An Application of Cointegration Analysis on Strategic Asset Allocation

Transcription

1 An Application of Cointegration Analysis on Strategic Asset Allocation (Jiahn-Bang Jang) (Yi-Ting Lai)* 12 (S&P 500) (NASDAQ) J.P. (J.P. Morgan bond) (M-V) (M-CVaR) Key wordcointegrationstrategic Asset AllocationConditional Value at Risk Efficient Frontier *

2 (Strategic Asset Allocation) (conditional information) (unconditional information) (Campbell et al.(2003)) (Bange and Thomas(2004)) (Brouwer and Philippe(2009)) Markowitz(1952) - (Mean-Variance, M-V) (Downside Risk) Duarte and Alcantara(1999) - (Mean-VaR Efficient Frontier) Artzner and et al.(1999) (coherent) (sub-additive) Artzner and et al. (1999)Rockafellar and Uryasev(2000) (Conditional Value at Risk, CVaR) Mean-CVaR(M-CVaR) M-V M-V (Kat, 2003) Engle and Granger(1987) Corhay et al. (1993) ( ) Arshanapalli and Doukas(1993) Engle-Granger(1987) Sanju n et al.(2009) Andros and Kontonikas (2010) Lucas(1997) (Tactical) (Strategic) F ss and Kaiser(2007) (M-V) (M-CVaR) M-V

3 () Augmented Dickey-Fuller(ADF) Dickey and Fuller(1979) DF AR(1) 1 (white noise) 1 DF Said and Dickey (1984) ADF(Augmented Dickey-Fuller) ARMA(p,q) (drift) (deterministic trend) p=0 DF α () Phillips and Perron (PP) ADF Phillips and Perron(1988) DF (non-parametric correction) DF (heteroscedasticity) (2004) ( ) 1 (white noise)e( )=0, Var( )=, t=1,2,3..., Cov(, )=0, t s

4 N ( ) (determinant of the regressor cross-product matrix) Engle and Granger(1987) (two-step) 1. n I (d ) I (d ) (integrated order) d 2. n d b CI (d, b) Engle and Granger Engle and Granger Johansen(1991) Johansen and Juselius(1990) (maximum likelihood estimationmle) Engle and Granger VAR(Vector Autoregressive) (rank) Johansen Johansen n I(1) k VAR

5 (6) Granger Representation VAR (Vector Error Correction Model, VECM) (7) (8) I (Error Correction Item) (Impact Matrix) Johansen (rank) rank( ) 1. rank( )n (Full Rank) VAR 2. rank( )0 VAR 3. rank( )r0rn r (nr) rank( ) (Characteristic roots)johansen(1991) 1. (trace test)

6 ) 2. (maximal eigenvalue test) T r r0 r Johansen(1991) (Brownian motion) Cheung and Lai(1993) Serletis(1993) Granger Representation (8) Johansen 0 n (9) 1 (m=2) (10)

7 (11) M-V M-CVaR M-V M-CVaR () M-V ( (2006)Mean-Variance ) Markowitz(1952) M-V n s.t. (13) (14) W

8 Step1 Lagrange L W Step2 W M-V () M-CVaR (2002) CVaR CVaR Rockafellar and Uryasev(2000) CVaR VaR - Step1 CVaR n R

9 m n t W t (m1) t VaR 2 VaR CVaR t1 CVaR Step2 t1 Step3 CVaR W CVaR CVaR (Investment Opportunity Set) CVaR CVaR M-CVaR 2 VaR VaR

10 12 (Credit Suisse Tremont Hedge Fund Index) (Greenwich Alternative Investments) 12 / 500 J.P / (-2.53%) (11.7%) (10.62%) (25.82%) J.P. (4.03%) / J.B. 1. J.B *** *** *** *** *** *** *** *** *** *** *** ln( 500 ) *** ln( ) *** ln(j.p. ) *** 1993/12~2009/12193 = 3 ln J.B. test H 0 *** 1%

11 ADF PP ADF text PP text 1% 5% 1% 5% () *** *** ( ) *** *** ( ) *** *** ( ) *** *** ( ) *** *** ( ) *** *** / ( / ) *** *** ( ) *** *** ( ) *** *** ** ( ) *** *** ( ) *** *** ( ) *** *** ( 500 ) *** *** ( ) *** *** J.P (J.P. ) *** *** Akaike s information criterion(aic) Schwartz s criterion(sc) H 0 *** 1% ** 5% 2 ADF PP I(1) (Non-stationary) 3 Johansen (Johansen 1991; Johansen and Juselius 1990) AIC (Akaike s information criterion) SC (Schwarz s criterion) (VECM) 3 3 1% I(1)

12 AIC ** SC ** / AIC ** SC ** AIC ** SC ** AIC ** SC ** AIC SC** 5% 3 4 AIC % 5% 500 J.P λ trace -λ max 5% 1% P 5% 1% P r = *** *** r *** * r ** r * r / r = ** ** r r r = ** *** r r r = *** *** r r *** 1% ** 5% * 10%

13 (VECM) ( 500 J.P. ) 4 5% 5 5% 500J.P. 5. χ 2 (m) Prob. χ 2 (m) Prob. β = ** α = * β 500 = α 500 = ** β J.P. = α J.P. = β = ** α = *** β = *** α = *** β = * α = *** β = * α = β = ** α = *** β = ** α = * *** 1% ** 5% * 10% / 5% / 500 J.P.

14 4 6. / / χ 2 (m) Prob. χ 2 (m) Prob. β = α = β 500 = ** α 500 = β J.P. = α J.P. = β / = α / = β = *** α = *** β = α = β 500 = α 500 = β J.P. = ** α J.P. = *** β = α = *** β = ** α = *** β = α = β 500 = α 500 = β J.P. = α J.P. = *** β = α = β = α = *** *** 1% ** 5% / M-V M-CVaR 5 (Tangent Portfolio) 7 / M-V M-CVaR 4 M-V M-CVaR %

15 / M-V M-CVaR J.P. /

16 500 J.P. 12 M-V M-CVaR / M-V M-CVaR / M-V M-CVaR / (M-V) (M-CVaR) 1. (2005) : : (2002) 3. (2004) 4. (2006) Mean-Variance VaR CVaR 5. Arshanapalli, B. and Doukas, J. (1993), International stock market linkage: evidence from pre- and post-october 1987 period, J. Bank. Finance. Vol. 17(1), pp Artzner, P., Delbaen, F., Eber, J.-M and Heath, D.(1999), Coherent measure of Risk, Mathematical Finance, Vol.9(3), pp Bange, Mary M. and Thomas W. Miller Jr., (2004) Return momentum and global portfolio allocations, Journal of Empirical Finance, Vol.11, No.4, p

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18 Rents and Land Prices in Japan: A Panel Cointegration Approach,Land Economics, Vol.85, No.4, p