Vol. 15 No. 6 Jun JOURNAL OF MANAGEMENT SCIENCES IN CHINA CAPM F J xmu. edu.

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1 JOURNAL OF MANAGEMENT SCIENCES IN CHINA Vol 5 No 6 Jun CAPM F830 9 A J Emal zlzheng@ xmu edu cn NYSE NASDAQ

2 Parlour Sepp 8 Parlour t ~ T Sepp 8 t 3 T Parlour Sepp 8 4 Parlour Sepp 8 t ~ T r T f P t T P T ~ N P T σ T W t θ t t n Θ B t Θ S t 3 4

3 n a T 2 Θ B t = 2 Θ S t Θ B t Θ B t Θ S t n W Θ B T Θ S T = B t Θ B tp LOB + r T f + T θ t Θ0 P S T + Θ B texe B TP T + 5 Θ B T = Θ B t exe B T Θ B t exe B T P LOB + r T f + Θ S T = Θ S t exe S T exe B T exe S T n Θ S texe S TP LOB + Θ S t exe S T P T exe B T 2 t T Pr B t Pr S 6 r T f 9 E t exe B T = Pr B t 3 B t Θ B tp LOB + r T f P LOB t T P LOB = n Tck n θ t Θ S t t Tck n 7 T n P LOB P LOB = P LOB + + θ t Θ S t P T t ~ T Tck 2 t ~ T W t t ~ T θ t P t B t 8 t ~ T T CARA U = e aw T 5 W t = θ t P t + B t W T = W t θ t P t + r T f + θ t P T T 6 Pr B t Pr S t 7 Tck P T 9 6

4 6 43 Θ B t exe S T P T + r T f P LOB + Θ s t exe S T P LOB P T T Θ B t Θ S t 7 EU = 0 EU = 0 Θ B t Θ S t exe B T P T + r T f P LOB E W T + a 2 Var W T = 0 exe B T P T exe S T P LOB + r T f P LOB PG B T P T PG S 瑏瑠 T T max EU = exp Θ B 0 ΘS 0 { } ae W T + a2 2 Var W T 8 6 W T E t W t = W t θ t P t + r T f + θ t P T + Θ B te t PG B T + Θ S te t PG S T E t PG B T = E t exe B TP T Pr B t + r T f P LOB E t PG S T = Pr B tp LOB E t exe S TP T W T Var W T =θ 2 t σ 2 T+var 2θ t cov P T = θ 2 t σ 2 T + Θ B tpg B T+ Θ S2 t var PG S T Θ B tpg B T + 9 Θ S tpg S T + Θ B2 t var PG B T + Θ S tpg S T Θ B tθ B tj cov PG B T PG B Tj + j = Θ S tθ S tjcov PG S T PG S Tj + j = Θ B tθ S tjcov PG B T PG S Tj + j = 2θ t [ Θ B tcov P T PG B T + Θ B t Θ S tcov P T PG S T ] E W T + a 2 Var W T = 0 Θ S t Θ B t E t PG B T + aθ t cov P T PG B T + [ a Θ B tj cov PG B T PG B Tj + Θ S tjcov PG B T PG S Tj ] = 0 Θ B t = var PG B T { E t PG B T a Θ B tj cov PG B T PG B Tj j = Θ S tjcov PG B T PG S Tj θ t cov P T PG B T } Θ S t = var PG S T { E t PG S T a Θ S tjcov PG S T PG S Tj j = Θ B tj cov PG B T PG S Tj θ t cov P T PG S T } 瑏瑠 PG B T PG S T T Potental Gan

5 βbb β SB β 2 3 CAPM CAPM beta 2 β BB = cov PG B T PG B Tj var PG B T cov PG S T PG B Tj var PG B T cov P T PG B T var PG B T = βbb j = βsb j = βpb 2 Θ B t = E t PG B T a var PG B T Θ B tj β BB j 4 Θ S tjβ SB j θ t β PB 5 5 CAPM Θ B t Θ 瑏瑡 [ ] B tn = S Θt Θ S t Θ S tn [ βbb β SB ] β [ β BB β SB ] β Θ S t3 5 β Θ S t = E t PG S T a var PG S T Θ S tjβ SS j Θ B tj β BS j θ t β PS 6 β 2n Θ B t Θ S t n [ βbb β SB β ] [ Θ B t S Θ ] t E t PG B T a var PG B T θ tβ PB = 7 E t PG S Tn a var PG S Tn θ tβ PS n [ ] β SB = β BB 2 β BB 3 β BB n β BB n β BB 2 β BB 23 β BB 2n β BB 2n β BB 3 β BB 32 β BB 3n β BB 3n β BB n β BB n2 β BB n3 β BB nn β SB 2 β SB 3 β SB n β SB n β SB 2 β SB 23 β SB 2n β SB 2n β SB 3 β SB 32 β SB 3n β SB 3n β SB n β SB n2 β SB n3 β SB nn Θ B t [ β BB β SB ] Θ B t [ S ] Θt [ ] = βbb β SB β E t PG B T a var PG B T θ tβ PB E t PG S Tn a var PG S Tn θ tβ PS n 8 瑏瑡 CAPM Jonhn H Cochrane Asset Prcng revsed edton

6 6 45 E t PG B T a var PG B T θ tβ PB 3 s = θ m t P m T + m = m = Θ Bs tj cov PG Bm j = T PG Bs Tj 9 Θ Ss tj cov PG Bm s = j = s = T PG Ss Tj [ βbb β SB ] θ s tcov P m T PG Bs β M Tj } 8 Θ B B B 2 B m B m t max EU = exp { ae W T + a2 Θ Bm 0 Θ Sm 2 Var W T } Θ S B 2 B 22 B 2m B 2m t 0 Θ B t Θ S t n = Θ BM B s B s2 B sm B sm t Θ Bm t Θ Sm t n m = M Θ SM t B m B m2 B mm B mm M m E t PG B T 9 a var PG B T θ t β PBs E t W T = W t s = θ m t P m t + r T f + m = E t PG SM Θ Bm t E t PG Bm Tn T + a var PG SM Tn θ M t β PMSs n s = [ ] Θ Sm t E t PG Sm T B sm = βbsbm β SsBm m = β BsSm s β m SsSm β BsBm 2 β BsBm n m β BsBm β BsBm 2 β BsBm 2n = s n m = M E W T + a 2 Var W T m = 0 Θ Bm t E W T + a 2 Var W T β BsBm j = cov PGBs T PG Bm Tj = 0 var PG Bs Θ Sm T t s m 2 j θ m Θ Bm t = var PG Bm T { E t PG Bm t m T a

7 CAPM 瑏瑢 P t θ [ t + ( t Θ B tp t 23 瑏瑣 exe B T t P t PG B T j = 0 23 CAPM P t P t CAPM PG B T = exe B T P T + r T f P LOB = P T + r T f P t PG S T = P t P T 20 E t r p r f E t PG B T = E t P T + r T f P t E t PG S T = P t = P t E t r p r T f E t P T = P t E t r p var t PG B T = var t PG S T = var P T + r T f P 2 = var P T = P 2 t var r p 22 beta 20 PG B Tj = P T +r f P t 4 β BB j β SB j β PB = cov P T PG B Tj var P T = = cov P T PG B Tj var P T = Θ B t = P t E t r p r f ap 2 t var r p θ t P LOB j > P t Θ B tj + P LOB j S Θtj < P t CAPM 5 E t r p r f CAPM 0 avar r p = P LOB j B Θ > P t S Θt j P LOB j < P t ) tj ] 23 CAPM avar r p [ = P m t s = Θ Ss tj ) ] PmPs β ( θ s t + Θ Bs tj t m 9 5 瑏瑢 瑏瑣

8 6 47 CAPM Markovtz H Portfolo selecton J Journal of Fnance Sharpe W F Captal asset prces A theory of market equlbrum under condtons of rsk J Journal of Fnance Grossman S J Stgltz J E On the mpossblty of nformatonally effcent markets J The Amercan Economc Revew L D Ng W L Optmal dynamc portfolo selecton Multperod meanvarance formulaton J Mathmatcal Fnance Easley D Hvdkjaer S O Hara M Is nformaton rsk a determnant of asset returns J Journal of Fnance Barber B Odean T Zhu Nng Do retal trades move markets J Revew of Fnancal Studes Copeland T E Gala D Informaton effects on the bdask spread J Journal of fnance Kyle A S Contnuous auctons and nsder tradng J Econometrca Journal of the Econometrc Socety Sepp D J Lqudty provson wth lmt orders and strategc specalst J Revew of Fnancal Studes Sandas P Adverse selecton and compettve market makng Emprcal evdence from a lmt order market J Revew of Fnancal Studes Parlour C A Prce dynamcs n lmt order markets J Revew of Fnancal Studes Foucault T Kadan O Kandel E Lmt order book as a market for lqudty J Revew of Fnancal Studes Goettler R L Parlour C A Rajan U Equlbrum n a dynamc lmt order market J Journal of Fnance Goettler R L Parlour C A Rajan U Informed traders and lmt order markets J Journal of Fnancal Economcs Rosu I A dynamc model of the lmt order book J Revew of Fnancal Studes J Chen We Qu Wenzhou Study of nvestors order placement strategy based on duraton J Journal of Management Scences n Chna n Chnese 7 J

9 Chen Shou L Shuangfe L Chuanguo Stock prce response to order mbalance and change of volume J Journal of Management Scences n Chna n Chnese 8 Parlour C A Sepp D J Lmt order markets A survey J Handbook of Fnancal Intermedaton and Bankng Order allocaton model A model combnng mcrostructure theory and asset allocaton theory ZHENG Zhenlong LIU Yangshu Department of Fnance School of Economcs Xamen Unversty Xamen Chna Abstract Ths paper extends asset allocaton model to order allocaton model whch brdges the gap between mcrostructure theory and asset allocaton theory In partcular by maxmzng nvestor s utlty of order submsson problem n the same way wth solvng asset allocaton problem we receve a closeform soluton on allocaton about order submsson In addton we prove that CAPM s a specal case of our model when submsson s constraned to be margnal market order Key words order submsson order allocaton asset allocaton 檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿檿 39 techncal reasons and s dfferent from the classcal batchng machne An nteger nonlnear programmng s proposed and a heurstc algorthm based on dynamc programmng s appled to the total weghted completon tme for the new batchng machne The worst case performance of the heurstc algorthm s proved to be at most 3 If any two steps processng tmes are the same the heurstc algorthm can obtan the optmal soluton If any one step s processng tme of all the jobs s the same the worst performance of the heurstc algorthm s proved to be at most 2 and the bound s tght We also analyze the worst case of the heurstc algorthm for the general case where jobs processng are composed of any stepprocessng Key words batchng machne bell type annealng furnace threestep processng tme dynamc programmng