I- Fama-French 3, Idiosyncratic (I- ) I- ( ) 1 I- I- I- 1 I- I- Jensen Fama-French 3 SMB-FL, HML-FL I- Fama-French 3 I- Fama-MacBeth Fama-MacBeth I- S
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2 I- Fama-French 3, Idiosyncratic (I- ) I- ( ) 1 I- I- I- 1 I- I- Jensen Fama-French 3 SMB-FL, HML-FL I- Fama-French 3 I- Fama-MacBeth Fama-MacBeth I- SMB-FL, HML-FL Fama-MacBeth 2, 3, 5 I- HML-FL 1 Fama-French (FF) 3 [7] (Capital Asset Pricing Model; CAPM [15, 18]) CAPM, yuji@gssm.otsuka.tsukuba.ac.jp, takaaki.yoshino@daiwa.co.jp, tetsuro.saito@daiwa.co.jp 1
3 ( [2, 14, 17, 19]) [20, 21] Idiosyncratic (I- ) I- FF 3 [3, 4, 10] [6, 11] [10] [20] I- I- 1 I- (1 ) 2 2 I I- I- I- (1) 2 I- (2) 2 I- 1, (3) I- I- [21] I- I- 1 I- 7 I- FF 3 SMB, HML (SMB-FL, HML-FL) I- SMB-FL, HML-FL Fama-MacBeth [8, 9] I- 2
4 2 2.1 CAPM n ( i = 1,..., n) M t R, i = 1,..., n R M,t ( ) R = r r f, R M,t = r M,t r f (2.1) R = r r i, R M,t = r M,t r M (2.2) 1. r i r f r i := E [r ], r M := E [r M,t ] i k C (k) 2 ] C (k) [R := Cov, RM,t k (2.3) (2.1) 1 CAPM [15, 18] r i r f = κ (1) ( r M r f ), κ (1) := C (1) Var [R M,t ] (2.4) [10] (2.4) r i r f 1 3. [10] κ (k) := C (k) k = 1, 2,..., (2.5) E [{R M,t E [R M,t ]} k+1], κ (2) i κ(3) [6, 11] ( ) 1 t = 1, 2,..., T r, r M,t ( i.i.d.) X, Y X = E [X] Var [X] Cov[X, Y ] X m X R m X. 2 r f [13] 3 CAPM. 1. 3
5 2.2 I- [20, 21] I- I- 1 (I- ) β (k) k I-. [ ] ε (0) β (k) := Cov ε (k 1) Var, RM,t k ], k = 1, 2, 3,... (2.6) [ R k M,t := R ε (k), k 1 ε (k) := ε (k 1) β (k) Rk M,t, k = 1, 2, 3,... (2.7) I- β (1) β(1) = κ (1) β(1) R M,t R M,t ε (0) := R ε (1) = R β (1) R M,t ε (1) β (1) R M,t 4. ε (1) 1 β (2) R2 M,t R2 M,t ε (2) RM,t k β(2) R2 M,t 1 ε(2) = ε (1) β(2) ε(k) ε(k 1) R2 M,t k k I- β(k) (2.6), (2.7) I- 1 R k I- k [20, 21] R = β (1) R M,t + β (2) R2 M,t + + β (k 1) Rk 1 M,t + β(k) Rk M,t + ε (k) (2.8) [ ] Cov ε (j), Rj M,t = 0, j = 1,..., k (2.8) (2.3) ] [ ] ] C (k) = β(1) [R Cov M,t, RM,t k + + β (k 1) Cov R k 1 M,t, Rk M,t + β (k) [R Var M,t k (2.9) (2.9) I- I- 2.3 I- [20, 21] I- 1 2 I- 0 β (k) = 0, k 2 (2.10) 4 2 X, Y X Y E [XY ] = 0. 4
6 1 2 I- [20, 21] w i > 0, n wi = 1 i=1 I- k I- k (k = 1, 2,...) n i=1 n i=1 w i β (k) = 0 (k 2) (2.11) w i ε (k) = 0 (k 1) (2.12) n i=1 w i β (1) = 1 (2.13) I- I- 2 2 I- 0 I- [20, 21] R, R M,t I- 1 I- I- 6. [21] I- 10 I- 1 I- 2 I- 3 I-. 5% ( ) 2 50%, 3 65% 5 w i > I- R M,t. 5
7 4 I- 25% 5 % 3 I- 2 I- 2 I- 3 I- B/P B/P 2 I- 3 I- 3 I- B/P I- [21] I- I- I- Fama-French 3 [7] I- Fama-French I- ᾱ i := r i r f β (1) ( r M,t r f ) (3.1) I- 7. ᾱ i c 2 β (2) + + c m 1β (m 1) + c m β (m) (3.2) m I- α := r r f β (1) (r M,t r f ) (3.3) 7 2 I- (= β (1) ), (3.1) (3.1) Jensen [12]. 6
8 CAPM α (= E [α ]) (2.1) R, R M,t α = ε (1) (3.2) A [16] CAPM I- I- (A.13) I- 3 I- ( ) 4 3 I- I- (A.13) I- ᾱ ( α ) 2 m I- 3.2 SMB HML FF 3 FF 3 SMB (Small Minus Big), HML (High Minus Low) 8,. 1. ( 1 ) 8 (Small) (Big) (B/P) 30% 70% B/P (Low), (Middle), (High) 2. Step 1 Small Low Small/Low Small Middle Small/Middle Small/Low, Small/Middle, Small/High, Big/Low, Big/Middle, Big/High 6 3. (a) (b) SMB (a) Small/Low, Small/Middle, Small/High 1/3 8 SMB/HML FF 3 [7] [14]. 7
9 (b) Big/Low, Big/Middle, Big/High 1/3 4. (a) (b) HML (a) Small/High, Big/High 1/2 (b) Small/Low, Big/Low 1/2 I- FF 3 (3.3) α α d 1 SMB t + d 2 HML t (3.4) SMB t HML t t SMB, HML (3.4) FF 3 r r f β 1 (r M,t r f ) + β 2 SMB t + β 3 HML t β 1 CAPM ( 1 I- β (1) ) (3.4) CAPM ( α ) SMB, HML (Factor Loading; FL) d 1, d 2 0 CAPM SMB, HML d 1, d 2 SMB, HML d 1, d 2 SMB, HML I- FF 3 SMB, HML (SMB-FL, HML-FL) SMB-FL, HML-FL (= β (1) ) α SMB, HML (3.4) i SMB, HML SMB-FL i = d 1, HML-FL i = d 2 SMB-FL i, HML-FL i ᾱ i c s SMB-FL i + c h HML-FL i (3.5) ᾱ i c 2 β (2) + + c m 1β (m 1) + c m β (m) + c ssmb-fl i + c h HML-FL i (3.6) I- (3.2) 8
10 NEEDS-FinancialQUEST ,121 R R M,t (2.1) 11. I- i R M,t β (1) (1 ) SMB-FL, HML-FL R 2 M,t β(2) 1 α (3.4) i SMB-FL i, HML-FL i k = 1 k = 2 k = 3 k = 4 k = 5 k = 6 k = t t (%) (%) Table 3.1: β (k). 5% t. Table 3.1 1,121 I- 7 Table β (i), i = 1,..., 7 t 2 0 t 5% ( ) 2 I- 3 I- ( ) 2 50%, 3 65% (2.2) (2.1). 9
11 25% 5 % 12. I- SMB-FL HML-FL Table 3.2 Table 3.1 I- SMB-FL, HML-FL, Panel A 7 I- Panel B SMB-FL, HML-FL Panel C t p Panel A C, F F p Panel A I- 2 I- 10% 3 4, 6 7 I- 1% I- 5 I- 5 I- VIF 7.06 VIF (A.13) I Panel A: I- : 0.107, F : , p : SMB-FL HML-FL 1.35e e e e e e e-04 t p < <.0001 Panel B: SMB-FL, HML-FL : 0.191, F : , p : e e e-04 t p < <.0001 Panel C: I- + SMB-FL, HML-FL : 0.211, F : , p : e e e e e e e e e-04 t p < <.0001 Table 3.2:. I-. SMB-FL, HML-FL I- 5 I- 5 I- 1% I- 3 7 I- I- 0 SMB-FL HML-FL 12 5 I- 7 I-. 10
12 I- Table 3.3 I SMB-FL HML-FL SMB-FL HML-FL Table 3.3:. SMB-FL, HML-FL HML-FL SMB-FL SMB-FL, HML-FL (3.4) SMB-FL, HML-FL 13 Fig. 3.1 SMB- FL, HML-FL 5% / SMB-FL, HML-FL All Table : 1978/10/ /07/08, 2: 1986/07/ /03/23 3: 1995/03/ /03/18, 4: 2004/03/ /03/ SMB-FL 90% HML-FL 85% (3.3) α (= ) SMB, HML SMB-FL HML-FL HML (= ᾱ i ) 13 (3.4) SMB t HML t , 1034, 1106,
13 0.000% プラス有意比率 マイナス有意比率 プラス有意比率 マイナス有意比率 % % % % % % % % % % % % % % % % % % % 0.000% ALL ALL SMB-FL HML-FL Fig. 3.1: (All) SMB-FL( ), HML- FL( ) 3.4 (B/P) B/P ( ) 5 ( 1 5 ) Table 3.4 ( 1 ) ( 5 ) 2 Panel A I- 1 I- 5 5 I- 1 SMB-FL, HML-FL 1 SMB-FL 1% HML-FL 10% 5 F 5 Panel C SMB-FL, HML-FL Panel A I- 1 Panel C SMB-FL, HML-FL I- 4 I- 10% 6 I- 1% Panel A, Panel B Table 3.5 B/P B/P ( 1 ) 12
14 1 Panel A: I- : , F : 4.339, p : SMB FL HML FL 3.25e e e e e e e-05 t p Panel B: SMB FL, HML FL : 0.108, F : , p : e e e-05 t p < Panel C: I + SMB FL, HML FL : 0.195, F : 7.759, p : e e e e e e e e e-04 t p < Panel A: I : 0.180, F : 9.163, p : SMB FL HML FL 5.62e e e e e e e-04 t p <.0001 Panel B: SMB FL, HML FL : , F : 2.595, p : e e e-04 t p <.0001 Panel C: I + SMB FL, HML FL : 0.173, F : 6.835, p : e e e e e e e e e-04 t p <.0001 Table 3.4:. I. ( : 1, : 5 ) 13
15 ( 5 ) Panel C HML-FL 1% 4 6 I- 1% I- 5% ( p 1% ) 1 5 SMB-FL 2 I- SMB-FL, HML-FL 5 10% B/P 1 Panel A: I : 0.142, F : 7.153, p : SMB FL HML FL 2.32e e e e e e e-04 t p <.0001 Panel B: SMB FL, HML FL : 0.211, F : , p : e e e-04 t p < <.0001 Panel C: I + SMB FL, HML FL : 0.261, F : , p : e e e e e e e e e-04 t p < <.0001 B/P 5 Panel A: I : 0.144, F : 7.265, p : SMB FL HML FL 5.80e e e e e e e-05 t p Panel B: SMB FL, HML FL : 0.203, F : , p : e e e-04 t p < Panel C: I + SMB FL, HML FL : 0.300, F : , p : e e e e e e e e e-04 t p < Table 3.5: B/P. I. ( : 1, : 5 ) 14
16 3.5 Table B/P 1 B/P 5 I- + 2 SMB-FL, HML-FL SMB-FL, HML-FL Panel C SMB-FL HML-FL + ( ) ( ) + (+ ) + ( ) 1 + ( ) + (+ ) ( ) + (+ ) 5 ( ) ( ) ( ) + (+ ) B/P 1 ( ) (+ ) ( ) B/P 5 ( ) ( ) + + (+ ) ( ) + (+ ) Table 3.6:. +,,, 1%, 5%, 10%. 3 I- 4 I- 6 7 I- 2 5 I- I- I- 2 5 I- SMB-FL SMB-FL 4 Fama-MacBeth Fama-MacBeth ( ). 15 I- SMB-FL, HML-FL (250 ) 15 Fama-MacBeth [8, 9] [5]. Fama-MacBeth. 15
17 1 Fama-MacBeth I ( ) I I- SMB, HML 8 1 ( ) SMB-FL, HML-FL 250 I- SMB-FL, HML-FL I- SMB-FL, HML-FL 1 I- SMB-FL, HML-FL 1 1,752. Fama-MacBeth [8, 9] t I- 4.2 Table 4.1 Fama-MacBeth Panel A 1 7 I Fama-MacBeth 1 3 t t p 4 7, 5% 5% 10% 10%. 17 Panel B SMB-FL, HML-FL Panel C SMB-FL, HML-FL Panel D 16 t, t+1 s r t+1,..., r t+s s i=1 (1 + rt+i) [14]. 17 1,
18 SMB-FL HML-FL Panel A: I- ( ): 6.018% ( ) 9.465e e e e e e e e-04 t p % ( ) % % % % % % % % 5% ( ) % % % % % % % % 10% ( ) % % % % % % % % 10% ( ) % % % % % % % % Panel B: I- + SMB-FL, HML-FL ( ): 8.739% ( ) 3.248e e e e e e e e e e-04 t p % ( ) % % % % % % % % % % 5% ( ) % % % % % % % % % % 10% ( ) % % % % % % % % % % 10% ( ) % % % % % % % % % % Panel C: (1 I- ) + SMB-FL, HML-FL ( ): 7.757% ( ) 2.364e e e e-04 t p % ( ) % % % % 5% ( ) % % % % 10% ( ) % % % % 10% ( ) % % % % Panel D: (1 I- ) ( ): 3.786% ( ) 2.390e e-04 t p % ( ) % % 5% ( ) % % 10% ( ) % % 10% ( ) % % Table 4.1: Fama MacBeth. I-. 17
19 1 I- Panel A Panel D Panel A Panel B Fama-MacBeth [8] 5% 36.7% 40.2% 80% ( ) 2 I- Panel A 2 7 I- 10% 3 5 I- 1% Panel B SMB-FL, HML-FL I- 5% I- 2 3 I- 5 I- 7 Panel A 5 I- 5 I- 3 I- 2 I- SMB-FL, HML-FL Panel C SMB-FL, HML-FL 3 HML-FL 1% HML-FL [8] B/P 18. HML-FL. (Table 3.2 ) HML-FL Fama-MacBeth SMB-FL [14] I- SMB-FL, HML-FL Fama-MacBeth 18 [8] Fama-MacBeth B/P B/P. B/P HML-FL HML-FL B/P HML-FL [8] B/P. 18
20 2 I- I- 5 I- 1 I- 7 I- 5 I- FF 3 SMB, HML (SMB-FL, HML-FL) 2 3 I- 5 I- SMB-FL, HML-FL 2 3 I- I- FF 3 FL I- Fama-MacBeth Fama- MacBeth 1 I- I- SMB-FL, HML-FL 2, 3, 5 I- I- HML-FL I- I- [1] P. Artzner, F. Delbaen, J. M. Eber, and D. Heath, Coherent Measures of Risk, Mathematical Finance, 9(3), , [2] M.M. Carhart, On persistence in mutual fund performance, Journal of Finance, 52(1), 57 82,
21 [3] R. Christie-David and M. Chaudhry, Coskewness and cokurtosis in futures markets, Journal of Empirical Finance 8, 55-81, [4] Y.P. Chung, H. Johnson and M. Schill, Asset pricing when returns are nonnormal: Fama-French factors vs. higher-order systematic comoments, Journal of Business, 79(2), , [5] J.H. Cochrane, Asset Pricing, Revised Edition, Princeton University Press, [6] R.F. Dittmar, Nonlinear pricing kernels, kurtosis preference, and evidence from the cross-section of equity returns, Journal of Finance 51, , [7] E.F. Fama and K.R. French, Common risk factors in the returns on stocks and bonds, Journal of Financial Economics, 33(1), 3 56, [8] E.F. Fama and K.R. French, The cross-section of expected stock returns, Journal of Finance, 47(2), , [9] E.F. Fama and J.D. MacBeth, Risk, Return, and Equilibrium: Empirical Tests, The Journal of Political Economy, 81(3), , [10] H. Fang and T.-Y. Lai, Co-kurtosis and capital asset pricing, Financial Review 32, , [11] C. Harvey and A. Siddique, Conditional skewness in asset pricing tests, Journal of Finance 55, , [12] M.C. Jensen, The Performance of Mutual Funds in the Period , Journal of Finance 23, , [13] A. Kraus and R. Litzenberger, Skewness preference and the valuation of risk assets, Journal of Finance 31, , [14],, Fama-French,, 22, 3 23, [15] J. Lintner, The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics, 13 37, [16] Y. Malevergne and D. Sornette, Extreme Financial Risks: From Dependence to Risk Management, Springer, [17] L. Pastor and R.F. Stambaugh, Liquidity risk and expected stock returns, Journal of Political Economy, 111(3), ,
22 [18] W. Sharpe, Capital asset prices: a theory of market equilibrium under conditions of risk, Journal of Finance 19, , [19],,, UFJ, , [20],,, Idiosyncratic, 2011 JAFEE, 49 60, [21],,,, JAFEE 12, pp , [22],, VaR, / / , , A (Generalized Capital Asset Pricing) [16] I- [16] CAPM ρ r i r f = ρ ( w r ) r M r f, i = 1, 2,..., n (A.1) w i ρ (r w =w M,t ) w i, i = 1, 2,..., n 1 w R n i r R n i r, i = 1,..., n w R n [16] ρ i (i = 1, 2,...) 1 1 X, Y, c, ρ 19. 1) 1 (Positive homogeneity): ρ (λx) = λρ (X) 0, λ > 0 2) (Convexity): ρ (λx + (1 λ) Y ) λρ (X) + (1 λ) ρ (Y ), λ [0, 1] 3) (Translation invariance): ρ (X + c) = ρ (X), ρ (0) = , [1] (Monotonicity; X Y ρ(x) ρ(y )) [22]. 21
23 ( [ (X ]) 2 1/2 ρ ρ (X) := E X) 1 ρ ( w r ) 1 w i ρ (r w =w M,t ) ( ) ( [ { ]) 2 1/2 ( [ 1/2 ρ w r = E w (r r)} = Var w r]) (A.2) = = = 1 2ρ (w r) w =w 1 [ 2ρ 2 (r M,t ) E 2 1 [ { } ] 2 E w (r r) w i } { w (r r) ρ 2 (r M,t ) E [(r M,t r M,t ) (r r i )] = Cov [r M,t, r ] Var [r M,t ] ] w (r r i ) =w w =w 1 ρ (r M,t ) (A.3) (A.3) (A.1) CAPM ρ ρ (X) := j 1 η j X X j, η j > 0 (A.4) j j X X l := ( [ E X l]) 1/l, l = 1, 2,..., (A.5) ρ 1 η 1 = 1, η j = 0 (j 2) (A.4) η 2 = 1, η j = 0 (j 2) (A.4) ρ R, R M,t (2.2) ρ ρ ( ) ρ w w r := η j (r r), j η j > 0 (A.6) {j=2,4,..., ˆm} ˆm w (r r) [ j {w j E (r r) } ] j w i = w i w =w [ w =w { j 1 = E j w (r r)} (r r i )] [ ] w =w = je R j 1 M,t R, j = 2, 4,..., ˆm w (r r) j j w i = j R M,t j 1 j w =w w (r r) j w i w =w 22
24 κ (j 1) = C(j 1) [ E R j M,t ] = C(j 1) R M,t j j, j = 2, 4,..., ˆm R, R M,t (2.2) w (r r) [ ] j E R j 1 M,t R = w i w =w R M,t j 1 j ( ) Cov R j 1 M,t, R = R M,t j 1 j C (j 1) = R M,t j 1 j = R M,t j κ (j 1) r i r f = ρ ( w r ) r M r f w i ρ (r w =w M,t ) = w (r r) j η j w i {j=2,4,..., ˆm} w =w = ( r M r f ) ω j κ (j 1) {j=2,4,..., ˆm} r M r f {j=2,4,..., ˆm} η j R M,t j (A.7) (A.8) (A.9) ω l, l = 2, 4,..., ˆm ω l := η l R M,t l {j=2,4,..., ˆm} η j R M,t j, l = 2, 4,..., ˆm (A.10) η l > 0 ω l > 0 (2.9) κ (j 1) = C(j 1) [ E R j M,t ω 2 + ω ω ˆm = 1 j 1 ] = l=1 [ ] E R j 1+l ϕ (j) M,t l := [ ], l = 1,..., j 1 E R j M,t ϕ (j) l β (l), j = 2, 4,..., ˆm (A.11) 23
25 (A.9) r i r f = ( r M r f ) = ( r M r f ) {j=2,4,..., ˆm} {j=2,4,..., ˆm} ω j κ (j 1) j 1 ω j l=1 ϕ l β (l) (A.12) I- r i r f r i r f = ( r M r f ) β(1) + + {j=4,6,..., ˆm} {j=6,8,..., ˆm} ω j ϕ (j) β (2) 2 ω j ϕ (j) 5 + {j=4,6,..., ˆm} ω j ϕ (j) β (3) 3 + β (5) + + ω ˆmϕ ( ˆm) ˆm 2) ˆm 2 β( + ω ˆm ϕ ( ˆm) ˆm 1 {j=6,8..., ˆm} ˆm 1) β( ω j ϕ (j) β (4) 4 (A.13) 4 2 I- 24
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濱田弘潤 : 多角化企業の利潤分析 77 多角化企業の利潤分析 多角化ディスカウントの寡占理論による説明 * 濱田弘潤 (diversification discount) Keywords: JEL classifications: D43, L13, L22, G
濱田弘潤 : 多角化企業の利潤分析 77 多角化企業の利潤分析 多角化ディスカウントの寡占理論による説明 * 濱田弘潤 (diversification discount) Keywords: JEL classifications: D43, L13, L22, G34 950-2181 2 8050 Tel. and fax: 025-262-6538 E-mail: khamada@econ.niigata-u.ac.jp
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