Question

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 94%. If it is known that returns are normally distributed with a mean of 6.2%, what is the risk, measured by standard deviation, that this investment manager assumes in his calculation? (Round "z" value to 2 decimal places and final answer to 2 decimal places.)

Answer 1

Given ba manger tell bis client ma king posihve the probability ㄧ-return(20)-with-his-sugested-portfolio that P(X > c) = o-34 is mean (A) = 6-2% To od słandard deviaion () Soluion ー| First nd -scoe Such that Sima Standard normal z-table we et z-score-correspondina-probablíh _066_- we knoc 6T O 6.2 Risk (standard-deviaton)一is. A oz

Number in the table represents PIZSz) 0.09 3.6 .0002 0002 000 00 0 00 0001 0001 0001 0001 3.5 0002 0002 0002 0002 .0002 0002 000 0002 00020002 3.4 .0003 0003 0003 0003.0003 0003 0003 0003 0003 0002 3.3 .0005 0005 0005 0004 0004 0004 .0004 0004 0004 0003 3.2 0007 0007 0006 0006 0006 0006 .0006 0005 0005 0005 -3.1 0010 .0009 0009 0009 0008 0008 0008 0008 0007 0007 3.0 0013 0013 0013 0012 0012 0 0 000010 2.9 0019 0018 0018 0017 .0016 0016 0015 0015 00140014 28 0026 0025 0024 0023 0023 0022 0021 002 0020 0019 2.7 0035 0034 0033 0032 0031 0030 .0029 0028 0027 0026 2.6 .0047 0045 0044 0043 0 004 0039 0038 0037 0036 2.5 0062 0060 0059 0057 0055 0054 0052 0051 0049 0048 2.4 0082 0080 0078 0075 .0073 007 069 0068 0066 0064 2.3 .0107 0104 0102 0099 0096 0094 0091 0089 0087 0084 2.2 0139 0136 0132 0129 0125 0122 0119 0116 0113 0110 -2.1 0179 0174 0170 0166 0162 0158 0154 0150 0146 0143 2.0 .0228 0222 0217 0212 0207 020 0197 0192 0188 0183 1.9 0287 0281 0274 .0268 .0262 0256 050 0244 02390233 -1.8 1.0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294 -1.7 0446 0436 0427 0418 0409 040 0392 .0384 0375 0367 -16 |.0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 1.5 0668 0655 0643 0630 0618 0606 0594 0582 0571 0559 1.4 .0808 0793 0778 0764 0749 0735 0708 06940681 1.3 0968 0951 0934 0918 0901 0885 0869 0853 0838 0823 1.2 115 1131 1112 1093 1075 1056 1038 1020 1003 0985 -1.11357 1335 1314 1292 1271 1251 1230 1210 1190 1170 1.01587 1562 1539 1515 1492 1469 1446 1423 14011379 0.9 .1841 .1814 1788 .1762 1736 71 1685 1660 16351611 0.8 .2119 .2090 2061 .2033 2005 19771949 1922 1894 1867 0.7 2420 2389 .2358 .2327 .2296 2266.2236 .2206 2177 2148 0.6 .2743 2709 .2676 2643 .2611 2578 .2546 2514 2483 2451 0.5 3085 3050 3015 298 2946 2912 28772843 2810 .2776 0.4 3446 3409 3372 3336 3300 3264 3228 3192 3156 3121 0.3 3821 3783 3745 3707 36693632 3594 3557 3520 3483 -0.2 1.4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859 0.1 4602 4562 4522 4483 4443 4404 4364 4325 4286 4247 0.05000 4960 4920 4880 4840 4801 4761 4721 4681 4641 z 0.00 0.01 0.02 0.03 0.00.05 0.06 0.07 0.08