1 CAPM: I-,,, I- ( ) 1 I- I- I- ( CAPM) I- CAPM I- 1 I- Jensen Fama-French 3 I- Fama-French 3 I- Fama-MacBeth I- SMB-FL, HML-FL Fama-MacBeth 1 Fama-Fr
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1 1 CAPM: I-,,, I- ( ) 1 I- I- I- ( CAPM) I- CAPM I- 1 I- Jensen Fama-French 3 I- Fama-French 3 I- Fama-MacBeth I- SMB-FL, HML-FL Fama-MacBeth 1 Fama-French (FF) 3 [5] (Capital Asset Pricing Model; CAPM [13, 16]) CAPM ( [2, 12, 15, 17]) [18, 19] Idiosyncratic (I- ) I- FF 3 I- ( ) 1 I- I- I- I- (1) 2 I- (2) 2 I- 1 [19] [14] CAPM I- 1 I- Jensen Fama-French 3 I- Fama-French 3 I- Fama-MacBeth I- SMB-FL, HML-FL Fama-MacBeth [6, 7]
2 2 2 I- 2.1 I- n ( i = 1,..., n) M t R i,t, i = 1,..., n R M,t ( ) R i,t = r i,t r f, R M,t = r M,t r f (2.1) R i,t = r i,t r i, R M,t = r M,t r M (2.2) 1. r i,t i r f r i := E [r i,t ], r M := E [r M,t ] i k C (k) 2 C (k) := Cov [ R i,t, RM,t k ] (2.1) 1 CAPM [13, 16] [8] r i r f 1 3. [8] κ (k) := C (k) (2.3) k = 1, 2,..., (2.4) k+1], E [{R M,t E [R M,t ]} κ (2) i κ(3) [4, 9] ( ) [18, 19] I- I- 1 (I- ) β (k) k I-. [ ] ε (0) i,t β (k) := Cov ε (k 1) i,t Var, RM,t k ], k = 1, 2, 3,... (2.5) [ R k M,t := R i,t ε (k) i,t, k 1 ε (k) i,t := ε(k 1) i,t β (k) Rk M,t, k = 1, 2, 3,... (2.6) I- β (1) β(1) = κ(1) β (1) R M,t R M,t ε (0) i,t := R i,t ε (1) i,t = R i,t β (1) ε (1) i,t β(1) R M,t 4. ε (1) i,t 1 β(2) R2 M,t R2 M,t ε (2) i,t = ε(1) i,t β(2) R2 M,t ε(2) i,t k I- β (k) Rk M,t β(2) R2 M,t ε(k 1) i,t R M,t 1 ε(k) i,t k 1 t = 1, 2,..., T r i,t, 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 [11] 3 CAPM X, Y X Y E [XY ] = 0.
3 3 (2.5), (2.6) I- 1 R i,t k I- k [18, 19] R i,t = β (1) R M,t + β (2) R2 M,t + + β (k 1) Rk 1 M,t + β(k) Rk M,t + ε (k) i,t (2.7) [ ] Cov ε (j) i,t, Rj M,t = 0, j = 1,..., k (2.7) (2.3) C (k) = β(1) Cov [ R M,t, RM,t k ] [ ] (k 1) + + β Cov R k 1 M,t, Rk M,t + β (k) Var [ RM,t k ] (2.8) I- I- (2.8) 2.2 I- [18, 19] I- 1 2 I- 0 β (k) = 0, k 2 (2.9) 1 2 I- [18, 19] w i > 0, n wi = 1 i=1 I- k I- k (k = 1, 2,...) n i=1 n wi β (k) = 0 (k 2), i=1 w i ε (k) i,t = 0 (k 1) (2.10) n i=1 w i β(1) = 1 I- I- 2 2 I- 0 I- [18, 19] R i,t, R M,t I- 1 I- I I- [14] I- [14] CAPM ρ r i r f = ρ ( w r ) r M r f, w i ρ (r w =w M,t ) i = 1, 2,..., n (3.1) 5 w i > I- R M,t.
4 4 w i, i = 1, 2,..., n 1 w R n i r R n i r i,t, i = 1,..., n w R n 7. 1 X, Y, c, ρ 8. 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) = 0 ρ X j X X ( [ j = E X X j]) j/l, j = 1, 2,..., (3.2) ρ 1 j = 1 j = 2 9. ρ j 1 R i,t, R M,t (2.2) ρ ρ ( w r ) := {j=2,4,..., ˆm} η j w (r r) j, η j > 0 (3.3) ˆm w (r r) j j w i = j R M,t j 1 j w (r r) j w i w =w w =w [ {w E (r r) } ] j [ ] = w i = je R j 1 M,t R i,t, j = 2, 4,..., ˆm w =w R i,t, R M,t (2.2) κ (j 1) w (r r) j = w i w =w [ ] E R j 1 M,t R i,t R M,t j 1 j (2.4) 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 ) {j=2,4,..., ˆm} = C(j 1) R M,t j 1 = R M,t j κ (j 1) j r M r f {j=2,4,..., ˆm} η j R M,t j (3.4) ω j κ (j 1) (3.5) 7 [14] ρ i (i = 1, 2,...) , [1] (Monotonicity; X Y ρ(x) ρ(y )) [20]. 9 ρ ρ (X) := X X 2 1 ρ ( w r ) 1 w i ρ ( ) = r w =w M,t ( ) ( [ ]) ( [ 1/2 { } ]) 2 1/2 ρ w r = Var w r = E w (r r) 1 2ρ ( w r ) w =w [ { } ] 2 E w (r r) w i w =w (3.1) CAPM. 1 ρ ( ) = Cov [ ] rm,t, r i,t r M,t Var [ ] r M,t
5 5 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 (3.6) η l > 0 ω l > 0 ω 2 + ω ω ˆm = 1 (2.8) κ (j 1) = C(j 1) [ E R j M,t j 1 ] = l=1 ϕ (j) l β (l), (3.5) r i r f = ( r M r f ) {j=2,4,..., ˆm} j = 2, 4,..., ˆm ϕ (j) l := ω j κ (j 1) = ( r M r f ) [ E E R j 1+l M,t [ R j M,t ] {j=2,4,..., ˆm} ], l = 1,..., j 1 (3.7) ω j j 1 I- r i r f l=1 ϕ l β (l) (3.8) 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 + {j=4,6,..., ˆm} ω j ϕ (j) 5 β (5) + + ω ˆmϕ ( ˆm) ˆm 2 ω j ϕ (j) β (3) 3 β( ˆm 2) + + ω ˆm ϕ ( ˆm) ˆm 1 {j=6,8..., ˆm} β( ˆm 1) ω j ϕ (j) β (4) 4 (3.9) 2 I- 4 I- I- Fama-French 3 [5] I- Fama-French I- ᾱ i := r i r f β (1) ( r M,t r f ) (4.1) I- 10. ᾱ i c 2 β (2) + + c m 1β (m 1) + c m β (m) (4.2) m I- α i,t := r i,t r f β (1) (r M,t r f ) (4.3) CAPM α i,t (= E [α i,t ]) (2.1) R i,t, R M,t α i,t = ε (1) i,t 10 2 I- (= β (1) ), (4.1) (4.1) Jensen [10].
6 6 (4.2) I- (3.9) I- 3 I- ( ) 4 3 I- I- (3.9) I- ᾱ i,t (4.2) 4.2 SMB HML FF 3 FF 3 SMB (Small Minus Big), (B/P) HML (High Minus Low), 11. I- FF 3 (4.3) α i,t α i,t d 1 SMB t + d 2 HML t (4.4) SMB t HML t t SMB, HML (4.4) FF 3 r i,t r f β 1 (r M,t r f ) + β 2 SMB t + β 3 HML t β 1 CAPM ( 1 I- β (1) ) (4.4) CAPM ( α i,t ) 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 i,t SMB, HML (4.4) 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 (4.5) ᾱ i c 2 β (2) + + c m 1β (m 1) + c m β (m) + c ssmb-fl i + c h HML-FL i (4.6) I- (4.2) 11 SMB/HML FF 3 [5] [12]. 8.
7 NEEDS- FinancialQUEST ,121 R i,t R M,t (2.1) 14. I- i R M,t β (1) (1 ) R2 M,t β (2) SMB-FL, HML-FL 1 α i,t (4.4) i SMB-FL i, HML-FL i k = 1 k = 2 k = 3 k = 4 k = 5 k = 6 k = t t (%) (%) Table 4.1: β (k). 5% t. Table 4.1 1,121 I- 7 Table β (i), i = 1,..., 7 t 2 0 t 5% ( ) 2 I- 3 I- ( ) 2 50%, 3 65% 4 25% 5 % 15. I- SMB-FL HML-FL Table 4.2 Table 4.1 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 (3.9) I (2.2) (2.1) I- 7 I-.
8 8 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 4.2:. I-. SMB-FL, HML-FL I- 5 I- 5 I- 1% I- 3 7 I- I- 0 SMB-FL HML-FL I- Panel A: SMB-FL HML-FL 1 + ( ) + (+ ) ( ) + (+ ) 5 ( ) ( ) ( ) + (+ ) B/P 1 ( ) (+ ) ( ) B/P 5 ( ) ( ) + + (+ ) ( ) + (+ ) + ( ) ( ) + (+ ) + ( ) Panel B: F I- SMB-FL + HML-FL I- + SMB-FL + HML-FL 1 R 2 : , F : R 2 : 0.108, F : R 2 : 0.195, F : R 2 : 0.180, F : R 2 : , F : R 2 : 0.173, F : B/P 1 R 2 : 0.142, F : R 2 : 0.211, F : R 2 : 0.261, F : B/P 5 R 2 : 0.144, F : R 2 : 0.203, F : R 2 : 0.300, F : R 2 : 0.107, F : R 2 : 0.191, F : R 2 : 0.211, F : Table 4.3: (Panel A) I- SMB- FL HML-FL F (Panel B). +,,, 1%, 5%, 10%. (B/P) Table 4.3 Panel A 1 5 B/P 1 B/P B/P ( ) 1 5.
9 9 2 SMB-FL, HML-FL SMB-FL, HML-FL Panel B F 3 I- 4 I- 6 7 I- 2 5 I- I- I- 2 5 I- SMB-FL SMB-FL 5 Fama-MacBeth Fama-MacBeth ( ). 17 I- SMB-FL, HML-FL (250 ) 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 [6, 7] t I- 5.2 Table A.1 Fama-MacBeth Panel A 1 7 I Fama-MacBeth 17 Fama-MacBeth [6, 7] [3]. Fama-MacBeth. 18 t, t + 1 s r t+1,..., r t+s s i=1 (1 + r t+i) [12].
10 t t p 4 7, 5% 5% 10% 10%. 19 Panel B SMB-FL, HML-FL Panel C SMB-FL, HML-FL Panel D 1 I- Panel A Panel D Panel A Panel B Fama-MacBeth [6] 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 [6] B/P 20. HML-FL. (Table 4.2 ) HML-FL Fama-MacBeth SMB-FL [12] I- SMB-FL, HML-FL Fama-MacBeth 2 I- I- 6 I- 1 I- 7 I- I- 19 1, [6] Fama-MacBeth B/P B/P. B/P HML-FL HML-FL B/P HML-FL [6] B/P.
11 11 Fama-MacBeth 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, [3] J.H. Cochrane, Asset Pricing, Revised Edition, Princeton University Press, [4] R.F. Dittmar, Nonlinear pricing kernels, kurtosis preference, and evidence from the cross-section of equity returns, Journal of Finance 51, , [5] 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, [6] E.F. Fama and K.R. French, The cross-section of expected stock returns, Journal of Finance, 47(2), , [7] E.F. Fama and J.D. MacBeth, Risk, Return, and Equilibrium: Empirical Tests, The Journal of Political Economy, 81(3), , [8] H. Fang and T.-Y. Lai, Co-kurtosis and capital asset pricing, Financial Review 32, , [9] C. Harvey and A. Siddique, Conditional skewness in asset pricing tests, Journal of Finance 55, , [10] M.C. Jensen, The Performance of Mutual Funds in the Period , Journal of Finance 23, , [11] A. Kraus and R. Litzenberger, Skewness preference and the valuation of risk assets, Journal of Finance 31, , [12],, Fama-French,, 22, 3 23, [13] 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, [14] Y. Malevergne and D. Sornette, Extreme Financial Risks: From Dependence to Risk Management, Springer, [15] L. Pastor and R.F. Stambaugh, Liquidity risk and expected stock returns, Journal of Political Economy, 111(3), , [16] W. Sharpe, Capital asset prices: a theory of market equilibrium under conditions of risk, Journal of Finance 19, , [17],,, UFJ, , [18],,, Idiosyncratic, 2011 JAFEE, 49 60, [19],,,, JAFEE 12, pp , [20],, VaR, / / , , A
12 SMB-FL HML-FL Panel A: I- ( ): ( ) 9.465e e e e e e e e-04 t p % ( ) % % % % % % % % 5% ( ) % % % % % % % % 10% ( ) % % % % % % % % 10% ( ) % % % % % % % % Panel B: I- + SMB-FL, HML-FL ( ): ( ) 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 ( ): ( ) 2.364e e e e-04 t p % ( ) % % % % 5% ( ) % % % % 10% ( ) % % % % 10% ( ) % % % % Panel D: (1 I- ) ( ): ( ) 2.390e e-04 t p % ( ) % % 5% ( ) % % 10% ( ) % % 10% ( ) % % Table A.1: Fama MacBeth. I-.
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