ACADEMIC ARTICLES ON THE TESTS OF THE CAPM

Transcription

1 ACADEMIC ARTICLES ON THE TESTS OF THE CAPM Page: o 5 The table below s a summary o the results o the early academc tests o the Captal Asset Prcng Model. The table lst the alpha correcton needed accordng to the test and the perod o market data used. Below the table s more detaled normaton on how the tests were perormed. Emprcal Evdence on the Alpha Factor n ECAPM Black (993) ) Author Alpha Estmate Perod reled upon % or betas between zero and Black, Jensen and Scholes 4.3% (972) 2) Fama and McBeth (972) 5.76% Fama and French (992) 3) 7.32% Ltzenberger and Ramaswamy (979) 4) 5.32% Ltzenberger, Ramaswamy and Sosn (98).63% to 3.9% Pettengll, Sundaram and 4.6% Mathur (995) 5) *) The gures reported n ths table are or the longest estmaton perod avalable and when applcable usng the authors recommended estmaton technque (unbased, ecent, consstent). Many o the artcles cted also estmate alpha or sub-perods and those alphas may der sgncantly. ) Black estmates alpha n a one step procedure rather than n an un-based two-step procedure.

2 Page: 2 o 5 2) Black, Jensen and Scholes estmate a negatve alpha or the subperod whch contan the depresson years and ) Calculated usng Ibbotson s data or the 3-day treasury yeld. 4) Relyng on Lzenberger and Ramaswamy s beore tax estmaton results. Comparable ater-tax estmaton results estmate alpha at 4.4%. 5) Pettengll, Sundaram and Mathur rely on total returns or the perod 936 through 99 to estmate the alpha parameter and use 9-day treasures. The 4.6% gure s calculated usng aucton averages 9-day treasures back to 94 as no other seres were ound ths ar back. Sources: Black, Fscher, Beta and Return, The Journal o Portolo Management, Fall 993, 8-8. Black, Fscher, Mchael C. Jensen and Myron Scholes, The Captal Asset Prcng Model: Some Emprcal Tests, rom Studes n the theory o Captal Markets, n Jensen, M. (ed.) Studes n the Theory o Captal Markets, Praeger, New York, 972, Fama, Eugene F. and James D. MacBeth, Rsk, Returns and Equlbrum: Emprcal Tests, Journal o Poltcal Economy, September 972, pp Fama, Eugene F. and Kenneth R. French, The Cross-Secton o Expected Stock Returns, Journal o Fnance, Vol. 47, June 992, pp Ltzenberger, Robert H. and Krshna Ramaswamy, The Eect o Personal Taxes and Dvdends on Captal Asset Prces, Theory and Emprcal Evdence, Journal o Fnancal Economcs, June 979, pp Ltzenberger, Robert H. and Krshna Ramaswamy and Howard Sosn, On the CAPM Approach to Estmaton o a Publc Utlty's Cost o Equty Captal, The Journal o Fnance, Vol. 35, No. 2, May 98, pp Pettengll, Glenn N., Srdhar Sundaram and Ike Mathur, "The Condtonal Relaton between Beta and Returns," Journal o Fnancal and Quanttatve Analyss, Vol. 3, No., March 995, pp. -6.

3 Appendx: Detals o the studes Page: 3 o 5 Note: All the ollowng academc studes, except Pettengll, Sundaram, & Mathur, 995, use 3-day rsk-ree rate. Pettengll, et al. uses the 9-day rate. Fsher Black, 993 Tme Seres Regressons: r r = α + β ( r r ) + ε m Concluson: α hgher (postve) or lower Exhbts or perod αˆ ranges rom 3.6% to 3.6% Look at table 4 or ull perod : β Alpha = % or betas n -.8 range Alpha = % 3% or betas n range.2 and up. Note, ths s a one-step procedure that s lkely to be based (at least regardng ecency). Black, Jensen & Scholes, 972 Fgures. 5: Graphs o excess monthly returns vs. β s Cross-sectonal Regresson: ( r γ γ β + ε r ) = + Table 4 γ *2 = 4.3% *2 = -9.6% *2 = 5.27% *2 = 9.32% *2 = 2.24% Fama & MacBeth, 973 Cross-sectonal regresson: rp = γ + γ ˆ β + ε p p Table 4 γ ˆ Rsk-ree Rate ˆ γ r ( ) * % % % %

4 Fama & French, 992 Cross-sectonal regresson: r = a + b ˆ β + ε Page: 4 o 5 Table AIV a r a - r *2 =.76% 4.44% 7.32% *2 =.8%.64% 8.44% *2 = 3.56% 7.24% 6.32% Rsk-ree rate rom Ibbotson. Ltzenberger & Ramaswamy, 979 Beore Tax Verson ( ): R r γ γ β + µ t t= + t t Table ~γ OLS.68*2 = 8.7% GLS.56*2 = 6.9% MLE.443*2 = 5.32% Pettengll, Sundaram, & Mathur, 995 Rsk-ree rate s the 9-day rate. Cross-sectonal regresson: ˆ γ r Table 6 9.% 4.5% = 4.6% r = γ + γ ˆ β + ε The average 3-month Treasury (aucton hgh, no TCM gong back to 936) rom 94 to 99) s 4.5%. The average -month rsk-ree rate rom Ibbotson s 4.4%. Ltzenberger, Ramaswamy & Sosn, monthly data Note: r t s excess return n the paper Table Bayesan: ˆ α = r =.36 *2 =.63% Raw: ˆ α =.326 *2 = 3.92% Table 2 Bayesan: ˆ α =.32*2 = 3.85% Raw: ˆ α =.42*2 = 5.4%

5 Page: 5 o 5 Table s estmated based on a consstent estmaton technque whle the hgher numbers n Table 2 are based on nconsstent GLS estmaton technques.