Question

A stock returned 13 percent, 18 percent, -16 percent and -1 percent annually for the past four years. The standard deviation of these returns is given as 15.29 percent. Assuming that the stock's returns are normally distributed, what is the 99.74 percent probability range for any one given year?

-42.4% to 49.4%

-27.1% to 34.1%

-11.8% to 18.8%

-47.1% to 52.3%

Answer 1

C34 X A F G H fi =B34-$B$39 B C D I Deviation Square of Returns from mean deviation 13% 0.09501 0.0090 At 99.74%: 18% 0.1450) 0.0210 Expected range of returns 33 Year 34 35 2 Mean-3* SD to Mean+3* SD -16% -0.1950 -0.0450 36 37 38 Sum 39 Arithmetic average -1% 0.0380 Expected range of returns 0.0020 0.0701 14% 3.5% (14%/4) 40 41 0.02337 0.0701/(4-1) 42 Variance 43 44 Standard deviation 45 (root of variance) 15.29%

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