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2 [ 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).

3 J. P.

4 J. P. 8

5 76 [1] 4 - ( C A L ) S = E(r P) r f P 1) ) market timing [ ] [1] William F. Sharpe, Mutual Fund Performance, Journal of Business, Supplement on Security Prices 39(January 1966). []

7 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 8 79 [1] / 3 r M r f r M r f P 1 P P 1 P 1 P 1 P P 1 0 P 1 P 1 P 1 0 C P 1 P 1 C [] 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 [] 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.

9 730 5) a. E(r M ) r f b. c. d. e ) ) - 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

10 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 )

11 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 )

12 8 733 ( 8-7 ) - Drex Portfolio Inc E(r M ) r f 8 M 0 ( ) (e) ( ) / (e) ( 8-7 ) (S P ) [ ( 8 / 0 ) ] 1 / 0. 0 ( 8 / 0 ) / (e) A = (e A ) / / / / / / n i =1 i (e i ) ( ) α A ( ) ( ) A ( ) σ(e A ) [ ( ) ] 1 / (e A ) ( ) K (e K ) 3 i=1 i (e i )

13 w 0 w * 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/ /0.04 = w * = 1+ (1 A )w 0 = w ( ) = S P = E(r M) r f M + A (e A ) = = 0.19 M ( 8-8 )

14 8 735 M [E(r P* ) r f ] [E(r M ) r f ] ( 8-9 ) M ( 8-7 ) ( ( 8-9 ) M a. M b. E(r M ) r f 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 )

15 736 n i M n i H n (e i ) n M 1 H 1 n(n 1 )/ C A P M 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 )

16 P 1 P 1 C (P 1 P 1 )C (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 )

17 738 Merton, Robert C. On Market Timing and Investment Performance: A Equilibrium Theory of Value for Market Forecasts. Journal of Business, July Tr e y n o r, Jack; and Fischer Black. How to Use Security Analysis to Improve Portfolio Selection. Journal of Business, January Ambachtsheen, Keith. Profit Potential in an Almost Efficient Market. Journal of P o rtfolio Management, Fall a. b. c. ( A 3 ) r M > r f A 78 B 86 r M < r f 9 A 57 B 50 a. P 1 P A B b. 4. ( ) A B C D

18 8 739 ( ) ( ) a. b. c. M d a. M b. ( A. 8 ) 6. ( ) M H A B C D ( ) ( ) 8 0 M 16 3 H a. b. M c. A. 8 M ( ) 7. 6 a. b. A F F 1 =

19 740 N 5 [ 1 r A ] N F 1 /F 0 r A (F 1 /F 0 ) 1 /N r A P 1 P 1 1 / 1 / a X / X / A A (e A ) ( ) 1 / W 0 ( / )/(0.08/0.04) W * /[1 ( ) ] S P = = S P = 0.44 M E(r P* ) r f S P σ M M E(r P* ) E(r M ) M b. W 0 (0.05 6/0.68 6)/( 0.1/0.04) W * /[1 ( ) ] S P = = S P =0.65 S M = 0.60

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