Qusos Ivsors Rsk Auds ad Prc Flucuao Asymmry Asa Sock Marks Wha s h sock rc flucuao asymmry? How o dscrb sm-quaavly? How o masur quaavly? Wha causs hs homo? Zhag Yu (Alc Dvso of Ecoomcs, School of Humas ad Socal Sccs, Nayag Tchologcal Uvrsy 1 Qualav dscro Th rc fallg sd s dffr from h rc rsg sd. Grally sakg, h fallg sd of rc s fasr ha h rsg sd. Tokyo, Jaa Hog Kog Shagha Cha Sgaor Mumba Ida *Daa from h://sg.fac.yahoo.com/. 3 4 Nw York, US Lodo, UK Two mhods of valuao Masur h rsg/fallg rags h sam m horzo. Masur h wag m o achv a fxd lvl of rur for h frs m. A coc from urbulc. I has b usd o sudy socks ad xchag ras*. I hls us g a dsrbuo of h wag m dd o oba a rdrmd rur for h frs m. Pars, Frac Frakfur, Grmay 5 *R.N. Maga ad H.E. Saly, Naur 383 (1996 587. I. Smos, M.H. Js, A. Johas, Eur. Phys. J. B 7 (00 583. M.H. Js, A. Johas, F. Pro I. Smos, Physca A 340 (004 678. 6 1
1A lvl of rur: Th wag m o achv hs rur for h frs m 0 3Wh 0 ravls alog h m axs, w ca g a dsrbuo of 1 3 a dsrbuo of Dsrbuo of ad Daly clos rcs of N5 from 04/01/1984 o 6/01/01. = 0.051, fv ms h avrag daly rc chag. 7 8 Daa Idx Locao Sar Ed Yars Grou 1: maur sock marks Asa N5 Tokyo, Jaa 1/4/1984 1/6/01 8 HSI Hog Kog 1/31/1986 1/6/01 5 SSEC Shagha Cha 19930104 1/0/01 19 Jaa US Frac US& Euro STI Sgaor 1/8/1987 1/6/01 4 KS11 7/1/1997 1/6/01 15 SENSEX Mumba Ida 7/1/1997 1/5/01 15 DJIA Nw York, US 10/1/198 1/6/01 84 FTSE Lodo, UK 4//1984 1/6/01 8 CAC40 Pars, Frac 3/1/1990 1/6/01 DAX Frakfur, Grmay 11/6/1990 1/6/01 Hog Kog UK Grmay 9 10 Grou : mrgg sock marks Cha Cocluso (1/3 I maur sock marks, wag m dsrbuos of h sam amou osv ad gav rurs show obvous asymmry. Whl mrgg marks Asa, such asymmry s ambguous. W d a quaav valuao o show a clarr cur of hs mrgg marks. Sgaor Ida 11 1
I s qual o h ra of rc fallg sd o rc rsg sd. Ecoomc uo Wh h asymmry valu s largr ha 1, mas ha rc fallg s fasr ha rc rsg. Wh h asymmry valu s smallr ha 1, mas ha rc rsg s fasr ha rc fallg. ŽƚŚĐŽŶĚŝƟŽŶƐƐŚŽǁ ƉƌŝĐĞŇƵĐƚƵĂƟŽŶĂƐLJŵŵĞƚƌLJ;ĂƐůŽŶŐĂƐтϭ Th asymmry valu s mor gral ha h dsrbuo fgur. Som dals fgur cao b cludd o h asymmry valu. 13 Idx Locao Yars Ex_au_lo Ex_au_ga ss Asa N5 Tokyo, Jaa 8 6.160 36.0453 1.3778 US& Euro HSI Hog Kog 5 9.7980 3.6644 1.096 SSEC Shagha Cha 19 35.184 33.5086 0.9539 STI Sgaor 4 1.1645 30.453 1.491 KS11 15 31.638 41.318 1.3034 SENSEX Mumba Ida 15 37.7361 35.4870 0.9404 DJIA Nw York, US 84 8.6853 9.9003 1.044 FTSE Lodo, UK 8 8.7841 39.603 1.3759 CAC40 Pars, Frac 3.8870 36.9811 1.548 DAX Frakfur, Grmay 4.4017 31.8657 1.3059 14 Idx Locao Prod Ex_au_loss Ex_au_ga SSEC Shagha Cha 4/1/1993 1/0/01 35.184 33.5086 0.9539 SENSEX Mumba Ida 7/1/1997 1/5/01 37.7361 35.4870 0.9404 DJIA Nw York, US 10/1/198 1/6/01 8.6853 9.9003 1.044 DJIA_1 198 1955 35.8885 31.6874 0.889 DJIA_ 1956 1983 7.0763 8.5445 1.054 DJIA_3 1984 01 30.5340 38.6419 1.655 15 Cocluso (/3 s of all sock marks (all 1 suor h graly of sock rc flucuao asymmry. I mos sock marks, h rc fallg s fasr ha h rc rsg. Whl Cha ad Ida, grally, h rc rsg s fasr ha h rc fallg, whch dcas hug dvlom oal. Th volvg asymmry valus of DJIA dffr m rods suggs ha h scal cas of Cha ad Ida may rrs a al sag of sock mark dvlom. 16 Wha causs hs asymmry? Ivsors bhavor Prosc hory* Pol s sychologcal rsoss o h qual amous of gas ad losss ar asymmrc. Pol ar mor ssv o losss ha o gas. Ca affc vsors rsk auds udr dffr vsm crcumsacs? W assum ca. Th, w d o vrfy by comarg our smulao wh mrcal aalyss. *D. Kahma, A. Tvrsky, Ecoomrca 47 (1979 63. 17 1 E ( V ( A mul-ag modl* D 1 E (, 1, (1, 1, 1 V ( E ( (1 r V ( 1 1 D, Ur ar: comar wh savg moy baks, wha you rdc o g by vsg socks. Lowr ar: valuao of rsk h fuur. x( ( ( x( k, ( 18 *W.A. Brock ad C.H. Homms, Joural of Ecoomc Dyamcs & Corol (1998135. k 3
Asymmrc rsk auds Numbr of rsky ass urchasd by vsors E ( (1 r 1, bv ( b : h rsk auds of vsors. I affcs rsk valuao. 1,( E ( (1 r 1 0 b 0,( E ( (1 r 1 0 Ecoomc uo 1 : ol ar mor ssv o rsk wh hy rdc a loss ad lss ssv o rsk wh hy rdc a ga. 0 1 : h oos suao. 19 Smulao Paramrs 100, 1, 0.6, r 4 1 10, 0.3, C 10, 0.8,, 0.5, 0.5,1,.3 0,0 0 Smulao Wh 1, hr s o asymmry. E E ( (1 r ( (1 r 1, bv ( V ( 1 Smulao Wh 1,...3 E ( (1 r bv ( 1 0.43,( 0 b.3,( 0 1 Pol ar mor (lss ssv o rsk wh hy rdc a loss (ga so hy wll ovrsma (udrsma h rsk, hrfor rduc (cras hr radg amou. Tha s, wh hy rdc a loss (ga hy wll sll (buy socks, bu sll lss (buy mor. Smlar wh mrcal daa aalyss rsul. Smulao Courxaml. Wh 0 1,.. 0.5 E ( (1 r 1, bv (,( 0 b 0.5,( 0 Oos wh mrcal daa aalyss rsul. Cocluso(3/3 Ivsors asymmrc rsk auds ca b a sourc of sock rc flucuao asymmry. Wh vsors rdc a loss h fuur, hy ar mor ssv o rsk. So hy wll ovrsma rsk ad d o sll lss socks. Wh vsors rdc a ga hy ar lss ssv o rsk. So hy wll udrsma rsk ad d o buy mor socks. 3 4 4
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