{"id":26243,"date":"2023-12-07T02:29:21","date_gmt":"2023-12-07T02:29:21","guid":{"rendered":"https:\/\/masterskills.org\/blog\/phan-phoi-chuan-normal-distribution-la-gi-phan-phoi-chuan-trong-tai-chinh.html"},"modified":"2023-12-22T11:30:18","modified_gmt":"2023-12-22T04:30:18","slug":"phan-phoi-chuan-normal-distribution-la-gi-phan-phoi-chuan-trong-tai-chinh","status":"publish","type":"post","link":"https:\/\/masterskills.org\/blog\/phan-phoi-chuan-normal-distribution-la-gi-phan-phoi-chuan-trong-tai-chinh.html","title":{"rendered":"Ph\u00e2n ph\u1ed1i chu\u00e2\u0309n (Normal Distribution) l\u00e0 g\u00ec? Ph\u00e2n ph\u1ed1i chu\u00e2\u0309n trong t\u00e0i ch\u00ednh"},"content":{"rendered":"
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Hi\u0300nh minh ho\u0323a. Ngu\u00f4\u0300n: 365datascience.com<\/i><\/p>\n<\/div>\n<\/div>\n

Ph\u00e2n ph\u1ed1i chu\u00e2\u0309n\u00a0<\/font><\/h2>\n

Kha\u0301i ni\u1ec7<\/span>m<\/b><\/p>\n

Ph\u00e2n ph\u1ed1i chu\u00e2\u0309n<\/b>\u00a0c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ph\u00e2n ph\u1ed1i Gaussian<\/b> trong ti\u00ea\u0301ng Anh la\u0300 Normal Distribution<\/b>.<\/p>\n

Ph\u00e2n ph\u1ed1i chu\u00e2\u0309n<\/b> l\u00e0 lo\u1ea1i ph\u00e2n ph\u1ed1i ph\u1ed5 bi\u1ebfn nh\u1ea5t hay \u0111\u01b0\u1ee3c du\u0300ng gi\u1ea3 \u0111\u1ecbnh trong ph\u00e2n t\u00edch ki\u0303 thu\u1eadt th\u1ecb tr\u01b0\u1eddng ch\u1ee9ng kho\u00e1n v\u00e0 trong c\u00e1c lo\u1ea1i ph\u00e2n t\u00edch th\u1ed1ng k\u00ea kh\u00e1c. Ph\u00e2n ph\u1ed1i chu\u1ea9n th\u00f4ng th\u01b0\u1eddng c\u00f3 hai tham s\u1ed1: gi\u00e1 tr\u1ecb trung b\u00ecnh v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n. \u0110\u1ed1i v\u1edbi ph\u00e2n ph\u1ed1i chu\u00e2\u0309n, 68% c\u00e1c quan s\u00e1t n\u1eb1m trong kho\u1ea3ng +\/- \u0111\u1ed9 l\u1ec7ch chu\u1ea9n c\u1ee7a gi\u00e1 tr\u1ecb trung b\u00ecnh, 95% n\u1eb1m trong +\/- hai l\u00e2\u0300n \u0111\u1ed9 l\u1ec7ch chu\u1ea9n v\u00e0 99,7% n\u1eb1m trong + – ba l\u00e2\u0300n \u0111\u1ed9 l\u1ec7ch chu\u1ea9n.<\/p>\n

M\u00f4 h\u00ecnh ph\u00e2n ph\u1ed1i chu\u00e2\u0309n\u00a0\u0111\u01b0\u1ee3c pha\u0301t tri\u00ea\u0309n b\u1edfi \u0110\u1ecbnh lu\u1ead<\/span>t gi\u1edbi h\u1ea1n trung t\u00e2m<\/b>. Li\u0301 thuy\u1ebft n\u00e0y n\u00f3i r\u1eb1ng c\u00e1c gi\u00e1 tr\u1ecb trung b\u00ecnh \u0111\u01b0\u1ee3c t\u00ednh to\u00e1n t\u1eeb c\u00e1c bi\u1ebfn ng\u1eabu nhi\u00ean \u0111\u1ed9c l\u1eadp va\u0300 gi\u1ed1ng h\u1ec7t nhau c\u00f3 ph\u00e2n ph\u1ed1i g\u00e2\u0300n v\u01a1\u0301i ph\u00e2n ph\u1ed1i\u00a0chu\u00e2\u0309n, b\u1ea5t k\u1ec3 lo\u1ea1i ph\u00e2n ph\u1ed1i cu\u0309a m\u00e2\u0303u ma\u0300 c\u00e1c bi\u1ebfn \u0111\u01b0\u1ee3c l\u1ea5y ra (mi\u1ec5n l\u00e0 n\u00f3 c\u00f3 ph\u01b0\u01a1ng sai h\u1eefu h\u1ea1n).\u00a0<\/p>\n

Ph\u00e2n ph\u1ed1i chu\u00e2\u0309n \u0111\u00f4i khi b\u1ecb nh\u1ea7m l\u1eabn v\u1edbi ph\u00e2n ph\u1ed1i \u0111\u1ed1i x\u1ee9ng. Ph\u00e2n ph\u1ed1i \u0111\u1ed1i x\u1ee9ng l\u00e0 m\u1ed9t ph\u00e2n ph\u00f4\u0301i trong \u0111\u00f3 m\u1ed9t \u0111\u01b0\u1eddng ph\u00e2n chia se\u0303 t\u1ea1o ra hai h\u00ecnh \u1ea3nh ph\u1ea3n chi\u1ebfu, nh\u01b0ng d\u1eef li\u1ec7u th\u1ef1c t\u1ebf c\u00f3 th\u1ec3 co\u0301 hai b\u01b0\u1edbu ho\u1eb7c nhi\u00ea\u0300u \u0111i\u00ea\u0309m nh\u00f4 l\u00ean tr\u00ean \u0111\u01b0\u1eddng cong h\u00ecnh chu\u00f4ng cu\u0309a ph\u00e2n ph\u1ed1i chu\u00e2\u0309n.<\/p>\n

\u0110\u1ed9 l\u1ec7<\/span>ch v\u00e0 \u0111\u1ed9<\/span> nho\u0323n<\/font><\/h3>\n

D\u1eef li\u1ec7u th\u1ef1c t\u1ebf hi\u1ebfm khi theo m\u1ed9t ph\u00e2n ph\u1ed1i chu\u00e2\u0309n<\/b> ho\u00e0n toa\u0300n. C\u00e1c h\u1ec7 s\u1ed1 \u0111\u1ed9 l\u1ec7<\/span>ch v\u00e0 \u0111\u1ed9<\/span> nho\u0323n \u0111o l\u01b0\u1eddng m\u1ee9c \u0111\u1ed9 kh\u00e1c bi\u1ec7<\/span>t c\u1ee7a m\u1ed9t ph\u00e2n ph\u1ed1i nh\u1ea5t \u0111\u1ecbnh so v\u1edbi ph\u00e2n ph\u1ed1i chu\u00e2\u0309n. \u0110\u1ed9 l\u1ec7ch \u0111o l\u01b0\u1eddng t\u00ednh \u0111\u1ed1i x\u1ee9ng c\u1ee7a m\u1ed9t ph\u00e2n ph\u1ed1i. Ph\u00e2n ph\u1ed1i chu\u1ea9n l\u00e0 \u0111\u1ed1i x\u1ee9ng v\u00e0 c\u00f3 \u0111\u1ed9 l\u1ec7ch b\u1eb1ng kh\u00f4ng. N\u1ebfu ph\u00e2n ph\u1ed1i c\u1ee7a t\u1eadp d\u1eef li\u1ec7u c\u00f3 \u0111\u1ed9 l\u1ec7ch nh\u1ecf h\u01a1n 0 ho\u1eb7c \u0111\u1ed9 l\u1ec7ch \u00e2m, th\u00ec \u0111u\u00f4i b\u00ean tr\u00e1i c\u1ee7a ph\u00e2n ph\u1ed1i d\u00e0i h\u01a1n \u0111u\u00f4i b\u00ean ph\u1ea3i; \u0111\u1ed9 l\u1ec7ch d\u01b0\u01a1ng ng\u1ee5 \u00fd r\u1eb1ng \u0111u\u00f4i b\u00ean ph\u1ea3i c\u1ee7a ph\u00e2n ph\u1ed1i d\u00e0i h\u01a1n \u0111u\u00f4i b\u00ean tr\u00e1i.<\/p>\n

\u0110\u1ed9<\/span> nho\u0323n \u0111o \u0111\u1ed9 d\u00e0y c\u1ee7a \u0111u\u00f4i ph\u00e2n ph\u1ed1i so v\u01a1\u0301i \u0111u\u00f4i c\u1ee7a ph\u00e2n ph\u1ed1i chu\u00e2\u0309n. Ph\u00e2n ph\u1ed1i v\u1edbi \u0111u\u00f4i l\u1edbn th\u1ec3 hi\u1ec7n d\u1eef li\u1ec7u \u01a1\u0309 \u0111u\u00f4i ph\u00e2n ph\u00f4\u0301i v\u01b0\u1ee3t qu\u00e1 d\u01b0\u0303 li\u1ec7<\/span>u \u01a1\u0309 \u0111u\u00f4i ph\u00e2n ph\u1ed1i chu\u00e2\u0309n (v\u00ed d\u1ee5 nhi\u00ea\u0300n h\u01a1n n\u0103m \u0111\u1ed9 l\u1ec7ch chu\u1ea9n so v\u1edbi gi\u00e1 tr\u1ecb trung b\u00ecnh). C\u00e1c ph\u00e2n ph\u1ed1i c\u00f3 \u0111\u1ed9<\/span> nho\u0323n th\u1ea5p cho th\u00e2\u0301y t\u1ead<\/span>p d\u1eef li\u1ec7u co\u0301 \u0111i\u00ea\u0309m c\u01b0\u0323c tri\u0323 th\u00e2\u0301p h\u01a1n c\u00e1c b\u1ea3n ph\u00e2n ph\u1ed1i chu\u00e2\u0309n.\u00a0<\/p>\n

Ph\u00e2n ph\u1ed1i chu\u00e2\u0309n c\u00f3 \u0111\u1ed9<\/span> nho\u0323n b\u0103\u0300ng ba, \u0111i\u1ec1u n\u00e0y cho th\u1ea5y ph\u00e2n ph\u1ed1i kh\u00f4ng c\u00f3 \u0111u\u00f4i m\u1ead<\/span>p hay m\u1ecfng. Do \u0111\u00f3, n\u1ebfu m\u1ed9t ph\u00e2n ph\u1ed1i quan s\u00e1t \u0111\u01b0\u01a1\u0323c c\u00f3 \u0111\u1ed9 nho\u0323n l\u1edbn h\u01a1n ba, ph\u00e2n ph\u1ed1i \u0111\u01b0\u1ee3c cho l\u00e0 c\u00f3 \u0111u\u00f4i m\u1ead<\/span>p khi so s\u00e1nh v\u1edbi ph\u00e2n ph\u1ed1i chu\u00e2\u0309n. N\u1ebfu ph\u00e2n ph\u1ed1i c\u00f3 \u0111\u1ed9<\/span> nho\u0323n nh\u1ecf h\u01a1n ba, n\u00f3 \u0111\u01b0\u1ee3c cho l\u00e0 c\u00f3 \u0111u\u00f4i m\u1ecfng khi so s\u00e1nh v\u1edbi ph\u00e2n ph\u1ed1i chu\u00e2\u0309n.<\/p>\n

Ph\u00e2n ph\u1ed1i chu\u00e2\u0309n trong t\u00e0i ch\u00ednh<\/font><\/h3>\n

Gi\u1ea3 \u0111\u1ecbnh v\u1ec1 ph\u00e2n ph\u1ed1i chu\u00e2\u0309n \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng cho gi\u00e1 t\u00e0i s\u1ea3n c\u0169ng nh\u01b0 h\u00e0nh \u0111\u1ed9ng gi\u00e1<\/b>. C\u00e1c nha\u0300 giao di\u0323ch c\u00f3 th\u1ec3 v\u1ebd c\u00e1c \u0111i\u1ec3m gi\u00e1 theo th\u1eddi gian \u0111\u1ec3 ph\u00f9 h\u1ee3p v\u1edbi h\u00e0nh \u0111\u1ed9ng gi\u00e1 g\u1ea7n \u0111\u00e2y th\u00e0nh m\u1ed9t ph\u00e2n ph\u1ed1i chu\u00e2\u0309n. H\u00e0nh \u0111\u1ed9ng gi\u00e1 ca\u0300ng di chuy\u1ec3n xa gi\u00e1 tr\u1ecb trung b\u00ecnh, c\u00e0ng c\u00f3 nhi\u1ec1u kh\u1ea3 n\u0103ng m\u1ed9t t\u00e0i s\u1ea3n b\u1ecb \u0111\u1ecbnh gi\u00e1 qua\u0301 cao ho\u0103\u0323c qua\u0301 th\u1ea5p. Nha\u0300 giao di\u0323ch c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng \u0111\u1ed9 l\u1ec7ch chu\u1ea9n \u0111\u1ec3 xem xe\u0301t c\u00e1c giao d\u1ecbch ti\u1ec1m n\u0103ng.\u00a0<\/p>\n

T\u01b0\u01a1ng t\u1ef1, nhi\u1ec1u li\u0301 thuy\u1ebft th\u1ed1ng k\u00ea c\u1ed1 g\u1eafng m\u00f4 h\u00ecnh h\u00f3a gi\u00e1 t\u00e0i s\u1ea3n theo gi\u1ea3 \u0111\u1ecbnh r\u1eb1ng ch\u00fang tu\u00e2n theo ph\u00e2n ph\u1ed1i chu\u00e2\u0309n<\/b>. Trong th\u1ef1c t\u1ebf, ph\u00e2n ph\u1ed1i gi\u00e1 c\u00f3 xu h\u01b0\u1edbng c\u00f3 \u0111u\u00f4i m\u1ead<\/span>p, v\u00e0 do \u0111\u00f3, chu\u0301ng c\u00f3 \u0111\u1ed9<\/span> nho\u0323n l\u1edbn h\u01a1n ba. C\u00e1c t\u00e0i s\u1ea3n nh\u01b0 v\u1eady c\u00f3 bi\u1ebfn \u0111\u1ed9ng gi\u00e1 l\u1edbn h\u01a1n ba \u0111\u1ed9 l\u1ec7ch chu\u1ea9n, v\u01b0\u1ee3t qu\u00e1 m\u1ee9c gia\u0301 tri\u0323 trung b\u00ecnh v\u01a1\u0301i t\u00e2\u0300n su\u00e2\u0301t th\u01b0\u1eddng xuy\u00ean h\u01a1n d\u1ef1 ki\u1ebfn theo gi\u1ea3 \u0111\u1ecbnh ph\u00e2n ph\u1ed1i chu\u00e2\u0309n. Ngay c\u1ea3 khi m\u1ed9t t\u00e0i s\u1ea3n \u0111\u00e3 t\u00f4\u0300n ta\u0323i m\u1ed9t th\u1eddi gian d\u00e0i va\u0300 ph\u00f9 h\u1ee3p v\u1edbi ph\u00e2n ph\u1ed1i chu\u00e2\u0309n thi\u0300 v\u00e2\u0303n kh\u00f4ng c\u00f3 g\u00ec \u0111\u1ea3m b\u1ea3o r\u1eb1ng hi\u1ec7u su\u1ea5t trong qu\u00e1 kh\u1ee9 th\u1ef1c s\u1ef1 d\u01b0\u0323u ba\u0301o chi\u0301nh xa\u0301c cho t\u0103ng tr\u01b0\u01a1\u0309ng trong t\u01b0\u01a1ng lai.<\/p>\n

Ca\u0301c y\u0301 chi\u0301nh<\/font><\/h3>\n

– Ph\u00e2n ph\u1ed1i chu\u00e2\u0309n<\/b> l\u00e0 thu\u1eadt ng\u1eef cho ph\u00e2n ph\u00f4\u0301i x\u00e1c su\u1ea5t co\u0301 \u0111\u01b0\u1eddng cong hi\u0300nh chu\u00f4ng.<\/p>\n

– Ph\u00e2n ph\u1ed1i chu\u00e2\u0309n l\u00e0 ph\u00e2n ph\u1ed1i \u0111\u1ed1i x\u1ee9ng, nh\u01b0ng kh\u00f4ng ph\u1ea3i t\u1ea5t c\u1ea3 c\u00e1c ph\u00e2n ph\u1ed1i \u0111\u1ed1i x\u1ee9ng l\u00e0 ph\u00e2n ph\u00f4\u0301i chu\u00e2\u0309n.<\/p>\n

– Trong th\u1ef1c t\u1ebf, h\u1ea7u h\u1ebft c\u00e1c ph\u00e2n ph\u1ed1i gi\u00e1 kh\u00f4ng pha\u0309i la\u0300 ph\u00e2n ph\u00f4\u0301i chu\u00e2\u0309n ho\u00e0n to\u00e0n.<\/p>\n

(Theo Investopedia<\/i>)<\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

\n Ph\u00e2n ph\u1ed1i chu\u00e2\u0309n (ti\u00ea\u0301ng Anh: Normal Distribution) l\u00e0 ph\u00e2n ph\u1ed1i x\u00e1c su\u1ea5t \u0111\u1ed1i x\u1ee9ng quanh gi\u00e1 tr\u1ecb trung b\u00ecnh, ca\u0301c d\u1eef li\u1ec7u g\u1ea7n gi\u00e1 tr\u1ecb trung b\u00ecnh xu\u00e2\u0301t hi\u00ea\u0323n th\u01b0\u1eddng xuy\u00ean h\u01a1n so v\u1edbi d\u1eef li\u1ec7u \u1edf xa gi\u00e1 tr\u1ecb trung b\u00ecnh.\n <\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[414],"tags":[],"_links":{"self":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/26243"}],"collection":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/comments?post=26243"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/26243\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=26243"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=26243"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=26243"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}