{"id":31496,"date":"2023-12-07T10:41:15","date_gmt":"2023-12-07T10:41:15","guid":{"rendered":"https:\/\/masterskills.org\/blog\/do-co-gian-maculay-macaulay-duration-la-gi-cong-thuc-xac-dinh.html"},"modified":"2023-12-23T08:18:02","modified_gmt":"2023-12-23T01:18:02","slug":"do-co-gian-maculay-macaulay-duration-la-gi-cong-thuc-xac-dinh","status":"publish","type":"post","link":"https:\/\/masterskills.org\/blog\/do-co-gian-maculay-macaulay-duration-la-gi-cong-thuc-xac-dinh.html","title":{"rendered":"\u0110\u1ed9 co gi\u00e3n Maculay (Macaulay Duration) l\u00e0 g\u00ec? C\u00f4ng th\u1ee9c x\u00e1c \u0111\u1ecbnh"},"content":{"rendered":"
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H\u00ecnh minh h\u1ecda<\/p>\n<\/div>\n<\/div>\n

\u0110\u1ed9 co gi\u00e3n Maculay (Macaulay Duration)<\/font><\/h2>\n

\u0110\u1ecbnh ngh\u0129a<\/b><\/p>\n

\u0110\u1ed9 co gi\u00e3n Maculay<\/b> trong ti\u1ebfng Anh l\u00e0 Macaulay Duration<\/b>. \u0110\u1ed9 co gi\u00e3n Maculay<\/i> hay th\u1eddi l\u01b0\u1ee3ng Macaulay<\/i> l\u00e0 th\u1eddi h\u1ea1n\u00a0trung b\u00ecnh c\u00f3 tr\u1ecdng s\u1ed1\u00a0\u0111\u1ebfn ng\u00e0y \u0111\u00e1o h\u1ea1n\u00a0c\u1ee7a d\u00f2ng ti\u1ec1n t\u1eeb\u00a0tr\u00e1i phi\u1ebfu.\u00a0Tr\u1ecdng s\u1ed1 c\u1ee7a m\u1ed7i d\u00f2ng ti\u1ec1n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1eb1ng c\u00e1ch chia gi\u00e1 tr\u1ecb hi\u1ec7n t\u1ea1i c\u1ee7a d\u00f2ng ti\u1ec1n cho gi\u00e1.<\/p>\n

B\u1ea3n ch\u1ea5t v\u00e0 v\u00ed d\u1ee5<\/font><\/h3>\n

– \u00dd t\u01b0\u1edfng \u0111\u1ea7u ti\u00ean v\u1ec1 duration c\u1ee7a tr\u00e1i phi\u1ebfu \u0111\u01b0\u1ee3c \u0111\u01b0a ra b\u1edfi m\u1ed9t nh\u00e0 kinh t\u1ebf h\u1ecdc t\u00ean l\u00e0 Frederick Macaulay v\u00e0o \u0111\u1ea7u th\u1ebf k\u1ef7 20, t\u1ee9c l\u00e0 ch\u1ec9 m\u1edbi g\u1ea7n \u0111\u00e2y. \u00dd t\u01b0\u1edfng c\u1ee7a \u00f4ng l\u00e0 t\u00ednh to\u00e1n kho\u1ea3ng th\u1eddi gian trung b\u00ecnh \u0111\u1ec3 m\u1ed9t tr\u00e1i ch\u1ee7 (ng\u01b0\u1eddi n\u1eafm gi\u1eef tr\u00e1i phi\u1ebfu) nh\u1eadn \u0111\u01b0\u1ee3c d\u00f2ng ti\u1ec1n t\u1eeb tr\u00e1i phi\u1ebfu.<\/p>\n

– M\u1ed7i d\u00f2ng ti\u1ec1n \u0111\u01b0\u1ee3c chi\u1ebft kh\u1ea5u v\u1ec1 gi\u00e1 tr\u1ecb hi\u1ec7n t\u1ea1i, v\u00e0 chia cho gi\u00e1 tr\u1ecb hi\u1ec7n t\u1ea1i c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c d\u00f2ng ti\u1ec1n \u0111\u1ec3 l\u1ea5y tr\u1ecdng s\u1ed1. Sau \u0111\u00f3 l\u1ea5y tr\u1ecdng s\u1ed1 n\u00e0y nh\u00e2n v\u1edbi th\u1eddi \u0111i\u1ec3m b\u1ea1n nh\u1eadn \u0111\u01b0\u1ee3c d\u00f2ng ti\u1ec1n, c\u1ed9ng t\u1ed5ng c\u00e1c k\u1ebft qu\u1ea3 n\u00e0y v\u00e0o, ch\u00fang ta \u0111\u01b0\u1ee3c \u0111\u1ed9 co gi\u00e3n Macaulay hay Macaulay Duration.<\/p>\n

– Macaulay Duration l\u00e0 \u0111\u1ea1i l\u01b0\u1ee3ng \u0111o l\u01b0\u1eddng th\u1eddi gian, v\u00e0 \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng n\u0103m.<\/p>\n

V\u00ed d\u1ee5 minh h\u1ecda<\/b><\/p>\n

M\u1ed9t tr\u00e1i phi\u1ebfu 5 n\u0103m, tr\u00e1i t\u1ee9c 6% tr\u1ea3 \u0111\u1ecbnh k\u00ec<\/span> h\u00e0ng n\u0103m, m\u1ec7nh gi\u00e1 $1.000 v\u00e0 m\u1ee9c l\u00e3i su\u1ea5t hi\u1ec7n t\u1ea1i (YTM) l\u00e0 4%.<\/p>\n

Gi\u00e1 tr\u1ecb c\u1ee7a tr\u00e1i phi\u1ebfu n\u00e0y l\u00e0:<\/p>\n

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Macaulay duration c\u1ee7a tr\u00e1i phi\u1ebfu n\u00e0y l\u00e0:<\/p>\n

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N\u00f3i c\u00e1ch kh\u00e1c, nh\u00e0 \u0111\u1ea7u t\u01b0 m\u1ea5t trung b\u00ecnh\u00a04,49 n\u0103m\u00a0\u0111\u1ec3 nh\u1eadn \u0111\u01b0\u1ee3c h\u1ebft t\u1ea5t c\u1ea3 c\u00e1c d\u00f2ng ti\u1ec1n.<\/p>\n

C\u00f4ng th\u1ee9c t\u1ed5ng qu\u00e1t c\u1ee7a Macaulay duration<\/p>\n

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\u01afu \u0111i\u1ec3m<\/font><\/h3>\n

\u01afu \u0111i\u1ec3m c\u1ee7a Macaulay duration l\u00e0 c\u00f3 th\u1ec3 d\u1ec5 d\u00e0ng th\u1ea5y vi\u1ec7c thay \u0111\u1ed5i d\u1eef li\u1ec7u \u0111\u1ea7u\u00a0v\u00e0o \u1ea3nh h\u01b0\u1edfng t\u1edbi k\u1ebft qu\u1ea3 nh\u01b0 th\u1ebf n\u00e0o, v\u00e0 tuy\u1ec7t v\u1eddi nh\u1ea5t l\u00e0 nh\u1eefng thay \u0111\u1ed5i n\u00e0y c\u00f3\u00a0\u1ea3nh h\u01b0\u1edfng gi\u1ed1ng h\u1ec7t\u00a0t\u1edbi\u00a0modified duration\u00a0v\u00e0\u00a0effective duration.<\/p>\n

* S\u1ef1 thay \u0111\u1ed5i c\u00e1c d\u1eef li\u1ec7u \u0111\u1ea7u v\u00e0o<\/b><\/p>\n

(1) Th\u1eddi gian \u0111\u00e1o h\u1ea1n (time to maturity)<\/i><\/p>\n

Khi th\u1eddi gian \u0111\u00e1o h\u1ea1n\u00a0t\u0103ng l\u00ean, Macaulay duration\u00a0t\u0103ng l\u00ean. \u0110i\u1ec1u n\u00e0y l\u00e0 \u0111\u01b0\u01a1ng nhi\u00ean b\u1ea1n s\u1ebd ph\u1ea3i \u0111\u1ee3i l\u00e2u h\u01a1n \u0111\u1ec3 nh\u1eadn ti\u1ec1n t\u1eeb tr\u00e1i phi\u1ebfu 30 n\u0103m, so v\u1edbi tr\u00e1i phi\u1ebfu 10 n\u0103m.\u00a0<\/p>\n

(2) Tr\u00e1i t\u1ee9c (coupon rate)<\/i><\/p>\n

Khi tr\u00e1i t\u1ee9c\u00a0t\u0103ng l\u00ean,\u00a0Macaulay duration\u00a0gi\u1ea3m \u0111i.<\/p>\n

N\u1ebfu tr\u00e1i t\u1ee9c l\u00e0 0%, Macaulay duration s\u1ebd b\u1eb1ng \u0111\u00fang th\u1eddi gian \u0111\u00e1o h\u1ea1n c\u1ee7a tr\u00e1i phi\u1ebfu, v\u00ec 100% d\u00f2ng ti\u1ec1n b\u1ea1n nh\u1eadn \u0111\u01b0\u1ee3c l\u00e0 t\u1ea1i th\u1eddi \u0111i\u1ec3m \u0111\u00e1o h\u1ea1n c\u1ee7a tr\u00e1i phi\u1ebfu. N\u1ebfu tr\u00e1i t\u1ee9c l\u1edbn h\u01a1n 0%, th\u00ec b\u1ea1n s\u1ebd nh\u1eadn l\u1ea1i \u0111\u01b0\u1ee3c m\u1ed9t \u00edt ti\u1ec1n tr\u01b0\u1edbc khi tr\u00e1i phi\u1ebfu \u0111\u00e1o h\u1ea1n, do \u0111\u00f3 th\u1eddi gian trung b\u00ecnh \u0111\u1ec3 nh\u1eadn l\u1ea1i to\u00e0n b\u1ed9 ti\u1ec1n s\u1ebd ng\u1eafn h\u01a1n th\u1eddi gian \u0111\u00e1o h\u1ea1n.\u00a0<\/p>\n

V\u00ec l\u00fd do n\u00e0y, khi tr\u00e1i t\u1ee9c t\u0103ng l\u00ean, Macaulay duration gi\u1ea3m \u0111i.\u00a0<\/p>\n

(3)\u00a0L\u1ee3i su\u1ea5t \u0111\u00e1o h\u1ea1n\u00a0(Yield To Maturity \u2013 YTM)<\/i><\/p>\n

Khi YTM\u00a0t\u0103ng l\u00ean, Macaulay duration\u00a0gi\u1ea3m \u0111i. Ph\u1ea7n n\u00e0y kh\u00f3 \u0111\u1ec3 suy lu\u1eadn h\u01a1n. V\u1ea5n \u0111\u1ec1 c\u1ed1t y\u1ebfu \u1edf \u0111\u00e2y l\u00e0 khi\u00a0l\u00e3i su\u1ea5t\u00a0t\u0103ng,\u00a0nh\u1eefng d\u00f2ng ti\u1ec1n ng\u1eafn h\u1ea1n (b\u1ecb\u00a0chi\u1ebft kh\u1ea5u m\u1ed9t kho\u1ea3ng th\u1eddi gian ng\u1eafn) s\u1ebd c\u00f3\u00a0gi\u00e1 tr\u1ecb hi\u1ec7n t\u1ea1i (PV)\u00a0gi\u1ea3m \u0111i\u00a0m\u1ed9t ch\u00fat;\u00a0nh\u01b0ng d\u00f2ng ti\u1ec1n d\u00e0i h\u1ea1n\u00a0(b\u1ecb chi\u1ebft kh\u1ea5u m\u1ed9t kho\u1ea3ng th\u1eddi gian d\u00e0i) s\u1ebd c\u00f3 PV\u00a0gi\u1ea3m \u0111i\u00a0nhi\u1ec1u h\u01a1n nhi\u1ec1u.\u00a0<\/p>\n

V\u00ec l\u00ed do n\u00e0y, khi\u00a0l\u00e3i su\u1ea5t\u00a0t\u0103ng l\u00ean,\u00a0nh\u1eefng d\u00f2ng ti\u1ec1n d\u00e0i h\u1ea1n ch\u1ec9 \u0111\u1ea1i di\u1ec7n cho m\u1ed9t ph\u1ea7n nh\u1ecf c\u1ee7a t\u1ed5ng gi\u00e1 tr\u1ecb PV, c\u00f2n\u00a0nh\u1eefng d\u00f2ng ti\u1ec1n ng\u1eafn h\u1ea1n \u0111\u1ea1i di\u1ec7n ph\u1ea7n l\u1edbn cho t\u1ed5ng gi\u00e1 tr\u1ecb PV, n\u00ean duration s\u1ebd\u00a0gi\u1ea3m \u0111i.\u00a0Sau \u0111\u00e2y l\u00e0 v\u00ed d\u1ee5 minh h\u1ecda:\u00a0<\/p>\n

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(4) M\u1eadt \u0111\u1ed9 tr\u1ea3 tr\u00e1i t\u1ee9c<\/i><\/p>\n

Khi m\u1eadt \u0111\u1ed9 t\u0103ng l\u00ean, Macaulay duration gi\u1ea3m \u0111i. Tr\u00e1i phi\u1ebfu tr\u1ea3 tr\u00e1i t\u1ee9c \u0111\u1ecbnh k\u00ec<\/span> 6 th\u00e1ng s\u1ebd \u0111em l\u1ea1i d\u00f2ng ti\u1ec1n s\u1edbm h\u01a1n so v\u1edbi tr\u00e1i phi\u1ebfu tr\u1ea3 tr\u00e1i t\u1ee9c \u0111\u1ecbnh k\u00ec<\/span> 12 th\u00e1ng. (d\u0129 nhi\u00ean l\u00e0 m\u1ed7i tr\u00e1i t\u1ee9c 6 th\u00e1ng kia ch\u1ec9 b\u1eb1ng m\u1ed9t n\u1eeda so v\u1edbi tr\u00e1i t\u1ee9c 12 th\u00e1ng). M\u1eadt \u0111\u1ed9 tr\u1ea3 c\u00e0ng d\u00e0y th\u00ec Macaulay duration c\u00e0ng gi\u1ea3m. V\u00ed d\u1ee5:<\/p>\n

Tr\u00e1i phi\u1ebfu 5 n\u0103m, tr\u00e1i t\u1ee9c 6% tr\u1ea3 h\u00e0ng n\u0103m v\u1edbi YTM 4% s\u1ebd c\u00f3 Macaulay duration l\u00e0 4.49 n\u0103m (\u0111\u00e3 t\u00ednh \u1edf tr\u00ean).<\/p>\n

Tr\u00e1i phi\u1ebfu 5 n\u0103m, tr\u00e1i t\u1ee9c 6% tr\u1ea3 m\u1ed7i 6 th\u00e1ng v\u1edbi YTM 4% s\u1ebd c\u00f3 Macaulay duration l\u00e0 4.42 n\u0103m (c\u00e1ch t\u00ednh t\u01b0\u01a1ng t\u1ef1).<\/p>\n

Tr\u00e1i phi\u1ebfu 5 n\u0103m, tr\u00e1i t\u1ee9c 6% tr\u1ea3 h\u00e0ng th\u00e1ng v\u1edbi YTM 4% s\u1ebd c\u00f3 Macaulay duration l\u00e0 4.37 n\u0103m.<\/p>\n

(T\u00e0i li\u1ec7u tham kh\u1ea3o:\u00a0Th\u1eddi gian \u0111\u00e1o h\u1ea1n b\u00ecnh qu\u00e2n (Duration), Tui h\u1ecdc t\u00e0i ch\u00ednh;\u00a0Macaulay Duration,\u00a0Investopedia)<\/i><\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

\n \u0110\u1ed9 co gi\u00e3n Maculay (ti\u1ebfng Anh: Macaulay Duration) l\u00e0 th\u1eddi h\u1ea1n trung b\u00ecnh c\u00f3 tr\u1ecdng s\u1ed1 \u0111\u1ebfn ng\u00e0y \u0111\u00e1o h\u1ea1n c\u1ee7a d\u00f2ng ti\u1ec1n t\u1eeb tr\u00e1i phi\u1ebfu. Tr\u1ecdng s\u1ed1 c\u1ee7a m\u1ed7i d\u00f2ng ti\u1ec1n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1eb1ng c\u00e1ch chia gi\u00e1 tr\u1ecb hi\u1ec7n t\u1ea1i c\u1ee7a d\u00f2ng ti\u1ec1n cho gi\u00e1.\n <\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[417],"tags":[],"_links":{"self":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/31496"}],"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=31496"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/31496\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=31496"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=31496"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=31496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}