373 51 1 1987 Niizeki 1998, 2005 1) 2005 2006 3 2003 I 1
52 374 58 3 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
375 53 Chen, Hong and Stein 2000 2) Kahneman and Tversky 1979 von Neumann and Morgenstern 1944 2001 7 11 2005 8 31 225 6 2 2002 Daniel Kahneman
54 376 58 3 225 2 Kahneman and Tversky 1979 Prospect Theory Risky Prospects Expected Utility Theory
377 55 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, 1979 1 B 2 A 4) Negative Prospects 3 Kahneman and Tversky 1979 0 4 x u(x) u(0)=0 1 B u(3000) / u(4000)>4 / 5 2 1 A B 1 / 4 A u(3000) / u(4000)<4 / 5
56 378 58 3 3 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, 1979 3 A 4 B Positive Prospects Reflection Effect S Value Function :v(x) v r x v(x)
379 57 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 25 2,000 B=(4000,0.25;2000,0.25) 6 A 25 6,000 A=( 6000,0.25) B 25 4,000 25 2,000 B=( 4000,0.25; 2000,0.25) Kahneman and Tversky, 1979 5 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
58 380 58 3 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
381 59 Loss Aversiveness Kahneman and Tversky, 1979 Tversky and Kahneman, 1991 7), 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
60 382 58 3 v ( x) v (x) v(x) x<0 8) v ( x) x<0 9), 2002 10) 8 9 10 1995 225 1,380
383 61 225 r 0 3 1,450 6 88 (2006) 2006 5 1998 2005 11) 2001 11 55
62 384 58 3 43 2006 10 6 1 52,514.63 12 2 11,146.56 12 3 225 10,322.72 1 4 TOPIX 9,488.30 1 5 3 8,294.59 12 6 7,662.53 12 7 DIAM 7,584.80 12 8 7,139.34 12 9 TOPIX 6,926.58 1 10 225 6,501.70 1 2006 2006 5
385 63 1 12) 3 3 1 +317.6 1 2 +315.5 1 3 +313.9 1 4 JF JP +269.1 1 5 +266.9 1 6 +258.8 1 7 +252.5 1 8 +247.1 1 9 +245.8 1 10 +235.9 1 2006 2006 5 Certainty Effect 12 CML CML 6 6,000 4,000 2,000 5 4,000 2,000 6,000 v(x) Thaler, 1985
64 386 58 3 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 1 1 2 (2) Kernel Regression Model f(x t ) 15) 13 Niizeki 1998 14 P t t P t 1 t 1 R t=log( P t/p t 1 ) 15 f(x t) Y t
387 65 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=1 6 16 h tradeoff Silverman (1986) 0.9T min(s,r/1.34) s R 17 smoothing Epanechnikov Silverman 1986
66 388 58 3 225 225 NIKKEI225 1 SOB PAT 225 NIK TOPIX TOP 18) 2 INB KOM 19) 2001 7 11 2005 8 31 1017 Date Index 225 2 2003 9 2 18 1 1 6 3 4 2 5 9 10 19 2 1 6 1
2001/7/11 2001/10/11 2002/1/11 2002/4/11 2002/7/11 2002/10/11 2003/1/11 2003/4/11 2003/7/11 2003/10/11 2004/1/11 2004/4/11 2004/7/11 2004/10/11 2005/1/11 2005/4/11 2005/7/11 Date NIK 140,000 120,000 100,000 80,000 60,000 40,000 20,000 0 Index 2001/7/11 2001/10/11 2002/1/11 2002/4/11 2002/7/11 2002/10/11 2003/1/11 2003/4/11 2003/7/11 2003/10/11 2004/1/11 2004/4/11 2004/7/11 2004/10/11 2005/1/11 2005/4/11 2005/7/11 Date TOP 140,000 120,000 100,000 80,000 60,000 40,000 20,000 0 Index NIKKEI225 14000 12000 10000 8000 6000 4000 2000 0 Index 2001/7/11 2001/11/11 2002/1/11 2002/3/11 Date 2001/9/11 2002/5/11 2002/7/11 2002/11/11 2003/1/11 2003/3/11 2002/9/11 2003/5/11 2003/7/11 2003/11/11 2003/9/11 2004/1/11 2004/3/11 2004/5/11 2004/7/11 2004/11/11 2004/9/11 2005/1/11 2005/3/11 2005/5/11 2005/7/11 389 67
58 3 2001/7/11 2001/10/11 2002/1/11 2002/4/11 2002/7/11 2002/10/11 2003/1/11 2003/4/11 2003/7/11 2003/10/11 2004/1/11 2004/4/11 2004/7/11 2004/10/11 2005/1/11 2005/4/11 2005/7/11 Date SOB 9,000 8,500 8,000 7,500 7,000 6,500 Index Date 2001/7/11 2001/10/11 2002/1/11 2002/4/11 2002/7/11 2002/10/11 2003/1/11 2003/4/11 2003/7/11 2003/10/11 2004/1/11 2004/4/11 2004/7/11 2004/10/11 2005/1/11 2005/4/11 2005/7/11 PAT 10,000 6,000 5,000 4,000 3,000 2,000 1,000 0 Index 7,000 8,000 9,000 2001/7/11 2001/10/11 2002/1/11 2002/4/11 2002/7/11 2002/10/11 2003/1/11 2003/4/11 2003/7/11 2003/10/11 2004/1/11 2004/4/11 2004/7/11 2004/10/11 2005/1/11 2005/4/11 2005/7/11 Date INB 35000 30000 25000 20000 15000 10000 5000 0 Index 68 390
391 69 Index 30000 25000 20000 15000 10000 5000 KOM 2001/7/11 2001/10/11 2002/1/11 2002/4/11 2002/7/11 2002/10/11 2003/1/11 2003/4/11 2003/7/11 2003/10/11 2004/1/11 2004/4/11 2004/7/11 2004/10/11 2005/1/11 2005/4/11 2005/7/11 Date 225 NIKKEI225P NIKP TOPP SOBP PATP INBP KOMP Mean S.D. Corr Vol 10490.66 105196.3 105061.3 7941.835 7927.777 15847.97 11187.73 1159.066 11570.40 12159.46 251.9038 606.8454 7875.016 6063.295 1 0.999739 0.979173-0.654578-0.501792 0.657566 0.694929 5766 7164 43580 8989 75 17 Mean S. D. Corr Vol NIKKEI225P 225 NIKP 225 TOPP TOPIX SOBP PATP INBP KOMP 7 (1) Kernel Density Estimate
70 392 58 3 Mean Max Min S.D. V 1/2 NIKKEI225R NIKR TOPR SOBR PATR INBR KOMR 5.59E-06 0.057352-0.068645 0.014111 0.006003 4 20) 225 TOPIX 7.85E-06 0.057139-0.068714 0.014082 0.005992 2.51E-05 0.046149-0.065418 0.012209 0.005167 5.25E-05 0.021716-0.026493 0.005236 0.002258-0.000127 0.024523-0.026726 0.005745 0.002484 0.000482 0.026876-0.045934 0.005918 0.005470 0.000402 0.035836-0.047447 0.006073 0.005391 Mean Max Min S. D. V 1/2 NIKKEI225R 225 NIKR 225 TOPR TOPIX SOBR PATR INBR KOMR (2) Return 20 1
393 71 Volatility 1 P 21).012 NIKKEI225.010 Volatility.008.006.004.002.000.08.04.00.04.08 Return Volatility.012.010.008.006.004.002 NK.000.08.04.00.04.08 Return Volatility TOP.009.008.007.006.005.004.003.002.001.000.08.06.04.02.00.02.04.06 Return 225 21 V t 1/2= 0 + 1 R t+u t u t iid) 1
72 394 58 3.004 SOB.0030 PAT Volatility.003.002.001 Volatility.0025.0020.0015.0010.0005.000.03.02.01.00.01.02.03 Return.0000.03.02.01.00.01.02.03 Return.020 INB.020 KOM.016.016 Volatility.012.008 Volatility.012.008.004.004.000.06.04.02.00.02.04 Return.000.06.04.02.00.02.04 Return 1 P-value NIKKEI225R NIKR TOPR SOBR PATR INBR KOMR -0.003984 0.0125-0.003989 0.0123-0.003665 0.0722-2.83E-05 0.9786 0.000596 0.5835-0.002246 0.7490 0.022698 0.0038 1 V t 1/2= 0 1 R t+u t P-value P 4
395 73 1 22) Reflection Effect Disposition Effect 23) Kick 0 0.2 0.2 0.2 Kick 22 23
74 396 58 3 Risky Assets Riskless Assets 5
397 75 2001 7 11 2005 8 31 4 225 225 TOPIX 3 225
76 398 58 3
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401 79 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.