リスクとリターンの実証分析―行動ファイナンスによるアプローチ―　新関三希代

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1 Niizeki 1998, ) I 1

2 Duffee 1995 Chen, Hong and Stein 2000 Black 1976 Chrisite 1982 Pindyck 1984 French, Schwert and Stambaugh 1987 Poterba and Summers 1986 Hong and Stein 1999

3 Chen, Hong and Stein ) Kahneman and Tversky 1979 von Neumann and Morgenstern Daniel Kahneman

4 Kahneman and Tversky 1979 Prospect Theory Risky Prospects Expected Utility Theory

5 Positive Prospects Negative Prospects Certainty Effect A B 3) Positive Prospects A B 1 A 80 4,000 A=(4000,0.8) B 100 3,000 B=(3000,1) 2 A 20 4,000 A=(4000,0.2) B 25 3,000 B=(3000,0.25) Kahneman and Tversky, B 2 A 4) Negative Prospects 3 Kahneman and Tversky x u(x) u(0)=0 1 B u(3000) / u(4000)>4 / A B 1 / 4 A u(3000) / u(4000)<4 / 5

6 A 80 4,000 A=( 4000,0.8) B 100 3,000 B=( 3000,1) 4 A 20 4,000 A=( 4000,0.2) B 25 3,000 B=( 3000,0.25) Kahneman and Tversky, A 4 B Positive Prospects Reflection Effect S Value Function :v(x) v r x v(x)

7 v x Reference Point r v(x) x>0 concave x<0 convex : r (x>0) (v) r v (x)<0 x<0 v (x)>0 5) 1 A B (v) 5 A 25 6,000 A=(6000,0.25) B 25 4, ,000 B=(4000,0.25;2000,0.25) 6 A 25 6,000 A=( 6000,0.25) B 25 4, ,000 B=( 4000,0.25; 2000,0.25) Kahneman and Tversky, B 6 A π(0.25) π(0.25)v(6000)<π(0.25)[v(4000)+v(2000)] π(0.25)v( 6000)>π(0.25)[v( 4000)+v( 2000)] 5 r 0

8 π(0.25) v(6000)<v(4000)+v(2000) v( 6000)>v( 4000)+v( 2000) x>0 v(x) x 0 4,000 2,000 6,000 4,000 2,000 6,000 6) Disposition Effect Weber and Camerer, 1998 r r v(x) x>0 x<0 v (x) 6 1,500 1,500

9 Loss Aversiveness Kahneman and Tversky, 1979 Tversky and Kahneman, ), 2002 x y 2 x>y 7 A 50 x 50 x A=(x,0.5; x,0.5) B 50 y 50 y B=(y,0.5; y,0.5) B π(0.5)v(y)+π(0.5)v( y)>π(0.5)v(x)+π(0.5)v( x) π(0.5) v(y)+v( y)>v(x)+v( x) v( y) v( x)>v(x) v(y) y=0 v(x)< v( x) 1 v (x)< v ( x) x<0 7

10 v ( x) v (x) v(x) x<0 8) v ( x) x<0 9), ) ,380

11 r 0 3 1, (2006) )

12 , , , TOPIX 9, , , DIAM 7, , TOPIX 6, ,

13 ) JF JP Certainty Effect 12 CML CML 6 6,000 4,000 2, ,000 2,000 6,000 v(x) Thaler, 1985

14 Disposition Effect v(x) 4 Kernel Regression Model Kernel Density Estimator 13) R t t 14) Z t DGP 1 z V t 1/2(z) 1/2 V t (z)=e R t 2 Z t =z (E R t Z t =z ) (2) Kernel Regression Model f(x t ) 15) 13 Niizeki P t t P t 1 t 1 R t=log( P t/p t 1 ) 15 f(x t) Y t

15 Y t =f(x t )+v t, t=1,,t 2 Y t X t v t (iid) Kernel Density Estimate T 1 f(x) Th t=1 K(w t ) 3 w t =(x X t )/h 4 T h band-width 16) K(w t ) box smooth bump (5) Epanechnikov 17) K(w t ) 4 3 (1 w 2 t ) I( w t 1) 5 K (2) Y t X t 6 (m(x)) x Simonoff 1996 x Y t X t T m(x) (Y t 0 1 (x X t )) 2 K(w t ) t= h tradeoff Silverman (1986) 0.9T min(s,r/1.34) s R 17 smoothing Epanechnikov Silverman 1986

16 NIKKEI225 1 SOB PAT 225 NIK TOPIX TOP 18) 2 INB KOM 19) Date Index

17 2001/7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/11 Date NIK 140, , ,000 80,000 60,000 40,000 20,000 0 Index 2001/7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/11 Date TOP 140, , ,000 80,000 60,000 40,000 20,000 0 Index NIKKEI Index 2001/7/ /11/ /1/ /3/11 Date 2001/9/ /5/ /7/ /11/ /1/ /3/ /9/ /5/ /7/ /11/ /9/ /1/ /3/ /5/ /7/ /11/ /9/ /1/ /3/ /5/ /7/

18 /7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/11 Date SOB 9,000 8,500 8,000 7,500 7,000 6,500 Index Date 2001/7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/11 PAT 10,000 6,000 5,000 4,000 3,000 2,000 1,000 0 Index 7,000 8,000 9, /7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/11 Date INB Index

19 Index KOM 2001/7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/ /10/ /1/ /4/ /7/11 Date 225 NIKKEI225P NIKP TOPP SOBP PATP INBP KOMP Mean S.D. Corr Vol Mean S. D. Corr Vol NIKKEI225P 225 NIKP 225 TOPP TOPIX SOBP PATP INBP KOMP 7 (1) Kernel Density Estimate

20 Mean Max Min S.D. V 1/2 NIKKEI225R NIKR TOPR SOBR PATR INBR KOMR 5.59E ) 225 TOPIX 7.85E E E Mean Max Min S. D. V 1/2 NIKKEI225R 225 NIKR 225 TOPR TOPIX SOBR PATR INBR KOMR (2) Return 20 1

21 Volatility 1 P 21).012 NIKKEI Volatility Return Volatility NK Return Volatility TOP Return V t 1/2= R t+u t u t iid) 1

22 SOB.0030 PAT Volatility Volatility Return Return.020 INB.020 KOM Volatility Volatility Return Return 1 P-value NIKKEI225R NIKR TOPR SOBR PATR INBR KOMR E V t 1/2= 0 1 R t+u t P-value P 4

23 ) Reflection Effect Disposition Effect 23) Kick Kick 22 23

24 Risky Assets Riskless Assets 5

25 TOPIX 3 225

27 Blac k, F., (1976) Studies of Stock Price Volatility Changes, Proceedings of the 1976 meetings of the Business and Economics Statistics Section, American Statistical Association, pp Che n, J., H. Hong, J. C. Stein, (2000) Forcasting Crashes: Trading Volume, Past Returns and Conditional Skewness in Stock Prices, NBER Working Paper, No Chri stie, A. A., (1982) The Stochastic Behavior of Common Stock Variances, Journal of Financial Economics, Vol.10, pp Duff ee, G. R., (1995) Stock Returns and Volatility: A Firm-level Analysis, Journal of Financial Economics, Vol.37, pp Fren ch, K. R., G. W. Schwert, and R. F. Stambaugh, (1987) Expected Stock Returns and Volatility, Journal of Financial Economics, Vol.19, pp Hon g, H., and J. C. Stein, (1999) Differences of Opinion, Rational Arbitrage and Market Crashes, NBER Working Paper, No Kah neman, D., and A. Tversky, (1979) Prospect Theory: An Analysis of Decision under Risk, Econometrica, Vol.47, pp Niiz eki, K. M., (1998) The Japanese Stock Rate of Return and Volatility: A Comparison of Methods to Estimate Volatilities, The Doshisha University Economic Review, Vol.55, pp Pind yck, R. S., (1984) Risk, Inflation, and the Stock Market, American Economic Review, Vol.74, pp Pote rba, J. M., and L. H. Summers, (1986) The Persistence of Volatility and Stock Market Fluctuations, American Economic Review, Vol.76, pp Silve rman, B. W., (1986) Density Estimation for Statistics and Data Analysis, London: Chapman and Hall. Simonoff, J. S., (1996) Smoothing Methods in Statistics, New York: Springer-Verlag. Thal er, R.H., (1985) Mental Accounting and Consumer Choice, Marketing Science, Vol.4, pp Tver sky, A., and D. Kahneman, (1991) Loss Aversion and Riskless Choice: A Reference

28 Dependent Model, Quarterly Journal of Economics, Vol.6, pp von Neumann, J., and O. Morgenstern, (1944) Theory of Games and Economic Behavior, Princeton : Princeton University Press. Web er, M., and C. Camerer, (1998) The Disposition Effect in Securities Trading: An Experimental Analysis, Journal of Economic Behavior and Organization, Vol.33, pp , (2006) H.P.., (2005) , pp.1-15., (2002).

29 The Doshisha University Economic Review Vol.58 No.3 Abstract Mikiyo Kii NIIZEKI, Empirical Tests between Risks and Returns: An Analysis with a Prospect Theory This paper investigates the correlation between the volatilities and the indices returns using daily data for Nikkei 225 and Japanese Open Stock Investment Trusts. Both a prospect theory and a nonparametric regression method are used to investigate a negative relationship between volatilities and returns. Three important features are found. First, the volatilities of both the Japanese stock index and the funds whose indices are connected with the stock market indices are found to depend negatively on the returns. This negative relationship is shown with a value function in the prospect theory. Second, the volatilities are not related to the returns of the funds with the monthly dividends and the funds whose returns are higher than the other funds. Third, the volatilities of the funds with the monthly dividends keep low levels at all the returns. This is a reason why the funds are the most popular.

Stepwise Chow Test * Chow Test Chow Test Stepwise Chow Test Stepwise Chow Test Stepwise Chow Test Riddell Riddell first step second step sub-step Step

Stepwise Chow Test * Chow Test Chow Test Stepwise Chow Test Stepwise Chow Test Stepwise Chow Test Riddell Riddell first step second step sub-step Stepwise Chow Test a Stepwise Chow Test Takeuchi 1991Nomura

リスクとリターンの実証分析―行動ファイナンスによるアプローチ― 新関 三希代

リスクとリターンの実証分析―行動ファイナンスによるアプローチ―　新関三希代