S12-18 Using Return Distributions [LO3] 1 Assume that the returns from holding small-company stocks are normally distributed. Refer to Figure 12.10 and Table A5 0.5 points a. What is the approximate probability that your money will double in value in a single year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What about triple in value? (Do not round intermediate calculations and enter your answer as a percent rounded to 7 decimal places, e.g...1616161.) eBook % References a. Probablity of doubling b. Probability of tripling % FIGURE 12.10 Historical Returns, Standard Deviations, and Frequency Distributions: 1926-2016 Average Return Standard Deviation Frequency Distribution Series Large-company stocks 12.0% 19.9% Small-company stocks 16.6 31.9 Helal Long-term corporate bonds 8.4 DO 6.0 9.9 Long-term government bonds 5.3 5.6 Intermediate-term government bonds II. U.S. Treasury bills 3.4 3.1 Inflation 3.0 4.1 The 1933 m.company stocks totalrein was 142.9 percent Source: Morningstar,200, author calculation TABLE A.S Cumulative normal distribution d Nid) d d d Nid) d 10013 Nid) 2230 Nid) -1.56 Nid) 5239 Nd) .0571 .0594 -3.00 -2.95 -.76 .08 .86 .8051 1.66 -1.56 -74 -.72 2297 2350 .68 .8106 9515 9536 .0016 .0019 .0022 -2.90 0818 .08 .10 -1.54 - 1.52 5319 5300 5478 8 1.68 1.70 9554 .0643 -70 .12 2420 2483 6159 8212 .8264 .9573 40026 -1.50 0668 .92 94 88 14 1.72 1.74 .9591 -2.85 -2.80 -2.75 -2.70 -2.65 0694 - 60 5557 5636 2546 - 1.48 -1.46 .16 96 8315 .0030 .0035 .0010 .9608 16 * 3 8 .98 2011 2676 8165 1.70 1.78 1.80 9625 -62 -1.44 -1.42 1.00 9641 -2.60 .0047 -.60 .5714 -5793 5871 594 8413 8-461 1.02 1.82 -1.40 .0054 .0062 0721 .0749 0778 0906 0830 0969 0901 0934 2743 2010 -58 1.04 -2.58 -2.50 -2.45 .9656 .9671 1.84 .8508 .6554 - 1.38 - 56 26 6026 1.06 1.80 9680 .0071 =1.30 - 54 1.08 .8599 1.66 0082 -1.34 -2.40 -2.35 9600 .9713 30 1.10 --52 -50 1.90 -1.32 6100 .6179 6255 6391 6643 .6686 1.12 1.92 .9726 -2.30 -1.30 45 94 0968 1003 1.94 .0094 0107 .0122 0139 .0158 .9738 -1.28 46 2877 2946 3015 3085 3156 3228 3300 3372 3446 3520 3594 36 1.90 8729 8770 8510 .9750 -2.20 -1.26 .1038 5406 6480 6554 1.16 1.18 1.20 se 40 9761 -2.15 1075 8849 1.98 2.00 2.05 .9772 .0179 .1112 -.40 - 1.24 - 1.22 1.20 -1.18 -2.10 -2.05 5626 1.22 .0202 1151 8888 .8925 6700 1.24 2.10 69798 .9621 se 42 -2.00 0228 .0239 65 .6772 1.25 -1.99 - 1.16 1190 1230 .1271 - 38 - 36 - 34 - 32 -.30 3660 49 .9601 -1.80 0250 -1.14 3745 50 2.15 2.20 2.25 2.30 8962 .8007 19032 9000 9099 .0262 .1314 3821 .6915 6986 -7054 -1.12 -1.10 .9878 .9893 -1.90 0274 .3897 1.29 1.30 1.32 1:34 1.36 1.38 1:40 2.35 .9900 1357 1401 .1446 - 26 -1.90 -1.50 3974 .7123 .0287 0301 .0314 9131 -24 .7190 -1.08 1.06 -1.04 -1.02 .9918 .0929 9162 2.40 2.45 2.50 4052 4129 4207 -22 .60 17257 9192 .9938 1530 - 20 7894 9222 2.55 -1.64 -1.82 -1.80 -1.00 .1567 -18 64 7380 9946 9953 9251 2.60 - 10 4354 .60 7454 1.46 9279 2.65 -1.78 -.90 1635 .1685 .1736 - 14 4443 1.48 2.70 0829 0944 0359 0375 0892 0409 0427 0446 0465 -7518 7580 -.94 9900 .9965 9970 9806 9332 -12 4522 -1.76 -1.74 1.72 2.75 .82 -1785 .1841 2.80 1.50 1.52 1.54 - 10 -08 .9974 2.55 9978 -1.70 7700 7754 1804 -06 4602 4681 4761 4640 4920 .78 1.50 .6857 .8382 9400 9-429 9.652 2.90 -. -88 -64 .9961 -1.69 -1.66 1,50 2.95 1940 2005 0984 0435 -02 7581 1.80 3.00 .9007 1.01 - Be 2061 00 5000 7930 9-174 3.05 9989 -1.62 -1.60 0506 0526 0548 5050 .7995 - BO -.70 1.04 9495 2119 2177 5160 This table shows the probability of observing a value loss than or equal to d. For example, as ilustrated, if dis-24, then Nais 4052. S12-18 Using Return Distributions [LO3] 1 Assume that the returns from holding small-company stocks are normally distributed. Refer to Figure 12.10 and Table A5 0.5 points a. What is the approximate probability that your money will double in value in a single year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What about triple in value? (Do not round intermediate calculations and enter your answer as a percent rounded to 7 decimal places, e.g...1616161.) eBook % References a. Probablity of doubling b. Probability of tripling % FIGURE 12.10 Historical Returns, Standard Deviations, and Frequency Distributions: 1926-2016 Average Return Standard Deviation Frequency Distribution Series Large-company stocks 12.0% 19.9% Small-company stocks 16.6 31.9 Helal Long-term corporate bonds 8.4 DO 6.0 9.9 Long-term government bonds 5.3 5.6 Intermediate-term government bonds II. U.S. Treasury bills 3.4 3.1 Inflation 3.0 4.1 The 1933 m.company stocks totalrein was 142.9 percent Source: Morningstar,200, author calculation TABLE A.S Cumulative normal distribution d Nid) d d d Nid) d 10013 Nid) 2230 Nid) -1.56 Nid) 5239 Nd) .0571 .0594 -3.00 -2.95 -.76 .08 .86 .8051 1.66 -1.56 -74 -.72 2297 2350 .68 .8106 9515 9536 .0016 .0019 .0022 -2.90 0818 .08 .10 -1.54 - 1.52 5319 5300 5478 8 1.68 1.70 9554 .0643 -70 .12 2420 2483 6159 8212 .8264 .9573 40026 -1.50 0668 .92 94 88 14 1.72 1.74 .9591 -2.85 -2.80 -2.75 -2.70 -2.65 0694 - 60 5557 5636 2546 - 1.48 -1.46 .16 96 8315 .0030 .0035 .0010 .9608 16 * 3 8 .98 2011 2676 8165 1.70 1.78 1.80 9625 -62 -1.44 -1.42 1.00 9641 -2.60 .0047 -.60 .5714 -5793 5871 594 8413 8-461 1.02 1.82 -1.40 .0054 .0062 0721 .0749 0778 0906 0830 0969 0901 0934 2743 2010 -58 1.04 -2.58 -2.50 -2.45 .9656 .9671 1.84 .8508 .6554 - 1.38 - 56 26 6026 1.06 1.80 9680 .0071 =1.30 - 54 1.08 .8599 1.66 0082 -1.34 -2.40 -2.35 9600 .9713 30 1.10 --52 -50 1.90 -1.32 6100 .6179 6255 6391 6643 .6686 1.12 1.92 .9726 -2.30 -1.30 45 94 0968 1003 1.94 .0094 0107 .0122 0139 .0158 .9738 -1.28 46 2877 2946 3015 3085 3156 3228 3300 3372 3446 3520 3594 36 1.90 8729 8770 8510 .9750 -2.20 -1.26 .1038 5406 6480 6554 1.16 1.18 1.20 se 40 9761 -2.15 1075 8849 1.98 2.00 2.05 .9772 .0179 .1112 -.40 - 1.24 - 1.22 1.20 -1.18 -2.10 -2.05 5626 1.22 .0202 1151 8888 .8925 6700 1.24 2.10 69798 .9621 se 42 -2.00 0228 .0239 65 .6772 1.25 -1.99 - 1.16 1190 1230 .1271 - 38 - 36 - 34 - 32 -.30 3660 49 .9601 -1.80 0250 -1.14 3745 50 2.15 2.20 2.25 2.30 8962 .8007 19032 9000 9099 .0262 .1314 3821 .6915 6986 -7054 -1.12 -1.10 .9878 .9893 -1.90 0274 .3897 1.29 1.30 1.32 1:34 1.36 1.38 1:40 2.35 .9900 1357 1401 .1446 - 26 -1.90 -1.50 3974 .7123 .0287 0301 .0314 9131 -24 .7190 -1.08 1.06 -1.04 -1.02 .9918 .0929 9162 2.40 2.45 2.50 4052 4129 4207 -22 .60 17257 9192 .9938 1530 - 20 7894 9222 2.55 -1.64 -1.82 -1.80 -1.00 .1567 -18 64 7380 9946 9953 9251 2.60 - 10 4354 .60 7454 1.46 9279 2.65 -1.78 -.90 1635 .1685 .1736 - 14 4443 1.48 2.70 0829 0944 0359 0375 0892 0409 0427 0446 0465 -7518 7580 -.94 9900 .9965 9970 9806 9332 -12 4522 -1.76 -1.74 1.72 2.75 .82 -1785 .1841 2.80 1.50 1.52 1.54 - 10 -08 .9974 2.55 9978 -1.70 7700 7754 1804 -06 4602 4681 4761 4640 4920 .78 1.50 .6857 .8382 9400 9-429 9.652 2.90 -. -88 -64 .9961 -1.69 -1.66 1,50 2.95 1940 2005 0984 0435 -02 7581 1.80 3.00 .9007 1.01 - Be 2061 00 5000 7930 9-174 3.05 9989 -1.62 -1.60 0506 0526 0548 5050 .7995 - BO -.70 1.04 9495 2119 2177 5160 This table shows the probability of observing a value loss than or equal to d. For example, as ilustrated, if dis-24, then Nais 4052