{"id":7457,"date":"2023-06-21T12:44:35","date_gmt":"2023-06-21T12:44:35","guid":{"rendered":"https:\/\/bjftradinggroup.com\/?p=7457"},"modified":"2026-09-25T19:02:04","modified_gmt":"2026-09-25T19:02:04","slug":"understanding-statistical-arbitrage-a-path-to-profitable-trading","status":"publish","type":"post","link":"https:\/\/bjftradinggroup.com\/vi\/understanding-statistical-arbitrage-a-path-to-profitable-trading\/","title":{"rendered":"Hi\u1ec3u v\u1ec1 arbitrage th\u1ed1ng k\u00ea: Con \u0111\u01b0\u1eddng \u0111\u1ebfn giao d\u1ecbch c\u00f3 l\u1ee3i nhu\u1eadn"},"content":{"rendered":"

Arbitrage th\u1ed1ng k\u00ea, th\u01b0\u1eddng \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u201cstat arb\u201d, l\u00e0 m\u1ed9t chi\u1ebfn l\u01b0\u1ee3c giao d\u1ecbch \u0111\u1ecbnh l\u01b0\u1ee3ng ph\u1ed5 bi\u1ebfn, \u0111\u01b0\u1ee3c c\u00e1c qu\u1ef9 ph\u00f2ng h\u1ed9 v\u00e0 c\u00f4ng ty giao d\u1ecbch t\u1ef1 doanh s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i. Kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n l\u00e0 khai th\u00e1c s\u1ef1 k\u00e9m hi\u1ec7u qu\u1ea3 v\u1ec1 gi\u00e1 gi\u1eefa c\u00e1c c\u00f4ng c\u1ee5 t\u00e0i ch\u00ednh c\u00f3 li\u00ean quan. C\u00e1c trader s\u1eed d\u1ee5ng stat arb d\u1ef1a v\u00e0o nh\u1eefng m\u00f4 h\u00ecnh to\u00e1n h\u1ecdc ph\u1ee9c t\u1ea1p \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh c\u01a1 h\u1ed9i giao d\u1ecbch, khi\u1ebfn chi\u1ebfn l\u01b0\u1ee3c n\u00e0y tr\u1edf th\u00e0nh m\u1ed9t ph\u1ea7n c\u1ee7a giao d\u1ecbch thu\u1eadt to\u00e1n.<\/p>\n

Ngu\u1ed3n g\u1ed1c c\u1ee7a arbitrage th\u1ed1ng k\u00ea<\/strong><\/h3>\n

Arbitrage th\u1ed1ng k\u00ea b\u1eaft ngu\u1ed3n t\u1eeb nh\u1eefng n\u0103m 1980, khi \u0111\u01b0\u1ee3c ti\u00ean phong b\u1edfi c\u00e1c nh\u00e0 ph\u00e2n t\u00edch \u0111\u1ecbnh l\u01b0\u1ee3ng \u1edf Ph\u1ed1 Wall, th\u01b0\u1eddng \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u201cquants\u201d. Ban \u0111\u1ea7u chi\u1ebfn l\u01b0\u1ee3c \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng tr\u00ean th\u1ecb tr\u01b0\u1eddng c\u1ed5 phi\u1ebfu, n\u01a1i c\u00e1c c\u1eb7p c\u1ed5 phi\u1ebfu \u0111\u01b0\u1ee3c ch\u1ecdn d\u1ef1a tr\u00ean t\u00ednh \u0111\u1ed3ng li\u00ean k\u1ebft (co-integration) \u2013 m\u1ed9t thu\u1ed9c t\u00ednh th\u1ed1ng k\u00ea cho th\u1ea5y kho\u1ea3ng c\u00e1ch gi\u00e1 gi\u1eefa hai c\u1ed5 phi\u1ebfu c\u00f3 xu h\u01b0\u1edbng h\u1ed3i quy v\u1ec1 trung b\u00ecnh theo th\u1eddi gian. T\u1eeb \u0111\u00f3, stat arb \u0111\u00e3 ph\u00e1t tri\u1ec3n v\u00e0 \u0111\u01b0\u1ee3c \u0111i\u1ec1u ch\u1ec9nh cho nhi\u1ec1u th\u1ecb tr\u01b0\u1eddng kh\u00e1c, bao g\u1ed3m forex v\u00e0 ti\u1ec1n m\u00e3 h\u00f3a.<\/p>\n

Nguy\u00ean t\u1eafc c\u1ed1t l\u00f5i<\/strong><\/h3>\n

Arbitrage th\u1ed1ng k\u00ea d\u1ef1a tr\u00ean nguy\u00ean l\u00fd h\u1ed3i quy v\u1ec1 trung b\u00ecnh v\u00e0 lu\u1eadt s\u1ed1 l\u1edbn. Ni\u1ec1m tin n\u1ec1n t\u1ea3ng l\u00e0 gi\u00e1 t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a c\u00e1c c\u00f4ng c\u1ee5 t\u00e0i ch\u00ednh c\u00f3 t\u01b0\u01a1ng quan trong l\u1ecbch s\u1eed s\u1ebd quay v\u1ec1 m\u1ee9c trung b\u00ecnh theo th\u1eddi gian. \u0110\u00e2y ch\u00ednh l\u00e0 n\u01a1i arbitrage th\u1ed1ng k\u00ea di\u1ec5n ra – n\u00f3 t\u1eadn d\u1ee5ng ch\u00eanh l\u1ec7ch gi\u00e1 gi\u1eefa c\u00e1c c\u00f4ng c\u1ee5 c\u00f3 t\u01b0\u01a1ng quan n\u00e0y khi ch\u00fang l\u1ec7ch kh\u1ecfi chu\u1ea9n m\u1ef1c l\u1ecbch s\u1eed.<\/p>\n

V\u00ed d\u1ee5, h\u00e3y x\u00e9t hai c\u1ed5 phi\u1ebfu v\u1ed1n bi\u1ebfn \u0111\u1ed9ng c\u00f9ng nhau trong l\u1ecbch s\u1eed. N\u1ebfu gi\u00e1 c\u1ee7a ch\u00fang ph\u00e2n k\u1ef3 – m\u1ed9t c\u1ed5 phi\u1ebfu t\u0103ng gi\u00e1 v\u00e0 c\u1ed5 phi\u1ebfu kia gi\u1ea3m – nh\u00e0 giao d\u1ecbch arbitrage th\u1ed1ng k\u00ea s\u1ebd b\u00e1n kh\u1ed1ng c\u1ed5 phi\u1ebfu t\u0103ng m\u1ea1nh h\u01a1n v\u00e0 mua c\u1ed5 phi\u1ebfu k\u00e9m h\u01a1n, \u0111\u1eb7t c\u01b0\u1ee3c r\u1eb1ng \u201cspread\u201d gi\u1eefa hai c\u1ed5 phi\u1ebfu cu\u1ed1i c\u00f9ng s\u1ebd h\u1ed9i t\u1ee5.<\/p>\n

Spread – ch\u00eanh l\u1ec7ch ho\u1eb7c \u0111\u1ed9 l\u1ec7ch gi\u00e1 gi\u1eefa hai c\u00f4ng c\u1ee5 t\u00e0i ch\u00ednh c\u00f3 li\u00ean quan.<\/strong><\/h3>\n

Trong arbitrage th\u1ed1ng k\u00ea, thu\u1eadt ng\u1eef \u201cspread\u201d th\u01b0\u1eddng d\u00f9ng \u0111\u1ec3 ch\u1ec9 ch\u00eanh l\u1ec7ch ho\u1eb7c \u0111\u1ed9 l\u1ec7ch gi\u00e1 gi\u1eefa hai c\u00f4ng c\u1ee5 t\u00e0i ch\u00ednh c\u00f3 li\u00ean quan. \u0110\u00f3 c\u00f3 th\u1ec3 l\u00e0 hai c\u1ed5 phi\u1ebfu kh\u00e1c nhau, h\u1ee3p \u0111\u1ed3ng t\u01b0\u01a1ng lai, c\u1eb7p ti\u1ec1n forex ho\u1eb7c th\u1eadm ch\u00ed token ti\u1ec1n m\u00e3 h\u00f3a.<\/p>\n

V\u00ed d\u1ee5, ng\u01b0\u1eddi ta c\u00f3 th\u1ec3 theo d\u00f5i spread gi\u1eefa hai c\u1ed5 phi\u1ebfu \u0111\u1ed3ng li\u00ean k\u1ebft trong l\u1ecbch s\u1eed b\u1eb1ng ph\u1ea7n m\u1ec1m chi\u1ebfn l\u01b0\u1ee3c giao d\u1ecbch c\u1eb7p<\/a> (m\u1ed9t d\u1ea1ng ph\u1ed5 bi\u1ebfn c\u1ee7a arbitrage th\u1ed1ng k\u00ea). Khi spread, t\u1ee9c ch\u00eanh l\u1ec7ch gi\u00e1 gi\u1eefa ch\u00fang, l\u1ec7ch \u0111\u00e1ng k\u1ec3 kh\u1ecfi m\u1ee9c trung b\u00ecnh l\u1ecbch s\u1eed, \u0111\u00f3 l\u00e0 t\u00edn hi\u1ec7u c\u01a1 h\u1ed9i giao d\u1ecbch.<\/p>\n

Gi\u1ea3 s\u1eed spread gi\u00e3n r\u1ed9ng qu\u00e1 m\u1ee9c, cho th\u1ea5y m\u1ed9t c\u1ed5 phi\u1ebfu b\u1ecb \u0111\u1ecbnh gi\u00e1 cao v\u00e0 c\u1ed5 phi\u1ebfu kia b\u1ecb \u0111\u1ecbnh gi\u00e1 th\u1ea5p so v\u1edbi m\u1ed1i quan h\u1ec7 l\u1ecbch s\u1eed c\u1ee7a ch\u00fang. Khi \u0111\u00f3, trader c\u00f3 th\u1ec3 b\u00e1n kh\u1ed1ng c\u1ed5 phi\u1ebfu b\u1ecb \u0111\u1ecbnh gi\u00e1 cao v\u00e0 mua c\u1ed5 phi\u1ebfu b\u1ecb \u0111\u1ecbnh gi\u00e1 th\u1ea5p. Ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu spread thu h\u1eb9p qu\u00e1 m\u1ee9c, h\u1ecd s\u1ebd l\u00e0m \u0111i\u1ec1u ng\u01b0\u1ee3c l\u1ea1i.<\/p>\n

Trong arbitrage th\u1ed1ng k\u00ea, spread \u0111\u01b0\u1ee3c k\u1ef3 v\u1ecdng s\u1ebd h\u1ed3i quy v\u1ec1 trung b\u00ecnh, ngh\u0129a l\u00e0 n\u00f3 dao \u0111\u1ed9ng quanh m\u1ed9t gi\u00e1 tr\u1ecb trung b\u00ecnh d\u00e0i h\u1ea1n. Trader k\u1ef3 v\u1ecdng r\u1eb1ng khi spread l\u1ec7ch \u0111\u00e1ng k\u1ec3 kh\u1ecfi m\u1ee9c trung b\u00ecnh n\u00e0y, cu\u1ed1i c\u00f9ng n\u00f3 s\u1ebd quay tr\u1edf l\u1ea1i, cho ph\u00e9p h\u1ecd ki\u1ebfm l\u1ee3i nhu\u1eadn t\u1eeb s\u1ef1 h\u1ed3i quy \u0111\u00f3.<\/p>\n

\"SharpTrader<\/p>\n

H\u00ecnh 1<\/strong> – Ch\u1ec9 b\u00e1o Spread c\u1ee7a SharpTrader\u2122<\/p>\n

Trong ph\u1ea7n m\u1ec1m SharpTrader\u2122 Arbitrage<\/a>, ch\u1ec9 b\u00e1o Spread \u0111\u01b0\u1ee3c d\u00f9ng \u0111\u1ec3 tr\u1ef1c quan h\u00f3a m\u1ed1i t\u01b0\u01a1ng quan gi\u1eefa hai t\u00e0i s\u1ea3n. Vi\u1ec7c t\u00ednh to\u00e1n t\u01b0\u01a1ng quan bao g\u1ed3m c\u00e1c th\u00e0nh ph\u1ea7n sau:<\/p>\n

    \n
  1. Spread: L\u00e0 ch\u00eanh l\u1ec7ch ho\u1eb7c kho\u1ea3ng c\u00e1ch b\u1eb1ng s\u1ed1 gi\u1eefa gi\u00e1 tr\u1ecb c\u1ee7a hai t\u00e0i s\u1ea3n.<\/li>\n
  2. SpreadMA: L\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh \u0111\u1ed9ng c\u1ee7a spread trong m\u1ed9t kho\u1ea3ng th\u1eddi gian nh\u1ea5t \u0111\u1ecbnh, \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi pi_SpreadMA_Period.<\/li>\n
  3. STD (\u0110\u1ed9 l\u1ec7ch chu\u1ea9n): T\u00ednh \u0111\u1ed9 l\u1ec7ch chu\u1ea9n c\u1ed5 \u0111i\u1ec3n c\u1ee7a spread so v\u1edbi SpreadMA. S\u1ed1 quan s\u00e1t \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng b\u1eb1ng pi_SpreadMA_Period.<\/li>\n<\/ol>\n

    \u0110\u1ec3 k\u00edch ho\u1ea1t vi\u1ec7c m\u1edf giao d\u1ecbch, ph\u1ea7n m\u1ec1m tu\u00e2n theo c\u00e1c nguy\u00ean t\u1eafc c\u1ee7a l\u00fd thuy\u1ebft arbitrage th\u1ed1ng k\u00ea.<\/p>\n

    M\u1ed9t ch\u00fat l\u00fd thuy\u1ebft v\u1ec1 c\u00e1ch t\u00ednh t\u01b0\u01a1ng quan<\/h3>\n

    \"C\u00f4ng<\/p>\n

    Arbitrage th\u1ed1ng k\u00ea – ma tr\u1eadn t\u01b0\u01a1ng quan<\/strong><\/h3>\n

    B\u1ea3ng t\u01b0\u01a1ng quan, c\u00f2n g\u1ecdi l\u00e0 ma tr\u1eadn t\u01b0\u01a1ng quan, l\u00e0 b\u1ea3ng th\u1ec3 hi\u1ec7n h\u1ec7 s\u1ed1 t\u01b0\u01a1ng quan gi\u1eefa nhi\u1ec1u bi\u1ebfn. M\u1ed7i \u00f4 trong b\u1ea3ng cho bi\u1ebft m\u1ee9c t\u01b0\u01a1ng quan gi\u1eefa hai bi\u1ebfn. Gi\u00e1 tr\u1ecb n\u1eb1m trong kho\u1ea3ng t\u1eeb -1 \u0111\u1ebfn 1.<\/p>\n

    N\u1ebfu hai bi\u1ebfn c\u00f3 t\u01b0\u01a1ng quan b\u1eb1ng 1, ch\u00fang bi\u1ebfn \u0111\u1ed9ng c\u00f9ng chi\u1ec1u, t\u1ee9c l\u00e0 khi bi\u1ebfn n\u00e0y t\u0103ng th\u00ec bi\u1ebfn kia c\u0169ng t\u0103ng, v\u00e0 ng\u01b0\u1ee3c l\u1ea1i. \u0110\u00e2y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 t\u01b0\u01a1ng quan d\u01b0\u01a1ng ho\u00e0n h\u1ea3o.<\/p>\n

    N\u1ebfu hai bi\u1ebfn c\u00f3 t\u01b0\u01a1ng quan b\u1eb1ng -1, ch\u00fang bi\u1ebfn \u0111\u1ed9ng ng\u01b0\u1ee3c chi\u1ec1u, t\u1ee9c l\u00e0 khi m\u1ed9t bi\u1ebfn t\u0103ng th\u00ec bi\u1ebfn kia gi\u1ea3m, v\u00e0 ng\u01b0\u1ee3c l\u1ea1i. \u0110\u00e2y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 t\u01b0\u01a1ng quan \u00e2m ho\u00e0n h\u1ea3o. T\u01b0\u01a1ng quan b\u1eb1ng 0 ngh\u0129a l\u00e0 kh\u00f4ng t\u1ed3n t\u1ea1i m\u1ed1i quan h\u1ec7 n\u00e0o gi\u1eefa c\u00e1c bi\u1ebfn.<\/p>\n

    D\u01b0\u1edbi \u0111\u00e2y l\u00e0 v\u00ed d\u1ee5 \u0111\u01a1n gi\u1ea3n v\u1ec1 b\u1ea3ng t\u01b0\u01a1ng quan cho ba bi\u1ebfn: A, B v\u00e0 C:<\/p>\n

    \"V\u00ed<\/p>\n

    H\u00ecnh 2<\/strong> – V\u00ed d\u1ee5 v\u1ec1 b\u1ea3ng t\u01b0\u01a1ng quan<\/p>\n

    Trong b\u1ea3ng n\u00e0y, t\u01b0\u01a1ng quan gi\u1eefa bi\u1ebfn A v\u00e0 B l\u00e0 0.5 (t\u01b0\u01a1ng quan d\u01b0\u01a1ng v\u1eeba ph\u1ea3i), trong khi t\u01b0\u01a1ng quan gi\u1eefa A v\u00e0 C l\u00e0 -0.7 (t\u01b0\u01a1ng quan \u00e2m m\u1ea1nh). \u0110\u01b0\u1eddng ch\u00e9o c\u1ee7a ma tr\u1eadn t\u1eeb g\u00f3c tr\u00ean b\u00ean tr\u00e1i \u0111\u1ebfn g\u00f3c d\u01b0\u1edbi b\u00ean ph\u1ea3i lu\u00f4n b\u1eb1ng 1 v\u00ec m\u1ed9t bi\u1ebfn lu\u00f4n t\u01b0\u01a1ng quan ho\u00e0n h\u1ea3o v\u1edbi ch\u00ednh n\u00f3.<\/p>\n

    C\u00e1c b\u1ea3ng n\u00e0y \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong nhi\u1ec1u l\u0129nh v\u1ef1c, bao g\u1ed3m t\u00e0i ch\u00ednh, n\u01a1i ch\u00fang gi\u00fap x\u00e1c \u0111\u1ecbnh m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c bi\u1ebfn t\u00e0i ch\u00ednh kh\u00e1c nhau ho\u1eb7c l\u1ee3i su\u1ea5t c\u1ee7a c\u00e1c t\u00e0i s\u1ea3n kh\u00e1c nhau, h\u1eefu \u00edch cho vi\u1ec7c \u0111a d\u1ea1ng h\u00f3a danh m\u1ee5c v\u00e0 qu\u1ea3n l\u00fd r\u1ee7i ro.<\/p>\n

    Th\u00f4ng th\u01b0\u1eddng b\u1ea1n c\u00f3 th\u1ec3 t\u1ea1o ma tr\u1eadn t\u01b0\u01a1ng quan n\u00e0y b\u1eb1ng ph\u1ea7n m\u1ec1m th\u1ed1ng k\u00ea ho\u1eb7c c\u00e1c ng\u00f4n ng\u1eef l\u1eadp tr\u00ecnh nh\u01b0 Python hay R. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 c\u00e1ch \u0111\u01a1n gi\u1ea3n \u0111\u1ec3 th\u1ef1c hi\u1ec7n v\u1edbi Python<\/a> b\u1eb1ng c\u00e1c th\u01b0 vi\u1ec7n pandas v\u00e0 numpy:<\/p>\n

    import pandas as pd<\/em><\/span><\/p>\n

    import numpy as np<\/em><\/span><\/p>\n

    # Gi\u1ea3 s\u1eed b\u1ea1n c\u00f3 d\u1eef li\u1ec7u l\u1ecbch s\u1eed trong hai danh s\u00e1ch<\/em><\/span><\/p>\n

    crude_oil_prices = […]<\/em><\/span><\/p>\n

    texas_oil_prices = […]<\/em><\/span><\/p>\n

    # T\u1ea1o DataFrame<\/em><\/span><\/p>\n

    df = pd.DataFrame({‘Crude Oil’: crude_oil_prices, ‘Texas Oil’: texas_oil_prices})<\/em><\/span><\/p>\n

    # T\u00ednh ma tr\u1eadn t\u01b0\u01a1ng quan<\/em><\/span><\/p>\n

    correlation_matrix = df.corr()<\/em><\/span><\/p>\n

    print(correlation_matrix)<\/em><\/span><\/p>\n

    \u0110o\u1ea1n script n\u00e0y s\u1ebd xu\u1ea5t ra m\u1ed9t ma tr\u1eadn t\u01b0\u01a1ng quan 2×2 v\u1edbi c\u00e1c h\u1ec7 s\u1ed1 t\u01b0\u01a1ng quan gi\u1eefa gi\u00e1 d\u1ea7u th\u00f4 v\u00e0 gi\u00e1 d\u1ea7u Texas.<\/p>\n

    Tri\u1ec3n khai chi\u1ebfn l\u01b0\u1ee3c arbitrage th\u1ed1ng k\u00ea<\/strong><\/h2>\n

    Tri\u1ec3n khai arbitrage th\u1ed1ng k\u00ea l\u00e0 m\u1ed9t nhi\u1ec7m v\u1ee5 ph\u1ee9c t\u1ea1p. N\u00f3 \u0111\u00f2i h\u1ecfi c\u00e1c c\u00f4ng c\u1ee5 v\u00e0 m\u00f4 h\u00ecnh th\u1ed1ng k\u00ea tinh vi, h\u1ec7 th\u1ed1ng t\u00ednh to\u00e1n t\u1ed1c \u0111\u1ed9 cao v\u00e0 thu\u1eadt to\u00e1n ti\u00ean ti\u1ebfn. C\u00e1ch ti\u1ebfp c\u1eadn bao g\u1ed3m:<\/p>\n