Chuyển động giá trên thị trường chứng khoán bước đi ngẫu nhiên hay hội tụ về giá trị trung bình

' A'' A' , TRlfO'NG D~I HQC KINH TE THANH PHO HO CHI MINH DE TAl NGHIEN CtJU KHOA HQC CAP CO' Sfr CHUYEN DONG GIA TREN THI• TRtrO'NG • CHirNG ~{HOAN , ~ "" "" ""' BtrO'C DI NGAU NHIEN flAY HOI VE • TU • GIA TRI• TRUNG BINH Ma so: CS-2012-41 Thanh vien de tai: TS Le D~t Chi Tp Ho Chi Minh~ thcing niim 2013 Ml}C Ll}C T6MTAT l Danh sach nhfrng til' viet tat Danh m1,1c bang bieu Gi6i thi~u Tong quan cac nghien cthl ve chuyen dl)ng gia 10 Ca s& ly thuyet 13 3.1 Gia trj CO' ban cua chfrng khmin , 13 3.1.1 Ly thuyet hi~u qua ca ban 13 3.1.2 Mo hinh djnh gia tai san 14 3.2.Ly thuyet Mean Reversion 14 3.2.1 Mean reversion 15 3.2.2 Mean reversion va thj trU'lrng hi~u qua 19 3.3 Toe dl) dieu chinh cua hi~n rugng Mean Reversion va hanh vi phong ngira rui ro bang quyen ChQn 20 Mo hinh kiem djnh Mean Reversion 22 4.1.Mo hinh hoi quy tY suat sinh lgi 22 4.2.Mo hlnh tY so phU'ang sai 23 4.3.Mo hinh hl)i t1,1 bien dl)ng 25 Mo hinh kiem djnh Mean Reversion tren Vn-Index 26 S.l.Khung phan tfch ~ 26 5.2.Ket qua mo hinh 28 ~ 5.3.Phan tich ket qua 35 Ket Iu~n 37 Pht.~ll;IC 38 TOM TAT Cac ly thuyet tai chinh da ph'an deu d\fa tren gif1 thuyet thj trtremg hi~u qua va ly thuyet btr&c di ng~u nhien lam nen tang, v&i CO' sa lu~n CO' ban Ia Sl;l' thay doi gia ca dO'n thuan Ia cac chuyen dc?ng ng~u nhien va gia qua khl.f khong the mang den chi d~n cho gia ttrO'ng lai Trong d6, mc?t quan diem m&i phu nh~n tinh dung dan cua gia thuyet thj trmrng hi~u qua Ia ly thuyet "f>ao ngtrQ'C gia ve gia trj trung binh" ll;li cho rang gia ca c6 moi tU'O'ng quan v&i va djch chuyen ve gia trj trung binh Bang each tr&c ltrgng chu6i dfr li~u chl.fng khoan Vi~t Nam 13 nam (tir 7/2000 - 2/2013) Ket qua cho thay: thl.f nhat, c6 S\f xuat hi~n hi~n ttrgng dao ngtrQ'C ve gia trj trung binh Doi v&i chu6i dfr li~u tuan thi hi~n ttrgng xuat hi~n (y hau nhtr tat ca cac de? tre (1-8) va chu6i dfr li~u thang chi the hi~n (y nhfrng de? tre dau tien (1-2), qua d6, ta thay dtrQ'C d~c diem thj trtrerng cua Vi~t Nam !3 hanh vi dau CO' ngan h(;ln Thu hai, hi~n ttrgng it chju anh htri'Yng bi'YI cu soc tir CUQC khung hoang Thl.f ba, quy mo m~u quan sat cang l&n thi tinh chinh xac d.ng cao Thl.f ttr, toe dQ dieu chinh cua hi~n ttrgng giam dan theo ki dQ tre Thl.f !'lam, xac djnh dtrQ'C toe de? dieu chinh C\1 the bang mo hinh hQi t\1 bien dc?ng Ia 185 Tir kh6a: Gia thuyet thj trtrerng hi~u qua, Dao ngtrgc gia ve gia trj trung binh, thj trtrerng chl.fng khoan Danh sach nhifng tir viet tit ARCH Mo hinh tl;f hoi qui phzrung sai thay doi c6 dieu ki~n ARMA ARIMA GARCH Mo hinh trung binh trzr(Yt va tl;f hoi qui Mo hinh trung binh trzrlJ't, dong lien ket, tl;f hoi qui Mo hinh tl;f hoi qui phzrung sai thay doi c6 dieu ki~n dzrlJ'c khai quat hoa DANH Ml)C BANG BIEU Bang 1: Tong hQ'p Reversion nghH~n cuu hrirng xac l'ljnh co S\1' xuat hi~n Mean Bang 2: Tong hQ'p nghien ctru ve l'ljnh nghia Mean Reversion Bang 3: Tom tat hU'ang phan tich Bang 4: Ket qua hoi qui mo hinh tuyen tinh theo tuan Bang 5: Ket qua hoi qui mo hinh tuyen tinh theo thang Bang 6: Ket qua hoi qui mo hinh tuyen tinh theo tuan cai tien Bang 7: Ket qua hoi qui mo hinh tuyen tinh theo thang cai tien Bang 8: Ket qua hoi qui mo hinh tuyen tinh ket hQ'p theo tuan chuy~n l'l()ng Brown Bang 9: Ket qua hoi qui mo hinh tuyen tinh ket hQ'p theo thang chuy~n l'l()ng Brown Bang 10: Ket qua mo hinh tY so phuang sai theo tuan cho giai l'lo~n 2000 - 2013 Bang 11: Ket qua 1no hinh tY so phuang sai theo thang cho giai l'lo~n 2000- 2013 Bang 12: Ket qua mo hinh khung hoang tY so phuang sai theo tuan cho giai do~n trll'cYC Bang 13: Ket qua mo hinh khung hoang tY so phuang sai theo thang cho giai 4o~n tru-6-c Bang 14: Ket qua mo hinh hoang tY so phuang sai theo tuan cho giai do~n khung Bang 15: Ket qua mo hinh tY so phuang sai theo thang cho giai hoang 4o~n khung Bang 16: Ket qua mo hinh khung hoang tY so phuang sai theo tuan cho giai l'lo~n sau Bang 17: Ket qua mo hinh khung hoang tY so phll'ang sai theo thang cho giai l'lo~n sau Bang 18: Ki~m 4jnh hoi quy h()i l\1 bien l'l()ng theo mo hinh GARCH Hinh 1: Tr\l'C quan Mean Reversion Hinh 2: Mo phong btrac di ng~u nhien chi so Vn-Index 2000 - 2013 theo chuyen dqng Brown Hinh 3: Mo phong toe dq dieu chinh hqi t\1 tY suat sinh IQ'i Hinh 4: Phan tach giai do~n phan tich GI6'1 THieu Vao cuoi nhfrng nam 1980, hai hQc gia Debondt va Thaler da xuat ban nhieu tai li~u lien quan den chien IU'Q'C rna nhieu ngU'ai quan tam hJ.c bay gia: chien IU'Q'C dau tU' di ngU'Q'C thj trU'ang va danh b(ili thi trU'ang Chien IU'Q'C d\fa vao qua khu, qua xay d\fng danh ffi\lC cua "nhfrng chfulg khoan lfi" mang l(ili tJ suat sinh IQ'i cao hO'n danh m1:1c cua "nhfrng ch1lng khoan lai" Chien IU'Q'C chinh Ia bieu hi~n cua hi~n tU'Q'ng "dao ngll'Q'C ve gia trj trung binh" (Mean Reversion), n6i mc}t each tr\l'C giac thi d6 Ia hi~n tU'Q'ng ben ton t(ili mc}t l\fC keo gia quay ve ml.fc trung binh sau no da VU'Q't len tren hay xuong thap hO'n gia trj trung binh Nhfrng nghien cl.fu cua hai hQC gia lam noi len nhieu tranh cai di lien v&i nhfrng cong trinh nghien cl.fu Ia li~u r~ng Mean Reversion c6 th\fc S\f ton t(ili tJ SUat sinh lQ'i hay tr\fC quan rna n6i li~u rang CO ton t(ili mQt l\fC keo gia Ve ml.fc gia trj trung binh mang l(ili S\f cong c6 tinh h~ thong cho chien lll'Q'C di ngll'Q'C thj trll'ang? Th\fC te Ia ban than hi~n tU'Q'ng khong ton t(ili l\fC "hfru hinh" hay "vo hinh" nao keo gia ve ml.fc trung binh, d6 chi Ia so sanh mang tinh tr\fC quan d~ hieu Ban than chuyen dc}ng cua PO ham chua tinh dirng va phan phoi dirng t(ilo nen cac dU'ang gi&i h(iln Nhfrng thay doi cua k}r tiep theo phan lhlg l(ili S\f thay doi cua k}r trU'ac d6, sau mc}t S\f thay dt1i "tich C\fc" lam tang t:Y suat sinh IQ'i di lien mc}t S\f thay doi "tieu C\fC lam giam tY suat sinh IQ'i va ngU'Q'C l(ili f>c}ng thai quay tr& ve c6 the xay v&i nhieu toe de} khac nhau, n6 c6 the lo(ili bo nhfrng thay doi di~n thai gian trU'&c d6 11 - - - - - -6 Hinh 1: Tr\fC quan Mean Reversion Ty suat sinh lgithj tnrem Ty suat sinh lgi cao c6 xu huang "tieu qrc" M1lc trung binh Ty suat sinh lgi thap c6 xu hu&ng "tfch qrc" Thaigian DeBondt va Thaler (1989), Lawrence Summers (1986) cung da chi rang c6 m(>t tac d(>ng h(>i tv keo dai gia chung khoan, thi n6 khong the phan bi~t dU'Q'C ve m~t thong ke v&i m(>t bU'&c di ng~u nhien Sau d6, Fama & French (1988) va Poterba & Summers (1988) da trinh bay m(>t bang chung cho thay tj suat sinh lgi k thc ve m~t thi tv ve gia trj trung binh m(>t each gian tiep thong qua vi~c hoi qui cac muc tY suat sinh lgi k thiri ki d\fa tren d(> tr~ ciia chinh n6 Hi~n tugng h(>i tv ve gia trj trung binh an chua moi tuang quan am t;;ti m(>t vai d(> tr~ k Poterba va Summers (1988) cung si'r dvng m(>t phll'ang phap gian tiep khac Ia si'r dvng h~ so phuang sai Neu khong ton t~i hi~n tll'gng h(>i tv, thi phuang sai ciia tY suat sinh lgi k kY se tY I~ v&i k Vi v~y, tj so gifra phll'ang sai ky c6 the dugc chuan h6a bang each lay phuang sai k ki chia cho k Tuy nhien, neu ton t;;ti hi~n tll'gng h(>i tv thi hi~p phU'ang sai se tj I~ nho han k - qua trinh gia bj day tr(r ve (khi n6 bj l~ch khoi gia trj trung binh) Vi v~y tj so phU'ang sai giam du&i mll'c dan vj Nhu v~y, vi~c dt chuyen d(>ng ng§u nhien, khong the dl;l' doan dU'Q'C Ly thuyet xay dl;l'ng d\fa tren gia djnh cua thj truerng hi~u qua v&i n(>i dung cot loi the hi~n qua kY vqng thuan nhat cua nha dau tu V&i kY vqng thuan nhat, nha dau ttr se c6 thong tin tuO'ng tg qua kh(r, theo d6 cac thong tin se phan anh het vao gia hom nay, ho~c gia sir hQ c6 thong tin de danh bCili thj truerng thi l~p tuc thj trtrerng se dieu chinh d~n den CaC "m~U ml;l'C" gia ca khong ton tCili nfra va cac thay doi gia ca mc;>t theri kY se d(>c l~p v&i S\f thay doi kY ke tiep Ngugc lCili, Mean Reversion lCili cho thay thj trtrerng "c6 tri nh&", thj truirng se dieu chinh ve muc can bang m(}t chu k}r nhat djnh tCilO CaC duerng gi&i hCiln ti~m C~n ve gia trj trung binh M(>t "m~u hinh" c6 the xay dgng thong qua Mean Reversion tCilO nen m(>t chien luge dau ttr c6 h~ thong d\fa tren cac thong tin qua khu Hinh Ia mc;>t mo phong dien hinh cho btr&c di ng~u nhien theo chuyen d(>ng Brown Ta thay ro rang bu&c di ng~u nhien kh.ong mo phong chinh xac S\f thay doi chi so Vn-Index giai do«iln 2000 - 2013, gia trj Vn-lndex c6 bieu hi~n cua hi~n ttrgng Mean Reversion dao d(>ng xung quanh muc trung binh (Mean) Hinh 2: Mo phong bU'ac di ngau nhH~n chi chuyen d()ng Brown 1500 so Vn-Index 2000 - 2013 theo -Real moving -Rd1 -Rd2 1000 -Rd3 -Rd4 -Rd5 500 -Mean (*) RD - Random Walk [Blrac ngdu nhien) Nhieu nghien cifu da chi S\f hi~n di~n cua Mean Reversion tren nhfeu lo~i gia ca tai san t~i nhfeu thj trll'erng khac tren the gi&i, tir nhfrng bang chU:ng chll'a th\fC S\f ro rang nhll' Fama French (1988), Lo va Mackinlay (1989) den nhfrng bang chifng ro rang nhll' Zivot & Andrews (1990), Kim, Nelson & Startz (1996) V&i nhfrng ket qua d6, nen tang cua Jy thuyet tai chinh bj lung lay rna gia thuyet thj trU'erng hi~u qua khong phai h.lc nao ciing dung tfil.i nhfeu thj trll'ao ngugc gia trj trung binh) Hi~n tuqng Mean Reversion Ia hi~n tll'gng d6 gia ca khong tuan theo bU'6-c di ng§u nhien rna c6 tinh t\1' tll'ang quan phu djnh, chuyen djch c6 xu hU'6-ng ve gia trj trung binh Mean Reversion xuat hi~n mang ham y khong chi llng d1;lng dau tU' va phong ngira rui ro rna Ia cong C\1 phfm bi~n ly thuyet nen tang - gia thuyet thj truerng hi~u qua ve D\fa tren cac djnh nghia Mean Reversion tir tr\fc quan den phan tich chi tiet phan, cac mo hinh kiem djnh dU'Q'C xay d~g nham nh~n di~n va danh gia hi~n tll'gng Mean Reversion Trong gi6-i h~n bai nghien c(ru nay, mo hinh tY so phll'O'ng sai to VU'f;rt tr()i hO'n SO v6-i cac mo hinh hoi qui V&i cac ket qua kiem djnh thu dU'Q'C, thj trll'irng chllng khoan Vi~t Nam, d~i di~n Ia chi so Vn-Index, cho thay S\f h(li t1;l ro rang tren hau het cac d() tr~, hay n6i each khac Mean Reversion xuat hi~n tren hau het cac quan sat dU'Q'C chQn f)ifu cho thay tam ly ciing nhll' chien IU'Q'C dau tu "ngan hc~m" cua cac nha dau tU' va qua d6 rut nhfrng chi d§n quan trQng phan tich rna ly thuyet thj truerng hi~u qua bj phu djnh bai S\f ton t~i cua Mean Reversion Dong thai, S\f khac bi~t danh gia Mean Reversion cac giai do~n khac nhau: trll'6-c, va sau khung hoang cho thay m()t thj trU'erng ganh chju cu soc, th! truerng lao doc, tY suat sinh lgi ch~ch khoi hoan toan gia trj trung binh, yeu to h()i t\1 I§.n ng§.u nhien hoan toan b! lo~i bo - 38 Ph1;111;1c 1: Tinh dirng Chulli Rt dtrQ'C gQi Ia c6 tinh dirng neu khong doi theo thai gian, d6 ta c6: kY VQng, phtrO'ng sai va hi~p phtrO'ng sai E(Rt) = J.l 'v't Var(Rt) cov(Rt, Rt+k) = E(Rt- J1.) = a \it = E[(Rt- Jl.)(Rt+k - J.J.)] = Yk \it V&i dieu ki~n thu 3, ta thay m()t chulli dtrgc gQi Ia dirng neu hi~p phtrO'ng sai hay h~ so tll'O'ng quan gifra Rt va Rt+k chi ph\l thu()c vao d() tr~ k rna khong ph\J thu()c vao thai diem t Va ngtrgc lc~li, neu vi ph~m m()t ba dieu ki~n tren thi Rt Ia chulli khong dirng hay gQi Ia btr&c ng~u nhien Xet m()t btr&c ng~u nhien dan gian: Rt = Rt-1 + Ut d6 Ut Ia nhi~u trang (White noise) c6 kyvQng bang 0, phtrO'ng sai khong doi bang a va hi~p phtrO'ng sai bang o (Ut Ia m()t chu6i dirng) E(Rt) = E(Rt-1) + E(Ut) = E(Rt_ 1) \it Dieu c6 nghia Ia k:Y vQng khong doi, nhien phtrO'ng sai l~i thay doi = R0 + U1 ~ Var(R 1) = Var(U1) = a R2 = R0 + U1 + U2 ~ Var(R 1) = 2Var(U1) = 2a R1 Rt = Ro + U1 + U2 + + Ut ~ Var(Rt) = tVar(U1) = ta (V&i R0 Ia hang so, cac Ui d()c l~p v&i nhau) M()t so mo hinh btr&c ng~u nhien phan tich: Qua trinh tv hoi qui (Autoregressive Process- AR) Qua trinh n, hoi quy b~c p c6 d~ng: p Rt = t/J0 + t/JiRt-i + Ut i=1 AR(p J h()i t\) hay dirng -1 < t/Ji < v&i mQi i Qua trinh trung binh trU'(;rt (Moving Average- MA) Qua trinh tung binh trugt b~c q c6 d~ng: 39 q Rt = ut + L eiut-i i=l Dfeu ki~n de chufii dirng -1 < 8i < v&i mQi i Qua trlnh trung blnh tnrc;rt va tl;l' hoi qui (Autoregressive Process Moving Average - ARMA) Qua trinh ARMA lei S\f ket hgp gifra qua trinh AR va qua trinh MA, ARMA(p,q) c6 p so hc;mg t\1' hoi quyva q so h~ng trung binh trU'Q't c6 d~ng: Rt = e + p q i=l i=O L aiRt-i + L fliUt-i Qua trinh trung blnh trU'c;rt, dong lien ket, tl;l' hoi qui (Autoregressive Integrated Moving Average- ARIMA) M(}t chu6i dugc gQi Ia dong lien ket b~c 1, kY hi~u 1(1), neu sai phan b~c nhat Ia chu6i dirng Va tU'O'ng t\f, m(}t chu6i dU'Q'C gQi Ia dong lien ket b~c d neu sai phan b~c d ciia n6 Ia m(}t chu6i dirng, Icy hi~u Ia I(d) Nhu v~y, qua trinh ARIMA chi dO'n gian Ia chu6i sai phan b~c bi~u di~n du&i d~ng ARMA Mo hinh ARIMA(p,d,q) nghYa Ia chu6i Rt c6 p so h~ng t\1' hoi quy, c6 sai phan b~c d Ia chu6i dirng va q so h~ng trung binh trU'gt: llRt =e + p q i=l i=O L aillRt-i + L fliUt-i Qua trinh tl;l' hoi qui phU'ung sai thay doi c6 dieu ki~n (AutoRegressive Conditional Heteroskedasticity- ARCH): Do Engle phat trien vao nam 1982 Mo hinh cho rang phuO'ng sai ciia cac so h~ng nhi~u t~i theri diem t ph\1 thu(}c vao cac so h(,lng binh phU'O'ng {y cac giai do~n trU'&c HO'n nfra, phuO'ng sai c6 dfeu ki~n khong chi ph\1 thu(}c vao m(}t d(} tr~ rna ph1;1c thu(}c vao rat nhfeu d(} tr~ Vi theta c6 mf> hinh tong quat ARCH(q) nhU' sau: ht =Yo + Y1U~-1 + Y2U~-2 + + YqU~-q (ht = a{) Ut-N(O, ht) Qua trinh tl;l' hoi qui phU'ung sai thay doi co dieu ki~n aU'c;rc khai quat hoa (Generalized AutoRegressive Conditional Heteroskedasticity -GARCH): 40 Do anh htrlrng cua ARCH c6 qua nhieu dQ tr~ c6 these lam ket qua u&c ltrgng giam so b~c t\l' do, d~n den vao nam 1995 Engle phat trien mo hinh GARCH (p, q) nhtr sau: Yt = P1 + P2Xt + ut ut'· N(O, ht) ht =Yo + Lr=l oiht-i + LJ=l YjU~-j (ht = at) 41 Ph\11\lc 2: Tien trinh MV hai phan Tien trinh Mean Reversion dU'C;rc C\J the bangphU'O'Dg trinh sau: Rt = xt + Wt Xt+l) = ( wtA.Xt+ Jl) + Zt+t (wt+1 (~) = (:t) + (~t ~) (~) + t-1 L(A~-i ~) zi + zt i=1 cov[(~)~(~)] = Vxx (As 1- A 0) ( -;1) (~t -1 ~) :~) (A~-i ~) 1-A2s 1-A2 Vxw ) SVww , Neus = t, q = ( Vxx Vxw Vxw) Vww cov(X5 + Ws,Xt + Wt) = (1 -A5 )(1 +At-s) _ A2 { Vxx + (1 +A) Vxwl + svww Neu gia toe bien thien gifra hai khoang theri gian reri r~c khong tU'O'Dg quan tuc Vxx + (1 +A) Vxw = 0, tien trinh chuyen d()ng gia se Ia m()t tien trinh ng~u nhien cov(R5 + Ws Rt + Wt) = s Vww 42 TAl LI~U THAM KIIAO Andrew, W L., & Craig, A M A Simple Specification Test of the Random Walk Hypothesis: Wharton School Rodney L White Center for Financial Research Andrew, W L., & Craig, A M A Simple Specification Test of the Random Walk Hypothesis: Wharton School Rodney L White Center for Financial Research Andrew, W L., & MacKinlay, A C (1989) Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test: National Bureau of Economic Research, Inc Annaert, J., & Hyfte, W V (2006) Long-Horizon Mean Reversion for the Brussels Stock Exchange: Evidence for the 19th Century: Ghent University, Faculty of Economics and Business Administration Ayres, I (1991) Back to basics: Regulating how corporations speak to the market Virginia Law Review, 77(5), 945-999 Halvers, R., Wu, Y., & Gilliland, E (2000) Mean Reversion across National Stock Markets and Parametric Contrarian Investment Strategies The journal of Finance, 55(2), 745-772 Bollerslev, Tim (1985) A conditionally heteroskedastic time series model for security prices and rates of return data, UCSD Discussion paper 85-32 Campbell, J (2000) Asset Pricing at the Millennium: Harvard University Department of Economics Campbell, J Y., & Mankiw, N G (1987) Are Output Fluctuations Transitory? 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