2000 11 Journal of Risk Management Vol.2 No.2 Nov. 2000 pp.89-118 * The Application of Contingent Portfolio Insurance in the Taiwan Stock Market ** (Hsinan Hsu) *** (Mi-Huan Lai) 1%9% Abstract The purpose of this paper is to propose a methodology of implementing contingent portfolio insurance. Specifically, based on the filter rule to judge while the market is bull or bear, we investigate the effect of contingent portfolio insurance on the portfolio of Taiwan Stock Exchange Capitalization Weighted Stock Index. The performance of the contingent portfolio insurance is compared with those of the standard portfolio insurance and the buy-and-hold strategy. Results indicate that, for filters 1% to 9%, the contingent portfolio insurance outperformed the other two strategies in various investment horizons for a 20-year sample period. Keywords: Contingent Portfolio Insurance, Filter Rule, Options, Dynamic Portfolio Strategies. * ** *** Professor, National Chengkou University, Tainan, Taiwan. Professor, National Chengkou University, Tainan, Taiwan.
90 1. 1 Black & Scholes (Option-Based Portfolio Insurance) Garcia and Gould (1987) (contingent portfolio insurance) 1 Garcia and Gould (1987)Zhu and Kavee (1988)Estep and Kritzman (1988) (1992) (1996)
2000 11 91 2. 2.1 protective put Black and Scholes (1973) Stoll (1969) = S + P rt = C + X e rt = S N d ) e X N( d ) + X e = S N ( 1 2 rt ( d1) + e X [1 N ( d2 )] rt (1) S N ( d 1 ) e rt X 1 N ( d )] [ 2 2 Black and Scholes (1973) (option-based portfolio insurance OBPI) (constant proportion portfolio insurancecppi) 2 Perold and Sharpe (1988), Rubinstein (1985),,60, 2000 6, forthcoming.
92 2.2 Garcia and Gould (1987) (1) (2) (3) (Etzioni,1986) ( (1991) (1992) (1993) (1995)) (1996) (CPPITIPP ) (1991) CPPI (1991) CPPI (1995) TIPP (1997) Clarke and Arnott (1987) (1) (2) (3) beta( β ) (4) Zhu and Kavee (1988) CPPI CPPI (1990) (1991) (1995)
2000 11 93 Black-Scholes (1990) Leland Rendleman and O Brien (1990) (1995) (1999) GARCH 3. (OBPI) 3.1 a. Black-Scholes (1973)
94 3 (1) (2) (3) (4) (5) 4 90 180 90 286 S t R = ln( ) t S 1 n R = n ) σ 2 t+ t 1 R t t= 1 1 t = ( R R) 1 i n 1 i= t n s 2 (2) s= σ ) t +1 286 (3) S t t R t σ ) t R t 2 t+1 t+1 n t+1 n 3 4 (1999) p.107,4 (1999) GARCH
2000 11 95 b. 5 70 1 88 12 AREMOS 3.2 a. Fama and Blume (1966) / Sweeney (1988) (1) / (i) K (go long) K (ii) K K (go short) (iii) K 5 (1) (2) ( )(3)
96 K / (2) (i) K (ii) K K (iii) K K ( ) (a) (b) (c) 3. Sharpe IndexTreynor Index Jensen Index - (mean-variance analysis) Clarke and Arnott (1987) Beta (upside capture) 3.1
2000 11 97 3.2 3.3 Zhu and Kavee (1988) CPPI 75 (Q3)25 (Q1) Clarke and Arnott (1987) - 4. 100 (overlapping) 70 1 1 1 1 70/1/1~71/12/3171/1/1~72/12/31 87/1/1~88/12/31 18 4.1 (i) Black & Scholes (1) S + P S N ( d 1 )
98 e rt X [ 1 N ( d2)] (ii) (iii) (1) () 6 (iv) ( ) (v) 1 HIGH LOW Indicator 1 HIGH S HIGH i HIGH Si HIGH 0 LOW S i 1 6 (1) SN(d ) 1 w s rt SN(d ) + e x 1 N ( d ) 1 2 w c 1w s
2000 11 99 4.2 (i) Black & Scholes Rubinstein Leland (ii) 7 (iii) (iv) 4.3 (i) (ii) (iii) 4. 4.1 (1985) 5 8 (1992) 10% 1%3%5%7%9% a. (1) 7 Etzioni1986 (time discipline): ( ) (market move disciple) (lag discipline)
100 S i Indicator=0 Indicator=1 Indicator=0 LOW=S i No S i >LOW S i <HIGH No Indicator=1 HIGH=S i Yes Yes Indicator=0 No S i /LOW >1+Filter S i /HIGH <1-Filter No Indicator=1 Yes Yes Indicator=1 Indicator=0 HIGH=S i LOW=S i 1
2000 11 101 1 1%9% 30% ( 79 81 ) 1% 76 77 50% 79 12000 4500 71 73 75 73 3% 75 5% (2) 40%
102 1 Filter=1% Filter=3% Filter=5% Filter=7% Filter=9% 19 19 19 19 19 () 1,417,796 1,379,454 1,338,893 1,321,644 1,356,952 () 749,836 672,516 627,786 624,722 703,387 2.0871 1.9191 1.6834 1.4925 1.9265 (%) 41.78 37.95 33.89 32.16 35.70 18 18 18 18 18 () 2,232,686 2,097,484 1,943,869 1,885,619 1,943,711 () 2,474,706 2,073,379 1,760,998 1,665,164 1,909,223 2.8383 2.6458 2.4839 2.4149 2.6822 (%) 61.64 54.88 47.20 44.28 47.19 15 15 15 15 15 () 6,639,436 6,104,181 5,016,235 4,651,527 4,700,814 () 7,566,641 6,708,755 5,159,465 5,054,731 4,908,488 1.3435 1.2744 1.3081 1.7457 1.3746 (%) 112.79 102.08 82.12 73.03 74.02 10 10 10 10 10 () 19,110,307 18,049,555 14,152,015 11,102,516 10,767,269 () 10,952,921 10,392,975 7,915,661 6,265,520 5,684,768-0.7932-0.6543-0.7397-0.5988-0.9885 (%) 181.10 170.50 131.52 101.03 97.67 5 5 5 5 5 () 42,710,217 38,393,056 27,998,263 21,566,351 21,852,948 () 7,529,046 6,843,706 4,316,952 3,866,264 7,599,875 0.2156-0.1425-0.4278 0.0209 1.7718 (%) 278.07 249.29 179.99 137.11 139.02 b. (1)
2000 11 103 1% 2 3% 1%9% 4.2 a. 3 ( 76 77 ) 79 84 79
104 2 Filter=1% Filter=3% Filter=5% Filter=7% Filter=9% 19 19 19 19 19 () 1,294,012 1,319,583 1,299,196 1,292,890 1,332,974 () 700,130 639,441 607,278 611,602 692,850 2.0904 1.8874 1.6344 1.4488 1.9119 (%) 29.40 31.96 29.92 29.29 33.30 () 123,784 59,871 39,697 28,753 23,978 18 18 18 18 18 () 1,933,623 1,955,399 1,852,416 1,823,145 1,892,017 () 2,244,446 1,943,986 1,675,538 1,609,628 1,858,795 2.8851 2.6523 2.4610 2.3945 2.6655 (%) 46.68 47.77 42.62 41.16 44.60 () 299,063 142,085 91,453 62,475 51,694 15 15 15 15 15 () 4,969,383 5,313,755 4,543,059 4,345,492 4,453,376 () 6,106,029 5,922,341 4,699,066 4,780,102 4,685,055 1.5657 1.3471 1.3869 1.8253 1.4312 (%) 79.39 86.28 70.86 66.91 69.07 () 1,670,053 790,401 525,790 306,027 250,427 10 10 10 10 10 () 10,363,062 14,075,946 12,002,615 9,811,552 9,781,279 () 6,583,250 8,263,693 6,740,481 5,573,503 5,142,638-0.2648-0.5165-0.6968-0.5221-0.9734 (%) 93.63 130.76 110.03 88.12 87.81 () 8,747,244 3,973,586 2,149,384 1,290,934 1,003,886 5 5 5 5 5 () 18,268,603 27,282,508 23,123,432 19,507,524 20,096,972 () 5,519,353 7,247,749 6,902,000 5,820,824 7,307,432 1.1183 1.1848 0.7850 0.2521 1.7630 (%) 115.12 175.22 147.49 123.38 127.31 () 20,164,372 8,201,910 4,220,904 2,452,611 1,812,189
2000 11 105 3 ( ) (filter=1%) ( ) 70 1,068,789 995,722 960,006 932,830 994,585 988,759 71 893,326 822,069 959,783 948,962 813,187 808,163 72 1,619,412 1,490,572 1,630,118 1,616,653 1,720,090 1,711,054 73 1,093,826 1,001,982 1,043,748 1,027,485 1,095,425 1,089,153 74 1,095,679 1,030,408 969,175 651,622 1,006,024 1,000,147 75 1,229,487 1,138,880 1,117,205 1,160,546 1,236,905 1,230,006 76 3,320,070 3,087,359 2,107,102 2,093,103 2,201,317 2,190,151 77 3,430,424 3,165,878 1,945,868 1,932,881 2,186,672 2,175,571 78 1,925,026 1,699,425 1,726,777 1,741,352 1,974,964 1,964,800 79 793,500 671,949 835,667 824,986 459,758 456,299 80 1,102,462 956,446 958,197 937,642 1,088,301 1,074,095 81 875,534 782,293 929,155 914,471 732,062 727,397 82 1,646,665 1,522,434 1,683,071 1,666,703 1,816,577 1,807,114 83 1,120,283 1,021,035 1,020,440 995,511 1,110,332 1,103,994 84 826,808 735,625 937,124 928,418 733,797 729,125 85 1,301,047 1,205,756 1,253,093 1,238,246 1,347,454 1,340,067 86 1,211,423 1,091,024 1,118,378 1,101,409 1,200,440 1,193,703 87 991,103 895,213 925,242 909,469 786,616 781,710 88 1,393,266 1,272,166 1,256,897 1,241,755 1,373,375 1,365,872 () 1,417,796 1,294,012 1,233,529 1,217,739 1,256,310 1,249,325 () 749,839 700,130 387,390 388,448 507,620 505,374 2.0871 2.0904 1.1282 1.1314 0.6024 0.6024 () 793,500 671,948 835,667 824,986 459,758 456,299 () 1,029,946 925,830 958,990 35,236 903,886 898,461 () 1,120,283 1,030,408 1,043,748 1,027,475 1,110,332 1,103,994 () 1,506,339 1,381,369 1,443,508 1,429,204 1,546,733 1,538,463 () 3,430,424 3,165,878 2,107,102 2,093,103 2,201,317 2,190,153 (%) 41.78 29.40 23.35 21.77 25.63 24.93
106 4 5 (1) (2) (3) 4 5 (4)
2000 11 107 (5) 1% 3% 8,201,910 (i) (ii) (iii) 4
108 (1%) () 1,417,796 1,233,529 1,204,819 1,256,310 () 749,836 387,390 390,810 507,620 2.0871 1.1282 1.4324 0.6024 (%) 41.78 23.35 20.48 25.63 () 161,486 0 0 0 () 0 22,781 51,491 0 () 2,232,686 1,534,937 1,469,101 1,618,842 () 2,474,706 1,038,764 977,609 1,180,746 2.8383 1.9732 1.9724 1.8247 (%) 123.27 53.49 46.91 61.88 () 613,844 0 0 0 () 0 83,905 149,741 0 () 6,639,436 2,896,014 2,816,018 3,165,189 () 7,566,641 2,815,275 2,734,728 3,010,554 1.3435 1.8283 1.6062 1.8171 (%) 563.94 189.60 181.60 216.52 () 3,474,247 0 0 0 () 0 269,175 349,171 0 () 19,110,307 5,351,559 5,091,518 5,910,130 () 10,952,921 2,728,519 2,619,008 2,954,211-0.7932-0.9203-0.9361-0.9677 (%) 1811.03 435.16 409.15 491.01 () 13,200,177 0 0 0 () 0 558,571 818,612 0 () 42,710,217 10,847,161 10,543,162 11,817,771 () 7,529,046 3,848,239 3,871,946 4,054,411 0.2156 1.5378 1.6098 1.4791 (%) 4171.02 984.72 954.32 1081.78 () 30,892,446 0 0 0 () 0 970,610 1,274,609 0
2000 11 109 5 (3%) () 1,319,583 1,217,739 1,196,805 1,249,325 () 639,441 388,448 389,683 505,374 1.8874 1.1314 1.4373 0.6024 (%) 31.96 21.77 19.68 24.93 () 70,258 0 0 0 () 0 31,586 52,520 0 () 59,871 15,132 8,015 6,984 () 1,955,399 1,511,480 1,456,932 1,610,253 () 1,943,986 1,039,206 974,742 1,175,521 2.6523 1.9671 1.9704 1.8247 (%) 95.54 51.15 45.69 61.03 () 345,146 0 0 0 () 0 98,773 153,321 0 () 142,085 23,457 12,170 8,588 () 5,313,755 2,861,189 2,794,899 3,149,758 () 5,922,341 2,807,572 2,724,462 2,997,232 1.3471 1.8220 1.6031 1.8171 (%) 431.38 186.12 179.49 214.98 () 2,163,997 0 0 0 () 0 288,569 354,859 0 () 790,401 34,825 21,120 15,431 () 14,075,946 5,305,665 5,058,914 5,882,553 () 8,263,693 2,722,883 2,609,522 2,941,138-0.5165-0.9231-0.9361-0.9677 (%) 1307.59 430.57 405.89 488.26 () 8,193,394 0 0 0 () 0 576,888 823,639 0 () 3,973,586 45,894 32,604 27,577 () 27,282,508 10,778,380 10,287,290 11,764,053 () 7,247,749 3,833,953 4,019,286 4,036,470 1.1848 1.5381 1.5304 1.4791 (%) 2628.25 977.84 928.73 1076.41 () 15,518,455 0 0 0 () 0 985,673 1,476,763 0 () 8,201,910 68,781 55,467 53,719
110 b. 1%3% 6 7 (1) (i) 76 1 6 76 10 1 1063 4673 (ii) 77 1 5 77 8 23 2341 8214 6 7 (2) (i) 79 2 5 79 10 1 12302 2560 (ii) 84 1 5 84 8 14 7051 4503 (3) (i) 78 5 25 78 12 28 9550
2000 11 111 (ii) 88 6 7 88 12 20 7850 6 Filter=1% Filter=3% () 4,045,763 3,896,659 4,232,2933,885,1254,396,049 76/01/06 (%) 304.58 289.67 323.23 288.51 339.60 () 0 0 0 0 0 76/10/01 () 350,286 499,390 163,756 510,924 0 () 3,353,234 3,383,687 3,168,3183,075,4533,508,757 77/01/05 (%) 235.32 238.37 216.83 207.55 250.88 () 0 0 0 0 0 77/08/23 () 155,523 125,070 340,439 433,304 0 79/02/05 () 402,548 411,683 888,196 856,482 208,096 (%) -59.75-58.83-11.18-14.35-79.19 () 194,452 203,587 680,100 648,386 0 79/10/01 () 0 0 0 0 0 () 758,882 711,944 951,340 934,045 638,633 84/01/05 (%) -24.11-28.81-4.87-6.60-36.14 () 120,249 73,311 312,707 295,412 0 84/08/14 () 0 0 0 0 0 () 1,054,551 1,080,668 904,952 894,2321,012,626 78/05/25 (%) 5.46 8.07-9.50-10.58 1.26 () 41,925 68,042 0 0 0 78/12/28 () 0 0 107,674 118,394 0 () 1,018,893 981,980 948,892 934,106 997,437 88/06/07 (%) 1.89-1.80-5.11-6.59-0.26 () 21,456 0 0 0 0 88/12/20 () 0 15,457 48,545 63,331 0
112 7 76/01/06 76/10/01 77/01/05 77/08/23 79/02/05 79/10/01 84/01/05 84/08/14 78/05/25 78/12/28 88/06/07 88/12/20 Filter=1% Filter=3% () 3,897,408 3,806,370 4,209,366 3,863,156 4,375,171 (%) 289.74 280.64 320.94 286.32 337.52 () 0 0 0 0 0 () 477,763 568,801 165,805 512,015 0 () 148,355 90,289 22,927 21,969 20,878 () 3,231,449 3,329,870 3,150,132 3,057,809 3,491,806 (%) 223.14 232.99 215.01 205.78 249.18 () 0 0 0 0 0 () 260,357 161,936 341,674 433,997 0 () 121,785 53,817 18,186 17,644 16,951 () 329,036 353,516 880,622 849,446 205,751 (%) -67.10-64.65-11.94-15.06-79.42 () 123,285 147,765 674,871 643,695 0 () 0 0 0 0 0 () 73,512 58,167 7,574 7,036 2,345 () 695,131 682,120 943,754 927,120 634,382 (%) -30.49-31.79-5.62-7.29-36.56 () 60,749 47,738 309,372 292,738 0 () 0 0 0 0 0 () 63,751 29,824 7,586 6,925 4,251 () 960,162 1,027,116 884,513 882,787 1,006,720 (%) -3.98 2.71-11.55-11.72 0.67 () 0 20396 0 0 0 () 46,558 0 122,207 0 0 () 94,389 53,552 20,439 11,445 5,906 () 953,788 949,647 928,915 921,973 991,598 (%) -4.62-5.04-7.11-7.80-0.84 () 0 0 0 0 0 () 37,810 41,951 62,683 69,625 0 () 65,105 32,333 19,977 12,133 5,839
2000 11 113 4.3 (1999) GARCH GARCH 90 180 ( 286 ) 8 9 1%3% t 1%3% t 8 90 180 1% 3% () 1,417,796 1,420,248 1,422,069 1,419,519 () 749,836 756,275 760,839 754,455 () 1,379,454 1,380,618 1,382,249 1,379,614 () 672,516 677,533 680,015 674,379 9 t 1 90 180 90 - - - - 1% 180-1.216 - - - -0.878-0.592 - - -0.509 0.352 1.396-90 - - - - 3% 180-0.773 - - - -0.831-0.739 - - -0.084 0.727 1.531-1. H 0.05 0
114 5. 1. 1%9% 1% 1% 3% 2. 1% 9% 3% 3. 4. 5. 6.
2000 11 115 7. 1. 2. 8
116 1. 1992 5 1-31 2. 1991 6 3. 1990 6 4. 1996 1 31-44 5. 1995 4 20-34 6. Strap Strip 1999, 101-127 7. 60 2000 6 102-127 8. 1997 6 9. 1995 6 10. (SRD) 1996 6 11. 1995 6 12. 1993 6 13. Black, Fischer and Robert Jones, 1987, Simplifying Portfolio Insurance, Journal of Portfolio Management, 48-51. 14. Black, Fisher and Myron Scholes, 1973, The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 637-659.
2000 11 117 15. Brennan, J. Michael and Eduardo S. Schwartz, 1988, Time-Invariant Portfolio Insurance Strategies, Journal of Finance, 283-299. 16. Choie, Kenneth S. and Eric J. Seff, 1989, TIPP: Insurance without complexity: Comment, Journal of Portfolio Management, 107-108. 17. Clarke, Roger G. and Robert D. Arnott, 1987, The Cost of Portfolio Insurance: Tradeoffs and Choices, Financial Analysts Journal, 35-47. 18. Cox, J. C. and S. A. Ross, 1976, The Valuation of Options for Alternative Stochastic Processes, Journal of Financial Economics, 3, 145-166. 19. Estep, Tony and Mark Kritzman, 1988, TIPP: Insurance without complexity, Journal of Portfolio Management, 38-42. 20. Etzioni, S. Ethan, 1986, Rebalance Disciplines for Portfolio Insurance, Journal of Portfolio Management, 59-62. 21. Fama, Eugene F. and Marshall E. Blume, 1966, Filter Rules and Stock-Market Trading, Journal of Business, 39, 226-241. 22. Garcia, C. B. and F. J. Gould, 1987, A Note on the Measurement of Risk in a Portfolio, Financial Analysts Journal, 61-69. 23. Leland, Hayne E., 1980, Who Should Buy Portfolio Insurance, Journal of Finance, 581-594. 24. Merton, R. C., 1973a, The Relationship Between Put and Call Option Prices: Comment, Journal of Finance, 28, 183-184. 25. Merton, R. C., 1973b, Theory of Rational Option Pricing, Bell Journal of Economics and Management Science, 4, 141-183. 26. Perold, Andre F. and William F. Sharpe, 1988, Dynamic Strategies for Asset Allocation, Financial Analysts Journal, 16-28. 27. Rendleman, Richard J. and Thomas J. O Brien, 1990, The Effects of Volatility Misestimation on Option-Replication Portfolio Insurance, Financial Analysts Journal, 60-70. 28. Rubinstein, Mark and Hayne E. Leland, 1981, Replicating Options with Positions in Stock and Cash, Financial Analysts Journal, 63-71. 29. Rubinstein, Mark, 1985, Alternative Paths to Portfolio Insurance, Financial Analysts Journal, 42-52.
118 30. Sharpe, William F., 1987, Integrated Asset Allocation, Financial Analysts Journal, 25-32. 31. Stoll, Hans R., 1969, The Relationship Between Put and Call Option Prices, Journal of Finance, 24, 801-824. 32. Sweeney, Richard J., 1988, Some New Filter Rule Tests: Methods and Results, Journal of Financial and Quantitative Analysis, 23, 285-300. 33. Zhu, Yu and Robert C. Kavee, 1988, Performance of Portfolio Insurance Strategies, Journal of Portfolio Management, 48-54.