 0. 015 0. 020 0. 013 0. 014 0. 027 0. 025 0. 007 ε 8 13 1 1 1 10 x 14 10 CSR 6 10 CSR 2007 ~ 2012 p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 000939-0. 103-0. 209 0. 554 0. 256 0. 107 0. 101 0. 465 1. 243 0. 097 0. 692 000510-0. 300-0. 258 0. 126 0. 115-0. 143 0. 067 0. 126 0. 131-0. 256 0. 125 600066 0. 257 0. 198-0. 043 0. 045 0. 164 0. 109-0. 020-0. 227 0. 212-0. 077 000158-0. 193-0. 364 0. 092 0. 100 0. 107 0. 101 0. 096 0. 065 0. 098 0. 086 600359 0. 139 0. 255 0. 081 0. 096 0. 112 0. 102 0. 087 0. 037 0. 114 0. 071 600789 0. 285 0. 411 0. 032 0. 075 0. 134 0. 105 0. 043-0. 062 0. 157 0. 014 600000 0. 428 0. 299-0. 042 0. 045 0. 164 0. 109-0. 020-0. 223 0. 212-0. 076 000977 0. 201 0. 223 0. 052 0. 083 0. 125 0. 103 0. 061-0. 021 0. 134 0. 037 600804-0. 050 0. 033 0. 093 0. 101 0. 107 0. 101 0. 098 0. 066 0. 093 0. 087 000767 0. 336 0. 412 0. 055 0. 084 0. 124 0. 103 0. 063-0. 010 0. 138 0. 042 0. 010 0. 011 0. 023 0. 018 0. 013 0. 015 0. 022 0. 043 0. 012 0. 026 0. 012 0. 011 0. 023 0. 021 0. 017 0. 019 0. 022 0. 027 0. 016 0. 024 ε 3 0. 321 0. 300 0. 348 0. 342 0. 339 0. 339 0. 346 0. 363 0. 339 0. 351 ε 4 0. 188 0. 184 0. 175 0. 175 0. 178 0. 175 0. 175 0. 178 0. 180 0. 176 ε 5 0. 196 0. 201 0. 122 0. 138 0. 156 0. 149 0. 126 0. 085 0. 163 0. 115 6 ε 3 ε 4 ε 5 CSR ε 3 ε 4 ε 5 p1

3 285 p2 p10 10 p1 p2 p10 p1 2-0. 103-0. 300 000939 000510 p1 0. 01 0. 0115 0. 321 ε 4 0. 188 ε 5 0. 196 6 2007 1 1 2012 12 31 10 2013 1 1 12 31 236 300 50 t 10 9 300 90% p8 7 7 2013 300 t p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 300 0. 002 0. 003 0. 001 0. 002 0. 002 0. 002 0. 001-0. 001 0. 002 0. 000 0. 000 0. 001 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 000 0. 000 0. 000 236 236 236 236 236 236 236 236 236 236 236 t Stat 1. 384 1. 647 0. 988 2. 299 2. 979 3. 137 1. 339-0. 580 2. 546 0. 523 1. 384 P T < = t 0. 084 0. 051 0. 162 0. 011 0. 002 0. 001 0. 091 0. 281 0. 006 0. 301 0. 084 ε 3 7 t p4 p5 p6 p9 P 0. 05 p1 p2 p7 P 0. 1 10 10 50 t 8 2013 50 t p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 50 0. 002 0. 003 0. 001 0. 002 0. 003 0. 002 0. 001-0. 001 0. 003 0. 001-0. 001 0. 001 0. 001 0. 000 0. 000 0. 000 0. 000 0. 000 0. 001 0. 000 0. 000 0. 000 236 236 236 236 236 236 236 236 236 236 236 t Stat 1. 647 1. 823 1. 136 2. 179 2. 870 2. 834 1. 425-0. 336 2. 610 0. 733 P T < = t 0. 051 0. 035 0. 129 0. 015 0. 002 0. 003 0. 078 0. 369 0. 005 0. 232 50 t 8 p2 p4 p5 p6 p9 P 0. 05 p1 p7 P 0. 1 10 CSR Markowitz Markowitz 10 6

286 2015 24 1 2 340007 470028 530019 530010 2011 3 15 340007 2011 000895 470028 3 300 50 1 CSR 2

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