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Over the past six years, a stock produced returns of 12 percent, 16 percent, -3 percent,...

Over the past six years, a stock produced returns of 12 percent, 16 percent, -3 percent, 7 percent, -5 percent, and 9 percent. Based on these six years, what range of returns would you expect to see 95 percent of the time?

-23.18 percent to 31.48 percent

-18.58 percent to 26.58 percent

-14.28 percent to 25.28 percent

-10.69 percent to 22.69 percent

-2.34 percent to 14.34 percent

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Answer #1

Returns over last six years are 12%, 16%, -3%, 7%, -5% and 9%

Average Return = [0.12 + 0.16 + (-0.03) + 0.07 + (-0.05) + 0.09] / 6
Average Return = 0.36 / 6
Average Return = 0.06 or 6.00%

Variance = [(0.12 - 0.06)^2 + (0.16 - 0.06)^2 + (-0.03 - 0.06)^2 + (0.07 - 0.06)^2 + (-0.05 - 0.06)^2 + (0.09 - 0.06)^2] / 5
Variance = 0.03480 / 5
Variance = 0.00696

Standard Deviation = (0.00696)^(1/2)
Standard Deviation = 0.08343 or 8.343%

95% Range of Returns = [Average Return - 2 * Standard Deviation, Average Return + 2 * Standard Deviation]
95% Range of Returns = [6.00% - 2 * 8.343%, 6.00% + 2 * 8.343%]
95% Range of Returns = [-10.69%, 22.69%]

So, you will expect to see return of -10.69% to 22.69%.

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