3. See Exhibit 3 in Jones and Wilson. Find the probability that an investment of $20,000 will result in a payoff between $125,000 and $142,750 in 15 years. EXHIBIT 3 Continued Per Year Investment Horizon 10 yn 15 y 20 yn 25 yn 30 ym. 40 ym. 1 yr. Jy Syn 17 0.3583 0.3749 0.3918 0.2648 0.2903 0.3171 0.2016 0.2379 0.2696 0.0799 0.1084 0.1437 0.1865 0.2362 2946 0.3585 0.0234 0.0403 0.0662 0.1039 0 1556 0.2225 0.3042 0.3978 0.0109 0.0218 0.0412 0.0729 0.1211 0.1889 0.2770 0.3744 0.4046 0.4356 0.4627 0.4811 0.49946 0.5321 0.3396 0.3776 0.4171 0.4579 0.4995 0.5415 0.5833 0.6247 0.6650 0.1256 01566 0.1925 0.2335 0.2794 0.3296 0.3837 0.4006 0.4993 0.55.85 0.6170 06734 0.7266 0.7756 05195 08580 08907 09179 0 5186 00523 0.0348 0.0769 0.0554 0.1097 0.0848 0.1519 0.1251 0.2041 0.1776 0.2664 0.2428 0 3378 0.3200 0.4163 0.40 0.4990 0.5R25 0.5920 66110 6810 0.7375 0.7613 0.8030 0.8297 0.8844 0.9018 0.9257 0.9351 0.95 0.9591 0.9741 0.9754 0.9861 0.4991 0.5715 0.6423 0.7070 0.7698 0.4985 0.6158 0.7242 0.8156 0.5972 0.6293 0.60046 0.6969 0.7818 0.8517 0.9052 0.9432 0.9682 0.9835 0.9920 0.6126 0 0.6916 0.7213 0.7498 0.7770 0.7408 0.7756 0.8079 0.8374 0.8684 .9052 0.9341 0.9558 0.9351 0.9662 0.9839 0.9931 0.9973 0.6700 0.6884 0.8026 0.8640 09399 0.97150 .9860 0.99300 .9964 0.9991 0.9823 0.9924 0 0.9985 0.9994 0.9998 0.9999 .0000 1.0000 1.0000 0.9940 0.9967 0.9983 0.9992 0.9996 0.9998 0.9999 1.0000 1 1.0000 -11 1.0000 0.2005 0.7243 0.7417 0.7586 0.7752 0.7912 0.8067 0.8216 0.810 0.8497 0.8627 0.8751 0.8869 0.8979 0.9082 0.9179 0.9269 0.9352 0.9428 0.9498 0.9759 0.9901 0.9967 0.999: 0.9998 1.000 0.8266 0.8459 08693 0.8880 0.9048 0.9198 09331 0.9448 0.9549 0.9635 0.9708 0.9769 0.9819 0.9861 0.9894 0.9920 0.9961 0.9952 0.9969 0.9978 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 0.8877 0.9571 0.9085 0.9702 0.9265 0.9799 0.9417 0.9869 0.9545 0.9916 0.9651 0.9948 0.9736 0.9969 0.9803 0.9982 0.9856 0.9997 0.9995 0.9927 0.9997 0.9950 0.9999 0.9766 0.9999 0.9977 1.0000 0.99851.0000 10000 0.9991 1.0000 0.9994 1.0000 0.9996 1.0000 0.9998 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.000 1.0000 1.0000 0.9961 9981 0.9992 0.9996 0.9999 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10000 1.0000 1.0000 1.000 1.0000 1.0000 0.9967 0.9985 0.9994 0.9998 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10000 1.0000 1.0000 1.0000 0.9997 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 16 -18 -19 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.000 1.0000 1.0000 -20 -25 -30 -35 40 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 -45 -50 1.0000 Geometric mean, R%, for the period is 9.98766%. The corresponding standard deviation is 21.38195% FALL THE MOURNAL OF PORTFOLIO MANAGEMENT Geometric mean, R%, for the period is 8.78258%. The corresponding standard deviation is 19.47527% EXHIBIT 3 Probabilities of Achieving, at Least, a Given Annual Nominal Geometric Mean Rate of Return over Various Investment Horizons, Based on the S&P Returns for 1926-1993 Per Year R% 1 yr. 3 yrs. Investment Horizon 10yrs. 15 yrs. 20 yrs. 5 yrs. 25 yrs. 3 yrs. 40 yrs. 60 50 45 40 0.0265 0.0383 0.0547 0.0769 0.1065 0.1452 0.1942 0.2545 0.3265 0.3422 0.0004 0.0011 0.0028 0.0067 0.0155 0.0335 0.0676 0.1264 0.2181 0.2407 0.0000 0.0000 0.0002 0.0007 0.0027 0.0090 0.0269 0.0699 0.1574 0.1817 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 .0032 0.0184 0.0775 0.0994 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0053 0.0408 0.0577 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0016 0.0222 0.0346 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0123 0.0211 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0069 0.0130 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0022 0.0051 0 FALL 1995 26 PROBABILITIES ASSOCIATED WITH COMMON STOCK RETURNS