A stock has returns of 7 percent, 12 percent, −24 percent, and 17 percent for the past 4 years. Based on this information, what is the 95 percent probability range for any one given year? −33.9 to 39.9 percent −70.8 to 76.8 percent −33.9 to 21.5 percent −15.5 to 21.5 percent −17.0 to 20.0 percent

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A stock has returns of 7 percent, 12 percent, −24 percent, and 17 percent for the past 4 years. Based on this information, what is the 95 percent probability range for any one given year? −33.9 to 39.9 percent −70.8 to 76.8 percent −33.9 to 21.5 percent −15.5 to 21.5 percent −17.0 to 20.0 percent

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Answer: percent −17.0 to 20.0 percent

Working notes for the above answer is as under

First of all we will find average return as follow

Year Return
1 0.07
2 0.12
3 -0.24
4 0.17
Total 0.12
Average Return 0.12/4
Average Return 0.03

NOw we will find

(0.07 – 0.03)2+ (0.12 – 0.03) 2+ (-0.24 – 0.03) 2+ (0.17 – 0.03) 2]

=0.1022

95% probability range =

=0.03 –  ( 2* 0.1022)

=0.03 -0.2044

=0.1744

So the answer is percent −17.0 to 20.0 percent

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