8 8 17 19 16
8 73 8.1 1 [ 1 ] 1 3 M y y= E(r M) r f 0.01 A M ( 8-1 ) E(r M ) r f M M A M E(r M ) E(r M ) M [1] Sanford J.Grossman and Joseph E.Stiglitz, On the Impossibility of Informationally E fficient Markets, American Economic Review 70 (June 1980).
74 60 3 10 8. J. P.
8 75 - - 8-1 J. P. 8
76 [1] 4 - ( C A L ) 8-1 8.3 S = E(r P) r f P 1) 197 1 1 1 000 30 30 3 5 1978 1 3 1 3 600 ) 197 1 1 1 000 1978 1 3 1 67 500 market timing 30 30 1 000 5 53. 6 [ ] [1] William F. Sharpe, Mutual Fund Performance, Journal of Business, Supplement on Security Prices 39(January 1966). []
8 77 1 1 96 1978 5 3 600 67 500. 55. 10 10. 70. 14 0. 8 5. 5 8 0. 5 5 0. 64. 37 0. 34 5. 89 3. 8 3. 55 38. 55 38. 55 30. 14 9. 1 0. 06 7. 06 0. 4 4. 8. 84 3. 8 5 50 0 5 0 5 1 5 7. 5 0. 5 5 1 0. 0 5 5. 0 1 1 1
78 0. 4 4. 8. 84-8.3.1 8-1 r f S 0 X S 0 ( 1 r f ) S T X X 8-1 S 0 S T X S T X S 0 ( 1 r f ) S 0 ( 1 r f ) 0 S T X S 0 ( 1 r f ) S T r f
8 79 [1] 8.3. 90 / 3 r M r f r M r f P 1 P P 1 P 1 P 1 P 1 1 1 00 P 1 0 P 1 P 1 P 1 0 C P 1 P 1 C 4 8.4 8.4.1 [] 1) ) 3) 4) [1] Robret C.Merton, On Market Timing and Investment Performance: An Equilibrium Theory of Value for Market Forecasts, Journal of Business, July 1981. [] Jack Treynor and Fisher Black How to Use Security Analysis to Improve Portfolio Selection, J o u r n a l of Business, January 1973.
730 5) a. E(r M ) r f b. c. d. e. 6. - 1) ) - 3) 8.4. i r i r f i (r M r f ) e i ( 8 - ) e i 0 T B ( 8 - ) M e i T B p a s s i v e p o r t f o l i o r M M r k r f k (r M r f ) e k k ( 8-3 ) k k k (e k ) k 0 M 0 - active portfolio)a
8 731 A A (e A ) A M (e A ) M C o v (r A, r M ) A M 8-0 C M L A 8 - A8- A [ A M (e A ) ] 1 / A E(r A ) A r f A [E(r M ) r f ] A M 8 A M A C A L A M P A w 1 w r p (w) w r A ( 1 w)r M w w * 8 - P w 0 w * = 1 + (1 A )w 0 ( 8-4 )
73 ( 8-4 ) 8 w 0 A 1 A (e A ) w 0 E(r M ) r f M A (e A ) A A 1. 0 ( 8-4 ) w * w * S P = S M + A w 0 = / (e A ) [E(r M ) r f ]/ M ( 8-5 ) ( 8-5 ) A/ (e A ) k w k = E(r M ) r f A (e A ) = E(r M) r f + ( 8-6 ) k (e k ) 1 ( 8-5 ) n i =1 M k / (e k ) i / A (e A ) M (e i ) A (e A ) n A (e A )
8 733 ( 8-7 ) - Drex Portfolio Inc. 15 0 7 E(r M ) r f 8 M 0 ( ) (e) ( ) / (e) 1 7 1. 6 4 5 0.155 6 5 1. 0 3 0.156 3 3 3 0. 5 6 0. 115 4 ( 8-7 ) (S P ) [ ( 8 / 0 ) 0. 1 5 5 6 0. 1 5 6 3 0. 11 5 4 ] 1 / 0. 0 ( 8 / 0 ) 0. 16 / (e) A = (e A ) 1 0. 0 7 / 0. 4 5 0.345 7 0.345 7/0.301 1.147 7 0. 0 5 / 0. 3 0.488 3 0.488 3/0.301 1.61 3 0. 0 3 / 0. 6 0.443 8 0.443 8/0.301 1.473 5 0. 3 0 1 1.000 0 n i =1 i (e i ) ( 1 114. 77 ) α A 1. 1 4 7 7 0. 0 7 ( 1. 6 1 ) ( 0. 0 5 ) 1. 4 7 3 5 0.03 0. 0 5 6 0. 5 6 A 1. 1 4 7 7 1. 6 ( 1. 6 1 ) 1. 0 1. 4 7 3 5 0. 5 0. 9 5 1 9 σ(e A ) [ 1. 1 4 7 7 0. 4 5 ( 1. 6 1 ) 0. 3 1. 4 7 3 5 0. 6 ] 1 / 0. 8 6 8. 6 (e A ) 0. 8 6 0. 6 8 6 ( ) K (e K ) 3 i=1 i (e i )
734 0. 56 1 5. 0 6 8. 6 1. 0 w 0 w * 15. 06 1 4. 95 1. 0 1. 0 1 0. 1 4 9 5 1. 1 4 7 7 0.171 6 0. 1495 1. 61 0.4 4 3 0. 1 4 9 5 1.4735 0.0 0.149 5 0.850 5 1.000 0 0.471 1 0. 40 M 4 M P P P * M M/ P P 1 M / P P * C A L (P * ) M E(r P* ) r f S P A w 0 = / (e A ) [E(r M ) r f ]/ M = 0.056/0.686 0.08/0.04 =0.1506 w * = 1+ (1 A )w 0 = w 0 0.1506 1 + (1 0.9519) 0.1506 = 0.1495 S P = E(r M) r f M + A (e A ) = 0.16 + 0.0619= 0.19 M 0. 4711 0. 0 0.094 9. 4 ( 8-8 )
8 735 M [E(r P* ) r f ] [E(r M ) r f ] 9. 4 8 1. 4 ( 8-9 ) 1. 4 1 55 M ( 8-7 ) ( 8-5 0.53 7 ( 8-9 ) M. 65 3 a. M b. E(r M ) r f 1 8.5-10 r i r f i i r M r f e i (r i ) i M (e i ) i j M M H r i r f i M r M r f i H r H r f i e i r i e i ( 8-10 ) i M i H M H r M r H r f r i ( 8-10 ) ( 8-10 ) (r i ) i M M i H H i M i H C o v (r M, r H ) (e i ) C o v (r i, r j ) i M j M M i H j H H ( i M j H j M i H ) C o v (r M, r H )
736 n i M n i H n (e i ) n M 1 H 1 n(n 1 )/ C A P M 8.6 0 r [r f (r ˆ M r f )]e a b ê 8-11 a * a b 8-11 b ( 8-11 ) a b ( 8-11 a ) ( b ) ˆ ˆ ˆ e ˆ ( 8-11 ) a ˆ b= Cov( + e, ˆ ) ( ˆ ) = Cov(, ˆ ) ( ) ( ) ( ˆ ) 8-1 ( 8-11 b ) 0 ( 8-1 ) b 0 = ( ) ( ˆ )
8 737-1.. 3. 4. 5. P 1 P 1 C (P 1 P 1 )C 6. - 7. - (e) 8. A (e A ) P 9. [ A/ (e A )] 10. [ i / (e i )] S P = E(r M) r f + M n i =1 i (e i ) 11. - 1.
738 Merton, Robert C. On Market Timing and Investment Performance: A Equilibrium Theory of Value for Market Forecasts. Journal of Business, July 1981. Tr e y n o r, Jack; and Fischer Black. How to Use Security Analysis to Improve Portfolio Selection. Journal of Business, January 1973. - Ambachtsheen, Keith. Profit Potential in an Almost Efficient Market. Journal of P o rtfolio Management, Fall 1974. 1. 1. 7 1. 3 8. 7 1 5. 5 1 7. 0 1 4. 4. 9 11. 9 8. 9 5. 4 a. b. c. ( A 3 ). 5. 5 1-3. r M > r f 1 3 5 A 78 B 86 r M < r f 9 A 57 B 50 a. P 1 P A B b. 4. ( ) A 0 1. 3 58 B 18 1. 8 71 C 17 0. 7 60 D 1 1. 0 55
8 739 ( ) 8 0 1 6 3 ( ) a. b. c. M d.. 8 5. 4 a. M b. ( A. 8 ) 6. ( ) M H A 0 1. 1. 8 58 B 18 1. 4 1. 1 71 C 17 0. 5 1. 5 60 D 1 1. 0 0. 55 ( ) ( ) 8 0 M 16 3 H 10 18 0. 6 a. b. M c. A. 8 M ( ) 7. 6 a. b. A. 8 6 8. 7 9. 0. 3 4 1. F 0 1 000 3 600 F 1 = 67 500 5 360 000 000
740 N 5 [ 1 r A ] N F 1 /F 0 r A (F 1 /F 0 ) 1 /N 1. 49 r A 8. 44 34. 71. P 1 P 1 1 / 1 / 1 0 3.a. 0.789 5 X 1 0.345 7/0.789 5 0.437 9 X 0.443 8/0.789 5 0.56 1 A 0.437 9 0. 0 7 0.56 1 0. 0 3 0.047 5 A 0.437 9 1. 6 0.56 1 0. 5 0.981 7 (e A ) (0.437 9 0. 4 5 0.56 1 0. 6 ) 1 / 0.45 3 0. 56 4. 75 8. 6 4. 53 W 0 (0.047 5/0.601 9)/(0.08/0.04) 0.394 6 W * 0.394 6/[1 ( 1 0.981 7) 0.394 6] 0.391 8 S P = 0.16 + 0.0457 = 0.197 5 S 0.453 P = 0.44 M E(r P* ) r f S P σ M 0. 0 7 0. 4 4 0. 0 0. 1 5 8 1 5. 8 M E(r P* ) E(r M ) 1 5. 8 1 5 0. 8 M b. W 0 (0.05 6/0.68 6)/( 0.1/0.04) 0.100 4 W * 0.100 4/[1 ( 1 0.951 9) 0.100 4] 0.099 9 S P = 0.1 + 0.056 = 0.41 9 0.0 0.86 S P =0.65 S M = 0.60