Suppose the returns on an asset are normally distributed. Suppose the historical

Question

Suppose the returns on an asset are normally distributed. Suppose the historical average annual return for the asset was 6.2 percent and the standard deviation was 8.3 percent. Refer to Table A.5.

What is the probability that your return on these bonds will be less than -2.1 percent in a given year? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What range of returns would you expect to see 95 percent of the time? (Enter your answers for the range from lowest to highest. Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

What range would you expect to see 99 percent of the time? (Enter your answers for the range from lowest to highest. Negative amounts should be indicated by a minus sign.Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

What is the probability that your return on these bonds will be less than -2.1 percent in a given year? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

TABLE A.5 Cumulative normal distribution -3.00 .0013 2236 -2.95 .016 1.56 .0594 5319 .5398 5478 8106 0019 2358 8159 1.70 9554 2420 92 9573 -2.80 0026 1.50 .0668 -2.75 0030 148 .0694 96 .5714 .98 2.70 -2.65 0040 -2.60 .0047 1.42 0778 -2.55 .0054-1.40 .0808 0749 2676 .5793 8413 1.02 1.82 9656 2810 8508 .8554 1' .9686 6026 6103 6179 6255 6331 1.88 9699 -2.35 .0094 1.32 0934 -2.30 0107 1.30 0968 48 3156 9726 1.94 .9738 1.96 9750 8770 -2.20 0139 1.26 1038 6480 0158 1075 1.20 2.00 .9772 9798 -2.10 0179 1.22 -2.05 0202 -2.00 0228 3520 6700 8925 1190 1.98 0239 1.16 1230 1271 1314 1.26 6962 9861 9878 9693 1.28 3745 6915 1.94 .0262 1.32 1.34 9099 2.35 9906 -1.92 0274 -110 3897 3974 2.40 9918 -1.88 0301 06 1446 1.38 .9162 .9929 4129 7257 9192 2.55 9946 2.60 .9953 .9279 2.65 9960 -1.84 0329 1.02 539 4286 -1.80 .0359 7518 1685 1736 1788 1841 0375 94 7580 1.50 9332 2.75 9970 2.80 9974 .9382 2.85 9978 72 4761 4840 4920 -1.68 .0465 6 1949 7823 1.58 9429 2.95.9984 84 3.00 .9987 -1.64 0505 1.62 2061 2119 2177 -1.62 .0526 04 04 5160 This table shows the probability [N(d)] of obeerving a value lees than or equal to d. For example, as illustrated, if d is 24, then N(d) is .4052.

Explanation / Answer

Asset return 6.20% Asset standard deviation 8.30% Using Excel Formula NORMDIST(x,mean,stdev,1) P (return < -2.1%) 0.16 95% level (Using Excel Formula NORMINV(probability,mean,stdev) -10.07% 22.47% 99% level (Using Excel Formula NORMINV(probability,mean,stdev) -15.18% 27.58%

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