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The Cross-Section of Expected Stock Returns

EUGENE F. FAMA and KENNETH R. FRENCH (1992)

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II. ¦Â and Size

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A. Informal Tests

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B. Fama-MacBeth Regressions

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±¾ÎÄÖ¤Ã÷¹æÄ£Ð§¹ûȷʵ´æÔÚ£¬¶øÇÒ¦ÂÓëÆ½¾ù»Ø±¨ÂÊȱ·¦Ïà¹ØÐÔ£¬ÓëSLBÄ£Ð͵ÄÖ÷ÕÅÏàì¶ÜµÄ£¬±¾ÎÄÀíÓ¦¼ìÑéÔÚ1963-1990Äê¼äµÄ½á¹ûÊÇ·ñÓÐÌØ±ðÖ®´¦¡£¸½Â¼ËµÃ÷1941-1990ÄêNYSEµÄ»Ø±¨ÂÊ£¬ÓëNYSE¡¢AMEX¡¢¼°NASDAQ 1963-1990ÄêµÄ»Ø±¨ÂÊÓÐÀàËÆµÄ±íÏÖ£»ÔÚÕâ50Äê¼äȷʵÓйæÄ£Ð§¹û´æÔÚ£¬µ«¦ÂÓëÆ½¾ù»Ø±¨ÂʼäµÄÏà¹ØÐÔС¡£ÓÐȤµÄÊÇ£¬1941-1965Äê¦ÂÓëÆ½¾ù»Ø±¨ÂʼäȷʵÓмòµ¥µÄÏà¹Ø¡£Õâ25ÄêÊÇÔçÆÚBlack, Jensen, and Scholes(1972) ¼°Fama and MacBeth (1973)Ñо¿ÖÐÖ÷ÒªµÄÑù±¾ÆÚ¼ä¡£È»¶ø£¬ÉõÖÁÊÇÔÚ1941-1965Ä꣬µ±±¾ÎÄ¿ØÖƹæÄ££¬¦ÂÓëÆ½¾ù»Ø±¨ÂʼäµÄ¹ØÏµÒ²ÏûʧÁË¡£

III. ÕËÃæÊÐÖµ±È, E/P, and Leverage

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A. Average Returns

±íIV˵Ã÷ÒÔÕËÃæÊÐÖµ±È (BE/ME)»òÊÇearnings-price ratio (E/P)Ëù¹¹½¨Í¶×Ê×éºÏ£¬1963Äê7Ôµ½1990Äê12ÔµĻر¨ÂÊ¡£±íIVÖÐBE/ME¼°E/PͶ×Ê×éºÏÊÇ

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E/PÓë¹ÉƱƽ¾ù»Ø±¨ÂʼäÓÐÒ»ÊìϤµÄUÐ͹ØÏµ¡£(ÀýÈçJaffe, Keim, and Westerfield (1989)¶ÔÃÀ¹ú¹ÉƱµÄÑо¿¡¢¼°Chan, Hamao, and Lakonishok (1991)¶ÔÈÕ±¾¹ÉƱµÄÑо¿)¡£ÔÂÆ½¾ù»Ø±¨ÂÊ´Ó¸ºE/PͶ×Ê×éºÏµÄ1.46%µ½µÍµ«ÎªÕýE/PµÄͶ×Ê×éºÏ1BµÄ0.93%¡£È»ºóƽ¾ù»Ø±¨Âʵ¥µ÷ÉÏÉý£¬ÔÚ×î¸ßE/PͶ×Ê×éºÏ´ïµ½Ã¿ÔÂ1.72%¡£

±íIV×îÏÔ×ŵÄÖ¤¾ÝΪ£¬ÕËÃæÊÐÖµ±ÈÓëÆ½¾ù»Ø±¨ÂʼäµÄÏÔÖøÕýÏà¹Ø¡£Æ½¾ù»Ø±¨ÂÊ´Ó×îµÍBE/MEͶ×Ê×éºÏµÄ0.3%µ½×î¸ßBE/MEͶ×Ê×éºÏµÄ1.83%£¬Ã¿¸öÔÂÓÐ1.53%µÄ²î¾à¡£Õâ¸ö²î¾àÊÇÁ½±¶ÓÚ±íIIÖÐ×îСÖÁ×î´ó¹æÄ£Í¶×Ê×éºÏ¼äƽ¾ù»Ø±¨ÂʵIJî¾à(0.74%)¡£Ò²ËµÃ÷ÁËÕËÃæÊÐÖµ±ÈÓëÆ½¾ù»Ø±¨ÂʼäÏÔÖøµÄ¹ØÏµ£¬²»¿ÉÄÜÊÇÊܦµÄDZÔÚÓ°Ïì¡£±íIVҲ˵Ã÷post-ranking Êг¡ ¦ÂsÔÚÒÔBE/ME¹¹½¨µÄͶ×Ê×éºÏ¼ä±ä¶¯ºÜС¡£

ƽ¾ù¶øÑÔ£¬£¨ÔÚ2317¼Ò¹«Ë¾£©Ã¿ÄêÖ»ÓÐ50¼Ò¹«Ë¾ÓиºµÄÕËÃæ¼ÛÖµ¡£¾ßÓиºÕËÃæ¼ÛÖµµÄ¹«Ë¾´ó¶à¼¯ÖÐÔÚÑù±¾ÖеÄ×îºó14Ä꣬1976-1989Ä꣬±¾ÎIJ»½«ÆäÄÉÈë¼ìÑéÖС£È»¶ø£¬¸ºBE¹«Ë¾µÄƽ¾ù»Ø±¨Âʸߣ¬¾ÍÏñÓиßBE/ME¹«Ë¾µÄƽ¾ù»Ø±¨ÂÊÒ»Ñù¡£¸ºBE(¸ºÓ¯ÓർÖµÄ)¼°¸ßBE/ME(Ò»°ãÈÏΪ¹ÉƱ¼Û¸ñ»áϵø)£¬½ÔÓжÔÓÚδÀ´Ó¯Óà¿´»µµÄѶºÅÔ¤²â¡£¸ºBE/MEÓë¸ßBE/ME¹«Ë¾µÄƽ¾ù»Ø±¨ÂÊÓëÕËÃæÊÐÖµ±ÈµÄ¼ÙÉèÒ»Ö£¬ ÕËÃæÊÐÖµ±È½âÊÍÆ½¾ùÊÕÒæµÄºá½ØÃæ±ä¶¯Óë²»Á¼Òò×ÓÓйء£

B. Fama-MacBeth Regressions

B.1. BE/ME

±íIIIµÄFM»Ø¹é֤ʵÁËÔÚ½âÊÍºá½ØÃæ¹ÉƱƽ¾ù»Ø±¨ÂÊÉÏ£¬ÕËÃæÊÐÖµ±ÈµÄÖØÒªÐÔ¡£Ö»ÒÔln(BE/ME)×öµÄÔÂ»Ø¹éÆ½¾ùбÂÊΪ0.5%£¬tͳ¼ÆÁ¿Îª5.71¡£ÕËÃæ¶ÔÊм۱ȵĹØÏµ±È¹æÄ£Ð§¹ûÏÔÖø£¬ÒòΪ½öÒÔln(ME)×öµÄ»Ø¹éÖ®tͳ¼ÆÁ¿Îª-2.58¡£µ«ÕËÃæÊÐÖµ±È²»ÄÜÈ¡´ú¹æÄ£ÔÚ½âÊÍ¹ÉÆ±Æ½¾ù»Ø±¨ÂÊÉϵĽÇÉ«¡£µ±ln(ME)¼°ln(BE/ME)¶¼±»°üº¬ÔڻعéʽÖУ¬¹æÄ£µÄƽ¾ùбÂʱê×¼ÎóÒÀÈ»ÊÇ-1.99£¬book-to-marketµÄбÂʱê×¼ÎóÔòΪÏÔ×ŵÄ4.44¡£

B.2. Leverage

FM»Ø¹éÀûÓøܸ˱äÁ¿½âÊͻر¨ÂÊ£¬ÌṩÁËÓÐȤµÄÒ»¸öÏë·¨ÉîÈëÁ˽âÕËÃæÊÐÖµ±ÈÓëÆ½¾ù»Ø±¨ÂʼäµÄ¹ØÏµ¡£±¾ÎÄʹÓÃÁËÁ½¸ö¸Ü¸Ë±äÁ¿£¬ÕËÃæ×ʲú¶ÔÊÐÖµ±È(A/ME)¡¢ÕËÃæ×ʲú¶ÔÕËÃæ¼ÛÖµ±È(A/BE)¡£½«A/MEÊÓΪºâÁ¿Êг¡¸Ü¸Ë¡¢A/BEÊÓΪºâÁ¿ÕËÃæ¸Ü¸Ë¡£»Ø¹éÓøܸ˱ÈÂʵÄ×ÔÈ»¶ÔÊý£¬ln(A/ME)¼° ln(A/BE)£¬ÒòΪ³õ²½¼ìÑéÏÔʾ³öÈ¡¶ÔÊý¶ÔÓÚ»ñµÃƽ¾ù»Ø±¨ÂÊÉϵĸܸËЧ¹û¶øÑÔ£¬ÊÇÒ»¸öºÃº¯ÊýÐÎʽ¡£Ê¹ÓöÔÊýÐÎʽҲÌṩÁËÔÚÆ½¾ù»Ø±¨ÂÊÖиܸË×÷ÓÃÓëÕËÃæÊÐÖµ±ÈµÄ¹ØÏµ¼òµ¥½âÊÍ¡£

»Ø±¨ÂʶԲÆÎñ¸Ü¸Ë±ÈÂÊ×öFM»Ø¹é(±íIII)£¬Ìá³öÁËһЩÀ§»ó¡£Á½¸ö¸Ü¸Ë±äÁ¿Óë»Ø±¨ÂÊÏà¹Ø£¬µ«È´ÓÐ×ÅÏà·´µÄ·ûºÅ¡£ÈçBhandari (1988)Ö÷ÕÅ£¬½Ï¸ßµÄÊг¡¸Ü¸ËÓ¦ÓÐ½Ï¸ßµÄÆ½¾ù»Ø±¨ÂÊ£¬ln(A/ME)µÄƽ¾ùбÂÊ×ÜΪÕýÇÒ´óÓÚ4±¶±ê×¼Îó¡£µ«¸ßÕËÃæÓ¦ÓÐ½ÏµÍµÄÆ½¾ù»Ø±¨ÂÊ£¬ln(A/BE)µÄƽ¾ùбÂÊ×ÜΪ¸ºÇÒ´óÓÚ4±¶±ê×¼Îó¡£

¹ØÓÚln(A/ME) ¼° ln(A/BE)ƽ¾ùбÂÊ·ûºÅÒìÏòÖ®ÃÕÓÐÒ»¸ö¼òµ¥µÄ½âÊÍ¡£Á½¸ö¸Ü¸Ë±äÁ¿µÄƽ¾ùбÂÊ·ûºÅÒìÏò£¬µ«ÓÐ×ÅÏà½üµÄ¾ø¶ÔÖµ£¬ÀýÈç0.5ºÍ-0.57¡£Òò´ËÊг¡¼°ÕËÃæ¸Ü¸Ë¼äµÄ²îÒ죬¿ÉЭÖú½âÊÍÆ½¾ù»Ø±¨ÂÊ¡£µ«Êг¡¼°ÕËÃæ¸Ü¸Ë¼äµÄ²îÒìÊÇÕËÃæÊÐÖµ±È, ln(BE/ME) = ln(A/ME) - ln(A/BE)¡£±íIIIÏÔʾFM»Ø¹é֮ƽ¾ùÕËÃæÊÐ

Öµ±ÈбÂʵÄÈ·ÓëÁ½¸öleverage±äÁ¿Ð±Âʵľø¶ÔÖµºÜ½Ó½ü¡£

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B.3. E/P

Ball (1978)¼ÙÉèE/P±ÈÂʰüº¬Ô¤ÆÚ»Ø±¨ÂÊÆäËû±»ºöÂԵķçÏÕÒò×Ó¡£¼ÙÈçÏÖÔÚÓ¯Óà´ú±í¶ÔδÀ´Ó¯ÓàµÄÔ¤ÆÚ£¬¾ßÓиßÔ¤ÆÚ»Ø±¨Âʵĸ߷çÏչɯ±£¬»áÓÐÏà¶ÔµÍÓÚÆäÓ¯ÓàµÄ¹É¼Û¡£Òò´Ë£¬ÎÞÂÛ±»ºöÂÔ·çÏÕÊÇʲô£¬E/PÓ¦ÓëÔ¤ÆÚ»Ø±¨ÂÊÏà¹Ø¡£È»¶ø£¬ÕâÏî¹ÛµãÖ»ÔÚ¹«Ë¾¾ßÓÐÕýÓ¯ÓàϲųÉÁ¢¡£µ±ÏÖÔÚÓ¯ÓàΪ¸º£¬¹É¼ÛÖв¢²»°üº¬¶ÔδÀ´Ó¯ÓàµÄÔ¤²â£¬Òò´ËE/P²»ÊÇÔ¤ÆÚ»Ø±¨ÂʵĴúÀí±äÁ¿¡£ÔÚFM»Ø¹éÖУ¬E/PÐëΪÕýÖµ£¬µ±E/PΪ¸ºµÄÇé¿öÏÂÔòʹÓÃÐéÄâ±äÁ¿¡£

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IV. A Parsimonious Model for Average Returns

½«½á¹û¼òµ¥ÕªÒªÈçÏ£º

(1) µ±¿¼Âǵ½¦ÂµÄ±ä¶¯Óë¹æÄ£Î޹أ¬¦ÂÓëÆ½¾ù»Ø±¨ÂʼäûÓпɿ¿µÄ¹ØÏµ¡£ (2) ƽ¾ù»Ø±¨ÂÊÖÐÊг¡¸Ü¸Ë¼°ÕËÃæ¸Ü¸ËËù°çÑÝÖ®Ïà¶Ô½ÇÉ«£¬¿ÉÓÉÕËÃæÊÐÖµ±È»ñµÃ¡£

(3) E/PÓëÆ½¾ù»Ø±¨ÂʼäÖ®¹ØÏµ£¬Ëƺõ¿ÉÓɹæÄ£¼°ÕËÃæÊÐÖµ±ÈµÄ×é³ÉËùÎüÊÕ¡£

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A. Average Returns, Size and Book-to-Market Equity

Table Vƽ¾ùÊÕÒæ¾ØÕóÀûÓüòµ¥µÄͼ±í˵Ã÷ÁË£¬Æ½¾ù»Ø±¨ÂÊÏÈÒÔ¹æÄ£·ÖÀà³É10µÈ·Ö¡¢ÔÙÒÔBE/ME·ÖÀà³É10¸öͶ×Ê×éºÏϵÄÁ½Î¬±ä¶¯¡£¹æÄ£·ÖÀàÖÐ(»Ø±¨ÂʾØÕóµÄÿһÐÐ)£¬»Ø±¨ÂÊËæ×ÅBE/MEÉÏÉý¶øÔö¼Ó£ºÆ½¾ù¶øÑÔ£¬ÔÚij¸ö¹æÄ£·ÖÀàÖУ¬×îµÍÓë×î¸ßBE/MEͶ×Ê×éºÏµÄ»Ø±¨ÂÊÏà²îԼΪÿÔÂ0.99%(1.63%-0.64%)¡£ÏàËÆµÄ£¬Óɻر¨ÂʾØÕóÿһÁеÄ×ÊÁϿɿ´³öƽ¾ù»Ø±¨ÂÊÓë¹æÄ£¼äµÄ¸ºÏà¹Ø£ºÆ½¾ù¶øÑÔ£¬

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B. The Interaction between Size and Book-to-Market Equity

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