68 Granger Granger
Abstract During the late 1980 s, the stock market and real estate market in Taiwan both went into enormous booms. The Taiwan Stock Market Weighted Price Index (TSMWPI) and real estate prices both reach the highest peaks that they never reach before. It seems that there is a certain relationship between the stock market and real estate market. Therefore, this thesis proposes to study the following two propositions: (1) if the stock market and real estate market are integrated, then a certain degree of asset substitution will occur. The price of the assets in the two markets will interacted due to the asset substitution. And this price interaction will reduce the effect of risk diversifying. (2) But if the two markets are segmented, the effect the diversifying risk will get significant increasing as long as having the assets of the two markets included in your portfolio simultaneously. Past studies commonly investigated the relationship between the price series in these two markets, and therefore make the conclusions of their relationships. However, any individual price series cannot represent the activities of the whole market. Consequently, we adopt the Arbitrage Pricing Model (APM) to examine the relationships between the stock market and the real estate market in Taiwan. Our study is the first one to discuss this topic from the view of the market. Our study also tests causality relationship between the price series, but we have some improvements compared to the past studies. Our model includes an exogenous variable which captures the influence affecting both the stock market and real estate market at the same time. The test of casualty is also based on the cointegration theory. We test four cities in Taiwan, including the Taipei City, Taipei County, Taichung City and Kaohsiung City. Our findings suggest that the house price of the Taipei City and the Taipei County are co-integrated with the TSMWPI, that is, there is a long-term equilibrium relationship between the two cities and TSMWPI. The test of Granger Causality indicates that TSMWPI only Granger causes the house price of the Taipei City. All other causality relationships are not existed in these four cities. Finally, we use the APM to examine the relationship between the two markets and find that no evidence of relationship is existed between the stock and the housing market, suggesting that the stock market and the housing market in Taiwan are segmented. Key Words: Real Estate Market, Stock Market, Causality, CAPM
1 3.3. 3 5 6 7. 7. 8..10..12..12..15...20.20.23.. 24.. 27.. 29..34.34
APT.35..39.39.42 Granger 43 Arbitrage Pricing Model-APT 45 47..48..50 Granger 51 APT..55..58..60...61...62.64
22 22 29 49 49 AEG...50 Granger.53 Granger.53 Granger.54 Granger.54 APT 57...4...9.21.21.47
12000 (1990) (1996) (1997) (2000)
(1995) (1996) (Vector Autoregression Model) (Engle and Granger, 1987) (Error Correction)
Granger (1969) 1 Granger Granger Capital Asset Pricing Model(CAPM) Asset Pricing Theory(APT) CAPM APT (portfolio) APT
(quality-fixed) 2 72 36 3 TEJ Ln 2 3
62 63 68 69 76 77 23 1. 62 63 1.5 2. 68 69 68 2
3. 76 77 75 76 78 2 4 79 82 83 85 14.5% 28.55% 23.08% 86 85 22.65% 87 86 26.11% 88 1500
1028.7 71 87 27% 88 104 114 66-69 74-78
1 51 55 60 79 12000 12495 80% 86 7 87 88 1500 89 2 4 NASDAQ 15.57% 1
90 4000 89 5 472 3.184 12.27
2 1. 2. 2
3. 4. 5. 6. 3 1. 2. 3 1977 27 1994 162 1992 107/108 1996 119
3. 4. 5. 4 1. 2. 3. 4
1. 2. 3. 4. 5.
1. 2. 3. 4. 5. 6.
7. 8. 9. 10. 20%
5 364 81 1. 15.2% 6 2. 20.8% 3. 24.6% 5 1989 1991 12 1992 1995 401 6
4. 16.6% 5. 22.8% 6. 22 16~20
180000 160000 140000 120000 100000 80000 60000 40000 20000 0 70q1 71q2 72q3 73q4 75q1 76q2 77q3 78q4 80q1 81q2 82q3 83q4 85q1 86q2 87q3 14000 12000 10000 8000 6000 4000 2000 0
63-66 67-74 75-82 83-90 62-90 0.0466-0.1246 0.3163-0.0835 0.2532 5324.8 34355.1 106610.46 19254.12 150394.91 237.9467 452.4233 10572.97 4646.077 11281.16 0.0545 NA 0.0376 57829.99 NA 3068.921 0 1 2 3 4 5 6 7 8 0.2532-0.1484-0.0449 0.2954-0.0747-0.2137 0.0895-0.2598 0.1695 0 1 2 3 4 5 6 7 8 0.2532 0.3839 0.0578-0.0329 0.2911-0.0825-0.0166 0.0877 0.0709 75 82 75 82 0.3163 75 82
1996 Hsiao 1981 5%
Breedon and Joyce (1992) Richard K.Green(1999) Markowitz Granger Ong 1995 Engle Granger (1987)
Adler Dumas (1983) Solnik(1977) - Liu Hartzell Greig Grissiom 1990 1978 1986 CAPM Patrick Wilson John Okunev Guy Ta 1995 CAPM Arbitrage Pricing Theory(APT) David C.Ling Andy Naranjo 1999 1978 1994 Arbitrage Pricing Model(APT) REITs 1990
Patrick Wilson John Okunev 1997 Real Estate Investment Trust (REITs) S&P500 mean reversion deterministic drift term fractionally integrated REITs 1999 1971 12 1993 12 22 fractional cointegration 1987 Daniel C.Quan Sheridan Titman 1999 17 16
( (1990) (1994) ) Chen and Patel (1998) ( ) 1991 74 1 78 12 12 12 1995 Granger 2 1996 VAR
Horng Jinh Chang Tueh Hua Lee 2000 Qkunev and Wilson (1997) (1999) 2000 80 88 John Okunev Goldstein and Nelling (1999)
( ) ( ) Crocker H. Liu David J.Hartzell Wylie Greig Terry V.Grissom (1990) Patrick Wilson John Okunev Guy Ta(1995) ONG SEOW ENG(1995) EREIT, FRC, NCREIF 1978 ~ S&P500, SMI, MGCI 1986 USMI, ACLI, ICM CAPM MA UI 1979 HI ~ 1993 PI (property transfer expense) AI Private Property Price Index SES-All Property Index CAPM Angler and 1977 Granger ~ 1992
Patrick Wilson John Okunev 1997 Patrick Wilson John Okunev 1999 David C. Ling Andy Naranjo (1999) REIT, Hybrid REIT, Equity REIT, Mortgage REIT 1993 S&P500 1979 All REITs ( ) FTAP Financial Times All Properties ( ) ~ Property Index( ) 1973 S&P500,S&P small Cap Index( ) FTSE (Financial Times Stock Exchange) ( ) All Ordinaries Index( ) ~ 1993 REITs form CRSP NCREIF, a combination of NCREIF and ACLI 1978 ~ 1994 mean reversion Fractional Cointergration APT REIT
Richard K. NYSE, AMEX, Nasdaq Green (1999) median price data from the California Association of REALTORS for San Francisco Country, Santa Clara Country, Los Angeles Country, Orange Country Russell2000 1989 ~ 1998 Granger 1991 1995 12 1985 ~ 1989 Granger 1980 ~ 1994
1996,82 Stock80 Stock90 from AREMOS 1986 ~ 1996 VAR 2000 1991 ~ 1999 John Okunev Horng Jihn Chang Tueh Hua Lee (2000) 1991 ~ 1998
70 90 (, 1995) (, 1996) CAPM APT
( ) ( ) Markowitz 1952
R t =f(s t-1,s t-2,s t-3,,e) R t S t-1,s t-2,s t-3 E 4.1 S t =f(r t-1,r t-2,r t-3,,e) (4.2 ) APT
Capital Asset Pricing Model(CAPM) Arbitrage Pricing Model(APT) CAPM APT CAPM i f i ( E( R R ) E( R ) = R + β ) 4.3 m f E(R i ) E(R m ) i i= im / 2 m im 2 m APT APT ( E( R1 ) Rf ) + β( i,2) ( E( R2) R f ) + L+ ( i, n ( E( Rn R f ) ei E = ) + ( Ri ) R f + β( i,1) β ) 4.4 R f (i,k) i k APT
APT Factor Analysis 4 4.4 ( E( Rm ) Rf ) + ( i,2 ( E( Rc R f ) ei E = β ) + (4.5 ) ( Ri ) R f + ( i,1) β ) E(R m ) E(R c ) 4.4 ( Rm Rf ) + β( i,2) ( Rc R f ) + ( i,3 GNPt ei R β + (4.6 ) i = R f + ( i,1) β ) 4.6 R m,t =a+b*r c,t + ν (4.7 ) c m ν R m 4.6 c m 4 ( ) Liu et al (1990) Ong (1995)
( νc / m R f ) + β( i,2) ( Rc R f ) + ( i,3 GNPt ei R β + 4.8 i = R f + ( i,1) β ) i
Granger (1969) Granger (Error Correction Term) (mis-specified) Granger APT Ln stationary (nonstationary) unit root
1 1 Stationary Augmented Dickey Fuller(ADF) 1979 Dickey Fuller t Dickey Fuller Dickey-Fuller (Dickey-Fuller unit root test) DF Y = ρ 1 + ε (4.9 ) t Y t t Y = α + ρ 1 + ε (4.10 ) t Y t t Y = α + βt + ρ 1 + ε (4.11 ) t Y t t = -1 t H 0 0 ( ) H 1 0 ( ) Dickey Fuller τ τ µ τ τ DF
t (White Noise) DF Dickey Fuller Augmented Dickey Fuller(ADF) Y = ρ Y + λ Y + ε t ADF t m i= 1 i t i Y = α + ρy + λ Y + ε t t m i= 1 i t i Y = α + βt + ρy + λ Y + ε t t m i= 1 i t t t i i t = -1 t (4.12 ) (4.13 ) (4.14 ) Y t Y t ADF DF Akaike information criterion(aic)(1974) AIC ' e e 2q AIC( q) = ln + 4.15 n n n: q: e e
AIC ADF Phillips-Perron(1988) DF Phillips Perron DF Phillips-Perron * * Y t = a0 + a1y t 1 + µ t 4.16 T Y t = a~ + a~ Yt + a~ 0 1 1 2( t ) + µ t 4.17 2 T t t: Phillips Perron DF * * Z(t a 1 )( a 1 =1) Z(t ~a 1 )( * ~a 1=1) Z(t ~a 2 )( ~a 2 =0) Z( 3 )( a 1 =1 ~a 2 =0) C( L) µ t = *εt 4.16 B( L) B(L)y t = * * a0 B(L)+ a1 B(L)y t-1 +C(L) t 4.18 Phillips-Perron DF
Co-integration X t Y t R t =X t - Y t X t Y t Augmented Engle-Granger (AEG) 1987 AEG X t = 0 + 1 *Y t + t (4.19 ) t ADF t t I(0) X t,y t t t I(0) X t,y t Granger Granger Granger X Y t t m m 0 + a j X t j + bjyt j + εt j= 1 j= 1 = α (4.20 ) m m 0 + c j X t j + d jyt j + νt j= 1 j= 1 = β (4.21 ) X t Y t t t m
Granger (4.20 ) Y t Y t X t (4.21 ) X t Y t X t Y t X t H 0 b 1 =b 2 =b 3 = =b m =0 H 1 b j X t Y t H 0 d 1 =d 2 =d 3 = =d m =0 H 1 d j Granger F Partial F 4.20 X t = a m 0 + a j X t j + µ t 4.22 j= 1 Reduce Form 4.19 Complete Form F F SSEr SSE df df SSE r c = 4.23 df c c c SSE c SSE r df r df c F F Y t X t Y t X t Yt Granger Cause
Xt X t Y t Y t X t (unidirectional) Y t X t X t, Y t AEG X Y t t m m 0 + α 1µ t 1 + a j X t j + bjyt j + εt j= 1 j= 1 = α (4.24 ) m m 0 + β 1µ t 1 + c j X t j + d jyt j + νt j= 1 j= 1 = β (4.25 ) t-1 4.19 Arbitrage Pricing Model APT Capital Asset Pricing Model(CAPM) Arbitrage Pricing Model(APT) CAPM Sharpe(1964) Lintner(1965) Mossion(1966) CAPM 7 1. 2. 3. 4. 5. 6. 7.
E(R i )=R f +(E(R m )-R f )* i E(R i ) (4.26 ) E R m i Security Market Line; SML APT Steven Ross APT (4.27 ) ( E( R1 ) Rf ) + β( i,2) ( E( R2) R f ) + L+ ( i, n ( E( Rn R f ) ei E = ) + ( Ri ) R f + β( i,1) β ) APT CAPM (4.27 )
Granger Granger APT APT Granger
Granger APT ADF Phillip-Perron (4.14 ) 0 I(0) (4.13 ) 1 I(1) AIC
ADF Statistic Phillip-Perron Statistic -1.1321 3-1.0728-2.5426 4-1.3797-2.6321* 1-4.2142** -4.2596*** 1-4.8426*** -1.5859 1-1.4272-1.7066 4-1.749 1%, 5%, 10% ADF Statistic Phillip-Perron Statistic -4.2405*** 2-8.1783*** -2.6873* 2-8.0597*** -5.5901*** 1-6.4557*** -3.3103** 3-11.8462*** 1%, 5%, 10% I(0) I(1)
(Error Correction Term) (mis-specified) Augmented Engle Granger(AEG) ADF I(0) I(1) I(1) AEG AEG u i AEG ADF Statistic Phillip-Perron Statistic -2.3364** 1-2.3949** -2.1235** 6-1.831* 1%, 5%, 10% I(0) Granger
Granger Granger I(1) m m=4 b j 0 c j 0
Granger T F R 2 0.3030 0.9213-0.2038-3.1526*** 2.9365** 0.5045 0.2576 0.2897 0.0346 0.1977 1.0082 0.1542 1%, 5%, 10% Granger T F R 2-0.1272-0.4057-0.0945-2.6838*** 1.3098 0.4080 0.4606 0.5606-0.204-2.2113** 1.4878 0.2336 1%, 5%, 10%
Granger T F R 2 1.0246 1.4897 1.5818 0.4420 1.4245 0.7033 1.4317 0.2578 1%, 5%, 10% Granger T F R 2 0.4065 0.9205 0.4210 0.2273 1.1996 0.6191 1.2293 0.3681 1%, 5%, 10% -0.2038 20.38%
1. 2. 3. 4. APT
APT APT APT ( νc / m R f ) + β( i,2) ( Rc Rf ) + ( i,3 GNPt ei R α + (5.1 ) i R f = 0 + β( i,1) β ) c/m R c GNP t R f i 0 CAPM Jensen s Abnormal Performance Index 1 (i,1) 0 (i,1) 1 Michael C.Jensen (1968), The Performance of Mutual Funds in the Period 1945-1964., Journal of Finance, May
APT T P-value R 2 DW 0-0.0350-2.2027 0.0310** (i,2) 0.1844 3.3946 0.0012** (i,1) 0.1216 0.8875 0.3780 (i,3) 0.1402 0.3698 0.7127 0.1640 2.1144 T P-value R 2 DW 0-0.0285-1.9678 0.0532* (i,2) 0.1127 2.2719 0.0263** (i,1) 0.1778 1.4212 0.1598 (i,3) 0.0009 0.0025 0.998 0.1055 2.0744 T P-value R 2 DW 0-0.0588-2.462 0.0194** (i,2) 0.0916 1.0806 0.2879 (i,1) 0.232 1.1376 0.2637 (i,3) 0.8065 1.7906 0.0828* 0.1309 1.3773 T P-value R 2 DW 0-0.0662-5.2188 0** (i,2) 0.093 2.0668 0.0469** (i,1) 0.0498 0.4602 0.6485 (i,3) 0.0851 0.3559 0.7242 * 10% 0 ** 5% 0 0.1188 1.2205 0 0
i (i,2) 0 (i,1) 0 APT APT APT
Granger Granger Granger
APT APT
Ljunj-Box Jarque-Bera White Heteroskedasticity L-B Q Statistic J-B Statistic R 2 *Obs 2.4312 36.4640** 1.4128 26.6811 Lag20 0.1543 24.3360 1.9121 33.9142** 1.3784 17.2110 Lag6,9,10 6.3138** 21.2702 2.7855 14.2980 Lag9,10 1.6017 18.3813 1% 5% 10%
1. 2. 3. 4. 5. 1.
2. 3. Granger
1.Alder, M. and B. Dumas (1983), International portfolio choice and corporation finance: A survey., Journal of Finance, No.38, pp925-984 2.Breedon, F. and Joyce, M. A. S. (1992), House prices, Arrears and Possessions, Bank of England Quarterly Bulletin, May, pp173-179. 3.Chen, M-C and Patel, K. (1998). House Price Dynamics and Granger Causality: An Analysis of Taipei New Dwelling Market., Journal of Asian Real Estate Society, 1(1), 101-126. 4.Chang, H. J. and T. H. Lee (2000), The dynamic relationship between house and stock market prices in Taiwan: An empirical study., International Journal of Management, Vol.17 Iss.2 June, pp143-150 5.Dickey, D. and W. A. Fuller (1979), Distribution of the estimates for autoregressive time series with a unit root., Journal of the American Statistical Association, No.74:June, pp427-31 6.Dickey, D. and W. A. Fuller (1981), Likelihood ratio statistics for autoregressive time series with a unit root, Econometrica, No.49:July, pp1057-1072 7.Enders, W. (1995), Applied Econometric Time Series, John Wiley&Sons Inc. 8.Engle, R. and C. W. J. Granger (1987), Co-integration and error-correction: Representation, Estimation, and Testing., Econometrica, 55:March, pp251-276 9.Granger, C. W. J. (1969), Investigating Causal Relations by Econometric Models and Cross-spectral Methods, Econometrica, Vol. 37, 424-438. 10.Green, R. K. (1999), Stock prices and house prices in California: New evidence of a wealth effect? A Note, November, University of Wilconsin-Madison 11. Gujarati, D. N. (1995), Basic Econometrics, McGRAW-Hill Inc.
12. Jensen, M. C. (1968), The Performance of Mutual Funds in the Period 1945-1964., Journal of Finance, May 13.Jorion, P. and E. Schwartz (1986), Integration vs. segmentation in the Canadian stock market, The Journal of Finance, July, pp603-616 14.Kim, H. L. (1997), The historical performance of Singapore property stocks, Journal of Property Finance, Vol.8 No.2, pp111-125 15.Liu, C. H. and D. J. Hartzell and W. Greig and T. V. Grissom (1990), The integration of the real estate market and the stock market: Some Preliminary evidence, Journal of Real Estate Finance and Economics, No. 3, pp261-282 16.Ling, D. C. and A. Naranjo (1999), The integration of commercial real estate markets and stock markets, Real Estate Economics, Vol.27, No.3, pp1-28 17.Liu, C. H., Grisson, T. V. and Hartzell, D. J. (1990). The impact of market imperfections on real estate returns and optimal investment portfolio., Journal of Real Estate Finance and Economics, 3, 261-82. 18.Madura, J. and A. M. Whyte (1991), Integration versus segmentation in real asset markets: Implications for direct foreign investment, Global Finance Journal, Vol.2, pp129-137 19.Ong, S. E. (1995), Singapore real estate and property stocks-a cointegration test, Journal of Property Research, No12, pp29-39 20.Phillips, P. and P. Perron (1988), Testing for a unit root in time series regression, Biometrica, Vol.75:June, pp335-346 21. Pindyck, R. S. and D. L. Rubinfeld (1997), Econometric Models and Economic Forecasts, McGRAW-Hill Inc. 22.Quan, D. C. and S. Titman (1997), Commercial real estate prices and stock market returns: An International Analysis, Financial Analysts Journal, May/June, pp21-34 23.Ross, S. A. and R. C. Zisler (1991), Risk and return in real estate, Journal of Real Estate Finance and Economics, No.4, pp175-190 24.Solnik, B. (1977), Testing International asset pricing models: Some
pessimistic views., Journal of Finance, No.32, pp503-512 25.Shilton, L. (2000), Random walks and the co-integration of the ACLI and NCREIF, Real Estate Economics, Vol.28 NO.3, pp435-465 26.Wilson, P. and J. Okunev and G. Ta (1996), Are real estate and securities markets integrated?, Journal of Property Valuation & Investment, Vol.14 No5, pp7-24 27.Wilson, P. and J. Okunev (1997), Using Nonlinear Tests to examine integration between real estate and stock markets, Real Estate Economics, Vol.25 No.3, pp487-503 28.Wilson, P. and J. Okunev (1999), Long-Term dependencies and long run Non-Periodic Co-Cycles: Real estate and stock markets, Journal of Real Estate Research, Vol.18 No.2, pp257-278 29.Wheaton, W. C. (1999), Real estate cycles: Some fundamentals, Real Estate Economics, Vol.27 No.2, pp209-230 1. (1989) 2. (1990) pp.220-24 3. (1991) 4. (1991) 12 5. (1992) 6. (1992) 107/108 7. (1994) 22 pp5-41 8. (1994)
pp.49-66 9. (1994) 27 10. (1994) 162 11. (1994) 12. (1995) 110 pp42-45 13. (1995) -Granger 14. (1995) 112 15. (1995) 401 16. (1996) 119 17. (1996) 18. (1997) - 19. (1997) 20. (1997) 21. (1997) 22. (1997) pp574-586 23. (1997) - -( ) pp1-21 24. (1998) - -( ) pp1-17 25. (1999) --- 26. (2000) 27. pp163-185
28. 216 29. 231