1 5 14 1994 5 % 8 % (term structure of interest rates)
15 369 15.1 15.1.1 short interest rate 15-1 15-1 0 8 2 11 1 1 0 3 11 1 000 1 / 1. 08 9 25. 93 P 1 000 /( 1. 08 1. 10 ) 8 41. 75 ( 15-1 ) 8 41. 75 1 000 8 41. 75 1. 08 9 09. 09 909. 0 1. 10 1 000 1 n 1 n P V 1 /[( 1 r 1 )( 1 r 2 ) ( 1 r n )] r i i 15-2 15-2 / 1 9 2 5. 9 3 8. 0 0 0 2 8 4 1. 7 5 8. 9 9 5 3 7 5 8. 3 3 9. 6 6 0 4 6 8 3. 1 8 9. 9 9 3 y 2 8 4 1. 7 5 1 000/(1 y 2 ) 2 ( 1 5-2 ) y 2 0.089 95 y 3 7 5 8. 3 3 1 000/(1 y 3 ) 3 y i e l d c u r v e 15-1
370 15-1 1 5-1 15-2 a ) 1997 11 b ) c 4 30 4 30 1 4 a) (1997 11 18 ) 1 4 b) (1989 10 4 ) c) (1989 10 17 15-2 a) b) c) ) Various editions of The Wall Street Journal. spot rate 15-2 15-3 8 1 0 18 9 15-2 8. 995
15 371 ( ) 1 2 3 4 15-3 15-1 15-2 8 4 1. 7 5 1 000/(1.08 1. 1 0 ) 1 000/(1 y 2 ) 2 ( 1 y 2 ) 2 1. 0 8 1. 1 0 1 y 2 ( 1. 0 8 1. 1 0 ) 1 / 2 1. 0 8 9 9 5 1 y 3 [ ( 1 r 1 ) ( 1 r 2 ) ( 1 r 3 ) ] 1 / 3 1 y 4 [ ( 1 r 1 ) ( 1 r 2 ) ( 1 r 3 ) ( 1 r 4 ) ] 1 / 4 ( 1 5-3 ) 15.1.2 1 5-2 925. 93 1 000 1 925. 93 74. 07 74. 0 / 925. 93 8 841. 75 10 1 000 / 1. 10 9 09. 09 ( 909. 0 8 41. 75 ) / 841. 75 8 8 758. 33 1 000 /( 1. 10 1. 11 ) 8 19. 00 8 19. 00 7 58. 33 / 758. 33 0. 08 8 1 8
372 15.1.3 15-2 15-4 1) 2) 3 1 3 2 2 2 1 1 15-4 100 1 9. 660 100(1.096 6) 3 1 31. 87 2 100 100(1.089 95) 2 11 8. 80 1 r 3 1 2 2 1 131. 87 118. 80 ( 1 r 3 ) ( 1 r 3 ) 1. 11 r 3 11 15-1 1 0 0 ( 1 y 3 ) 3 1 0 0 ( 1 y 2 ) 2 ( 1 r 3 )
15 373 1 r 3 ( 1 y 3 ) 3 /( 1 y 2 ) 2 1 r n ( 1 y n ) n / ( 1 y n 1 ) n 1 ( 1 5-4 ) n y n n n n n 1 n 1 15-4 forward interest r a t e n f n 1 f n ( 1 y n ) n / ( 1 y n 1 ) n 1 f n ( 1 y n ) n ( 1 y n 1 ) n 1 ( 1 f n ) ( 1 5-5 ) n (n 1 ) n f n n (n 1 ) 15.2 15-4 15-5 2 A 3 B 12 15-1 A ( 30 / 1. 08 ) [1 030 /( 1. 08 1. 10 )] 8 94. 78 8. 98 B ( 120 / 1. 08 ) [1 120 /( 1. 08 1. 10 )] 1 053.87 8. 94 B
374 1 8 986. 10 1 10 1 004.78 1 d 1 1 d 2 d d 1 1 /( 1 r 1 ) r 1 9 8 6. 1 0 d 1 4 0 d 2 1 040 1 004.78 d 1 5 0 d 2 1 050 d 1 0.956 94 d 2 0. 911 37 r 1 d 1 1 /( 1 r 1 ) 0.956 94 r 1 0. 045 d 2 1 /[( 1 r 1 )( 1 f 2 )] 1 /[( 1. 045 )( 1 f 2 )] 0. 911-37 f 2 0. 05 4. 5 2 10 000 9 700 4 1 000 1 [1] i P i i t / C F i t 1 t d t P 1 d 1 C F 11 d 2 C F 12 d 3 C F 13 e 1 P 2 d 1 C F 21 d 2 C F 22 d 3 C F 23 e 2 P 3 d 1 C F 31 d 2 C F 32 d 3 C F 33 e 3 ( 15-6 ) P n d 1 C F n1 d 2 C F n2 d 3 C F n3 e n e i [ 2 d t ] d t 1 t d t 1 [1] [2] M c C u l l o c h J. Huston McCulloch, Measuring the Term Structure of Interest Rates, Journal of Business 44 (January 1971); and The Tax Adjusted Yield Curve, Journal of Finance 30 (June 1975).
15 375 15-6 15-6 15-6 15-6 15.3 2 ( 1 r 1 ) ( 1 r 2 ) ( 1 y 2 ) 2 r 2 15-1 r 1 8 E(r 2 ) 1 0 1 000 / 1. 08 9 25. 93 2 1 000 /( 1. 08 1. 10 ) 8 41. 75 15-2 8 1 000 2 8 10 909. 09 8 2 10 909. 09 r 2 10 909. 09 8 2 8 2 841. 75 819 2 11 ( 909. 09 / 819 1. 11 ) 2 3 11 8 1
376 f 2 E(r 2 ) E(r 2 ) 1 0 f 2 1 3 2 819 10. 5 1 f 2 [ ( 1 y 2 ) 2 / ( 1 y 1 ) ] ( 1. 1 0 5 2 ) / ( 1. 0 8 ) 1. 1 3 E(r 2 ) f 2 r 2 f 2 E(r 2 ) liquidity premium 3 1 f 2 1 0 E(r 2 ) 2 1 000 2 841. 75 y 2 9 1 841. 75 841. 7 ( 1. 08 )( 1 r 2 ) r 2 10 841. 75 ( 1. 08 )[ 1 E(r 2 )] E(r 2 ) f 2 2 2 ( 1. 0 8 ) [ 1 E(r 2 ) ] ( 1. 0 9 ) 2 ( 1. 0 8 ) ( 1 f 2 ) E(r 2 ) f 2 10 E(r 2 ) 11 f 2 E(r 2 0 11 1 15.4 15.4.1 expectations hypothesis
15 377 f 2 E(r 2 ) 0 f 2 E(r 2 ) 15-5 ( 1 y 2 ) 2 ( 1 r 1 )( 1 f 2 ) ( 1 y 2 ) 2 ( 1 r 1 ) [1 E(r 2 )] 1 4 15.4.2 f 2 E(r 2 ) E(r 2 ) f 2 liquidity preference theory f 2 E(r 2 ) 5 ( ) ( ) a) b) ( ) c) d) ( ) 15-5 a) 1 b) c) d)
378 r 1 1 0 E(r 2 ) 1 0 E(r 3 ) 1 0 2 ( 1 y 2 ) 2 ( 1 r 1 ) [ 1 E(r 2 ) ] 1. 1 0 1. 1 0 y 2 1 0 1 f 2 E(r 2 ) f 2 11 1 2 ( 1 y 2 ) 2 ( 1 r 1 ) ( 1 f 2 ) 1. 1 0 1. 11 1. 2 2 1 1 y 2 1. 105 f 3 11 ( 1 y 3 ) 3 ( 1 r 1 ) ( 1 f 2 ) ( 1 f 3 ) 1. 1 0 1. 11 1. 11 1.355 31 1 y 3 1.106 7 15-5 a 1 5-5 b d 15.4.3 market segmentation theory preferred habitat theory 15.5 1 15-3 1 y n [ ( 1 r 1 ) ( 1 r 2 ) ( 1 r n ) ] 1 /n 1 y n [ ( 1 r 1 ) ( 1 f 2 ) ( 1 f 3 ) ( 1 f n ) ] 1 /n ( 1 5-7 )
15 379 f n 1 y n n 9 ( 1 y 4 ) 4 ( 1. 0 9 ) 3 ( 1 f 4 ) f 4 0. 09 y 4 0. 09 f 4 9 y 4 9 6 15-1 1 5-2 4 3 y 3 9. 66 y 4 y 3 f n E(r n ) E(r n ) 15-5 a 10 1 11 10 11 11 15-5 a 1 11 10
380 15-6 1971 15-6 term premiums Conference Board 1989 11 1 0 8 1 8
15 381 Michael Boldin 10 1 1 0 A r t u r o E s t r e l l a S. Frederic S. Mishkin 10 3 1. 21 5 % 10 2. 4 90 % Michael M. Philips, Makeup of Leading Indicators May Shift The Wall Stre e t J o u r n a l, August 12, 1996. 90 15-7 90 1 5-7 90 2/3 1980 ~ 1982 90 1 ( 1 )( 1 )
382 1. 2. 3. 4. ( 1 y n ) n ( 1 f n 1 ) ( 1 f n 1 ) n 1 n ( 1 y n ) n ( 1 r 1 ) ( 1 f 2 ) ( 1 f 3 ) ( 1 f n ) 5. 6. H o m e r, Sidney; and Martin Liebowitz. Inside the Yield Book: New Tools for Bond Market Strategy. Englewood Cliffs, N.J.: Prentice Hall,1972. Cox, John; Jonathan Ingersoll; and Stephen Ross. A Reexamination of Tr a d i t i o n a l Hypotheses about the Term Structure of Interest Rates. Journal of Finance 3 6
15 383 (September 1981). Fama, Eugene. The Information in the Term Structure. Journal of Financial Economics 13 (1984). M a n k i w, N. Gregory. The term structure of Interest Rates Revisited. B ro o k i n g s Papers on Economic Activity 61 (1986). McCulloch, J. Houston. The Tax-Adjusted Yield Curve. Journal of Finance 3 0 (June 1975). 1. ( 1 ) ( 2 ) ( 3 ) ( 1 ) ( 2 ) 2. a. b. c. d. 3. a. b. c. d. 4. 5. 6. / / / / 1 9 4 3. 4 0 3 8 4 7. 6 2 2 8 9 8. 4 7 4 7 9 2. 1 6 7. 6 8. 1996 1 1 / / 1 3. 5 0 4 5. 5 0 2 4. 5 0 5 6. 0 0 3 5. 0 0 1 0 6. 6 0 a. 1999 1 1 b. 1999 1 1 c. 1995 1 1 1999 1 1 1996 1 1
384 9. 10. 4 5 a. 3.0 b. 4. 5 c. 5. 5 d. 6. 0 11. A B A B 3 3 ( ) 10 6 ( ) 10. 65 10. 75 / 98. 40 88. 34 / ( )( ) / 1 5 3 11 2 8 ( )( ) 12. / / 1 1 0 3 1 2 2 11 a. b. ( ) c. ( ) d. 12 ( ) 13. / / 1 4 3 6 2 5 / / 1 5 3 7 2 6 a. b. 14. 7 8 9 100 a.
15 385 b. c. d. 1 ( c ) 15. 15 A A A / 3 5. 5 0 5. 8 0 5 6. 0 0 6. 6 0 7 6. 7 5 7. 2 5 1 0 7. 2 5 7. 6 0 1 5 7. 4 0 7. 8 0 3 0 7. 7 5 8. 2 0 16. / 1 9 4 3. 4 0 2 8 7 3. 5 2 3 8 1 6. 3 7 1 000 ( )/ a. 1 000 8. 5 3 b. 8 1 17. 1 5 3 8 2 7 1 000 60 a. b. c. d. 7 18. 1 6. 1 3 6. 3 2 6. 2 4 6. 4 a. b. 19.
386 a. 1 5. 0 0 5. 0 0 5. 0 0 2 5. 2 0 5. 2 1 5. 4 2 3 6. 0 0 6. 0 5 7. 7 5 4 7. 0 0 7. 1 6 1 0. 5 6 5 7. 0 0 b. i. ii. iii. c. 20. 5 6 12 ( ) 5. 8 21. 100 94. 34 84. 99 100 12 a. b. c. d. 1. 683. 18 ( 15-2 ) 1 000 /( 1. 10 1. 11 1. 11 ) 737. 84 1 r 7 37. / 683. 18 1. 08 r 8 2. 300 /9 700 0.030 93 3. 093 1 000 (40/1.030 93) [1 040/(1.030 93)(1 f) ] f 0.049 52 4. 952 3. 10 1 9 4. 5. 6. r 4 9. 66 1 000 /( 1. 08 1. 10 1. 11 1. 0966 ) 691. 53 691. ( 1 y 4 ) 4 1 000 y 4 9. 66 r 4 r 4