2010 2 3 :,,,,,, 2004 2007,, :,,,,,, ;,,,,, ;,,,,,, (relationship lending) 90 (Berger & Boot,1995), :,, ;,, ;, 3,, :410083, : dengchao @mail. csu. edu. cn, hong2ao @chalco. com. cn, wangx0202 @126. com ;,,, :100818, :beijinghuwei @126. com ( [ 2007 ]24 ) (05BR22),, 83
:,,,, (Petersen & Rajan,1994 ;Berger &Udell,1995 ;Cole,1998 ), (2003) 2005, Yasuda (2005),Ljungqvist et al. (2006), Bharath et al. (2007), (Small Bank Advantage),, (Berger & Udell, 1998) (Hauswald &Marquez,2002) (Berger,2002), (Petersen & Rajan,2002) (Strahan & Weston,1998) (Stein,2002),, Dietsch (2002) Hannagan (2004),, (2003),,, (2004),,,,, : ;, ; 2004 2007,,, ;,,,,,, ( ) Berger &Udell (1995),,,,,, :,,, ; 84
2010 2, ;,,,,,,,, (Dewatripont &Maskin,1995),,,,,,,,, ( ),, (Berger & Udell,1998) (1),,, (2),, (3),,,,,,, (4),,,,, ( ),,,,, (,2004),,,,,, (1), (2),, (3),, (4),,,, (5),,, (6),,, 85
: ( ),,, :, 1 1,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ( ),,,,,,,,,, 86
2010 2,,,,,,, S, X S X,, ; S X,, t,t,, R P, C( S), P, : R p + C( S) P (1),,,, (1) : R p + C( S) = P (2), : R p = I 1 - C 1, I 1, C 1 Black2Scholes, C ( S) = S 0 [ N ( d 1 ) ] - X 0 [ N ( d 2 ) ],, C( S) ; S 0 = PV ( S) ; X 0 = PV ( X) ; N ( d) d, R p + C( S) = P, : I 1 - C 1 + S 0 [ N ( d 1 ) ] - PV ( X) [ N ( d 2 ) ] = P (3),, i,,,,,, ; ( ) (2), R P C ( S) P, 1 1. R P R p = I 1 - C 1, I 1 = ( L i T + F) (1 - t),,l ; i ; T ;, = 1 ; F ; t C 1 : C 11 C 12 C 13 C 11,,, ( IFTP, 87
: 1 Internal Funds Transfer Pricing),,,,,, IFTP, C 11 : C 11 = L IFTP T C 12, n,, C 12 = C f + C v = C f + E i N i, i = 1, C f ; C v ; E i i ; N i i C 13 C 11,,, C 13, C 13, EAD = PD LGD EAD,, PD,LGD, : 88 R p = I 1 - C 1 = (L i T + F) (1 - t) - ( C 11 + C 12 + C 13 )
2010 2 n = ( L i T + F) (1 - t) - (L IFTP T + C f + E i N i + PD LGD EAD) i = 1 2. C(S) X Black2Scholes, S 0 S 0 S, R,,,,,,,,,, 9 R 1 = p (L i T + F) (1 - t) ; R 2 = p ( f n k n ) (1 - n = 1 t) ; R 3 = p [ r 1 (1 - s 1 - s 2 ) D + r 2 ( s 1 + s 2 ) D ] 1 - t, p ( p ) ; f n n ; k n n ; r 1 ; s 1, s 2 ; D ; r 2, r m, : S 0 = PV ( R) = ( R 1 + R 2 + R 3 )Π(1 + r m ) (5) X, X 1 X 2 X 3 : n X = X 1 + X 2 + X 3 = p ( L IFTP T + PD LGD EAD + r 3 D + C i K i ) i = 1, r 3, C i i, K i i 3. P P,, P = ROE a L,, ROE, a, 2004 2007,,, (4) (6) 89
: ( ),,, (,2001) : (1),,,, (2),,, (3),,,, (4),,,,,,,,, 1., ( loanrel ) m i loanrel = i 2,, 0169,, 1 32123 %,,,, 2 25 th 75 th The number of relation bank per loan 114 115 0 0 1 2 4 Loanrel 0169 0128 0 0136 0162 1 1 2.,, capital, 1000, 0 ;1000 2000, 1 ; 3000, 2, industry, 1, 2, 3, 0 3,, 230, 46 %, 90 110,,, 54 %,,,,,78 % BBB BB, 55, 11 % A,, 90
2010 2 3 230 0. 46 90 0. 18 110 0. 22 70 0. 14 32 0. 06 90 0. 18 270 0. 54 108 0. 22 ( ) A 20 0. 04 BBB 280 0. 56 BB 110 0. 22 B 35 0. 07 55 0. 11 < 1000 60 0. 12 1000 2000 160 0. 32 2000 3000 280 0. 56,56 % 2000 3000 (, ), 1000 12 % 3.,,,, premium,, maturity Loanamount, 500, 0 ;500 1000, 1 ; 1000, 2,, Mortgage,, 1, 0 Investment,,,,, 1, 0 4,, 36 %, 58 %,, 4 25th 75th Premium 0. 36 0. 23 0 0. 12 0. 30 0. 40 0. 58 Loan amount 864. 7 665. 41 30 400 700 1125 3800 Maturity 7. 75 4. 02 1 5 6 12 24 Mortgage 0. 76 0. 43 0 0 1 1 1 Investment 0. 79 0. 41 0 1 1 1 1,, 86417 1000 67 %,, 500 37 %,500 1000 30 %,, 7175, 91
:,, 76 %, 24 % 4.,,, i, (CHOSEN) m, m, 1 ; 0 ( ), logit Logit ( CHOS EN) = 0 + 1 loanrel + 2 industry + 3 premium + 4 maturity + 5 capital + 6 mortgage + 7 investment + 8 loanamount + 2004 2007, 5 5 Wald Sig. OR constant - 3. 7112 1. 0930 11. 8990 0. 0010 loanrel 3. 6320 1. 8251 7. 2916 0. 0269 37. 7883 industry 0. 0054 0. 0027 0. 6765 0. 4108 1. 0054 premium - 0. 0443 0. 0387 1. 6688 0. 1964 0. 9567 maturity 0. 0780 0. 0340 0. 2614 0. 2392 1. 0811 capital - 0. 4169 0. 1189 4. 3516 0. 0370 0. 6591 mortgage - 0. 0619 0. 0418 0. 2614 0. 6092 0. 9400 investment - 0. 0948 0. 0081 1. 1463 0. 2843 0. 9096 loanamount 0. 2869 0. 0504 7. 2916 0. 0694 1. 3323 Pseudo R 2 0. 28 5 Logit,,, Wald, OR 5,loanrel 316320, 5 %, loanrel,loanrel = 1 loanrel = 0 3717883, OR ( 5 ) loanamount, OR 113323, capital, OR 016591,capital 0 1 ( 1000 1000 2000 ), 016591,,, premium mortgage,,, 6, loanrel = 0, 2191 % ; loanrel = 1, 53110 %,,, 92
2010 2 50119 %, ( ),,, 6 = capital = 0 capital = 1 capital = 2 loanrel = 0 2191 % 4198 % 3134 % 2123 % loanrel = 1 53110 % 66144 % 56161 % 46124 % 50119 % 61146 % 53127 % 44101 % ( ) A B 1500,, 2000, 800, 2007 80 %, 20 %,,, A B BBB,, 1500,A? 1., 2008 9 16 712 % 0122 %,BBB 1125 %, = 0 B A, 0 A 115 %, I 1 = + = 712 % + 0122 % + 1125 % + 115 % = 10117 %, 41125 % 2. R P I 1 = ( L i T + F) (1 - t) = 1500 i 1 1 (1-515 %) = 141715 3 i ( ), C 11 = L IFTP T = 1500 1 4186 % 1 = 7219 ( ), C f = 4175 + 3150 = 8125, C v = 20112, C 12 = 8125 + 20112 = 28137 BBB PD = 2184 %, (LGD) = 20 %, EAD = 1500, C 13 = EDF LGD EAD = 2184 % 20 % 1500 = 8152, C 1 = C 11 + C 12 + C 13 = 7219 + 28137 + 8152 = 109179,A B R p = I 1 - C 1 = 141715 i - 109179( ) C( S) (1) S A, B 75 %, loanrel = 0175, Logit A p = 58192 %, B L = 2000 (1 + 15 %) = 2300, 712 %, R 1 = p ( L i T + F) (1 - t) = 58192 % 2300 712 % 1 (1-515 %) = 92121,B A, R 2 9 = p ( f n k n ) (1 - t) = 5155 ; n = 1 93
:,B 120, R 3 = p [ r 1 (1 - s 1 - s 2 ) D + r 2 ( s 1 + s 2 ) D ] 1 - t = 58192 % [ 416 % (1-1715 %) 120 + 1189 % 1715 % 120 ] (1-515 %) = 2175, S = R 1 + R 2 + R 3 = 92121 + 5155 + 2175 = 100151 (2) X :A B B, B, B A, PD = 1108 %, LGD = 24 %, X 1 n = p [ L IFTP T + C i K i + PD LGD EAD ] = 58192 % (2300 4186 % i = 1 1 + 2415 + 1108 % 24 % 2300) = 83182, X 2 n = p C i k i = 4168 n : X 3 = p ( r 3 D + C i k i ) = 58192 % (1172 % 120 + 213) = 2157 i = 1,B X = X 1 + X 2 + X 3 = 83182 + 4168 + 2157 = 91107 S(100151 ) X(91107 ), A B (3) C( S) A r m = 712 %, S 0 = SΠ(1 + r m ) = 100151Π(1 + 712 %) = 93176 r f = 3136 %, X 0 = XΠ(1 + r c ) = 91107Π(1 + 3136 %) = 88111 = 47 %, d 1 i = 1 = ln ( S 0 ΠPV ( X) )Π t + tπ2 = ln (93176Π88111)Π(0147 1) + 0147 1Π2 = 0137, d 2 = d 1 - t = 0137-0147 1 = - 0110, N ( d 1 ) = 016443, N ( d 1 ) = 014602,, C 0 = S 0 [ N ( d 1 ) ] - PV ( X) [ N ( d 2 ) ] = 93176 016443-88111 014602 = 19186 3. A P A,A ROE = 15 %, a = 8 %, P = ROE a L = 15 % 8 % 1500 = 18 4. B, R p + C ( S) = P, 141715 i - 109179 + 19186 = 18, i = 7161 %, 5175 %, A, 10117 %, 41125 %, B, 7161 %, 5175 %, B A, A,, ( ) 7, loanrel 94
2010 2 = 0, 9102 %, 25121 % loanrel = 1, 7116 %,, 7 0100 8160 % 0100 9102 % 25121 % 0125 18192 % 6138 8157 % 18196 % 0150 36165 % 12135 8114 % 13111 % 0175 58192 % 19186 7161 % 5175 % 1100 78105 % 26131 7116 % - 0157 %,,,,,,,,,,,,,,,,,,,,,,,,,,2004 :, 7,2003 :, 3,2003 :,,2001 :,,2004 :, 11 Berger A. N., Udell, Gregory F., 1995, Relationship Leading and Lines of Credit in Small Firm Finance, Journal of Business,Vol. 68, 351 381. Berger A. N. and Udell G. F, 1998, The Economics of Small Business Finance : The Roles of Private Equity and Debt Markets in the Financial Growth Cycle, Journal of Banking and Finance,Vol. 22,613 673. Berger,Udell, 2002, Small Business Credit Availability and Relationship Lending : The Importance of Bank Organizational Structure, Economic Journal. Vol. 112,32 53. 95
: Boot,2000, Relationship Banking : What do We Know?, Journal of Financial Intermediation, (9) :7 25. Cole, Rebel, 1998, The Importance of Relationships to the Availability of Credit, Journal of Banking and Finance, (22) :959 977. Dewatripont M. and Maskin E. 1989 Credit and Efficiency in Centralized and Decentralized Economics,Mimeograph, Harvard University. Fama,E. 1985, What s Different about Bank?, Journal of Monetary Economics, (15) :29 39. Hauswald R. and Marquez R. 2000, Relationship Banking, Loan Specialization and Competition, Indiana University Working Paper. Ljungqvist, F. Marston and W. J. Wilhelm, 2006, Competing for Securities Underwriting Mandates : Banking Relationships and Analysts Recommendations, Journal of Finance,Vol. 61,301 340. Michel Dietsch and Joel Petey. 2002, The Credit Risk in SME Loans Portfolios : Modeling Issues, Pricing and Capital Requirements, Journal of Banking and Finance, 26 :303 322. Sreedhar Bharath, Sandeep Dahiya, Anthony Saunders, et al.,2007, So What Can We Get? The Bank s View of Lending Relationships, Journal of Financial Economics,Vol. 85, 368 419. Petersen M. A., Rajan R. G.. 2002, Does Distance Still Matter? The Information Revolution in Small Business Lending, Journal of Finance Vol. 57,2533 2570. Petersen,M.,Rajan,R.,1994, The Benefit of Credit Mark Competition on Lending Relationships, Journal of Finance, (49) :3 37. S. Greenbaum and A. Thakor, 1995, Contemporary Financial Intermediation, Dryden Press, New York. Strhan P. E., Weston J. P., 1998, Small Business Lending and Bank Consolidation : Is There Course for Concern? Current issue in Economics and finance, Federal Reserve Bank of New York, (22) :821 845. Stein Jeremy C. 2002, Information Production and Capital Allocation : Decentralized versus Hierarchical Firms, Journal of Finance Vol. 57 (5),1891 1921. Thomas A. Hannagan, 2004, Loan and Relationship Pricing Practice, The RMA Journal,Vol. 87 (4),60 62. Von Thadden, 1995, Long2Tern Contracts, Short2Term Investment and Monitoring, Review of Economic Studies,Vol. 62,57 575. Yasuda, 2005, Do Bank Relationships Affect the Firmπs Underwriter Choice in the Corporate2bond Underwriting Market?, Journal of Finance,Vol. 60,1259 1292. Research on Pricing of Relationship Lending from Big Banks to Small Firms Deng Chao, Ao Hong, Hu Wei and Wang Xiang (Business School of Central South University) Abstract :Nowadays, the external environment of big banks and small firms has changed greatly. Big banks need to further exploit the market of small firms and small businesses also need comprehensive financial service offered by big banks. Deep into the symbiosis between big banks and small businesses, this paper finds that the relationship lending is the best way to connect big banks and small businesses, and that big banks have more advantages to grant relationship lending. We also find that the long2term cooperation between big banks and small businesses can bring big banks potential earnings2relationship rents. Based on the implicit contract of relationship lending, we formulate the pricing model of relationship lending, which can distribute the rents of relationship lending and realize the revenue compensation spreading periods. At last, we calculate the rents of relationship lending with the data of some small businesses from one big bank between 2004 and 2007, and demonstrate the process of pricing the relationship lending. Key Words :Relationship Lending ; Big Bank ; Small Firms ;Pricing Model JEL Classification : E47, G21,M21 ( : ) ( : ) 96