{"id":26282,"date":"2023-12-07T02:30:14","date_gmt":"2023-12-07T02:30:14","guid":{"rendered":"https:\/\/masterskills.org\/blog\/hiep-phuong-sai-covariance-la-gi-cong-thuc-tinh-hiep-phuong-sai.html"},"modified":"2023-12-22T14:42:49","modified_gmt":"2023-12-22T07:42:49","slug":"hiep-phuong-sai-covariance-la-gi-cong-thuc-tinh-hiep-phuong-sai","status":"publish","type":"post","link":"https:\/\/masterskills.org\/blog\/hiep-phuong-sai-covariance-la-gi-cong-thuc-tinh-hiep-phuong-sai.html","title":{"rendered":"Hi\u1ec7p ph\u01b0\u01a1ng sai (Covariance) l\u00e0 g\u00ec? C\u00f4ng th\u01b0\u0301c ti\u0301nh hi\u00ea\u0323p ph\u01b0\u01a1ng sai"},"content":{"rendered":"
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Hi\u0300nh minh ho\u0323a. Ngu\u00f4\u0300n: Hadrienj.github.io<\/i><\/p>\n<\/div>\n<\/div>\n

Hi\u1ec7p ph\u01b0\u01a1ng sai<\/font><\/h2>\n

Kha\u0301i ni\u00ea\u0323m<\/b><\/p>\n

Hi\u1ec7p ph\u01b0\u01a1ng sai<\/b> trong ti\u00ea\u0301ng Anh la\u0300 Covariance<\/b>.<\/p>\n

Hi\u1ec7p ph\u01b0\u01a1ng sai<\/b> \u0111o l\u01b0\u1eddng m\u1ed1i quan h\u1ec7 \u0111\u1ecbnh h\u01b0\u1edbng gi\u1eefa l\u1ee3i nhu\u1eadn tr\u00ean hai t\u00e0i s\u1ea3n. Hi\u1ec7p ph\u01b0\u01a1ng sai d\u01b0\u01a1ng c\u00f3 ngh\u0129a l\u00e0 l\u1ee3i nhu\u1eadn cu\u0309a hai t\u00e0i s\u1ea3n di chuy\u1ec3n c\u00f9ng nhau trong khi hi\u1ec7p ph\u01b0\u01a1ng sai \u00e2m c\u00f3 ngh\u0129a l\u00e0 ch\u00fang di chuy\u1ec3n ng\u01b0\u1ee3c l\u1ea1i.\u00a0<\/p>\n

Hi\u1ec7p ph\u01b0\u01a1ng sai \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00e1ch ph\u00e2n t\u00edch c\u00e1c bi\u00ea\u0301n \u0111\u1ed9ng v\u00ea\u0300 la\u0303i su\u00e2\u0301t (\u0111\u1ed9 l\u1ec7ch chu\u1ea9n\u00a0so v\u1edbi l\u1ee3i nhu\u1eadn k\u00ec<\/span> v\u1ecdng) ho\u1eb7c b\u1eb1ng c\u00e1ch nh\u00e2n m\u1ed1i t\u01b0\u01a1ng quan gi\u1eefa hai bi\u1ebfn v\u1edbi \u0111\u1ed9 l\u1ec7ch chu\u1ea9n c\u1ee7a t\u1eebng bi\u1ebfn.<\/p>\n

Hi\u1ec3u v\u00ea\u0300 hi\u1ec7p ph\u01b0\u01a1ng sai<\/font><\/h3>\n

Hi\u1ec7p ph\u01b0\u01a1ng sai <\/b>xa\u0301c \u0111i\u0323nh c\u00e1c gi\u00e1 tr\u1ecb trung b\u00ecnh c\u1ee7a hai bi\u1ebfn di chuy\u1ec3n c\u00f9ng nhau nh\u01b0 th\u00ea\u0301 na\u0300o. N\u1ebfu l\u1ee3i nhu\u1eadn c\u1ee7a c\u1ed5 phi\u1ebfu A t\u0103ng b\u1ea5t c\u1ee9 khi n\u00e0o l\u1ee3i nhu\u1eadn c\u1ee7a c\u1ed5 phi\u1ebfu B t\u0103ng v\u00e0 hi\u00ea\u0323n t\u01b0\u01a1\u0323ng t\u01b0\u01a1ng t\u1ef1 cu\u0303ng xa\u0309y ra khi l\u1ee3i nhu\u1eadn c\u1ee7a m\u1ed7i c\u1ed5 phi\u1ebfu gi\u1ea3m, th\u00ec c\u00e1c c\u1ed5 phi\u1ebfu n\u00e0y \u0111\u01b0\u1ee3c cho l\u00e0 c\u00f3 hi\u1ec7p ph\u01b0\u01a1ng sai d\u01b0\u01a1ng. Trong t\u00e0i ch\u00ednh, hi\u1ec7p ph\u01b0\u01a1ng sai \u0111\u01b0\u1ee3c t\u00ednh to\u00e1n \u0111\u1ec3 gi\u00fap \u0111a d\u1ea1ng h\u00f3a n\u1eafm gi\u1eef c\u00f4\u0309 phi\u00ea\u0301u.<\/p>\n

Khi m\u1ed9t nh\u00e0 ph\u00e2n t\u00edch c\u00f3 m\u1ed9t t\u1eadp h\u1ee3p d\u1eef li\u1ec7u, m\u1ed9t c\u1eb7p gi\u00e1 tr\u1ecb x v\u00e0 y, hi\u1ec7p ph\u01b0\u01a1ng sai c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng 5 bi\u1ebfn t\u1eeb d\u1eef li\u1ec7u \u0111\u00f3. C\u00f4ng th\u01b0\u0301c ti\u0301nh la\u0300:<\/p>\n

Cov (x, y) = SUM [(xi<\/sub> – xm<\/sub>) * (yi<\/sub> – ym<\/sub>)] \/ (n – 1)
<\/b><\/p>\n

xi<\/sub> = m\u1ed9t gi\u00e1 tr\u1ecb x \u0111\u00e3 cho trong t\u1eadp d\u1eef li\u1ec7u<\/p>\n

xm<\/sub> = gi\u00e1 tr\u1ecb trung b\u00ecnh ho\u1eb7c trung b\u00ecnh c\u1ee7a c\u00e1c gi\u00e1 tr\u1ecb x<\/p>\n

yi<\/sub> = gi\u00e1 tr\u1ecb y trong t\u1eadp d\u1eef li\u1ec7u t\u01b0\u01a1ng \u1ee9ng v\u1edbi xi<\/sub><\/p>\n

ym<\/sub> = gi\u00e1 tr\u1ecb trung b\u00ecnh ho\u1eb7c trung b\u00ecnh c\u1ee7a c\u00e1c gi\u00e1 tr\u1ecb y<\/p>\n

n = s\u1ed1 \u0111i\u1ec3m d\u1eef li\u1ec7u<\/p>\n

\u1ee8ng d\u1ee5ng hi\u1ec7p ph\u01b0\u01a1ng sai<\/font><\/h3>\n

Hi\u1ec7p ph\u01b0\u01a1ng sai c\u00f3 c\u00e1c \u1ee9ng d\u1ee5ng quan tr\u1ecdng trong t\u00e0i ch\u00ednh v\u00e0 l\u00ed<\/span> thuy\u1ebft danh m\u1ee5c \u0111\u1ea7u t\u01b0 hi\u1ec7n \u0111\u1ea1i<\/b>. V\u00ed d\u1ee5, trong m\u00f4 h\u00ecnh \u0111\u1ecbnh gi\u00e1 t\u00e0i s\u1ea3n v\u1ed1n (CAPM)<\/b>, \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ednh l\u1ee3i nhu\u1eadn k\u00ec<\/span> v\u1ecdng c\u1ee7a m\u1ed9t t\u00e0i s\u1ea3n, hi\u1ec7p ph\u01b0\u01a1ng sai gi\u1eefa ch\u01b0\u0301ng khoa\u0301n v\u00e0 th\u1ecb tr\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong \u0111\u00ea\u0309 ti\u0301nh m\u1ed9t trong nh\u01b0\u0303ng bi\u1ebfn ch\u00ednh c\u1ee7a m\u00f4 h\u00ecnh, beta (\u03b2).\u00a0<\/b><\/p>\n

Trong CAPM, beta \u0111o l\u01b0\u1eddng m\u1ee9c \u0111\u1ed9 bi\u1ebfn \u0111\u1ed9ng ho\u1eb7c r\u1ee7i ro h\u1ec7 th\u1ed1ng c\u1ee7a ch\u1ee9ng kho\u00e1n so v\u1edbi th\u1ecb tr\u01b0\u1eddng n\u00f3i chung, \u0111\u00f3 l\u00e0 m\u1ed9t vi\u0301 du\u0323 th\u1ef1c t\u1ebf \u01b0\u0301ng du\u0323ng hi\u1ec7p ph\u01b0\u01a1ng sai \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 m\u1ee9c \u0111\u1ed9 r\u1ee7i ro c\u1ee7a nh\u00e0 \u0111\u1ea7u t\u01b0 \u0111\u1ed1i v\u1edbi m\u1ed9t ch\u1ee9ng kho\u00e1n c\u1ee5 th\u1ec3.<\/p>\n

Trong khi \u0111\u00f3, l\u00ed<\/span> thuy\u1ebft danh m\u1ee5c \u0111\u1ea7u t\u01b0 s\u1eed d\u1ee5ng hi\u1ec7p ph\u01b0\u01a1ng sai \u0111\u1ec3 gi\u1ea3m thi\u1ec3u r\u1ee7i ro t\u1ed5ng th\u1ec3 c\u1ee7a danh m\u1ee5c \u0111\u1ea7u t\u01b0 b\u1eb1ng c\u00e1ch loa\u0323i bo\u0309 s\u1ef1 bi\u1ebfn \u0111\u1ed9ng th\u00f4ng qua \u0111a d\u1ea1ng h\u00f3a th\u00f4ng tin t\u01b0\u0300 hi\u1ec7p ph\u01b0\u01a1ng sai.<\/p>\n

V\u00ed d\u1ee5 v\u1ec1 hi\u1ec7p ph\u01b0\u01a1ng sai<\/font><\/h3>\n

Gi\u1ea3 s\u1eed m\u1ed9t nh\u00e0 ph\u00e2n t\u00edch trong m\u1ed9t c\u00f4ng ty c\u00f3 b\u1ed9 d\u1eef li\u1ec7u 5 qu\u00ed<\/span> cho th\u1ea5y m\u1ee9c t\u0103ng tr\u01b0\u1edfng t\u1ed5ng s\u1ea3n ph\u1ea9m qu\u1ed1c n\u1ed9i (GDP) h\u00e0ng qu\u00ed<\/span> theo t\u1ef7 l\u1ec7 ph\u1ea7n tr\u0103m (x) v\u00e0 t\u0103ng tr\u01b0\u1edfng d\u00f2ng s\u1ea3n ph\u1ea9m m\u1edbi c\u1ee7a c\u00f4ng ty theo t\u1ef7 l\u1ec7 ph\u1ea7n tr\u0103m (y). T\u1eadp d\u1eef li\u1ec7u c\u00f3 th\u1ec3 tr\u00f4ng nh\u01b0 sau:<\/p>\n

Q1: x = 2, y = 10<\/p>\n

Q2: x = 3, y = 14<\/p>\n

Q3: x = 2,7, y = 12<\/p>\n

Q4: x = 3,2, y = 15<\/p>\n

Q5: x = 4,1, y = 20<\/p>\n

Gi\u00e1 tr\u1ecb x trung b\u00ecnh b\u1eb1ng 3 v\u00e0 gi\u00e1 tr\u1ecb y trung b\u00ecnh b\u1eb1ng 14,2. \u0110\u1ec3 t\u00ednh hi\u1ec7p ph\u01b0\u01a1ng sai, ti\u0301nh t\u1ed5ng c\u00e1c gi\u00e1 tr\u1ecb xi <\/sub>tr\u1eeb \u0111i gi\u00e1 tr\u1ecb x trung b\u00ecnh, nh\u00e2n v\u1edbi c\u00e1c gi\u00e1 tr\u1ecb yi<\/sub> tr\u1eeb \u0111i c\u00e1c gi\u00e1 tr\u1ecb y trung b\u00ecnh sau \u0111o\u0301 chia cho (n-1), nh\u01b0 sau:<\/p>\n

Cov (x, y) = ((2 – 3) x (10 – 14.2) + (3 – 3) x (14 – 14.2) + … (4.1 – 3) x (20 – 14.2)) \/ 4 = (4.2 + 0 + 0,66 + 0,16 + 6,38) \/ 4 = 2,85<\/p>\n

Khi k\u00ea\u0301t qua\u0309 cho\u00a0hi\u1ec7p ph\u01b0\u01a1ng sai<\/b>\u00a0d\u01b0\u01a1ng, nh\u00e0 ph\u00e2n t\u00edch c\u00f3 th\u1ec3 n\u00f3i r\u1eb1ng s\u1ef1 t\u0103ng tr\u01b0\u1edfng c\u1ee7a d\u00f2ng s\u1ea3n ph\u1ea9m m\u1edbi c\u1ee7a c\u00f4ng ty c\u00f3 m\u1ed1i quan h\u1ec7 t\u00edch c\u1ef1c v\u1edbi t\u0103ng tr\u01b0\u1edfng GDP h\u00e0ng qu\u00ed<\/span>.<\/p>\n

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

\n Hi\u1ec7p ph\u01b0\u01a1ng sai (ti\u00ea\u0301ng Anh: Covariance) \u0111o l\u01b0\u1eddng m\u1ed1i quan h\u1ec7 theo h\u01b0\u1edbng gi\u1eefa l\u1ee3i nhu\u1eadn tr\u00ean hai t\u00e0i s\u1ea3n.\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\/26282"}],"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=26282"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/26282\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=26282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=26282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=26282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}